Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Management procedure evaluation of a data-limited multispecies fishery with application to the Hawaiian… Bryan, Meaghan Darcy 2012

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2012_spring_bryan_meaghan.pdf [ 4.2MB ]
Metadata
JSON: 24-1.0103460.json
JSON-LD: 24-1.0103460-ld.json
RDF/XML (Pretty): 24-1.0103460-rdf.xml
RDF/JSON: 24-1.0103460-rdf.json
Turtle: 24-1.0103460-turtle.txt
N-Triples: 24-1.0103460-rdf-ntriples.txt
Original Record: 24-1.0103460-source.json
Full Text
24-1.0103460-fulltext.txt
Citation
24-1.0103460.ris

Full Text

MANAGEMENT PROCEDURE EVALUATION OF A DATA-LIMITED MULTISPECIES FISHERY WITH APPLICATION TO THE HAWAIIAN BOTTOMFISH FISHERY  by  MEAGHAN DARCY BRYAN B.A., Smith College, 1999 M.Sc., North Carolina State University, 2003  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in  THE FACULTY OF GRADUATE STUDIES (Zoology) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  APRIL 2012 © Meaghan Darcy Bryan, 2012  Abstract Multispecies fisheries with technical interactions and sparse data present a challenge for assessment scientists, many of whom are now legally required to provide species-specific management advice. A key question is can these data be used to provide species-specific assessments and management advice? Secondly, in light of new assessment approaches, how would new management procedures perform with respect to the status quo? This thesis uses a novel multispecies model to reconstruct historical abundances using fishery-dependent data from the Hawaiian bottomfish fishery. In this handline fishery, hook competition and time spent handling fish limits catch rates, resulting in nonlinear relationships between CPUE and abundance. The model is jointly fit to species-specific catch and is conditioned on historical fishing effort. The model allows for hook competition and partitions time spent fishing and time spent handling fish, h. Simulation experiments showed this approach provided nearly unbiased parameter estimates unless an incorrect assumption was made about h. Empirical h estimates were unavailable, so a range of h values were imputed from information on fishing gears and sensitivity to h was evaluated. Species-specific information was disentangled using h, but no single value best described all species-specific catch equally. Leading and management parameter estimates were relatively insensitive to the assumed value of h, except for catchability at low stock size. Given the uncertainty about h, management procedure evaluation was used to evaluate management performance of the multispecies model to an aggregate model and evaluate alternative management procedures (MPs), defined by the decision rule, assessment model, and data types. Trade-offs among management objectives describing stability in catch, fishery productivity, and over-exploitation risk were compared. Trade-offs between catch and conservation objectives were largely determined by the decision rule. MPs associated with an aggregate assessment represented a balance from the aggregate perspective, but led to overii  exploitation of one or more species. Average annual variation in catch was high for all MPs and highest for MPs using the multispecies approach in combination with a tag-recapture program. These results were largely robust to the assumptions about h in the assessment model and demonstrated the difficulty of co-managing multiple species.  iii  Table of Contents Abstract .......................................................................................................................................... ii Table of Contents ......................................................................................................................... iv List of Tables .............................................................................................................................. viii List of Figures ............................................................................................................................... xi Acknowledgements .................................................................................................................... xxi Chapter 1 General Introduction .................................................................................................. 1 Trade-offs in fisheries management................................................................................................ 3 Output controls and the evaluation of management strategies ....................................................... 5 Hawaiian bottomfish fishery ........................................................................................................... 9 Target species ......................................................................................................................9 Gear....................................................................................................................................10 Bottomfish management ....................................................................................................11 Data ....................................................................................................................................12 Traditional stock assessments ............................................................................................14 Problems with the aggregate assessment approach, ..........................................................15 Aims of the project and thesis structure ........................................................................................ 18 Chapter 2 Derivation of a multispecies assessment model that accounts for non-stationarity in catchability .............................................................................................................................. 27 Introduction ................................................................................................................................... 27 Methods......................................................................................................................................... 33 Simulation model ...............................................................................................................33 State dynamics ...................................................................................................... 33 Observation dynamics and derivation of the catch equation ................................ 35 Behaviour of the simulation model ....................................................................... 39 Estimation model ...............................................................................................................40 Simulation-estimation experiments ...................................................................................42 Bias in parameter estimation and reference points ............................................................43 Comparison to the status quo .............................................................................................43 Results ........................................................................................................................................... 44 Influence of average handling time on CPUE and time-varying catchability ...................44 iv  Measured bias in leading and management reference parameters .....................................45 Incorrect assumptions about average handling time ..........................................................47 Estimated MSY from status quo approach compared to the true ......................................47 Discussion ..................................................................................................................................... 48 Performance of the multispecies assessment model ..........................................................52 Assumptions and expected directional bias .......................................................................55 A comparison of species-specific and aggregate management reference points ...............58 Chapter 3 Assessment of the Hawaiian bottomfish fishery while accounting for nonstationarity in catchability ......................................................................................................... 94 Introduction ................................................................................................................................... 94 Methods......................................................................................................................................... 99 Data ....................................................................................................................................99 Analytical methods ..........................................................................................................100 State dynamics .................................................................................................... 100 Observation dynamics ......................................................................................... 101 Average handling time per fish ........................................................................... 102 Estimated leading parameters, likelihood, and priors ......................................................103 Management parameters ..................................................................................................105 Results ......................................................................................................................................... 106 Trends in predicted biomass, depletion, fishing mortality rate, and catchability ............106 Model fit and maximum likelihood estimates of the leading parameters ........................108 Posterior density estimates and correlation in the estimated parameters ........................109 Posterior density estimates and correlation in management parameters .........................111 Discussion ................................................................................................................................... 113 Assumptions pertaining to observation dynamics ...........................................................115 Information contained in fishery-dependent data ............................................................121 Model comparison and future research ............................................................................125 Final remarks ...................................................................................................................126 Chapter 4 Management procedure evaluation for the Hawaiian bottomfish fishery ........ 166 Introduction ................................................................................................................................. 166 Methods....................................................................................................................................... 171 Overview of the management procedure evaluation .......................................................171 v  Management procedures ..................................................................................................173 Operating model ..............................................................................................................174 Multispecies population dynamics ...................................................................... 175 Observation dynamics of the fishery: Fishery dependent data and targeting behaviour............................................................................................................. 176 Fishery independent data .................................................................................... 178 Assessment models ..........................................................................................................179 Aggregate assessment ......................................................................................... 179 Multispecies assessment ..................................................................................... 181 Harvest control rules ........................................................................................................183 Evaluating performance ...................................................................................................184 Results ......................................................................................................................................... 186 Short-term performance measures ...................................................................................186 Average annual variation in total catch, precautionary harvest control rule ...... 186 Average annual variation in total catch, weak stock harvest control rule .......... 187 Average total catch, precautionary harvest control rule ..................................... 188 Average total catch, weak stock harvest control rule ......................................... 189 Depletion level of total biomass, precautionary harvest control rule ................. 190 Depletion level of total biomass, weak stock harvest control rule ..................... 191 Long-term performance measures ...................................................................................192 Average annual variation in total catch, precautionary harvest control rule ...... 192 Average annual variation in total catch, weak stock harvest control rule .......... 193 Average total catch, precautionary harvest control rule ..................................... 194 Average total catch, weak stock harvest control rule ......................................... 195 Depletion level of total biomass, precautionary harvest control rule ................. 196 Depletion level of total biomass, weak stock harvest control rule ..................... 197 Total biomass and total catch projections ........................................................................198 Perfect information ............................................................................................. 198 Precautionary harvest control rule ...................................................................... 199 Weak stock harvest control rule.......................................................................... 200 Average catch and depletion per species .........................................................................201 Short-term projections ........................................................................................ 201 vi  Long-term projections ......................................................................................... 202 Fundamental trade-offs ....................................................................................................202 Discussion ................................................................................................................................... 205 Management performance and harvest control rules .......................................................205 Data, assessment model assumptions, and performance .................................................210 Assessment model assumptions .......................................................................................213 Uncertainty ......................................................................................................................216 Conclusions......................................................................................................................219 Chapter 5 Summary ................................................................................................................. 255 Future avenues of research ..............................................................................................259 References .................................................................................................................................. 261 Appendix A: Supplementary information for Chapter 3 ...................................................... 273 Appendix B: Supplementary information for Chapter 4 ...................................................... 294  vii  List of Tables Table 1.1 List of Hawaiian bottomfish target species. The * indicates species belonging to the Deep-7 complex. The following symbols indicate the three different depth categories to which the species belong according to Ralston and Polovina (1982), † 30m-140m, ‡ 80m-240m, §200m-350m. ................................................................................................................................ 20 Table 2.2 The operating model used for the simulation-estimation experiments. The state dynamics were parameterized according to the delay difference model (Deriso, 1980), recruitment was described by the Beverton-Holt model, and the observation model was derived from Holling’s disc equation. ....................................................................................................... 65 Table 2.3 Derivation of Holling’s disc equation for multiple species. ........................................ 68 Table 2.4 Equilibrium analysis to determine reference management points. ............................... 69 Table 2.5 Parameter values that were systematically varied to measure non-proportionality in species-specific and total CPUE. All other state dynamic parameters in the model were fixed and the same for each species. ...................................................................................................... 71 Table 2.6 Data scenarios used for the simulation-estimation experiments to determine bias in the estimated leading parameters Θ. ................................................................................................... 72 Table 2.7 Parameter combinations used for the simulation-estimation experiments. Parameter combinations built upon one another to make the results comparable among the scenarios with two-, six-, and 12-species.............................................................................................................. 73 Table 2.8 Measure of non-proportionality (m) for individual species and the resulting aggregate for fisheries simultaneously capturing 2 species. The recruitment compensation Κ, the von Bertalanffy growth coefficient k, and catchability at low stock size q0 differed for each species. The relative difference between species is expressed as parameter specific ratios. ..................... 74 Table 2.9 Hypothetical true MSY values for individual species that make-up a multispecies fishery and the resulting aggregate MSY. Data were generated without contrast with an h = 0.0833. Predicted aggregate MSY resulted from the status quo approach where average handling time h is assumed to equal zero. Results are reported for two-, six- and 12-species scenarios at three levels of error expressed as the total standard deviation (η = 0.1, η = 0.5, η = 1). .............. 75 Table 3.1 Parameter symbols and descriptions used to describe the state and observation dynamic models for the Hawaiian bottomfish fishery. ............................................................... 127 Table 3.2 Species-specific growth parameter values used and the sources from which they came. L∞ is the asymptotic length, k is the von Bertalanffy growth coefficient, a and b parameters describing the length-weight relationship, and WAi is the mean weight-at-recruitment. Symbols next to the values refer to footnotes below the table .................................................................. 130 Table 3.3 The joint posterior probability of the estimated leading parameters across the different average handling time hypotheses. ............................................................................................. 131 viii  Table 3.4 State and observation dynamic models used to assess the Hawaiian bottomfish. The state dynamics were modeled using a delay difference model (Deriso, 1980), recruitment was described by the Beverton-Holt stock-recruitment model, and the observation model was derived from Holling’s disc equation. ..................................................................................................... 132 Table 3.5 Initial values and the upper and lower bounds for the estimated parameters. * indicates value was fixed and not estimated. ............................................................................................. 133 Table 3.6 The likelihood of the catch given the estimated model parameters L(Ci | Θ) for hypotheses of h. The values in bold are the lowest value of L(Ci | Θ) for each species. ........... 134 Table 4.1 Management procedure descriptions. Management procedures were defined by the harvest control rule, data used as part of the assessment in projection years, observation error levels, and the average handling time per fished used in the assessment model hassess. C & E refers to annual catch by species (measured in kg) and total, annual effort (measured in trips). MSDD is short-hand for multispecies delay-difference model. ................................................. 222 Table 4.2 Model parameter symbols and descriptions used in this chapter................................ 224 Table 4.3 The observation dynamics sub-model used to simulate species-specific catch, speciesspecific relative indices of abundance from a research survey, and the numbers of recaptured tags per species for forward projections. ............................................................................................ 230 Table 4.4 Aggregate surplus production model to represent the status quo assessment method. .... ..................................................................................................................................................... 231 Table 4.5 Estimated parameters of interest, the observation dynamics sub-models, and the likelihoods used as part of the multispecies delay difference assessment model. ...................... 232 Table 4.6 Equilibrium analysis to obtain an estimate of the total effort to obtain total maximum sustainable yield ‫ ݐܻܵܯܧ‬for each projection year (2006-2030) that is applied to the harvest control rule within the management procedure evaluation. ........................................................ 234 Table 4.7 Performance measures used to evaluate the relative performance of each management procedure over short- and long-term projections ........................................................................ 236 Table 4.8 The interquartile range, median, and mean for the percent difference in average projected short-term catch for all management procedures relative to the perfect information management procedure. Results are shown for operating model scenario one (h = 0 minutes) and operating model scenario two (h = 7 minutes). Negative values represent a loss and positive values represent a gain in catch relative to the perfect information management procedure. .... 237 Table 4.9 The interquartile range, median, and mean for the percent difference in average projected long-term total catch for all management procedures relative to the perfect information management procedure. Results are shown for operating model scenario one (h = 0 minutes) and operating model scenario two (h = 7 minutes). Negative values represent a loss and positive values represent a gain in catch relative to the perfect information management procedure. .... 238 Table A.1 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the average handling time per fish h = 0. .................................................. 273 ix  Table A.2 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 2 minutes per fish. .......................................................... 273 Table A.3 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 5 minutes per fish. .......................................................... 274 Table A.4 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 7 minutes per fish. .......................................................... 274 Table A.5 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 9 minutes per fish. .......................................................... 275 Table A.6 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 15 minutes per fish. ........................................................ 275 Table A.7 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 20 minutes per fish. ........................................................ 276 Table A.8 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 25 minutes per fish. ........................................................ 276 Table A.9 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 30 minutes per fish. ........................................................ 277 Table A.10 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 42 minutes per fish. ............................................. 277 Table A.11 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 60 minutes per fish. ............................................. 278 Table B.1 The 95% confidence interval, median, and mean for the percent difference in average projected short-term catch for the management procedures under the modified weak-stock harvest control rule relative to the perfect information management procedure. Results are shown for operating model scenario one (h = 0 minutes) and operating model scenario two (h = 7 minutes). Negative values represent a loss and positive values represent a gain in catch relative to the perfect information management procedure. ........................................................................ 295 Table B.2 The 95% confidence interval, median, and mean for the percent difference in average projected long-term catch for the management procedures under the modified weak-stock harvest control rule relative to the perfect information management procedure. Results are shown for operating model scenario one (h = 0 minutes) and operating model scenario two (h = 7 minutes). Negative values represent a loss and positive values represent a gain in catch relative to the perfect information management procedure. .............................................................................. 296  x  List of Figures Figure 1.1 Three relationships between CPUE and abundance. The dashed line represents hyperstability, the solid line represents a proportional relationship, the dotted line represents hyperdepletion............................................................................................................................... 21 Figure 1.2 Map of the Hawaiian Islands. The analysis of this thesis focuses on the Main Hawaiian Islands. The Northwestern Hawaiian Islands is divided into two management zones; the Mau and Ho’omalu zones. The Mau zone includes Nihoa, Necker Island and is highlighted by the red circle. All other islands in the Northwestern Hawaiian Islands belong to the Ho’omalu zone. .............................................................................................................................................. 22 Figure 1.3 Summary of the fishery dependent catch and effort statistics reported for the Main Hawaiian Islands collected by the State of Hawaii Department of Aquatic Resources for 19482005. a) Total catch (summed across all species, excluding Ta’ape) measured in kilograms, b) total effort measured in the number of trips per year, and c) catch per unit effort (CPUE = kg/trip) for bottomfish species assemblage excluding Ta’ape. ..................................................... 23 Figure 1.4 Annual number of trips and active licenses participating in the Hawaiian bottomfish fishery in the Main Hawaiian Islands from 1948 to 2005. ........................................................... 24 Figure 1.5 Reported, species-specific catch, measured in kilograms from the Main Hawaiian Islands for years 1948-2005. The * indicates species belonging to the Deep-7 species complex. .. ....................................................................................................................................................... 25 Figure 1.6 Species composition of observed catch, measured as a proportion of the total observed catch, from the Main Hawaiian Islands for years 1948-2005. The * indicates species belonging to the Deep-7 species complex. .................................................................................................... 26 Figure 2.1 A flow chart of the simulation-estimation framework used for this chapter. Eighteen data scenarios were evaluated using this framework. Data scenarios were determined by the combination of average handling time per fish, effort series (with or without contrast), error level, and number of species. One hundred Monte Carlo simulations were performed for each scenario. ........................................................................................................................................ 76 Figure 2.2 Examples of the catch observations and biomass trajecotries generated by the simulation model. The example depicted in the figure represents a two species fishery, either (a, c, e) with or (b, d, f) without contrast. Panels a and b depict simulated fishing mortality rates with and without contrast, respectively. Panels c and d show examples of catch and biomass for species one, while panels e and f show catch and biomass for species two. ................................ 77 Figure 2.3 A systematic search over the recruitment compensation ratio Κ, the von Bertalanffy growth coefficient k, and catchability at low stock size qo (see Table 2.5 for parameter combinations) and the resulting relationship between aggregate CPUE and aggregate biomass as measured by ݉. An ݉ = 1 indicates the relationship is proportional, ݉ < 1 indicates hyperstability, and ݉ > 1 indicates hyperdepletion. Simulations were done for a hypothetical fishery targeting two species simultaneously. .............................................................................. 78 xi  Figure 2.4 Example of the CPUE-biomass and the corresponding time-varying catchabilitynumbers relationships for a hypothetical two species fishery where handling time is part of the fishing process. a, b) Species have a higher catchability at low stock size qo than that of the species in panels c and d. .............................................................................................................. 79 Figure 2.5 Estimated bias for unfished biomass Bo, the recruitment compensation ratio Κ, catchability at low stock size qo, and the reference points MSY and FMSY. Results are from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The data were generated for a two species fishery, with three different levels of error: (a, b) η = 0.1; (c, d) η = 0.5; and (e, f) η = 1, and either (a, c, e) with or (b, d, f) without contrast. Parameter combinations used to simulate the data can be found in Table 2.7. Note the t y-axis scales for panels a and b are the same, but differ from panels c-f. . 80 Figure 2.6 Estimated bias for unfished biomass Bo resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ....... 81 Figure 2.7 Estimated bias for unfished biomass Bo resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ....... 82 Figure 2.8 Estimated bias for the recruitment compensation ratio Κ resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ........................................................................................................................ 83 Figure 2.9 Estimated bias for the recruitment compensation Κ resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ...................................................................................................................................... 84 Figure 2.10 Estimated bias for catchability at low stock size qo resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six xii  species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ...................................................................................................................................... 85 Figure 2.11 Estimated bias for catchability at low stock size qo resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ...................................................................................................................................... 86 Figure 2.12 Estimated bias for MSY resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ....... 87 Figure 2.13 Estimated bias for MSY resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ....... 88 Figure 2.14 Estimated bias for FMSY resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ....... 89 Figure 2.15 Estimated bias for FMSY resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7. ....... 90 Figure 2.16 Estimated bias for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo, MSY, and FMSY. Results are from 100 Monte Carlo simulations. The data were generated for a two species fishery. Data were generated at three different levels of error a) η = 0.1, b) η = 0.5, and c) η = 1and generated without contrast. Data were generated  xiii  with handling time and parameters were estimated without handling time (i.e. htrue > 0 and hest = 0). Parameter combinations used to simulate the data can be found in Table 2.7. ...................... 91 Figure 2.17 Estimated bias for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo, MSY, and FMSY. Results are from 100 simulation-estimation experiments. The data were generated for a two species fishery. Data were generated without contrast at three different levels of error a) η = 0.1, b) η = 0.5, and c) η = 1. Data were generated with handling time and the parameters were estimated with handling time that was larger than the true handling time (i.e. hest > htrue). Parameter combinations used to simulate the data can be found in Table 2.7. ........................................................................................................................ 92 Figure 2.18 Measured bias between the true aggregate MSY and the estimated aggregate MSY from the status quo approach for a) two-, b) six-, and c) 12-species scenarios when handling time is assumed to be known. Each bar represent the distribution in measured bias for data generated at three levels of error (η = 0.1, η = 0.5, and η = 1). ..................................................................... 93 Figure 3.1 Example of the penalty used to constrain the fishing mortality rate of the individual Hawaiian bottomfish fishery. ...................................................................................................... 137 Figure 3.2 Annual predicted biomass measured in metric tons for each species for five hypotheses of average handling time per fish h. ......................................................................... 138 Figure 3.3 Annual estimated depletion (Bit/Boi; solid lines, primary axis) and fishing mortality (Fit, dashed lines, secondary axis) from the MLEs of the leading parameters for each species for five hypotheses of average handling time per fish h................................................................... 139 Figure 3.4 The relationship between the ratio of species-specific catchability and catchability at low stock size (qit /qoi) and depletion (Bit/Boi) for each species and five hypotheses of average handling time per fish h. ............................................................................................................. 140 Figure 3.5 The relationship between species-specific catchability and catchability at low stock size (qit/qoi) and the ratio of species-specific biomass and total biomass for five average handling time hypotheses. Stars indicate the starting point ....................................................................... 141 Figure 3.6 Profile of the negative log-likelihoods of species-specific catch, L(Ci | Θi), against the average handling time per fish values h (minutes per fish). Values plotted in this figure are presented in Table 3.7. ................................................................................................................ 142 Figure 3.7 Observed and predicted (solid lines) catch for each species and five hypotheses of average handling time per fish (h). ............................................................................................. 143 Figure 3.8 Catch residuals (ln‫ ݐ݅ܥ‬− 	ln‫ )ݐ݅ܥ‬on a natural logarithmic scale for each species and five hypotheses of average handling time per fish h................................................................... 144  Figure 3.9 Estimated, annual recruitment anomalies (ωit) for each species and five hypotheses of average handling time per fish h. ................................................................................................ 145 Figure 3.10 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size  xiv  qo estimated for five hypotheses of average handling time per fish h for Ehu. Posteriors were generated from 20,000 random samples. .................................................................................... 146 Figure 3.11 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Gindai. Posteriors were generated from 20,000 random samples. .................................................................................... 147 Figure 3.12 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Hapu’upu’u. Posteriors were generated from 20,000 random samples. ........................................................................... 148 Figure 3.13 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Kahala. Posteriors were generated from 20,000 random samples. .................................................................................... 149 Figure 3.14 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Kalekale. Posteriors were generated from 20,000 random samples. ........................................................................... 150 Figure 3.15 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Lehi. Posteriors were generated from 20,000 random samples. .................................................................................... 151 Figure 3.16 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Onaga. Posteriors were generated from 20,000 random samples. .................................................................................... 152 Figure 3.17 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Opakapaka. Posteriors were generated from 20,000 random samples. ........................................................................... 153 Figure 3.18 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Uku. Posteriors were generated from 20,000 random samples. .................................................................................... 154 Figure 3.19 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for White ulua. Posteriors were generated from 20,000 random samples. ........................................................................... 155  xv  Figure 3.20 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Ehu. Posteriors were generated from 20,000 random samples. .................................................................................... 156 Figure 3.21 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Gindai. Posteriors were generated from 20,000 random samples. .................................................................................... 157 Figure 3.22 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Hapu’upu’u. Posteriors were generated from 20,000 random samples. ........................................................................... 158 Figure 3.23 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Kahala. Posteriors were generated from 20,000 random samples. .................................................................................... 159 Figure 3.24 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Kalekale. Posteriors were generated from 20,000 random samples. .................................................................................... 160 Figure 3.25 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Lehi. Posteriors were generated from 20,000 random samples. .................................................................................... 161 Figure 3.26 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Onaga. Posteriors were generated from 20,000 random samples. .................................................................................... 162 Figure 3.27 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Opakapaka. Posteriors were generated from 20,000 random samples. ........................................................................... 163 Figure 3.28 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Uku. Posteriors were generated from 20,000 random samples. .................................................................................... 164 Figure 3.29 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal)  xvi  estimated for five hypotheses of average handling time per fish h for White ulua. Posteriors were generated from 20,000 random samples. ........................................................................... 165 Figure 4.1 Species groupings based on the reported average beginning and end catch depths. . 239 Figure 4.2 Plot of the precautionary harvest control rule. The effort ratio is E/EMSY and the biomass ratio is B/BMSY. ............................................................................................................. 240  Figure 4.3 Short term projections for AAV, ‫ݐܥ‬, and ‫ ݐܦ‬for 21 management procedures (see Table 4.1 for shorthand notation) that fall under two harvest control rules (precautionary and weak-stock) and two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). Each box summarizes the performance measures estimates resulting from 100 MPE realizations. .......... 241 Figure 4.4 Long-term projections for AAV, ‫ݐܥ‬, and ‫ ݐܦ‬for 21 management procedures (see Table 4.1 for shorthand notation) that fall under two harvest control rules (precautionary and weak-stock) and two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). ........... 242 Figure 4.5 Total catch (top panels) and biomass (bottom panels) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030 for the two operating model (OM) scenarios. The projected trajectories represent years in which catch was set to MSY under the perfect information management procedure. The solid lines represent three individual trajectories and the shaded region represents the 95 percent confidence region. ....................... 243 Figure 4.6 Total catch (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the precautionary harvest control rule was implemented. The solid lines represent three individual trajectories and the shaded region represents the 95 percent confidence region. Each panel represents a different management procedure. ........................................................................... 244 Figure 4.7 Total biomass (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the precautionary harvest control rule was implemented and for two scenarios (hsim = 0 minutes and hsim = 7 minutes). The solid lines represent three individual trajectories and the shaded area represents the 95 percent confidence region. Each panel represents a different management procedure..................................................................................................................................... 245 Figure 4.8 Total catch (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the weak stock harvest control rule was implemented. The solid lines represent three individual trajectories and the shaded region represents the 95 percent confidence region. Each panel represents a different management procedure. ........................................................................... 246 Figure 4.9 Total biomass (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the weak stock harvest control rule was implemented. The solid lines represent three individual  xvii  trajectories and the shaded area represents the 95 percent confidence region. Each panel represents a different management procedure ............................................................................ 247 Figure 4.10 Short-term species-specific average catch for 21 management procedures falling under two harvest control rules (precautionary and weak-stock) and two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). Each row represents one species: a) Hapu’upu’u, b) Kahala, c) Kalekale, d) Opakapaka, e) Uku, f) Ehu, g) Onaga, h) Lehi, i) Gindai, and j) White ulua. ........................................................................................................................ 248 Figure 4.11 Short-term species-specific mean depletion for 21 management procedures falling under two harvest control rules (precautionary and weak-stock) and two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). Each row represents one species: a) Hapu’upu’u, b) Kahala, c) Kalekale, d) Opakapaka, e) Uku, f) Ehu, g) Onaga, h) Lehi, i) Gindai, and j) White ulua. The dashed line represents overfishing (i.e., Bcurrent/Bo = 0.2). ................... 249 Figure 4.12 Long-term projections for species-specific average catch for two harvest control rules (precautionary and the weak stock) and two scenarios (hsim = 0 minutes and hsim = 7 minutes). Each row represents one species: a) Hapu’upu’u, b) Kahala, c) Kalekale, d) Opakapaka, e) Uku, f) Ehu, g) Onaga, h) Lehi, i) Gindai, and j) White ulua. ............................ 250 Figure 4.13 Long-term species-specific mean depletion for 21 management procedures falling under two harvest control rules (i.e., precautionary and weak-stock) and two operating model scenarios (i.e., h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). Each row represents one species: a) Hapu’upu’u, b) Kahala, c) Kalekale, d) Opakapaka, e) Uku, f) Ehu, g) Onaga, h) Lehi, i) Gindai, and j) White ulua. The dashed line represents overfishing (i.e., B = 0.2 Bo). ............................ 251 Figure 4.14 Trade-off curve between long-term catch and stock size for the two operating model scenarios; a) the fishery-dependent data were simulated to be proportional to abundance and b) the fishery-dependent data were simulated to be hyperstable. Refer to Table 4.1 for management procedure short-hand, which is used to indicate where the individual management procedures lie on the trade-off curve. ................................................................................................................. 252 Figure 4.15 Trade-off curves separated into regions of high catch and depletion (a, b) and low catch and depletion (c, d) for the operating model scenarios: fishery-dependent data were simulated to be proportional to abundance (a, c) and fishery-dependent data were simulated to be hyperstable (b, d). The cut-off represents the balanced trade-off A1. Refer to Table 4.1 for management procedure short-hand, which is used to indicate where the individual management procedures are along the trade-off curve. ................................................................................... 253 Figure 4.16 Trade-off between long-term total catch and the number of overfished species (B<0.2Bo) for two operating model scenarios a) the fishery-dependent data were simulated to be proportional to abundance and b) the fishery-dependent data were simulated to be hyperstable. Refer to Table 4.1 for management procedure short-hand, which is used to indicate where the xviii  individual management procedures along the trade-off curve. A total of ten species were considered for analysis. ............................................................................................................... 254 Figure A1 Traceplots of 20,000 random samples for per species unfished biomass, Boi, when it was assumed average handling time per fish, h, was equal to zero. ........................................... 279 Figure A.2 Traceplots of 20,000 random samples for the per species recruitment compensation ratio, Κi, when it was assumed average handling time per fish, h, was equal to zero. ............... 280 Figure A.3 Traceplots of 20,000 random samples for the per species catchability at low stock size, qoi, when it was assumed average handling time per fish, h, was equal to zero. ................ 281 Figure A.4 Traceplots of 20,000 random samples for per species unfished biomass, Boi, when it was assumed average handling time per fish, h, was equal to two minutes per fish. ................. 282 Figure A.5 Traceplots of 20,000 random samples for the per species recruitment compensation ratio, Κi, when it was assumed average handling time per fish, h, was equal to two minutes per fish............................................................................................................................................... 283 Figure A.6 Traceplots of 20,000 random samples for the per species catchability at low stock size, qoi, when it was assumed average handling time per fish, h, was equal to two minutes per fish............................................................................................................................................... 284 Figure A.7 Traceplots of 20,000 random samples for per species unfished biomass, Boi, when it was assumed average handling time per fish, h, was equal to five minutes per fish. ................. 285 Figure A.8 Traceplots of 20,000 random samples for the per species recruitment compensation ratio, Κi, when it was assumed average handling time per fish, h, was equal to five minutes per fish............................................................................................................................................... 286 Figure A.9 Traceplots of 20,000 random samples for the per species catchability at low stock size, qoi, when it was assumed average handling time per fish, h, was equal to five minutes per fish............................................................................................................................................... 287 Figure A.10 Traceplots of 20,000 random samples for per species unfished biomass, Boi, when it was assumed average handling time per fish, h, was equal to seven minutes per fish. .............. 288 Figure A.11 Traceplots of 20,000 random samples for the per species recruitment compensation ratio, Κi, when it was assumed average handling time per fish, h, was equal to seven minutes per fish............................................................................................................................................... 289 Figure A.12 Traceplots of 20,000 random samples for the per species catchability at low stock size, qoi, when it was assumed average handling time per fish, h, was equal to seven minutes per fish............................................................................................................................................... 290 Figure A.13 Traceplots of 20,000 random samples for per species unfished biomass, Boi, when it was assumed average handling time per fish, h, was equal to nine minutes per fish. ................ 291 Figure A.14 Traceplots of 20,000 random samples for the per species recruitment compensation ratio, Κi, when it was assumed average handling time per fish, h, was equal to nine minutes per fish............................................................................................................................................... 292 xix  Figure A.15 Traceplots of 20,000 random samples for the per species catchability at low stock size, qoi, when it was assumed average handling time per fish, h, was equal to nine minutes per fish............................................................................................................................................... 293  Figure B.1 Short term AAV, ‫ݐܥ‬, and ‫ ݐܦ‬for 10 management procedures that are the same as the weak-stock MPs in Chapter 4 (see Table 4.1, for shorthand notation), except the harvest control rule is a modified weak-stock harvest control rule. Results are presented for two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish) and for the perfect information management procedure (far right panels). .................................................................................. 298  Figure B.2 Long- term AAV, ‫ݐܥ‬, and ‫ ݐܦ‬for 10 management procedures that are the same as the weak-stock MPs in Chapter 4 (see Table 4.1, for shorthand notation), except the harvest control rule is a modified weak-stock harvest control rule. Results are presented for two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish) and for the perfect information management procedure (far right panels). .................................................................................. 299 Figure B.3 Total catch (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the modified weak-stock harvest control rule was implemented. The solid lines represent three individual trajectories and the shaded region represents the 95 percent confidence region. Each panel represents a different management procedure. .................................................................. 300 Figure B.4 Total catch (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the modified weak-stock harvest control rule was implemented. The solid lines represent three individual trajectories and the shaded region represents the 95 percent confidence region. Each panel represents a different management procedure. .................................................................. 301 Figure B.5 Short-term species-specific average depletion for two operating model scenarios and the modified weak-stock harvest control rule and the management procedure described by perfect information...................................................................................................................... 302 Figure B.6 Long-term species-specific average depletion using a modified weak-stock harvest control rule for two operating model scenarios for two operating model scenarios and the modified weak-stock harvest control rule and the management procedure described by perfect information. ................................................................................................................................. 303  xx  Acknowledgements This research could not have been completed without the assistance and support of many people. First, I would like to sincerely thank my supervisor and supervisory committee. My supervisor, Dr. Steve Martell, provided me with this opportunity and thoughtful insights along the way. I thank him for teaching me most of what I know about fisheries modeling and programming in R and ADMB. Dr. Carl Walters played an integral role in the development of this thesis and provided sage advice at every stage. My committee members Drs. Pierre Kleiber (US National Marine Fisheries Service), Murdoch McAllister (UBC Fisheries Centre), and Ian Perry (Department of Fisheries and Oceans Canada) also provided invaluable insight and feedback on my thesis. Funding for this work was provided by the Pacific Islands Fishery Science Center (PIFSC) part of the US National Oceanic and. Atmospheric Association (NOAA)/ National Marine Fisheries Service (NMFS). I thank Dr. Gerard DiNardo for making this opportunity possible and Robert Moffitt and the staff at the PIFSC for sharing their insight about this fishery. I thank Drs. Clay Porch and Todd Gedamke for having the confidence in my abilities and hiring me as part of the Sustainable Fisheries Division at the US NOAA/NMFS Southeast Fisheries Science Center prior to finishing this thesis. I am incredibly grateful to them for providing me with the time to complete my thesis. I am incredibly fortunate to have a supportive network of friends and family. Drs. Rob Ahrens, Robyn Forrest, Bob Lessard, and Nathan Taylor were always there to be sounding boards and provided valuable perspectives and insights. Drs. Robyn Forrest, Mike Melnychuk, Sunny Snider, and Nathan Taylor read parts of this thesis and provided invaluable input. I am extremely grateful to Rachael Louton and Tom Porteus for not only their friendship, but also xxi  allowing me to use their computers for several weeks to complete my simulations. I am also incredibly grateful for the moral support and friendship of many fellow graduate students; Megan Bailey, Line Christensen, Robyn Forrest, Carey McGilliard, Mike Melnycuk, Kerrie O’Donnell, Erin Rechisky, Nathan Taylor, Brett van Poorten, Valeria Vegara, and Chad Wilkinson. My time off was spent with a wonderful group of people and I thank them for the adventures and good times we have shared. Thank you, Stacy Connole, Robyn Forrest , Bob Lessard, Ian McCulloch, Mike Melnycuk , Chris O’Grady, Erin Rechisky, Nathan Taylor , Valeria Vegara, and Sims Weymuller. Finally, I owe the world to my husband, David Bryan. Thank you for your constant support, love, and encouragement, and reminding me to enjoy everything the Pacific Northwest has to offer.  xxii  Chapter 1 General Introduction The Magnuson-Stevens Reauthorized Fisheries Conservation and Management Act (MSA) is the main regulatory legislation for fisheries management in the United States. It outlines and defines management objectives for US fisheries and provisions for rebuilding in the event of a stock collapse. The mandates of the MSA are diverse, but a main goal of National Standard 1 is to prevent overfishing while achieving optimal yield for each US fishery. This mandate is an attempt to sustainably use fisheries resources and provide economic stability for fishers and fishing communities. The MSA was last amended in 2007 and outlines the requirements to prevent overfishing. Under the new federally mandated requirements, all domestic fisheries will be managed by an output control system in the form of annual catch limits (ACLs) by the year 2011 and an ACL will be developed for each stock that makes up a fishery. The definition of stock is crucial to the development and implementation of ACLs, especially for fisheries that target more than one species. The MSA defines a stock of fish as "a species, subspecies, geographical grouping, or other category of fish capable of management as a unit." This definition of unit stock allows for many interpretations. For example, a unit stock can be defined by a single species or multiple species that are fished within a distinct geographic area. The MSA therefore allows for multispecies fisheries, which often target species with disparate biology and ecology, to be managed as one management unit. This is at odds with a discretionary provision in section 303 of the MSA, which outlines the requirements and optional provisions of fishery management plans (FMPs). FMPs may “include management measures that conserve target and non-target species”. This discretionary provision implies the potential need for managing on a per species basis. Other federal legislation, such as the Endangered Species Act (ESA) also points to the potential need for having knowledge about stock status on a 1  per species basis. The ESA focuses specifically on the conservation of threatened and endangered species (i.e., individual species). The ability to develop management measures for individual species will depend on the ability to determine their abundance. In many multispecies fisheries this is a difficult task given the variability in the quality and quantity of data that are available for assessments. Fisheries are often described on a scale from data-poor to data-rich indicating how well stock status and reference points can be determined (Restrepo and Powers 1999). Data-poor scenarios can be defined as those where stock assessments are minimal and estimates of maximum sustainable yield (MSY) and stock status are unreliable due to a lack of basic information, such as a relative index of abundance or life-history information (Restrepo and Powers 1999). Data-limited scenarios are described as those where stock status and reference points can be determined, but similar to data-poor scenarios they may be unreliable (Restrepo and Powers 1999). Unreliable estimates may be due to the lack of contrast in the catch and effort data, temporally inconsistent catch and effort series, and specifically for multispecies fisheries, data for several species may be aggregated to mask changes in species-specific catch or catch rates (Restrepo and Powers 1999, Cheung and Sadovy 2004). Many multispecies fisheries, especially those in sub-tropical and tropical regions, are considered to be data-poor or datalimited (Pauly 1982, Johannes 1998, Cheung and Sadovy 2004). Fisheries in these regions generally target many more species than their temperate counterparts; therefore, catch and effort statistics on a per species basis are often minimal (Ketchen 1964, Pauly 1982, Sadovy 2005). Additionally, although a greater number of species are targeted and captured by fisheries in tropic regions they also are perceived to be of lesser value often negating economic justification for fishery monitoring or fishery-independent research (Ketchan 1964, Sadovy 2005).  2  In lieu of fisheries-independent scientific surveys for establishing unbiased estimates of relative abundance, catch statistics from commercial fisheries are typically the best information or the only information that can be used in the estimation of abundance. The level of detail for catch and effort reporting is of real importance for stock assessments. For example, when fishery-dependent catch and effort data are available effort is often a cumulative metric over species and a given unit of time (e.g., a day of fishing). Unfortunately, total effort from multispecies fisheries does not provide information about targeting and effective fishing effort (i.e., the effort directed at catching each species) is unknown (Rjinsdorp et al. 2006). Without knowledge about effective fishing effort it is difficult to develop an unbiased index of abundance for the individual species that make up a multispecies fishery (He et al. 1997). In turn, it is difficult to obtain estimates of abundance that are needed to develop reference points (e.g., MSY) for individual species. A key question is can the species-specific reference points be developed from fishery-dependent data when only total effort is known? If so, can speciesspecific management objectives be met simultaneously in a multispecies fishery? In answering this question, it is important to consider and evaluate trade-offs with respect to how a stock is defined. Trade-offs in fisheries management Finding a balancing among management trade-offs is at the core of fisheries management. The MSA National Standards and FMP provisions represent a multitude of tradeoffs that managers have to regularly consider. Some of these trade-offs are summarized in Chapter 2 of Walters and Martell (2004). Examples of common management trade-offs include: short-term versus long-term catch; system biodiversity versus productivity; profit versus employment opportunities; expenditure on fisheries research versus expenditure on other public services; harvest of prey species versus the abundance of predator species; and destructive versus 3  selective fisheries. The biodiversity-productivity trade-off is a central trade-off in the management of multispecies fisheries. The biodiversity-productivity trade-off is characterized by the conflict between managing for maximized long-term catch versus protecting one or more species from overfishing at the expense of fishing for more productive target species. The latter is sometimes referred to as weak-stock management (Hilborn et al. 2004). These authors showed that significant reductions in yield (approximately 90% of the west coast groundfish yield) would be required in order to protect one or more less productive species from being overfished. Ecosystem simulation models have shown similar results, i.e., when managing fisheries to optimize profit generally some biodiversity is lost (Christensen and Walters 2004, Cheung and Sumaila 2008). Christensen and Walters (2004) showed that this loss of biodiversity was due to maintaining a system structured to promote the productivity of the most economically valuable species and resulted in the loss of their competitors and predators. Cheung and Sumaila (2008) demonstrated that this trade-off could be quite severe for tropical marine ecosystems. In their study, a small increase (~10%) in the biodiversity index led to a quite large loss in economic benefits (~62% reduction in net present value). Management aimed at both economic and biodiversity objectives is difficult, especially if non-selective gear types that indiscriminately capture multiple species are used. Interactions among species that are caused by indiscriminate capture are sometimes referred to as technological interactions (Murawski 1984). Simulation studies have shown that managing for long-term total yield will lead to optimal harvest rates heavily influenced by more productive species (Paulik et. al 1967, Hilborn 1976, Hilborn1985). Managers may attempt to implement separate optimal fishing policies for individual species. Although this may lead to greater total yield, it is likely that one or more lower-productivity species will be overfished due to incidental 4  catch (Mackinson et. al. 2009). Implementing a management strategy that optimizes for high economic return through optimal catch will most likely lead to the potential extirpation of less productive species while sustainably fishing more productive species. The converse would be to avoid overfishing the less resilient species by implementing a weak-stock management approach, which will likely lead to substantial loss in catch (Christensen and Walters 2004; Hilborn et al. 2004). The intermediate compromise between the two management objectives would be to maintain catch of the more productive or abundant species, while reducing the incidental catch of less resilient species. Dankel et al. (2009) compared the ability of the New England groundfish fishing fleet to meet the objectives of the MSA while using one of three trawl types. Their simulation study employed a multispecies yield per recruit model that incorporated technical interactions among species through species-specific and gear-specific catchability coefficients. Although the results were theoretical and dependent on estimating species- and gear-specific catchability coefficients, yield and employment opportunities were sustained while reducing the impact on non-target species dependent on the availability of highly selective gear types. Investment in innovation of highly selective gear types may be an important way for this compromise to be realized and ensure that fishing mortality or catch quota limits are met without overfishing less resilient species (Walters and Martell 2004, Dankel et.al. 2009, Ainsworth and Pitcher 2010). Output controls and the evaluation of management strategies The MSA in the United States mandates that all managed fisheries will be managed by a catch quota system (i.e., ACLs). This type of management strategy is an example of an output control. Output controls aim to limit removals by implementing catch quotas, such as total 5  allowable catch (TAC) or some proportion of the TAC (e.g., individual quotas (IQs) or individual transferable quotas (ITQs)). A perceived benefit of this type of strategy is that, if adequate monitoring of catch is in place, catch quotas are an easily understandable and implemented policy (DiCosimo et al. 2010). Predictions of sustainable catch (as opposed to sustainable fishing mortality) are heavily dependent on the ability to estimate abundance of a population and as such, there is a need for accurate and precise annual stock assessments to develop these catch quotas (Walters and Pearce 1996). Stock assessment models are mathematical/statistical representations of the population dynamics of target species and of the dynamics of observing a fishery. They are used to make quantitative predictions about how a population responds to management choices (Hilborn and Walters 1992). Assessment models are confronted with time series data, such as catch and effort, and are used to estimate key parameters such as the population scale (unfished reference abundance) and productivity (e.g., recruitment rate and natural mortality) along with historical estimates of fishing mortality consistent with the historical catch or effort. Given estimates of population scale and productivity, management reference points such as maximum sustainable yield (MSY) and MSY-derivatives (i.e., levels of effort, fishing mortality, and biomass that achieve MSY) are determined. The accuracy and precision of these estimates is dependent on how informative the available data are, as well as the underlying model assumptions inherent in stock assessment (Hilborn and Walters 1992). A common assumption is that fishing mortality is proportional to fishing effort, and catch rates are proportional to biomass, which are shown in equations 1 and 2: ‫ܨ‬௧ = 	‫ܧݍ‬௧  ‫ܧܷܲܥ‬௧ = 	‫ܤݍ‬௧  (1) (2) 6  where F is fishing mortality, q is the catchability coefficient, E is effort, B is biomass, and CPUE is catch per unit effort. Traditionally, it has been assumed that changes in fishing mortality are proportional to changes in observed effort (eq. 1) and catch rates are proportional to abundance (eq. 2). Equation 1 represents the relationship between fishing mortality and effort and equation 2 represents the relationship between catch per unit effort and abundance. The catchability parameter (q) is defined as fishing mortality per standard unit of effort. Equations 1 and 2, as written, imply that q is time-invariant and independent of density. This tenuous assumption is predicated on a number of further incorrect assumptions, including: i) fishing is a truly random process (i.e., spatial distribution of fishing effort is distributed randomly); ii) fish are randomly distributed throughout the fishing area (or clumped if effort is randomly distributed); iii) efficiency of the fishing fleet is stable over space and time; and iv) there is no gear saturation (i.e., no limits on the maximum rate that gear can capture fish or the hold capacity to keep them) (Paloheimo and Dickie, 1964, Rothschild 1967, Cooke and Beddington 1984). Incorrectly assuming proportionality when the underlying relationship is non-linear is not uncommon and can have major implications on assessment outcomes (Harley et al. 2001). Harley et al. (2001) conducted a meta-analysis of an ICES database containing fishery-dependent catch rate data and fishery-independent estimates of abundance. They showed that 147 of 209 (70%) catch rate series were hyperstable, whereas 62 (30%) were hyperdepleted. Hyperdepletion is described by catch rates declining more quickly than abundance and leads to an overly pessimistic outlook on stock abundance (Figure 1.1a, Hilborn and Walters 1992). Hyperdepletion can occur, for example, when a portion of a population is more vulnerable to the fishing process leaving the remainder of the population relatively invulnerable (Walters and Bonfil 1999). This may be the case for the South Australian rock lobster fishery where catch 7  rates have shown a declining trend (Linnane and Crosthwaite 2009). This is most likely due to localized depletion because fishers have spatially concentrated targeted effort on the inshore lobster population foregoing targeted effort and catch opportunities in the offshore environment (Linnane and Crosthwaite 2009). Interference competition, where competing fishing activities reduces fishing efficiency, can also lead to hyperdepletion (Swain and Wade 2003). In a hyperdepleted system, under the assumption of proportionality, abundance would be underestimated and this would lead to overly conservative management strategies and foregone catch. Hyperstability is considered to be the more concerning relationship with regard to fisheries management. Hyperstability is described by relatively stable catch rates as abundance declines (Figure 1.1a, Hilborn and Walters 1992). Under an assumed proportional relationship, this signal would be interpreted as minimal stock decline. It would lead to the over-estimation of abundance and under-estimation of fishing mortality. Using optimistic estimates of population scale and productivity will in turn lead to optimistic estimates of MSY and MSY based reference points. Hyperstability is the result of exponentially or non-linearly increasing catchability as abundance declines (Hilborn and Walters 1992). Paloheimo and Dickie (1964) demonstrated for a hypothetical purse seine fishery that the interaction among the aggregative behaviour of the target species, changes in the target species distribution, as well as the time spent searching for aggregations leads to catchability being inversely related to abundance. Empirical studies have shown that this inverse relationship exists for Pacific sardines (MacCall 1976), George’s Bank haddock (Crecco and Overholtz 1990) , and Atlantic cod in the north Gulf of Saint Lawrence (Rose and Leggett 1991). Cooke and Beddington (1984) presented various theoretical models evaluating mechanisms such as, handling time and the resulting relationship between catch rates and abundance. They demonstrated that variability in catchability over time and handling time, 8  would lead to a non-linear relationship between catchability and abundance. The theoretical work of Swain and Sinclair (1994) also suggests that as the spatial distribution of fish contracts with declining abundance catchability increases exponentially. These studies point to a number of mechanisms that degrade the catch rate-abundance relationship and indicate that catchability is seldom constant. Using biased reference points in managing fisheries has major implications for the ability to meet management objectives. Developing quotas based on positively biased estimates of MSY can lead to depensatory fishing, regardless of whether catches are implemented as a TAC or an IQ or an ITQ (Walters and Pearse 1996). This is particularly worrisome for multispecies fisheries with strong technological interactions and spatial overlap among species. Catch quotas for multispecies fisheries can be implemented on a species basis or as a total quota (i.e., not apportioned by species). The common problem between the two approaches is that the individual species are rarely equally resilient to fishing pressure, as described earlier. This risk is worrisome even if quotas are precisely estimated. The Hawaiian bottomfish fishery embodies some of these problems inherent in managing multispecies fisheries. As such, the following section describes this fishery to provide justification for its use as a case study and justify the intended goals of this thesis. Hawaiian bottomfish fishery Target species The Hawaiian bottomfish fishery targets a multispecies complex made-up of 12 native species from the Lutjanid, Carangid, and Serranid families (Table 1.1) and Lutjanus kasmira, a non-native species that was introduced in the early 1960s but was not caught commercially until the late 1960s. The depth distribution for this species complex is quite wide, between 30m and 9  greater than 200m, with overlapping species-specific depth distributions (Ralston and Polovina 1982, Moffitt et al. 1989, Haight et al. 1993). Using cluster analysis methods, Ralston and Polovina (1982) defined the depth distributions of three separate species assemblages (Table 1.1). The adults of all the species are often associated with hardbottom structures and deepwater headlands (Ralston et al. 1985). Overall, these fish are relatively long lived (20+ years), slow growing species (von Bertalanffy k ~ 0.15-0.25 yr-1) with moderate natural mortality rates (M ~ 0.25-0.5 yr-1; Manooch 1987, Ralston 1987, Morales-Nin and Ralston 1990, Manooch and Potts 1997). Gear The Hawaiian fisheries, including the deep-water bottomfish fishery, have operated since ancient times (~300A.D.; Cobb 1905, Impact Assessment Inc. 2007). Bottomfish were traditionally caught from canoe fishing platforms using handlines outfitted with hand carved wooden hooks. Canoes were used until the late 1800s when the Japanese introduced the larger more modern wooden sampan platforms that were eventually motorized in the early 1900s (Impact Assessment Inc. 2007). The progression to more modern fishing platforms resulted in a transition from mainly subsistence to commercial fishing. Cobb (1905) summarizes the commercial fishery operations throughout the Hawaiian Islands in the late 1800s, early 1900s. The records included in his summary provide evidence that a number of bottomfish species were commercially captured prior to 1900. The present day fishing fleet consists of a mix of 50ft-200ft motorized sampans and generic modern fishing boats (Kawamota pers. comm. 2006). Handlines have always been the gear type used to fish for bottomfish. Overtime the technique has become increasingly more 10  efficient. Traditional handlines were set and retrieved manually by hand, Samoan reels were used until the 1970s-1980s, when electric handlines became the primary fishing gear (Kawamota pers. comm. 2006). The electric handline system is made up of an electric base outfitted with a single weighted line with ~5-10 baited circle hooks. Commonly used baits included squid, fish, and chum (Kawamota pers. comm. 2006). Anecdotal evidence suggests that fishers will use certain fish types to target certain species, but this is not apparent from the data. The line is dropped to the seafloor or just above hardbottom structures to target bottomfish. Bottomfish management The Hawaiian Island archipelago is divided into three management areas, the Main Hawaiian Islands (MHI), the Mau zone and the Ho’omalo zone (Figure 1.2). The Mau and Ho’omalu zones make up the Northwestern Hawaiian Islands (NWHI). Management of the bottomfish fishery has varied among the zones. Fishing in the NWHI zones was managed as a limited entry system until 2010. The limited entry program started in 1988 for the Ho’omalu zone and 1998 for the Mau zone. Approximately 11 licenses fished within the NWHI and no limitations were placed on the catch amount. Fisheries management in the NWHI changed in 2006 with the creation of the Papahaതnaumokuaതkea Marine National Monument. Bottomfish  fishing was allowed to continue after the initial designation of the national monument; however, as part of the fishery management plan the NWHI were closed to bottomfish fishing in 2010. Therefore, all future fishery developments and fisheries management plans will solely pertain to the MHI. Management of the commercial bottomfish fleet in the MHI has consisted of a commercial fishing license program and area closures that represent 20% of the available bottomfish habitat in state waters, both implemented by the HDAR. Limitations were not placed 11  on catch numbers, weights, or effort in the MHI until 2006. The Western Pacific Fisheries Management Council (WesPac), responding to concerns about overfishing (Moffitt et al. 2006), implemented a total allowable catch (TAC) management system for seven of the Hawaiian bottomfish species in 2006 (Deep-7, see Table 1.1). This TAC program is currently in operation and is not partitioned among the seven species; therefore, the composition of TAC can be made up of any mixture of the seven species. The fishery for the Deep-7 species is closed for the remainder of the year once the TAC has been reached. Interestingly, no restrictions have been placed on the species that do not belong to the Deep-7 complex. Fishers can continue to fish for the five other species that make-up the bottomfish fishery even after the Deep-7 fishery is closed; this provision likely results in additional bycatch of Deep-7 species. Fishers are legally required to release Deep-7 species if they are caught after the Deep-7 quota is met. Data The data available for stock assessment of the Hawaiian bottomfish complex are fishery dependent and have been collected by the State of Hawaii Department of Aquatic Resources (HDAR) since 1948. Initially the main goal of this data collection program was to evaluate the economic development of the fishery rather than for use in stock assessments. Commercial fishers are required to submit monthly reports detailing fishing date, license number (that changed every year), species-specific catch in pounds and numbers, fishing location (large statistical areas) and the corresponding sales information. HDAR revised their data collection program in 2002 and fishers are now required to submit daily fishing reports that included the aforementioned data, as well as information about depths fished, sub-area fished, and bank quadrant fished. Between 2002 and 2005 a total of 19,522 trips were reported, of these 216 trips (approximately one percent) provided depth information, subarea information was never reported, and 184 trips provided information about bank quadrant in which fishing took place. 12  Collection of these new data was an initial attempt to collect more detailed information about the spatial aspects of the fishery. Compliance with all the changes in daily fishing reports seems limited. The catch and effort statistics for the Hawaiian bottomfish fishery for the years 19482005 are summarized in Figure 1.3 through Figure 1.6. Aggregate catch declined throughout the 1950s and early 1960s, was stable but with low catches throughout the 1960s and 1970s, increased in the late 1970s and 1980s, then peaked in 1988 which was followed by a decline (Figure 1.3). Trends in aggregate catch correspond with reported effort trends and the number of licenses actively fishing on an annual basis (Figure 1.3, Figure 1.4). The pattern in the total number of licenses and total effort were almost identical except for a slight lag in the decline in effort during the mid- to late-1950s (Figure 1.4). Aggregate CPUE trends show a general declining trend as effort increases (i.e., one-way trip, Figure 1.3). Catch has been consistently dominated by P. filamentosus (Hawaiian common name is opakapaka), A. virescens (uku), and E. coruscans (onaga) (Figure 1.5, Figure 1.6). S. dumerili (kahala) catches were generally high until the late 1980s after which it was implicated as a cause of ciguatera poisoning and catches rapidly declined (Figure 1.5, Figure 1.6). C. ignobilis (white ulua) also seems to make up a large portion of the reported catch over time and made up a disproportionate amount of the catch in 1968 (Figure 1.5). It is important to note that white ulua and C. lugubris (black ulua) have been reported by species or jointly reported as “ulua” over the entire timespan of data collection. The annual catch estimates of “ulua” were assigned to white and black ulua according to the average catch proportion (over all years) of these two species.  13  Traditional stock assessments Stock status for the Hawaiian bottomfish complex has been determined using an aggregate surplus production model (i.e., all species captured in this fishery are pooled together as a single species; Moffitt et al. 2006). Although this has been done on an archipelagic scale, I will focus on the modeling approach used for the MHI since it is the focal area for future assessment and management and this thesis. The surplus production model estimates next year’s aggregate biomass bt+1 as a function of the aggregate carrying capacity K, aggregate intrinsic rate of growth r, the previous year’s aggregate biomass bt and annual observed aggregate removals ct: ܾ௧ାଵ = ܾ௧ + ‫ܾݎ‬௧ ቀ ௄೟ቁ − ܿ̂௧ . ௕  (3)  The predicted removals ܿ̂௧ represent total annual catch of all species combined and bt is the total annual biomass of all species combined. Notice that a single intrinsic rate of growth parameter is used to describe the productivity of this species assemblage. This assumes either that r is the same for all species or that the proportional contribution of all species with different r values remains stable, and therefore all species are equally resilient to fishing. The model was fit to observed, annual catch ct, where predicted catch ܿ̂௧ was a function of total annual biomass and annual survival from fishing mortality: ܿ̂௧ = ܾ௧ (1 − ݁ ி೟ ).  (4)  Errors in observed catch were assumed to be lognormal. Fishing mortality was calculated as the product of the catchability coefficient q and observed total effort Et: ‫ܨ‬௧ = ‫ܧݍ‬௧ .  (5)  14  The equation for annual fishing mortality Ft indicates that Ft is proportional to Et through a constant catchability coefficient q that is also estimated. Due to known changes in vessel power and gear efficiency, three separate catchability parameters were estimated, one for each arbitrary time period that corresponded to significant changes in technologies. Therefore, it was assumed that within a given time period Ft and Et were proportional as is indicated by (2). This observation model is a simplification of reality and completely disregards species-specific differences in catchability and the effects of targeting high valued species and competition among species for baited hook space (Rothschild 1967, Somerton and Kikkawa 1995, Rodgveller et al. 2008). Problems with the aggregate assessment approach, Warnings against using nominal aggregate catch and effort data to assess communities are extensive (see Hampton et al. 2005, Maunder et al. 2006, Polacheck 2006, Kleiber and Maunder 2008). Changes in aggregate catch and effort statistics will never represent changes in total abundance due to spatial expansion (Walters 2003), changing fleet efficiency, changing targeting behaviours (Maunder et al. 2006, Polacheck 2006), as well as relative differences in productivity and catchability among species (Kleiber and Maunder 2008). Additionally, the management advice that stems from aggregate assessments using these data will not be sustainable for all species. Methods to address these issues in multispecies fisheries include ordination and classification methods to analyse multispecies datasets and subset these datasets for trips that are most representative for individual species (Murawski et al. 1983, Rogers and Pikitch 1992, Lewy and Vinther 1994, Pelletier and Ferraris 2000, Glazer and Butterworth 2002, Stephens and MacCall 2004, Branch et al. 2005). Murawski et al. (1983) used hierarchical cluster analysis 15  (HCA) to identify species assemblages that could be managed as a single unit; the clusters were based on area fished, depth, and month fished. Similarly, Rogers and Pikitch (1992) used an ordination method, as well as two cluster analysis methods to identify groundfish assemblages targeted by the US west coast groundfish fishery. Although it is important to understand which species most often co-occur in the catch, the assemblages will most likely represent species of disparate productivities making some more vulnerable to overfishing than others. Their approaches do not lend themselves to developing management procedures for individual target species. Lewy and Vinther (1994) used cluster analysis to define directed fisheries for the Danish North Sea trawl fishery. Directed fisheries were defined by similarities in vessel size, mesh size and gear, and the landed weight of the species caught. Pelletier and Ferraris (2000) developed an iterative process that used a combination of ordination and clustering methods to define fishing tactics that were based on gear, species composition of the catch, fishing location, and month fished. Once a fishing tactic was defined, monthly effort (i.e., total number of trips per tactic) was totalled according to the target species associated with a given fishing tactic. Branch et al. (2002) used cluster analysis to define fishing opportunities, which was based on the starting and ending distance between trawls. Once fishing opportunities were identified, the species composition of the catch for the total number of trips per fishing opportunity was used to identify target species. Generally for all of these studies, the one species making up the largest proportion of the catch was recognized as the target species. Stephens and MacCall (2004) developed a method to subset larger multispecies databases for trips that are most representative of a particular target species using logistic regression. In their model, the probability of encountering an individual species was determined by the presence of co-occurring species. The CPUE for the target species was then calculated from a 16  subset of trips that was predicted to have a high probability of encountering the target species and co-occuring species. Although a novel approach to this complex problem, there is potential to over-estimate the decline in CPUE of the target because those trips that catch only the target species are not included in the resulting subset because the trip is not associated with a cooccurring species. The resulting effort also continues to represent effort directed at multiple species and does not account for the influence other species may have on the resulting catch rates, which is true for all the studies previously mentioned. Although these studies attempt to define targeted fishing effort from typical fisheries dependent data within a rigorous statistical framework, a drawback is that by subsetting the data to be more “representative” of a particular species unintended bias in the resulting CPUE index could be introduced. For example, if the goal is to separate the data into groups representing one target species the clustering methods will reduce within group variance by selecting and grouping high catch trips for a given species. Selecting for high catch trips will inflate the resulting catch rate for a species and may introduce hyperstability (i.e. CPUE remains relatively stable at high abundances) into the index invalidating its use to represent proportional changes in abundance. Another drawback is that the statistical methods ignore potentially important underlying mechanisms that will influence the resulting catch of one species as it relates to another. For example, gear saturation and handling time effects are two mechanisms in which the density of one or more species will influence the catch of another species. A high density species can exclude another from the gear effectively reducing the catch rate of the lower density species. Similarly, the time spent handling one species will reduce the effort spent catching other potentially vulnerable species. Both mechanisms are known to cause hyperstability in relative abundance.  17  Aims of the project and thesis structure The Hawaiian bottomfish fishery exemplifies a multispecies fishery that is characterized by data limitations and assessment problems in the face of increasing management mandates. This fishery is used as a case study to propose and test a potential method for disaggregating species-specific abundance information from total effort and species-specific catch data and using a feedback simulation technique to compare the outcome of alternative management procedures in relation to the current management procedure. The main goals of this thesis are to (1) develop a tool to disaggregate abundance information from total effort and species-specific catch data as an attempt to move away from the current aggregate assessment approach, (2) evaluate the ability of aggregate and speciesspecific quota policies to meet management objectives, and (3) evaluate the current fisherydependent, as well as fishery-independent data collection programs in terms of meeting management objectives. Chapter 2 presents a mechanistic approach that accounts for technological interactions in the observation dynamics sub-model of the assessment framework. The approach stems from a simple hypothesis about the process of fishing. It is a hypothesis well documented in the predator-prey literature and eloquently describes the functional relationship between a predator’s catch rate of its prey species and the prey species density, namely, Holling’s disc equation (Holling 1959b). Borrowing from predator-prey theory and incorporating Holling’s disc equation into an integrated stock assessment framework allows for two problems that plague current stock assessments to be addressed; (1) non-stationarity in catchability and (2) the ability to predict the catch of an individual species and in turn estimate the historical abundance of individual species given information on total effort and catch by species. Monte Carlo 18  simulation experiments are conducted to quantify bias and precision and justify the use of this approach to meet the first goal of this thesis. Chapter 3 explores the application of this approach to the fishery-dependent data from the Hawaiian bottomfish fishery. Chapter 4 presents a management procedure evaluation to evaluate alternative data collection programs that may resolve current assumptions about the historical data, as well as evaluate alternative quota based policies in terms of meeting fisheries management objectives; e.g., maximizing catch, minimizing the risk of over-exploitation, and maintaining stable catch over time. Chapter 5 provides a synopsis of the main findings of this thesis and future avenues of research.  19  Tables Table 1.1 List of Hawaiian bottomfish target species. The * indicates species belonging to the Deep-7 complex. The following symbols indicate the three different depth categories to which the species belong according to Ralston and Polovina (1982), † 30m-140m, ‡ 80m-240m, §200m-350m. Hawaiian name  Family  Scientific name  Common name  Black ulua†  Carangidae  Caranx lugubris  Black jack  Butaguchi†  Carangidae  Psuedocaranx dentex  White trevally  Ta’ape†  Lutjanidae  Lutjanus kasmira  Bluestripe snapper  Uku†  Lutjanidae  Aprion virescens  Green jobfish  White ulua†  Carangidae  Caranx ignobilis  Giant trevally  Ehu*§  Lutjanidae  Etelis carbunculus  Ruby snapper  Kalekale*§  Lutjanidae  Pristipomoides sieboldii  Lavender jobfish  Onaga*§  Lutjanidae  Etelis coruscans  Flame snapper  Gindai*‡  Lutjanidae  Pristipomoides zonatus  Oblique banded snapper  Hapu’upu’u*‡  Serranidae  Epinephelus quernus  Hawaiian grouper  Kahala‡  Carangidae  Seriola dumerili  Greater amberjack  Lehi*‡  Lutjanidae  Aphareus rutilans  Rusty jobfish  Opakapaka*‡  Lutjanidae  Pristipomoides filamentosus  Crimson jobfish  20  0.03 0.02 0.00  0.01  CPUE  0.04  0.05  Figures  0.0  0.2  0.4  0.6  0.8  1.0  Abundance Figure 1.1 Three relationships between CPUE and abundance. The dashed line represents hyperstability, the solid line represents a proportional relationship, the dotted line represents hyperdepletion.  21  Figure 1.2 Map of the Hawaiian Islands. The analysis of this thesis focuses on the Main Hawaiian Islands. The Northwestern Hawaiian Islands is divided into two management zones; the Mau and Ho’omalu zones. The Mau zone includes Nihoa, Necker Island and is highlighted by the red circle. All other islands in the Northwestern Hawaiian Islands belong to the Ho’omalu zone. 22  Total catch (kgs)  5e+05 4e+05 3e+05 2e+05 1e+05  Total Effort (trips)  0e+00 10000  b)  8000  6000  4000  2000 100  Total CPUE (kgs/trip)  a)  c)  80 60 40 20 0 1950  1960  1970  1980  1990  2000  Years Figure 1.3 Summary of the fishery dependent catch and effort statistics reported for the Main Hawaiian Islands collected by the State of Hawaii Department of Aquatic Resources for 19482005. a) Total catch (summed across all species, excluding Ta’ape) measured in kilograms, b) total effort measured in the number of trips per year, and c) catch per unit effort (CPUE = kg/trip) for bottomfish species assemblage excluding Ta’ape.  23  Effort Licenses  Effort(10s of trips), Number of licenses  1200  1000  800  600  400  200  1950  1960  1970  1980  1990  2000  Year Figure 1.4 Annual number of trips and active licenses participating in the Hawaiian bottomfish fishery in the Main Hawaiian Islands from 1948 to 2005.  24  Hapu'upu'u* Kalekale* Opakapaka* Ehu* Onaga* Lehi*  4e+05  Gindai* Uku Kahala White Ulua Butaguchi Black Ulua  Catch (kgs)  3e+05  2e+05  1e+05  0e+00 1948  1954  1960  1966  1972  1978  1984  1990  1996  2002  Years Figure 1.5 Reported, species-specific catch, measured in kilograms from the Main Hawaiian Islands for years 1948-2005. The * indicates species belonging to the Deep-7 species complex.  25  1.2  Hapu'upu'u* Kalekale* Opakapaka*  Ehu* Onaga* Lehi*  Gindai* Uku Kahala  White Ulua Butaguchi Black Ulua  Proportion of total catch  1.0  0.8  0.6  0.4  0.2  0.0 1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003  Years Figure 1.6 Species composition of observed catch, measured as a proportion of the total observed catch, from the Main Hawaiian Islands for years 1948-2005. The * indicates species belonging to the Deep-7 species complex.  26  Chapter 2 Derivation of a multispecies assessment model that accounts for non-stationarity in catchability Introduction Relative abundance data derived from commercial fisheries are often inherently biased because of non-random fishing behavior. In spite of this, commercial catch-per-unit-effort (CPUE) data are still widely used because they are often the only data available for making inferences about changes in abundance of fish populations. In single-species fisheries, a nominal CPUE index can be defined as total catch divided by total effort, albeit it is naïve to do so, over a fixed time period. It is then assumed, again naively, that this index is proportional to abundance: ஼  ா  = ‫ܤݍ‬,  (1)  where q is the average catchability coefficient (i.e., the proportion of the population biomass, B, caught by one average unit of fishing effort), and E is fishing effort. Although very unlikely in most cases, catchability is most often assumed constant over time allowing for the assumption that catch per unit effort is proportional to biomass. A number of mechanisms can lead to changes in catchability. Changes in the spatial distribution of the target species, gear efficiency, targeting preferences, and fisher behaviors, such as search and handling time can lead to changes in catchability over time (Paloheimo and Dickie 1964, Mangel and Beder 1985, Crecco and Overholtz 1990, Hilborn and Walters 1992, Swain and Sinclair 1994). To develop relative indices of abundance, fishery independent surveys are sometimes conducted using consistent sampling gear under a random, systematic, or stratified random survey design. Given random or systematic sampling, the goal of fishery independent surveys is to provide an index of abundance that is proportional to abundance. In 27  the absence of relative indices of abundance developed from fishery independent surveys, CPUE standardization techniques are often employed. These include the use of generalized linear, generalized additive, or generalized linear mixed models to account for the effects of covariates such as sea surface temperatures, ex-vessel price for fish, gear type, area fished, vessel size, vessel horsepower, and season on catchability (Maunder 2001, Maunder and Punt 2004). In essence, the goal of CPUE standardization is to remove the impact of spatial, temporal, and environmental factors on catchability, so that it can then be assumed constant. Detailed timeseries or logbooks are often needed for CPUE standardization, but these are often unavailable. The problem with using CPUE as a relative abundance index becomes more complicated for multispecies fisheries, in which a number of species are targeted simultaneously. Fisheries dependent data from multispecies fisheries typically consist of species-specific catch and total effort, but information about the time spent fishing for one species versus another (i.e., targeting) is rarely, if ever, known. Without fisheries independent survey information it is very difficult to develop an unbiased relative abundance index for the individual species in a multispecies fishery. One approach has been to aggregate catch statistics over many species (i.e., the multispecies complex is treated as if it were a single species), thereby aggregating CPUE, to assess populations (e.g., Ralston and Polovina 1982, Agnew et al. 2000, Myers and Worm 2003). Ralston and Polovina (1982) conducted analyses at different levels of aggregation to determine which best explained the observed commercial catch of the Hawaiian bottomfish fishery. Agnew et al. (2000) conducted an aggregated assessment for 11 rajid species prosecuted around the Falkland Islands. Myers and Worm (2003), most notably, conducted a global analysis to evaluate the biomass trajectories of large predatory species prosecuted in several shelf and oceanic systems. A disadvantage of aggregation is that it does not provide information about  28  how the individual species are affected by fishing, which has important management implications. In one of the largest scale applications of aggregate CPUE data, Myers and Worm (2003) conducted a global assessment of commercial exploited fish species. Criticisms of their work included their use of the Japanese longline CPUE index to represent changes in abundance of important commercial pelagic species (i.e., tuna), the lack of spatially-corrected CPUE, and their assumption that catchability was constant over time, which allowed them to assume that aggregate CPUE represented changes in abundance of the global community of predatory species (Walters 2003, Hampton et al. 2005, Maunder et al. 2006, Polacheck 2006, Kleiber and Maunder 2008). This last assumption is likely to be erroneous because of changes in preferential targeting of species over time, improvements in fishing efficiency, changes in species distributions, changes in conspecific and inter-specific abundance, and inter-specific differences in productivity and catchability among species (Hampton et al. 2005, Maunder et al., 2006; Polacheck, 2006, Kleiber and Maunder 2008). Using a simple two-species model, Kleiber and Maunder (2008) demonstrated that ignoring inter-specific differences in productivity and catchability among species leads to a non-linear relationship between aggregate CPUE and abundance, even if fishing is random. More specifically, they showed that depending on the relative difference between productivity and catchability among species, the aggregate CPUEabundance relationship will either be hyperstable (CPUE remains high while biomass declines) or hyperdepleted (CPUE declines as abundance remains relatively high; Hilborn and Walters, 1992). Hyperstable indices lead to overestimates of abundance, whereas hyperdepleted indices lead to underestimates of abundance. In general, aggregate indices will not truly represent changes in aggregate abundance unless all species have the same catchability and productivity (Kleiber and Maunder 2008). 29  Sustainable yield and harvest rates are highly dependent on the population scale (i.e., carrying capacity) and productivity of the management unit, with less productive species expected to have a lower optimal harvest rate than more productive species. Simulation studies conducted by Paulik et al. (1967), Hilborn (1976, 1985) all demonstrated that treating a community of species or multiple stocks as a single unit leads to an overall optimal harvest rate that is heavily influenced by more productive species. Management policies based on a multispecies or mixed-stock harvest rate could therefore lead to the potential extirpation of less productive species that are not as resilient to fishing pressure as more productive species. Their results clearly demonstrate the trade-off between maximizing the productivity of a system and maximizing biodiversity (Walters and Martell 2004). Managers must consider the trade-off between overall productivity and biodiversity when developing fisheries management objectives. If there is little concern about the loss of weaker (i.e., least productive) species and instead greater interest in maximizing overall yield, an aggregate assessment approach may be adequate. Conversely, if maintenance of biodiversity and avoidance of overfishing for one or more species are stronger management objectives, policies could be designed to protect weaker stocks. Hilborn et al. (2004) demonstrated that “weak stock management” can lead to substantial losses in potential yield (e.g., the B.C. groundfish fishery would suffer a 90% reduction in yield to avoid overfishing the least productive species). This result does not consider the influence of fisher targeting behaviour. Branch and Hilborn (2008) demonstrated that fishers can adjust the composition of their catch to accommodate changes in fishing regulations (i.e., they targeted certain species less when those species’ quotas were reduced) by changing their targeting behavior. The ability of fishers to adjust their practices and targets to achieve species-specific quotas can potentially lead to a sustainable yield summed across species that is greater than the aggregate sustainable yield (Paulik et al. 1967). 30  Development of species-specific management policies for multispecies fisheries often depends on whether species-specific abundance information can be extracted from fishery dependent data sources. Many multispecies fisheries collect species-specific catch data, but only total effort data. Effort is a strong determinant of catch, and it has been recognized that if total effort is broken down using a time budget approach, the catching power of individual vessels or a fleet can be determined (Hilborn and Walters 1992). In simplest terms, total effort can be separated into components representing the total time spent searching for fishing locations and total time spent handling the gear and catch using the same basic derivation used by Holling for his disc equation (Holling 1959a, 1959b), which has been used extensively in the ecology literature to predict catch rates of prey by predators. The disc equation or the Type II functional response (Holling 1959a, 1959b) describes a hyperbolic relationship between the capture rate at which a predator will deplete its prey’s density. Using blind-folded human subjects searching for and handling paper “discs” and experimental parasite-host data, Holling showed that captures rates will not increase linearly with increasing prey density, rather capture rates will generally decline non-linearly with increasing prey density. Time consuming behaviours such as, the time spent searching and handling prey effectively limited the capture rate at higher prey densities causing this non-linear relationship. This relationship is predicated on two assumptions (i) the effective rate of search and (ii) the average time spent handling a prey item are independent of prey density. There are several reasons to expect why fishers might behave like an animal predator. Under higher prey densities, catch rates should be higher, but the relationship is expected to saturate at a maximum catch rate limited by how quickly fish can be landed and processed or simply handling time. Further, in a multispecies fishery at the simplest level, interspecific interactions are through a shared predator. Shared predation can sometimes result in apparent 31  competition and can lead to the depressed abundance of non-focal species as the abundance of the focal species declines (Holt, 1977). From a fisheries standpoint, this interaction can cause an initial suppression in the catch rate of a non-focal species. The initial suppression would then be followed by an increase in the catch rate of the non-focal species as the abundance of the focal species declines. This result could be misinterpreted as increasing abundance if catch rates are assumed proportional to abundance (Deriso and Parma 1987) and could lead to unintended depensatory fishing. The disc equation can be modified for multispecies scenarios (Walters and Martell 2004, also see Methods section). Modifying the disc equation to account for multiple prey species explicitly models the effects of inter-specific abundance on species-specific catch rates due to processes such as hook competition or territorial displacement on reefs. This equation predicts that the relative catchability of a non-focal species will increase as the abundance of a target species declines due to reduced hook competition. The result is an apparent increase in catch rate for the non-focal species This chapter proceeds in four phases. First, a stochastic, multispecies simulation model incorporating handling time is presented. Second, a systematic approach is used to evaluate how inter-specific differences and handling time influence the interpretation of aggregate catch rate data. Third, simulation-estimation experiments are used to evaluate the performance of the model in terms of its ability to estimate parameters describing the scale, productivity, and catchability at low stock size, as well as management reference points for individual populations from aggregate effort data. Fourth, the approach presented in this chapter is compared to the status quo approach of aggregating species data as is currently done in the Hawaiian bottomfish fishery.  32  Methods Simulation model A stochastic, multispecies simulation model was developed to generate typical fisheries dependent data (i.e., species-specific catch and total effort data). The simulation model includes a population dynamics sub-model for the individual fish populations and an observation submodel to generate species-specific catch data. All model parameters and variables used in this chapter are defined in Table 2.1. State dynamics The delay difference model (Deriso, 1980) was used to simulate the population dynamics of two, six, or 12 individual species in a multispecies fishery (Table 2.2). The delay difference model assumes that growth in weight follows the Ford-Brody growth equation, where weight-atage wa has a linear relationship to the previous weight-at-age wa+1: ‫ݓ‬௔ାଵ = 	ߙ	 + 	ߩ‫ݓ‬௔  (2)  for age Ai fish that are fully recruited to the fishery. The parameters ρ and α represent the slope (i.e., the negative log of the metabolic rate) and intercept parameters, respectively. Assuming the underlying length-age relationship can be described by the von Bertalanffy growth model, ρ and α can be approximated from the von Bertlanffy growth parameters k and w∞, which represent the metabolic rate coefficient and asymptotic weight (equations T2.2.2 and T2.2.3 in Table 2.2). The asymptotic weight for each species was calculated from known growth coefficients ai and bi for the length-weight relationship (eq. T2.2.4 in Table 2.2). Another assumption of the delay difference model is that fish age Ai and older are fully vulnerable to the fishery and are sexually mature. It is also assumed that fish age Ai and older 33  have the same natural mortality Mi. Natural mortality was assumed equal to 1.5 times the growth rate, commonly assumed from life history theory (Beverton and Holt 1959, Jensen 1996, T2.2.5). Natural survival Si was calculated as a function of fixed natural mortality, and annual total survival sit for species i at time t was calculated as a negative exponential function of total mortality Zit (eqs.T2.2.6, T2.2.7, T2.2.8). Total mortality was calculated as the sum of natural and fishing mortality Fit, where Fit was assumed to be the product of effort Et and speciesspecific, time varying catchability qit (eqs.T2.2.8, T2.2.9). It was assumed that the initial population biomass ‫ܤ‬௢೔ and numbers ܰ௢೔ 	were at equilibrium in the unfished state. Equations T2.2.10 through T2.2.13 were used to derive the age at recruitment Ai, numbers of an unfished stock Noi, mean weight of the unfished population wi , and recruits when the population is at an unfished state Roi, respectively. Assuming that weight followed the von Bertalanffy growth function and that growth parameters and weight at recruitment ‫ݓ‬஺೔ were known, the following equation can be solved for Ai: ‫ݓ‬஺೔ = 	 ‫ݓ‬ஶ೔ (1 − ݁ ି௞೔ ஺೔ )௕೔ ,  (3)  with Ai rounded to the nearest integer (eq. T2.2.10). The numbers for each species when the  population was at an unfished state ܰ௢೔ were calculated as the quotient of unfished biomass  ‫ܤ‬௢೔ and the mean weight of the unfished population ‫ݓ‬ ഥ ௜ (eq. T2.2.11). Mean weight of the unfished population ‫ݓ‬ ഥ ௜ was derived from the delay difference equation for biomass (eq.  T2.2.12). The recruits of an unfished population for each species ܴ௢೔ were calculated as a function of the numbers of an unfished population and natural survival (eq. T2.2.13). It was assumed that recruitment followed the Beverton-Holt relationship and was simulated as a stochastic process with independent, lognormal recruitment anomalies (eq. T2.2.14). Annual recruitment anomalies were randomly generated normal deviates, ωit 34  (eqs.T2.2.15). The standard deviations of the species-specific recruitment anomalies ߪఠ೔ 	were calculated as the component of the total standard deviation not associated with observation error (eq. T2.2.16), while the remainder of the total standard deviation was attributed to observation error. Recruitment at each time step was calculated as a function of biomass lagged by Ai years.  The Beverton-Holt recruitment parameters ‫ݏ‬௢೔ and βi in equation T2.2.14 represent the maximum juvenile survival rate and density dependence terms for each species i and were derived from recruitment compensation Κi (Myers et al. 1999) and recruitment and biomass of the unfished population, ܴ௢೔ and ‫ܤ‬௢೔ (eqs. T2.2.17, T2.2.18). Equations T2.2.19 and T2.2.20 were used to  update population numbers and biomass of species i over time t. Observation dynamics and derivation of the catch equation The observation dynamics sub-model was used to generate fishery dependent data similar to what are commonly collected. Catch by species and total effort are the most common fishery dependent data collected from multispecies fisheries, so the observation model was used to simulate species-specific catch data. To avoid the assumption that catchability is constant and therefore catch rates are proportional to abundance, the disc equation was used to generate the data to account for handling time and inter-specific hook competition. First, consider a fishery where total effort can be separated into two components representing i) the time spent searching for fishing locations and trying to catch fish and ii) the time spent handling the gear and processing the catch. The total time then is the sum of these two activities as described by Holling (1959b), i.e., 	்ܶ௢௧௔௟ = 	 ܶ௦ + 	 ܶ௛ .  (4)  Total handling time is the product of total catch, Ct, and the average time spent retrieving the fishing gear, removing fish from the gear, and redeploying the gear for each fish caught, h: 35  ܶ௛ = ℎ‫ܥ‬.  (5)  Assuming that catch (C) is proportional to abundance (N) and total search time Tsearch, the catch per total time fishing is given by: C = qNTs,  (6)  where q is a catchability coefficient. Substituting equation (6) into (5) yields: Th = h qNTs,  (7)  and then substituting equation (5) into (4) and solving for total search time yields: ೅೚೟ೌ೗ ܶ௦ = 	 ଵା௛௤ே .  ்  (8)  The full equations for catch and CPUE are thus: ‫	= ܥ‬  ௤ே்೅೚೟ೌ೗ ଵା௛௤ே  and  ஼  ்೅೚೟ೌ೗  =  ௤ே  ଵା௛௤ே  .  (9)  Following this derivation of Holling’s disc equation in Holling (1959b) and Walters and Martell (2004), total effort Et is partitioned into total time spent searching Tst and total time spent handling the catch and gear Tht (eq. T2.3.1). Total handling time is the product of the total  number of captured fish ∑௜ ‫ܥ‬௜௧ 	 ∑୧ C୧୲ and the average time spent handling h one unit of catch (i.e.,  one fish, eq. T2.3.2). It was assumed that average handling time was the same for all species. Assuming that catch is proportional to abundance while actively searching gives the catch equation T2.3.3. Through a series of substitutions (substitute eq. T2.3.3 into eq. T2.3.2, then substitute the result into eq. T2.3.1) total effort Et is given by equation T2.3.4. Equation T2.3.4 can then be solved for search time Tst (eq. T2.3.5), which is substituted into equation T2.3.3 to give an updated catch equation (eq. T2.3.6). Equation T2.3.6 implies that catch is weighted by the proportion of time spent searching. Dividing both sides of equation T2.3.6 by NitEt results in 36  the time-varying catchability coefficient (eq. T2.3.7 and eq. T2.2.21). Time varying, speciesspecific catchability was used to calculate annual, species-specific fishing mortality (eq. T2.2.9). Catch was simulated using the Baranov catch equation with independent log-normal  observation error ݁ జ೔೟ (eq. T2.2.22). Observation error νit was randomly generated from a normal distribution with mean 0 and standard deviation συi (eq. T2.2.23). The standard deviation among observations was calculated as the product of the total standard deviation ηi and the proportion of the total standard deviation associated with observation error ξi (Meyer and Millar 1999, eq. T2.2.24). Changes in mean weight of the catch can inform relative changes in survival and recruitment. A decline in mean weight of the catch may indicate a reduction in the survival of older, larger individuals or an increase in recruit, and vice versa (Schnute 1987). The speciesspecific catch mean weights were generated using equation T2.2.25, where ݁ ௪೔೟ represent  lognormal errors. The error terms for mean weight were randomly generated from a normal distribution with mean 0 and standard deviation σwi (eq. T2.2.26). An important aspect of any fisheries modeling exercise is to determine reference points on which management policies can be based. True reference points, maximum sustainable yield and the fishing mortality rate that achieves maximum sustainable yield, were also generated by the simulation model. A numerical relaxation technique similar to Walters et al. (2007) was used to find these reference points. Table 2.4 outlines the system of equations used to find these values. The approach involves an iterative search over hypotheses of total effort, beginning with an initial guess for species-specific catchability that is a function of the average handling time  per fish, the true catchability at low stock size ‫ݍ‬௢೔ and unfished numbers ܰ௢೔ . In other words, the initial guess for the catchability at equilibrium was: 37  ‫ݍ‬௘೔೙೔೟೔ೌ೗ =  ௤೚೔  ଵା௛ ∑ ௤೚೔ ே೚೔  (T2.4.1).  This initial value for catchability at equilibrium was used to solve equations T2.4.2 through T2.4.6 for long-term, species-specific total survival, mean weight, biomass, numbers, and catchability. Equations T2.4.2 and T2.4.3 follow the delay-difference calculations for total survival and mean weight of the unfished population that were previously specified in Table 2.2. This was done by first calculating equilibrium biomass. Equilibrium biomass (i.e.,  ௗ஻ ௗ௧  = 0) for  given hypotheses of total effort was obtained by substituting ‫ܤ‬௘೔ for Bit, the Beverton-Holt ஻೐  equation for Rit and ௪ഥ ೔ for Nit into annual biomass equation for each species t into equation ೐೔  T2.2.20, resulting in: ‫ܤ‬௘೔ = 	 ‫ݏ‬௘೔ ൬ߙ௜  ஻೐೔  ഥ ೐೔ ௪  + ߩ௜ ‫ܤ‬௘೔ ൰ + ‫ݓ‬஺ ௜  ௦೚೔ ஻೐ ೔  ଵା	ఉ೔ ஻೐ ೔  	.  (10)  Solving the above equation for ‫ܤ‬௘೔ gives T.2.4.4 for equilibrium biomass. Equilibrium numbers were then calculated as the quotient of equilibrium biomass and equilibrium mean weight (eq. T2.4.5). The value obtained for equilibrium numbers was applied to equation T2.4.6 to get the next iteration’s estimate of catchability at equilibrium, which was combined with the previous estimate of catchability using a relaxation weight sor. More specifically, the previous step was weighted by a value equal to 1-sor and the next iterate was weighted by sor (eq. T2.4.6). The new weighted value of catchability was then recycled through equations T2.4.2-T2.4.6 until catchability at equilibrium no longer changed. Catchability converged to a stable value within 20-30 iterations, with a sor of 0.9. Once convergence was obtained, equations T2.4.7 through T2.4.9 were used to calculate fishing mortality, total mortality and catch for each species and hypothesis of total effort. The 38  resulting catch curve (catch plotted against total effort) was used to determine MSY and EMSY for each species (eq. T2.4.10, T2.4.11). The maximum value of each catch curve across effort hypotheses was the MSY and the effort associated with the maximum catch value was EMSY for each species. FMSY was simply the product of EMSY and the associated equilibrium catchability after convergence (eq. T2.4.12). Catch for each effort hypothesis was then summed over all species to determine the aggregate catch curve (eq. T2.4.13). The maximum value of the aggregate catch curve across all effort hypotheses represented the MSY for the aggregate (eq. T2.4.14). Behaviour of the simulation model The behaviour of the simulation model was explored to show the influence of handling time on the catch rates of individual species with respect to changing abundance. Additionally, to evaluate the influence of handling time and the relative differences in productivity and catchability among species on aggregate CPUE and aggregate biomass, a systematic search over the recruitment compensation ratio Κ, the von Bertalanffy growth parameter k, and the catchability at low stock size qo was conducted. Species-specific catch was simulated using equation T2.2.22 and the parameters values outlined in Table 2.5. Aggregate biomass was simulated according to the population dynamics outlined in Table 2.2, where species-specific biomass is given by equation T2.2.20. Aggregate CPUE and aggregate biomass were then given by: ܿ‫	 = ݁ݑ݌‬  ∑೔ ஼೟ ா೟  (11)  and ‫∑ 	 = ܤ‬௜ ‫ܤ‬௜௧  (12) 39  The relationship between CPUE and biomass can be represented as a power function: ܿ‫ ܤݍ = ݁ݑ݌‬௠ ,  (13)  where the power parameter m determines the shape of the relationship between CPUE and biomass. A value of m equal to one would indicate proportionality, a value of m less than one would lead to hyperstability, and a value of m greater than one would lead to hyperdepletion (Hilborn and Walters 1992, Harley et al. 2001). Using a log-transformation, this equation can also be written as: ln ܿ‫ ݉	 = ݁ݑ݌‬ln ‫ ܤ‬+ 	 ln ‫ݍ‬.  (14)  where m is the slope of the linear relationship between the ln CPUE and ln B. The relationship between aggregate CPUE and biomass, which was a function of handling time and the relative differences between species-specific productivity and catchability, was determined by estimating m. This value was estimated using the linear modelling function in the stats package in R (R Core Development Team 2011). Estimation model An estimation model was used to predict simulated observations to determine the impact of fishing on historical abundance. The estimation model consisted of the same population and observation sub-models as those used in the simulation model. The estimation model was driven by observed effort (days fished) through the calculation of fishing mortality (eq. T2.2.9) and was  fit to the simulated catch and mean weight data. Predicted species-specific catch ‫ܥ‬መ௜௧ 	and species-  ෡௜௧ 	were calculated using equations T2.27 and T2.28, specific mean weight of the catch ܹ  respectively. It was assumed that errors in the observed catch and observed mean weight were normally distributed in log space and the residuals δCit between predicted Cˆit and observed catch 40  Cit were calculated using T2.2.29. The residuals δWit between predicted and observed mean weight were calculated using T2.2.30. The leading model parameters estimated by the estimation model were unfished biomass Boi, recruitment compensation Κi, catchability at low stock size qoi, and annual recruitment anomalies for each species ωit (eq. T2.2.1). The von Bertalanffy growth coefficient ki, growth parameters ai, bi, and weight at recruitment wki for each species as well as handling time were all assumed to be known. The negative log likelihoods of the catch and mean weight data given the model parameters Θi were calculated using equations  T2.2.31 and T2.2.32, respectively, where n is the number of years of catch observations and ߪఔଶ೔ and σ2wi are the observation error variance in catch and mean weight observations. The  recruitment anomalies were assumed to be distributed lognormally with a mean 0 and variance σ2ωi T2.2.33. Both σ2υi and σ2ωi were calculated as functions of total variance ηi and the proportion of the variance associated with observation error ξi, which were assumed to be known in this simulation study. The objective function to be minimized and used to obtain the most likely parameter combination for Θi was made up by the combination of the negative log likelihoods for the catch and weight observations and the recruitment anomalies and is given by equation T2.2.34. Predicted reference points were found using the approach outlined in Table 2.4. This is the same approach as previously explained for the simulation model, the only difference being that the initial guess for species-specific catchability was a function of average handling time per fish (assumed to be known) and the maximum likelihood estimates of ‫ݍ‬௢೔ and ܰ௢೔ .  41  Simulation-estimation experiments Simulation-estimation experiments were conducted to evaluate bias and precision in the estimated parameters and associated reference points used in policy. The simulation model was used to generate catch and average weights by species from true leading parameter and life history values (see Figure 2.1 for a diagrammatic representation). Several datasets were generated, differing in the number of target species (2, 6, or 12 species), effort scenario (i.e., contrasting effort or without contrast), and error level (ηi was equal to 0.1, 0.5, or 1; Table 2.6). This resulted in 18 scenarios. Differences among species were based on randomly generated combinations of unfished biomass Bo, the recruitment compensation ratio Κ, catchability at low stock size qo and the von Bertalanffy growth parameters (Table 2.7). Average handling time per fish was assumed to be the same for all species, all scenarios, and constant over time. An example of simulated datasets for a two-species fishery where data were generated with and without contrast is shown in Figure 2.2. Datasets with contrast were generated with a total effort series that gradually increased to a peak and then declined over time, causing fishing mortality and catch to have the same qualitative pattern. As a result, biomass declined as fishing mortality rates increased and then recovered as fishing mortality declined. Datasets without contrast were generated so that total effort increased over time, causing fishing mortality to also increase. Catch increased, reached a plateau as fishing mortality continued to increase, and in turn biomass declined over time. Table 2.6 summarizes the data scenarios used for the simulation-estimation experiments. The estimation model was applied to each dataset to estimate the leading and management parameters. Three assessment scenarios were explored in the estimation phase; i.e., in the estimation model, average handling time per fish h was assumed to be (i) equal to the true h, (ii) equal to zero (implying constant catchability), or (iii) greater than the true value. These 42  scenarios were explored in an attempt to evaluate bias when making the wrong structural assumption about h and therefore about catchability during the assessment process. A total of 54 simulation-estimation scenarios were considered. One hundred Monte Carlo simulations were carried out for each of the 54 scenarios. Bias in parameter estimation and reference points The suitability of the above approach to effectively estimate species-specific information describing population scale and productivity from total effort data was determined by examining the bias in species-specific leading parameter estimates Θi (T2.2.1) and management reference points. The ability to estimate these parameters was determined by calculating the differences between true and estimated values, using bias ratios calculated on a log2 scale (Schnute and Richards 1995, Fu and Quinn 2002): ܾ݅ܽ‫ 	 = ݏ‬log ଶ ቀ  ௉௥௘ௗ௜௖௧௘ௗ ்௥௨௘  ቁ  (15)  Bias ratios equal to 1 indicate a two-fold over-estimation, whereas a bias ratio of -1 indicates a two-fold under-estimation. Comparison to the status quo As a final step, the approach outlined in this chapter was compared to the status quo approach (i.e., an aggregate data set consisting of the sum of catches over all species). The same data generated for the 54 scenarios were used in this part of the analysis. The following modifications were done to make the multispecies data applicable to the status quo approach. First, species-specific catch was aggregated to represent total catch CTot: ‫்ܥ‬௢௧೟ = ∑௜ ‫ܥ‬௜௧ .  (16)  Annual total mean weight was calculated as follows: 43  ഥ ்௢௧ = ܹ ೟  ∑೔ ௐ೔೟  ே௨௠௕௘௥	௢௙	௦௣௘௖௜௘௦  .  (17)  Lastly, parameters such as the von Bertalanffy growth coefficient k, asymptotic weight ‫ݓ‬ஶ ,	and the growth parameters a and b were needed to derive other population dynamics variables in the estimation model. The mean value of each parameter was calculated from the values for individual species and applied to equations T2.2.2 through T2.2.5 and T2.2.10. The estimation model for the status quo approach was the same as that used for the simulation experiments, except that the assessment was done for an assumed single species and the average handling time per fish was assumed negligible (i.e., h = 0) in the observation dynamics submodel. This implies constant catchability, a common assumption in stock assessments. The model was fit to total catch and total mean weight data, and driven by total effort through the fishing mortality equation (FTot = qETot). The leading estimated parameters were unfished biomass Bo, the recruitment compensation ratio Κ and the assumed constant  catchability coefficient q, as well as annual recruitment anomalies ݁ ఠ೟ . A multispecies (i.e., aggregate) MSY was also predicted and compared to the individual-species MSY estimates outlined in this chapter. Results Influence of average handling time on CPUE and time-varying catchability Simulated datasets were examined to determine the influence of handling time on the relationships between CPUE and abundance for individual species and the aggregate population. It is often assumed that CPUE is proportional to abundance because catchability is assumed constant over time. Including handling time in the observation model resulted in a hyperstable CPUE-biomass relationship for individual species regardless of the differences among species (Table 2.8). The aggregate CPUE-biomass relationship, however, was either hyperstable or 44  hyperdepleted depending on the differences among species in the two-species scenario (Table 2.8, Figure 2.3). The majority of parameter combinations of the recruitment compensation ratio, von Bertalanffy growth coefficient, and maximum catchability led to hyperstability in the aggregate CPUE-biomass relationship (Figure 2.3). There was, however, evidence of hyperdepletion across a small range of parameter combinations (Figure 2.3). The aggregate CPUE-biomass was hyperdepleted across all Κ-ratios and k-ratios when the q-ratio was generally <1(Figure 2.3). The relationship was hyperdepleted across q-ratios > 1 when the Κ-ratio was ≤ 1 and the k-ratio was < 1 (Figure 2.3a, b). The domain of hyperdepletion widened for Κ-ratios > 1 in combination with k-ratios > 5 (Figure 2.3c, d). Although the CPUE-biomass relationship for individual species was always hyperstable, it should be pointed out that occasionally the difference among species in terms of recruitment compensation, von Bertalanffy growth coefficient, and maximum catchability led to an increase in CPUE as biomass declined for at least one species (Figure 2.4). This generally resulted from one species having a much higher maximum catchability than the other species. Measured bias in leading and management reference parameters Figures 2.5- 2.15 demonstrate the estimation performance of the model for each leading parameter and management reference point under the various scenarios. Overall, the leading parameters and reference points were estimated relatively well when the correct average handling time per fish was assumed in the estimation model. Contrast or lack of contrast in the simulated data was not particularly influential on the estimates. The magnitude of error used to generate the data, however, was highly influential on the precision of the parameter estimates. The number of species considered in the simulation-estimation experiments influenced the level 45  of bias in only some of the estimated parameters. Each of these factors is described further below. Figures 2.5-2.7 show the measured bias between true and predicted unfished biomass Bo for scenarios with two, six, and 12 target species, respectively. Accuracy was not influenced by the number of species, but there was a small loss in accuracy for datasets generated with larger error. Uncertainty in the estimates was larger for datasets generated with larger error, regardless of the number of species. Within a scenario for a given number of species, results were similar across datasets generated with and without contrast. Figures 2.5, 2.8, and 2.9 show the measured bias in the predicted recruitment compensation ratio Κ for the two-, six-, and 12-species scenarios, respectively. Of all parameters, the recruitment compensation ratio was estimated with the least accuracy and precision. It was well-estimated at the lowest error (η = 0.1), regardless of the number of species or whether the data were generated with or without contrast. Scenarios generated with larger error, however, generally led to a loss of accuracy and increased uncertainty in estimated recruitment compensation, for all scenarios regardless of the number of species or contrast/ lack of contrast in the data. Where accuracy was lost, there was a tendency to overestimate Κ. Figure 2.5, 2.10, and 2.11 show the estimated bias between the true and predicted catchability at low stock size qo for the two-, six-, and 12-species scenarios, respectively. This parameter was estimated with minimal bias for all scenarios. Uncertainty in qo estimates was greater for scenarios generated with larger error. Within a given level of error, qo was estimated with greater uncertainty for datasets generated with a greater number of species. The accuracy in qo estimates was not greatly influenced by the level of error for most scenarios. The 12-species  46  scenario associated with larger levels of error resulted in overestimates of qo. Estimates were similar for datasets generated with and without contrast in fishing effort. Bias in the reference points, MSY and FMSY, was minimal (Figure 2.5, Figures 2.122.15). Neither contrast in the data nor number of species seemed to influence the measured bias in the reference points. Similar to the measured bias in the leading parameters, inaccuracies and imprecision were greater, albeit minimal, for datasets simulated with higher levels of error. Inaccuracies in MSY generally were skewed towards under-estimation, whereas, inaccuracies in FMSY were skewed towards over-estimation. Incorrect assumptions about average handling time The estimated leading parameters and derived management points were inaccurately estimated when the incorrect handling time was assumed in the estimation model. Imprecision in the estimates increased as would be expected at higher levels of error (Figures 2.16, 2.17). Unfished biomass Bo was underestimated when it was assumed that handling time was either zero or greater than the average handling time used to generate the data (Figures 2.16, 2.17). The parameters Κ and qo tended to be underestimated when average handling time was assumed to be negligible in the assessment model ( Figure 2.16). Conversely, Κ and qo were overestimated when the assumed average handling time in the assessment model was greater than the handling time used to generate the data (Figure 2.17). Estimated MSY from status quo approach compared to the true Bias was measured between true aggregate MSY and the aggregate MSY predicted from the status quo approach. The status quo approach overestimated aggregate MSY regardless of 47  number of species, level of contrast, or level of error (Figure 2.18). The median value of measured bias was between 0.5 and 1 across all levels of error and levels of contrast for the two species scenario (Figure 2.18a). The same was true for the six and 12 species scenarios, except at the lowest level of error when the data were not simulated with contrast (Figure 2.18b, c). The median measure of bias indicates a six and 10 fold overestimation when data were generated at the lowest level of error for the six and 12 species scenarios, respectively. Discussion A stochastic, multispecies estimation model that allows for species-specific estimates of scale, productivity, catchability at low stock size, and management parameters while accounting for non-stationarity in catchability due to handling time effects was presented in this chapter. The approach was demonstrated using a delay-difference model to describe the population dynamics for multiple species and the catch equation based on Holling’s disc equation. This represented a step away from an aggregate assessment approach for fisheries targeting multiple species, in which the only fishery dependent data available are species-specific catch and total effort, life history and age-composition data are limited, and information about directed targeting does not exist. In the absence of targeting information, catch was predicted using the disc equation, which accounts for time limitations in gear operation. As an initial step, the model was used as part of a simulation framework to evaluate how handling time and inter-specific differences in productivity and catchability influence the interpretation of aggregate catch rate data (i.e., using total CPUE to represent changes in community abundance). The influence of handling time and changes in community composition on the catch rates of individual species was also evaluated. It was shown that the aggregate CPUE-biomass relationship is never proportional and therefore that assuming a constant, mean 48  catchability coefficient for the community does not accurately represent changes in community abundance. It was also shown that in some instances, catch rates of one species will actually increase as its abundance and the abundance of other species decline (Figure 2.4). Simulationestimation experiments were used to evaluate the performance of the model. Performance was quantified and evaluated as bias in the estimated parameters describing the scale, productivity, maximum catchability, and management reference points for individual species from aggregate effort data. It was shown that in general the leading parameters and reference points can be estimated reliably for individual species from aggregate effort data using this approach. Finally, the approach presented in this chapter was also compared to the status quo approach. It was shown that estimates of aggregate MSY were biased towards over-estimation when estimated by the status quo approach as compared to the multispecies approach developed in this chapter. This finding has strong implications for the management of multispecies fisheries. The use of aggregate abundance indices to represent changes in community abundance has been controversial, especially over the past several years. Examples of the aggregate approach include analyses done on the Hawaiian bottomfish fishery (Ralston and Polovina 1982, Moffitt et al. 2006), the ray fishery around the Falkland Islands (Agnew et al. 2000), and the global assessment of predatory species of Myers and Worm (2003). All assumed aggregate CPUE was directly proportional to aggregate abundance. There are two problematic assumptions implicitly made through this initial assumption. First, inter-specific differences in scale, productivity, and catchability were effectively ignored. This implies that rates of depletion in a community of species were the same as rates of depletion for each species. Second, it was assumed that catchability is constant over time. There are numerous case studies documenting changes in catchability (e.g., Peterman and Steer 1981, Crecco and Overholtz 1990, Swain and Sinclair 1994, Harley et al 2001, Polacheck 2006, to name a few) and it is highly unlikely that 49  catchability has remained constant in this fishery with the adoption of new technologies and fishing gear in Hawaiian bottomfish fishery. Through simulations, Kleiber and Maunder (2008) characterized the expected bias in aggregate CPUE. Simulations were done using the Schaefer production model to represent the population dynamics of two species that differed in terms of productivity and catchability. Their results showed that aggregate CPUE and aggregate abundance will always be non-linear unless the catchability and the productivity of each species are identical. More specifically, over time aggregate CPUE will be hyperstable when the ratio of productivity is greater than the ratio of catchability and hyperdepleted when the ratio of productivity is less than the ratio of catchability. Given the structural and parameterization differences between Kleiber and Maunder (2008) and the model used in this chapter, a direct comparison of the results cannot be made. The results presented in this chapter, however, confirm that the aggregate CPUE-biomass relationship will be either hyperdepleted or hyperstable depending on the inter-specific differences in productivity and catchability. Scenarios where one species was slower growing and had a higher underlying catchability than the other species led to hyperdepletion in aggregate CPUE. All other parameter combinations led to hyperstability in aggregate CPUE. The catch equation in this chapter accounted for time-varying catchability by incorporating information about average handling time per fish and changes in community composition, whereas Kleiber and Maunder (2008) assumed that catchability for each species was constant. Their assumption is convenient and directly relates changes in CPUE with abundance or changes in fishing mortality with effort. Various mechanisms pertaining to the biology of the target species as well as fisher behavior cause this assumption to be erroneous. These mechanisms include changing spatial distribution of the target population, changes in targeting, handling time, and increased gear efficiency (Paloheimo and Dickie 1964, Bannerot 50  and Austin 1983, Cooke and Beddington 1984, Crecco and Overholtz 1990, Swain and Sinclair 1994). Without detailed logbook information or fishery independent surveys it is difficult to know the magnitude of change in these factors and the resulting change in catchability. It has been shown theoretically and in applied situations that handling time causes hyperstability in catchability for single and multiple species scenarios (Paloheimo and Dickie 1964, Sinoda 1983, Cooke and Beddington 1984, and Deriso and Parma 1987). In other words, as abundance declines catchability will increase non-linearly. This corresponds to a larger proportion of the population being removed by a unit of effort as abundance declines. Handling time represents the combined limitation of the fishing gear’s capacity to capture fish and the fishers’ ability to process the catch. It also represents a loss of effective fishing time. Over a gradient of high abundances, there is a limit to the number of fish that can be caught given the gear limitations, therefore, handling time and effective fishing time will remain relatively stable resulting in relatively stable catch rates even though abundance may be declining from unfished abundance. With further declining abundance, total handling time declines while total effective fishing time increases. The increase in effective fishing time corresponds with a non-linear increase in catchability as abundance declines. This results in an asymptotic relationship between catch rates and abundance. The same asymptotic relationship holds true for multiple species scenarios. The combination of handling time and the abundance of other target species will also influence catchability of individual target species. For example, as the abundance of one target species increases, effective fishing time of other species declines due to increased handling time of the target species, leading to suppressed catch rates of the other species. Deriso and Parma (1987) illustrated that handling time effects can lead to negatively correlated catch rates (i.e., CPUE of one species declined while the CPUE of another increased) among species. In this chapter it was 51  demonstrated that this negative correlation is also dependent on the relative difference in the catchability at low stock size among species. This result has interesting ramifications: misinterpreting an increase in CPUE as an increase in abundance due to incorrectly assuming a proportional relationship between the two could lead to potential overfishing of the species with increasing CPUE when in fact it is declining. Given the simultaneous capture of multiple species, continued fishing of this species could lead to depensatory fishing of another species due to their incidental catch. In other words, if these species were not managed in tandem the more vulnerable species could be extirpated. Performance of the multispecies assessment model The simulation results point to the importance of moving away from an aggregate approach as well as accounting for time-varying catchability of individual species for assessment purposes. To this end, simulation-estimation modeling was done to quantify bias in the estimated leading parameters Θ (T2.2.1) when using the disc equation to predict species-specific catch from total effort data within a stock assessment framework. The ability to accurately estimate leading parameters relies on informative data, which is often synonymous with contrasting relative abundance indices (Hilborn 1979, Hilborn and Walters 1992). Hence, datasets simulated with good contrast were expected to render more accurate parameter estimates than datasets simulated without contrast (i.e., one-way trip), especially for the recruitment compensation ratio Κ. Accuracy of parameter estimates was fairly similar between datasets simulated with or without contrast, which was unexpected. The greatest effect on both accuracy and precision of parameter estimates seemed to be the magnitude of the total standard deviation with which the data were generated. The one-way trip datasets were simulated so that the individual populations were depleted to at least 20 percent of their unfished biomass, so the stock recruitment curves for most species were well defined, making them informative about the 52  recruitment compensation ratio Κ. Also, observations at low effort and high biomass, as well as high effort and low biomass were available and therefore informative about Bo and qo (Hilborn and Walters 1992). At the lowest level of total standard deviation, all parameters were estimated with high accuracy and precision. Moreover, Bo and qo were estimated accurately at all levels of error, but Κ was not. The ability to estimate Κ relies on either a recovery signal in the data, which is provided in datasets containing contrast (i.e., as effort declines, biomass increases or recovers), or observations of recruitment when stock size is very low. Observations at low stock size lead to a well-defined stock-recruitment curve, which provides information about maximum juvenile survival and mean recruitment at unfished stock size; the ratio of the two is equal to Κ. Higher levels of error in the form of recruitment anomalies may have distorted the stock recruitment curve leading to less accurate estimates of Κ. Hence, in absence of a strong depletion signal Κ was estimated less accurately than when a strong depletion signal was available. These findings are not that different from a single species assessment model where there is a lack of information in the relative abundance data to resolve confounding between stock size and productivity. The number of species did not greatly influence the accuracy or precision of parameter estimates, except for qo at the highest level of error and the fishery targeting 12 species. Although the bias was minimal, qo was overestimated to a greater extent (bias ~ 0.5) than scenarios with fewer species (bias ~ 0.1). FMSY is a function of catchability at low stock size; therefore an over-estimation of qo would in turn lead to the overestimation of FMSY. If fisheries management is based on input controls (i.e., limits effort instead of total catch) or the harvest control rule is based on estimates of FMSY this could lead to overfishing.  53  It should be reiterated that total standard deviation ηi was separated into components associated with observation error (ξiηi) and process error ((1–ξi)ηi). Total standard deviation was an estimated parameter, but given catch, effort, and mean weight data it was not possible to estimate ξi. As a freely estimated parameter, global maxima of the likelihood could be found when ξi = 0 (i.e., process error only model) or ξi = 1 (i.e., observation error only model), as was demonstrated in the errors-in-variables case presented by Schnute and Kronlund (2002). Preliminary simulation-estimation experiments were in agreement with the Schnute and Kronlund (2002) result, therefore, ξi was specified a priori. Alternatively an informative prior for ξi could also be defined. The magnitude of total standard deviation used to simulate the data were the main cause of imprecision in the parameter estimates. At higher levels of total error parametric uncertainty increased leading to greater imprecision in the parameter estimates. The apparent negative correlation between MSY and FMSY, was directly related to the negative correlation between Bo and Κ. Bias in Bo was skewed towards under-estimation and bias in Κ was skewed towards over-estimation, with maximum likelihood estimates for these parameters generally indicating that the stocks were small and productive. Species with higher productivity (i.e., high Κ), all else being equal, can withstand higher rates of fishing mortality than less productive species. An overestimate in Κ implies an upward bias in FMSY. A downward bias in Bo will lead to more conservative estimates of MSY. The accuracy and precision in the estimates of MSY and FMSY have important implications for management policies that use MSY-based reference points. Generally, where inaccuracies were observed, there was a small downward bias in estimates of MSY. Imprecision was variable and dependent on the level of error used to simulate the data. Considering the results with the least precision, the downward bias in MSY would mainly lead to management policies that avoid overfishing and would be considered precautionary. 54  Assumptions and expected directional bias The same model used to simulate the multispecies data was also used as the estimation model. In the estimation model, a number of assumptions were made with respect to the underlying “true” dynamics that may have led to optimistic results. The biological parameters describing the growth of each species (i.e., the von Bertalanffy growth parameters and weight-atrecruitment), were assumed to be known without error in the estimation model. A number of growth and mortality relationships were derived from these parameters, so that they were also assumed known without error. Biological parameters are never known with full certainty and the underlying relationships are rarely static. The population dynamics were described by the delaydifference model. Therefore, all assumptions inherent to the delay-difference model were assumed in both the simulation and estimation models. The goal of this chapter was to evaluate the sensitivity of the assessment model to different structural assumptions about catchability by adjusting handling time effects, as well as the interaction of species with different life histories. The assumptions made about the population dynamics of the simulated multispecies systems were employed and to keep the results tractable. Although, model sensitivity to these assumptions was not evaluated it is worth discussing the expected directional bias if assumptions were violated. Life history, productivity, maturity, and selectivity parameters are all factors that influence MSY-based reference points used as targets or limits of fisheries management policies. The life history of many species are often described by trade-offs between productivity and survival (Adams 1980, Roff 1984, Jensen 1996). A broad classification system indicates that species can be long-lived and slow growing (low von Bertalanffy growth coefficient, k), have low natural mortality rates, and have high age, length, and weight at maturity or can be shortlived and fast growing (high k), have high natural mortality rates, and have low age, length, and 55  weight at maturity (Adams 1980, Roff 1984). Adams (1980) evaluated the correlation between these measures and showed these basic relationships for anchovies, salmon, cods, rockfishes and flatfishes. Long-lived, slower growing species are generally considered less productive than their short-lived, faster growing counterparts. Adams (1980) showed that long-term yield and fishing mortality was lower for long-lived and slower growing species than short-lived and faster growing species. All else being equal, the fishing mortality to achieve MSY (FMSY) for an individual species will be positively correlated with k. FMSY would be expected to be overestimated when incorrectly assuming a species has a faster growth rate (larger value of k) in the estimation model. Under repeated simulation testing, the estimate of FMSY would be positively biased. Conversely, FMSY would be expected to be underestimated if incorrectly assuming a slower growth rate (smaller value of k) in the assessment model and under repeated simulation testing this would manifest as a negative bias. The size at recruitment is also positively correlated with fishing mortality, but negatively correlated with k (Beddington and Kirkwood 2005). All else being equal, incorrectly assuming a larger size at recruitment would lead to an overestimate of long-term fishing mortality. Given the negative correlation between size at recruitment and k, it would be difficult to speculate about directional bias as a combined pair. Selectivity, the effectiveness with which fishing gear captures fish with respect to age or size, also influences the long-term average fishing mortality a particular species can withstand (Myers and Mertz 1998, Quinn and Deriso 1999). The selectivity schedule was assumed to be known and constant over time in the estimation model. The assumed shape of the selectivity schedule relative to the “true” underlying relationship is a source of potential bias in the fishing mortality estimate. For example, assuming knife-edge selectivity in the estimation model, as is done for the delay-difference model, when the “true” selectivity relationship is dome-shape 56  (which is generally due to a strong spatial segregation of a stock relative to ontogeny or due to a size-refuge from the fishing gear) will overestimate the fishing mortality of older individuals and underestimate their numbers. In this example, BMSY would be expected to be overestimated and FMSY underestimated. Butterworth and Rademeyer (2008) compared the stock status estimates for the Gulf of Maine (GOM) cod stock when assuming asymptotic and dome-shape selectivity. Stock status estimates were highly dependent on the assumed selectivity relationship and the GOM cod population was considered overfished due to lower estimated of abundance when assuming an asymptotic selectivity curve than when assuming a dome shape curve. Fully vulnerable fish are also assumed to be fully mature in the delay-difference model. Myers and Mertz (1998), using a theoretical example, demonstrated that the age at selectivity with respect to the age of maturity is also an important determinant of the long-term average fishing mortality. They specifically showed that higher fishing mortality can be achieved by modifying the age at selectivity so that fish are allowed to reproduce (i.e., reach maturity) prior to becoming fully vulnerable to the fishing gear. An overestimate of long-term average fishing mortality would be expected if age at maturity and vulnerability to the fishing gear were incorrectly assumed the same while the “true” age at maturity was greater than the “true” age at full vulnerability. An assumption made in the observation dynamics sub-model was that average handling time per fish h is constant over time. A decline in h would be expected with increased gear efficiency and as fishers become more experienced. All else being equal, the catchability of a species at time t would be underestimated, as would fishing mortality at time t, if h was incorrectly assumed to be larger than the “true” h. In turn, biomass would be overestimated. If h was assumed to be larger than the true value over the entire time series, the estimation model  57  would tend to bias towards a small, productive population. This relationship would in turn lead to an over-estimation of FMSY and under-estimation of BMSY. A comparison of species-specific and aggregate management reference points The “true” aggregate MSY and the MSY estimated by the status quo approach were greater than any of the species-specific MSYs, which is not surprising. Less productive species could be subject to overfishing in the absence of management policies that allocate the aggregate MSY among species. Using the status quo approach, aggregate MSY was grossly overestimated. An inherent assumption of aggregate assessments and management policies is that the aggregate data or an assumed mean relationship for scale and productivity parameters adequately represent the individual species that make-up a multispecies fishery. Predicted aggregate MSY was much greater than the true aggregate as well as the MSYs for individual species. The status quo approach assumed that effort and fishing mortality rates were proportional (i.e., handling time was negligible). This assumption combined with ignoring the differences among species led to the over-estimation of MSY, which in turn would undoubtedly lead to overfishing of less productive species. Hilborn (1976) and Hilborn (1985) demonstrated that less productive species will be overfished when treating a community of species as a single species. Recently, Worm et al. (2010) considered the impacts of exploitation on fish communities and demonstrated that as exploitation rates increased total catch increased to a multispecies MSY (in this chapter multispecies MSY has been referred to as aggregate MSY). As total catch approached multispecies MSY, approximately 40 percent of the stocks collapsed and catch was then dominated by more productive species. In other words, managing with a multispecies MSY policy inevitably leads to less productive stocks collapsing. In the United States, management 58  policies are guided by the Magnuson-Stevens Act, which indicates that a fishery must enter a recovery plan if a species is being over-fished (i.e., weak stock management). Continued use of aggregate assessments will inadvertently lead to some species being over-fished, so this policy goal will not be met. Weak stock management is a debated management approach. Although the goal is to protect less productive species, it may lead to loss of potential catch of more productive species. Hilborn et al. (2004) determined that in order to avoid overfishing less productive species, weak stock management policies would lead to a 90% loss of potential catch by the west coast groundfish fishery. Hilborn (1976), Hilborn (1985), and Hilborn et al. (2004) assume that the scale and productivity of the target species are the main determinants of catch and not the targeting behavior exhibited by fishermen. Branch and Hilborn (2008), in contrast, demonstrated for the British Columbia groundfish fishery that fishermen will modify their fishing practices to adjust the mixture of species making up their catch in accordance to quota adjustments. They also showed that when quotas were reduced fishers targeted species with higher quotas. The work presented in this chapter does not account for targeting of specific species. This chapter, however, outlines an assessment method that can be used to develop species-specific quotas using the most common type of multispecies fishery dependent data available, species-specific catch and total effort. By incorporating information about handling time in the catch equation, effective fishing time for each species is accounted for and allows for the prediction of speciesspecific catch from total effort. This approach relies on having an estimate of handling time. If data about handling can be collected from the fishery, either through interviews with fishermen or direct observations of fishing vessels, this information can be easily incorporated into a stock assessment framework and ultimately provide estimates of abundance and management reference points for individual 59  species making up a multispecies fishery. Moreover, this approach allows for the development of species-specific management policies to protect less productive species without the complete loss of catch of more productive species.  60  Tables Table 2.1 Parameter symbols and descriptions used to describe the state and observation dynamics models. Notation  Description  Units  Subscripts i  Species  t  Year  Estimated Parameters ‫ܤ‬௢೔  Unfished biomass  kg  Recruitment compensation ratio  -  Catchability at low stock size  days-1  Asymptotic weight  kg  von Bertalanffy growth coefficient  -  Length-weight scalar  cm/kg  Length-weight power parameter  -  Age of recruitment  years  h  Average handling time per fish  days  Et  Annual fishing effort  days  Observed landings  kg  Observed mean weight of landed fish  kg  Κ௜  ‫ݍ‬௢೔ Growth Parameters ‫ݓ‬ஶ೔ ݇௜  ܽ௜ ܾ௜  ‫ܣ‬௜ Observed States  ‫ܥ‬௜௧  ܹ௜௧  Continued on the next page  61  Table 2.1 continued Notation  Description  Units  Biomass  kg  Unfished numbers, Numbers  numbers  Unfished recruits, Recruits  numbers  qit  Time varying catchability  days-1  Fit  Annual fishing mortality  -  sit  Annual survival  -  Predicted landings  kg  Predicted mean weight of landed fish  kg  ρi  Slope of the Ford-Brody growth function (metabolic rate parameter)  -  αi  Intercept of the Ford-Brody growth function  kg  Mi  Natural mortality  -  Si  Natural survival  -  Mean weight at Ai  kg  Mean weight of unfished population  kg  Maximum juvenile survival rate  recruit/spawner  Unobserved States Bit  ܰ௢೔ Nit ܴ௢೔ Rit  ‫ܥ‬෢ ప௧  ෢ప௧ ܹ Derived Parameters  ‫ݓ‬஺೔ ‫ݓ‬௜  ‫ݏ‬௢೔ βi  Recruitment scalar  recruit/spawner Continued on next page  62  Table 2.1 continued Notation  Description  Units  νit  Observation error  kg  ωit  Process error  number of recruits  Error in mean weight observations  kg  ηi  Total standard deviation  -  ξi  Proportion of ηi associated with observation error  -  Catch residuals  kg  Weight residuals  kg  Standard deviation of νit  kg  Standard deviation of ωit  number of recruits  Error and likelihood parameters  ‫ݓ‬௜௧  ߜ஼೔೟  ߜௐ೔೟ ߪజ೔  ߪఠ೔ ߪ௪೔  Standard deviation of ‫ݓ‬௜௧  kg  Equilibrium parameters ‫ݏ‬௘೔ೕ  ‫ݓ‬ ഥ௘೔ೕ ‫ܤ‬௘೔ೕ  ܰ௘೔ೕ ‫ݍ‬௘೔ೕ ‫ܨ‬௘೔ೕ  ܼ௘೔ೕ  Total survival at effort hypothesis e Mean weight of the unfished population at hypothesis e  kg  Biomass at hypothesis j  kg  Number at hypothesis j  numbers  Catchability at hypothesis j  days-1  Fishing mortality at hypothesis j  -  Total mortality at hypothesis j  -  63  Table 2.1 continued Notation  Description  Units  Catch at hypothesis j  kg  Aggregate catch at hypothesis j  kg  Aggregate maximum sustainable yield  kg  Effort that obtains aggregate MSY  days  Fishing mortality that obtains MSY  -  Equilibrium parameters continued ‫ܥ‬௘೔ೕ  ‫ܥ‬௘ೌ೒೒  ೕ  MSYagg ‫ܧ‬ெௌ௒ೌ೒೒ ‫ܨ‬ெௌ௒೔  64  Table 2.2 The operating model used for the simulation-estimation experiments. The state dynamics were parameterized according to the delay difference model (Deriso, 1980), recruitment was described by the Beverton-Holt model, and the observation model was derived from Holling’s disc equation. Equation number Description Subscripts i  Species  t  Time  Estimated Parameters T.2.2.1  Θ = (‫ܤ‬௢ ௜ , ߈௜ , ‫ݍ‬௢೔ , ߟ௜ , ߱௜௧ )  Growth Parameters  T.2.2.2 T.2.2.3 T.2.2.4  ߩ௜ = 	 ݁ ି௞೔  ߙ௜ = 	 ‫∞ݓ‬೔ (1 − 	 ߩ௜ ) ‫ݓ‬ஶ೔ = 	 ܽ௜ ‫ܮ‬ஶ೔ ௜ ௕  Mortality and survival T.2.2.5 T.2.2.6  Mi = 1.5ki  ܵ௜ = 	 ݁ ିெ೔  T.2.2.7  ‫ݏ‬௜௧ = 	 ݁ ିெ೔ ି	ி೔೟ or ‫ݏ‬௜௧ = 	 ݁ ି	௓೔೟  T.2.2.8  Zit = Fit +Mi  T.2.2.9  Fit = qitEt Continued on next page  65  Table 2.2 continued Equation number  Description  State dynamics model  T2.2.10 T2.2.11  T2.212 T2.2.13 T2.2.14 T2.2.15 T2.2.16 T2.2.17  T2.2.18 T2.2.19 T2.2.20  ‫ܣ‬௜ = 	 − ܰ௢೔ =  ‫ݓ‬ ഥ௜ =  ‫ܤ‬௢೔ ‫ݓ‬ ഥ௜  ‫ۉ‬  ௪ಲ ೔ ቇ ௪ಮ೔ ௕೔  ݇௜  + 	1‫ۊ‬ ‫ی‬  ܵ௜ ߙ௜ + 	 ‫ݓ‬஺೔ (1 − ܵ௜ ) 1 − ߩܵ௜  ܴ௢೔ = 	 (1 − ܵ௜ )ܰ௢೔ ܴ௜௧ =  ‫ݏ‬௢ ௜ ‫ܤ‬௜௧ି஺೔ ఠ ݁ ೔೟ 1 + ߚ௜ ‫ܤ‬௜௧ି஺೔  	߱௜௧ ~	ܰ൫0, 	ߪ௪೔ ൯  ߪఠ ௜ = 	 (1 − 	 ߦ௜ )ߟ௜ ‫ݏ‬௢೔ = ߚ௜ =  Κ ௜ ܴ௢೔ ‫ܤ‬௢೔  Κ ௜ − 	1 ‫ܤ‬௢೔  ܰ௜௧ = ‫ݏ‬௜ ܰ௜௧ିଵ + ܴ௜௧ିଵ  ‫ܤ‬௜௧ = 	 ‫ݏ‬௜௧ିଵ (ߙ௜ ܰ௜௧ିଵ + 	 ߩ௜ ‫ܤ‬௜௧ିଵ ) + 	 ‫ݓ‬஺ ௜ ܴ௜௧ିଵ  Observation dynamics model T2.2.21  ln ‫ۇ‬−݁  ୪୬ቆ  ‫ݍ‬௜௧ =  ‫ݍ‬௢ ௜ 1 + ℎ ∑௜ ‫ݍ‬௢ ௜ ܰ௜௧  Continued on next page  66  Table 2.2 continued Equation number  Description  Observation dynamics model T2.2.22 T2.2.23 T2.2.24  ‫ܥ‬௜௧ =  ‫ܨ‬௜௧ (1 − ݁ ି௓೔೟ )‫ܤ‬௜௧ ݁ ఔ೔೟ ܼ௜௧  ߥ௜௧	 ~	ܰ൫0, ߪఔ೔ ൯ ߪఔ೔ = 	 ߦ௜ ߟ௜  ‫ܤ‬௜௧ ௪ ݁ ೔೟ ܰ௜௧  T2.2.25  ܹ௜௧ =  T2.2.26  wit ~ N(0,σwi)  T2.2.27  ‫ܥ‬෢ ప௧ =  T2.2.28 Likelihood T2.2.29 T2.2.30 T2.2.31  T2.2.32  T2.2.33  T2.2.34  ‫ܨ‬௜௧ (1 − ݁ ି௓೔೟ )‫ܤ‬௜௧ ܼ௜௧  ෢ప௧ = ܹ  ‫ܤ‬௜௧ ܰ௜௧  ߜ஼೔೟ = 	 ln ‫ܥ‬௜௧ − 	 ln ‫ܥ‬෢ ప௧  ෢ప௧ ߜௐ೔೟ = 	 ln ܹ௜௧ − 	 ln ܹ  ∑௧ ߜ஼ ௜௧ ଶ ݊ ‫ܥ(ܮ‬௜௧ |ߠ௜ ) = 	 ln ߪఔ೔ + 2 2ߪఔ೔ ଶ  ∑௧ ߜௐ ௜௧ ݊ ‫ܮ‬൫ܹ௜ |ߪ௪೔ ൯ = 	 ln ߪ௪೔ + 2 2ߪ௪೔ ଶ  ଶ  ∑௧ ߱௜௧ ଶ ݊ ‫ܮ‬൫߱௜ |ߪఠ೔ ൯ = 	 ln ߪఠ೔ + 2 2ߪఠ೔ ଶ  Ψ௜ = 	 ෍ ‫ܥ(ܮ‬௜௧ |	߆) + ෍ ‫ܮ‬൫ܹ௜௧ |ߪ௪೔ 	൯ 	 + ෍ ‫ܮ‬൫߱௜௧ |σఠ೔ ൯ ௜  ௜  ௜  67  Table 2.3 Derivation of Holling’s disc equation for multiple species. Equation number T2.3.1 T2.3.2 T2.3.3  Description  ‫ܧ‬௧ = ܶ௛೟ + ܶ௦೟  ܶ௛೟ = ℎ	 ෍ ‫ܥ‬௜௧ ௜  ‫ܥ‬௜௧ = 	 ‫ݍ‬௢೔ 	ܶ௦೟ 	ܰ௜௧  T2.3.4  ‫ܧ‬௧ = 	 ܶ௦೟ + 	ℎ ෍ ‫ݍ‬௢೔ ܶ௦೟ ܰ௜௧  T2.3.5  ܶ௦೟ =  ‫ܧ‬௧ 1 + ℎ ∑௜ ‫ݍ‬௢೔ ܰ௜௧  ‫ݍ‬௜௧ =  ‫ݍ‬௢೔ 1 + ℎ ∑௜ ‫ݍ‬௢೔ ܰ௜௧  T2.3.6  T2.3.7  ‫ܥ‬௜௧ =  ௜  ‫ݍ‬௢೔ ܰ௜௧ ‫ܧ‬௧ 1 + ℎ ∑௜ ‫ݍ‬௢೔ ܰ௜௧  68  Table 2.4 Equilibrium analysis to determine reference management points. Equation number  Description  Subscripts i  Species  j  Effort hypothesis  T2.4.1  ‫ݍ‬௘೔೙೔೟೔ೌ೗ =  T2.4.2  ‫ݏ‬௘೔ೕ = 	 ݁  T2.4.3  ‫ݓ‬ ഥ௘೔ೕ =  T2.4.4  ‫ܤ‬௘೔ೕ = 	 −  T2.4.5  ܰ௘೔ೕ =  T2.4.6 T2.4.7 T2.4.8 T2.4.9  T2.4.10 T2.4.11  ‫ݍ‬௢೔ 1 + ℎ ∑ ‫ݍ‬௢೔ ܰ௢೔  ିெ೔ ି	ாೕ ௤೐೔ೕ  ‫ݏ‬௘೔ೕ ߙ௜ + ‫ݓ‬஺೔ ቀ1 − ‫ݏ‬௘೔ೕ ቁ 1 − ߩ௜ ‫ݏ‬௘೔ೕ  −‫ݓ‬ ഥ௘೔ೕ + ‫ݏ‬௘೔ೕ ቀߙ௜ + ߩ௜ ‫ݓ‬ ഥ௘೔ೕ ቁ + ‫ݓ‬஺೔ ‫ݏ‬௢೔ ‫ݓ‬ ഥ௘೔ೕ ߚ௜ ൬−‫ݓ‬ ഥ௘೔ೕ + ‫ݏ‬௘೔ೕ ቀߙ௜ + ߩ௜ ‫ݓ‬ ഥ௘೔ೕ ቁ൰  ‫ܤ‬௘೔ೕ  ‫ݓ‬ ഥ௘೔ೕ  ௤೚  ‫ݍ‬௘೔ೕ = 	 (1 − ‫ݍ)ݎ݋ݏ‬௘೔ೕ + 	‫ ݎ݋ݏ‬ଵା௛ ∑ ௤೔  ೚೔ ே೐೔ೕ  ‫ܨ‬௘೔ೕ = 	 ‫ܧ‬௝ ‫ݍ‬௘೔ೕ  ܼ௘೔ೕ = ‫ܨ‬௘೔ೕ + ‫ܯ‬௜ ‫ܥ‬௘೔ೕ =  ‫ܨ‬௘೔ೕ  ܼ௘೔ೕ  ቀ1 − ݁  ି௓೐೔ೕ  ‫ܻܵܯ‬௜ = max	ቀ‫ܥ‬௘೔ೕ ቁ  ,sor = 0.9  ቁ ‫ܤ‬௘೔ೕ  ‫ܧ‬ெௌ௒೔ = 	 ‫ܧ‬௝ 	|	max	ቀ‫ܥ‬௘೔ೕ ቁ  Continued on next page  69  Table 2.4 continued Equation number T2.4.12 T2.4.13  T2.4.14  Description  ‫ܨ‬ெௌ௒೔ = 	 ‫ܧ‬ெௌ௒೔ ‫ݍ‬௘  ‫ܥ‬௘ೌ೒೒	 = 	 ෍ ‫ܥ‬௘೔ೕ ೕ  ௜  ௜  ‫ܻܵܯ‬௔௚௚ = max	ቀ‫ܥ‬௘ೌ೒೒	 ቁ ೕ  70  Table 2.5 Parameter values that were systematically varied to measure non-proportionality in species-specific and total CPUE. All other state dynamic parameters in the model were fixed and the same for each species. Parameter  Species 1  Species 2  Κ  2, 5, 20, 40  5  qo  0.05, 0.1, 0.2, 0.3, 0.4, 0.5  0.1  k  0.05, 0.15, 0.3, 0.45, 0.6, 0.75  0.1  Bo  1  1  71  Table 2.6 Data scenarios used for the simulation-estimation experiments to determine bias in the estimated leading parameters Θ. Number of species 2  6  12  x  Total standard deviation ηi  Data type  0.1  Contrast  0.5  1  x  x  x x  x  x x  x  x  x  x  x x  x  x x  x  x  x  x x  x  x  x x  x  x  x  x  x x  x  x x  x  x  x  x x  x x  x  x x  One-way trip  x x  x  x x  x  x x  x  72  Table 2.7 Parameter combinations used for the simulation-estimation experiments. Parameter combinations built upon one another to make the results comparable among the scenarios with two-, six-, and 12-species. Number of species Bo Κ qo L∞ k a b 479.92  38.21  0.294  131.93  0.118  0.007  333.74  5.22  0.245  100.63  0.177  0.013  479.92  38.21  0.294  131.93  0.118  0.007  333.74  5.22  0.245  100.63  0.177  0.013  150.45  8.23  0.213  143.35  0.138  0.006  692.65  3.78  0.263  140.84  0.137  0.007  735.22  26.99  0.299  181.80  0.122  0.008  412.97  44.26  0.258  195.26  0.175  0.013  479.92  38.21  0.294  131.93  0.118  0.007  333.74  5.22  0.245  100.63  0.177  0.013  150.45  8.23  0.213  143.35  0.138  0.006  692.65  3.78  0.263  140.84  0.137  0.007  735.22  26.99  0.299  181.80  0.122  0.008  412.97  44.26  0.258  195.26  0.175  0.013  3 2  6  3  3 12  536.37  5.76  0.225  131.36  0.250  0.007  766.16  7.07  0.228  160.84  0.244  0.008  348.39  2.39  0.263  160.49  0.346  0.015  728.67  3.02  0.274  132.51  0.147  0.007  87.85  2.66  0.269  140.12  0.334  0.009  985.62  2.53  0.227  122.35  0.319  0.010  73  Table 2.8 Measure of non-proportionality (m) for individual species and the resulting aggregate for fisheries simultaneously capturing 2 species. The recruitment compensation Κ, the von Bertalanffy growth coefficient k, and catchability at low stock size q0 differed for each species. The relative difference between species is expressed as parameter specific ratios. Κratio  0.4  0.4  0.4  kratio  0.5  3  6  qratio  mspecies1  mspecies2  maggregate  0.5  0.9973  0.9979  1.0048  2  0.9994  0.9967  1.0043  5  0.9998  0.9938  1.002  0.5  0.9817  0.9980  1.0143  2  0.9965  0.9952  0.9828  5  0.9982  0.9891  0.9758  0.5  0.9257  0.9977  1.1019  2  0.9758  0.9883  0.9657  5  0.9806  0.9733  0.9413  0.5  0.9754  0.9979  1.0445  2  0.9970  0.9964  0.9526  5  0.9994  0.9932  0.9453  0.5  0.8869  0.9991  1.1687  2  0.9534  0.9971  0.8634  5  0.9727  0.9918  0.7862  0.5  0.7440  0.9992  1.4510  2  0.9063  0.9972  0.8385  5  0.9263  0.9873  0.6598  6 0.5  6 3  6 6  74  Table 2.9 Hypothetical true MSY values for individual species that make-up a multispecies fishery and the resulting aggregate MSY. Data were generated without contrast with an h = 0.0833. Predicted aggregate MSY resulted from the status quo approach where average handling time h is assumed to equal zero. Results are reported for two-, six- and 12-species scenarios at three levels of error expressed as the total standard deviation (η = 0.1, η = 0.5, η = 1). Number of species η = 0.01 η = 0.5 η=1 2 21.9723 24.6216 19.6646 16.4429  21.4245  9.1726  True MSYagg  38.4121  46.036  28.6839  Predicted MSYagg  80.8738  67.039  58.3407  6  24.4361  22.7043  30.165  15.7723  24.3119  18.0132  6.43356  5.19155  7.59606  19.9204  7.56937  36.3887  31.9155  43.8306  18.7544  28.3629  24.3756  26.0081  True MSYagg  120.622  119.343  132.718  Predicted MSYagg  1509.64  192.085  246.193  12  18.7076  20.6172  15.0767  12.5771  14.5665  6.17099  5.80168  6.74081  6.32879  20.5425  21.0626  8.39041  29.7557  40.1208  27.6805  19.7382  27.862  7.8141  23.7387  23.7587  28.8465  34.6127  28.159  52.161  12.1015  30.1175  12.7135  25.4055  22.1581  45.9439  3.72884  1.61229  4.04047  38.0421  15.3103  31.6348  True MSYagg  244.746  249.647  246.431  Predicted MSYagg  8218.88  9624.53  477.248  75  Figures  Number of species True handling time True life history and population parameters Total effort series Error level  100 random seeds  Simulation Model  True reference points MSYi, FMSYi  True handling time Observed catch and weight by species Life history data Total effort series  Estimation Model  Predicted reference points MSYi, FMSYi  Predicted Boi, qoi, Κi , ωit  Figure 2.1 A flow chart of the simulation-estimation framework used for this chapter. Eighteen data scenarios were evaluated using this framework. Data scenarios were determined by the combination of average handling time per fish, effort series (with or without contrast), error level, and number of species. One hundred Monte Carlo simulations were performed for each scenario.  76  1.2 0.4 0.0  20  30  40  50  60  Catch Biomass  10  20  30  40  50  60  10  20  30  40  50  60  10  20  30  40  50  60  d)  0  0  200  c)  10  20  30  40  50  60  0 300  0  f)  100 0  0  100  200  e)  200  300  0  400  10  200  400  0  Catch and Biomass  b)  0.8  0.8 0.4 0.0  Fishing mortality  Species 1 Species 2  a)  0  10  20  30  40  50  60  0  Year  Figure 2.2 Examples of the catch observations and biomass trajecotries generated by the simulation model. The example depicted in the figure represents a two species fishery, either (a, c, e) with or (b, d, f) without contrast. Panels a and b depict simulated fishing mortality rates with and without contrast, respectively. Panels c and d show examples of catch and biomass for species one, while panels e and f show catch and biomass for species two.  77  b)  κratio = 0.4  1.6  7  4  0.8  3 2 1 6  1  1.2 1.0  4  0.8  0.6  3  0.6  0.4  2  0.4  0.2  1  0.0 4  1.4  0.2 1  1  1  5 kratio  kratio  1.0  1.6  6  1.2  5  8  2  qratio  d)  κratio = 2  m  1.6  8  0.8  5  kratio  1.0 1.2  m  1.6 1.4  6  1.2 0.8  κratio = 6  7  1.4  6  1.2  5  1.0  4  0.8  3  0.6  3  2  0.4  2  0.4  0.2  1  0.2  1  1  0.0  1  2  4 qratio  6  8  0.8  1  kratio  6  qratio  7  4  4  0.0  1.2  c)  m  7  1.4  6  2  κratio = 1  m  1.2  a)  0.6  0.0 2  4  6  8  qratio  Figure 2.3 A systematic search over the recruitment compensation ratio Κ, the von Bertalanffy growth coefficient k, and catchability at low stock size qo (see Table 2.5 for parameter combinations) and the resulting relationship between aggregate CPUE and aggregate biomass as measured by ݉. An ݉ = 1 indicates the relationship is proportional, ݉ < 1 indicates hyperstability, and ݉ > 1 indicates hyperdepletion. Simulations were done for a hypothetical fishery targeting two species simultaneously.  78  b)  0.12 0.08  100  200 300  400  10  30  50  70  d)  3.0  0.025 0.030 0.020  4.0  Catchability  5.0  0.035  c)  CPUE  0.10  Catchability  15 5  10  CPUE  20  25  0.14  a)  100 150 200 250 300 Biomass  30  40  50  60  Numbers  Figure 2.4 Example of the CPUE-biomass and the corresponding time-varying catchabilitynumbers relationships for a hypothetical two species fishery where handling time is part of the fishing process. a, b) Species have a higher catchability at low stock size qo than that of the species in panels c and d.  79  0.4 0.0 -0.4 1.0  d)  0.0 -0.5 f)  0.0 -0.5 -1.0  -1.0  -0.5  0.0  0.5  1.0 -1.0  0.4 0.0  e)  0.5  1.0 -1.0  -0.5  log2  b)  0.5  c)  0.5  1.0  -0.4  0.0  a)  Bo1BBo2 κ 1Κκ 2 qo1 MSY 1 F2MSY1 MSY2 qoqo2MSY FFMSY MSY o  BB MSY FMSY2 o1 Bo2 κ 1Κκ 2 q o1 1 F2MSY1 qoqo2MSY FMSY MSY o  Figure 2.5 Estimated bias for unfished biomass Bo, the recruitment compensation ratio Κ, catchability at low stock size qo, and the reference points MSY and FMSY. Results are from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The data were generated for a two species fishery, with three different levels of error: (a, b) η = 0.1; (c, d) η = 0.5; and (e, f) η = 1, and either (a, c, e) with or (b, d, f) without contrast. Parameter combinations used to simulate the data can be found in Table 2.7. Note the t y-axis scales for panels a and b are the same, but differ from panels c-f.  80  1.0 0.0  d)  f)  0.0 -1.0  0.5  0.0  e)  1.0  -1.0  0.0  0.5  1.0  -1.0  0.0 -1.0 1.0 -1.0  0.0  0.5  c)  -1.0  0.5  1.0  Bias in Bo (log2)  b)  0.5  a)  0.5  1.0  \  Figure 2.6 Estimated bias for unfished biomass Bo resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  81  d)  1.0  0.0  0.0 -1.0  e)  1.0  -1.0  0.0  0.5  1.0  -1.0  0.0  0.5  b)  f)  0.5  1.0 1.0 -1.0  0.0  0.5  c)  -1.0  0.5  1.0  Bias in Bo (log2)  -1.0  0.0  0.5  a)  Figure 2.7 Estimated bias for unfished biomass Bo resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  82  1.0 0.0 -1.0 2 2  -2  -1  0  1  d)  1  f)  -1  -1  -2  -2  0  1  e)  0  b)  0.5  1.0 -2  -1  0  1  c)  2  Bias in K (log2)  2  -1.0  0.0  0.5  a)  Figure 2.8 Estimated bias for the recruitment compensation ratio Κ resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  83  d)  1.0  -0.5  -0.5 -1.5  e)  1.5  -1.5  -0.5  0.5  1.5  -1.0  0.0  0.5  b)  f)  0.5  1.0 -1.5  -0.5  0.5  c)  -1.5  0.5  1.5  Bias in K (log2)  1.5  -1.0  0.0  0.5  a)  Figure 2.9 Estimated bias for the recruitment compensation Κ resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  84  d)  1.0  0.0  0.0 -1.0  e)  1.0  -1.0  0.0  0.5  1.0  -1.0  0.0  0.5  b)  f)  0.5  1.0 -1.0  0.0  0.5  c)  -1.0  0.5  1.0  Bias in qo (log2)  1.0  -1.0  0.0  0.5  a)  Figure 2.10 Estimated bias for catchability at low stock size qo resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  85  d)  1.0  -0.5  -0.5 -1.5  e)  1.5  -1.5  -0.5  0.5  1.5  -1.0  0.0  0.5  b)  f)  0.5  1.0 -1.5  -0.5  0.5  c)  -1.5  0.5  1.5  Bias in qo (log2)  1.5  -1.0  0.0  0.5  a)  Figure 2.11 Estimated bias for catchability at low stock size qo resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  86  d)  1.0  0.0  0.0 -1.0  e)  1.0  -1.0  0.0  0.5  1.0  -1.0  0.0  0.5  b)  f)  0.5  1.0 1.0 -1.0  0.0  0.5  c)  -1.0  0.5  1.0  Bias in MSY (log2)  -1.0  0.0  0.5  a)  Figure 2.12 Estimated bias for MSY resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  87  d)  1.0  0.0  0.0 -1.0  e)  1.0  -1.0  0.0  0.5  1.0  -1.0  0.0  0.5  b)  f)  0.5  1.0 1.0 -1.0  0.0  0.5  c)  -1.0  0.5  1.0  Bias in MSY (log2)  -1.0  0.0  0.5  a)  Figure 2.13 Estimated bias for MSY resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  88  d)  1.0  0.0  0.0 -1.0  e)  1.0  -1.0  0.0  0.5  1.0  -1.0  0.0  0.5  b)  f)  0.5  1.0 1.0 -1.0  0.0  0.5  c)  -1.0  0.5  1.0  Bias in Fmsy (log2)  -1.0  0.0  0.5  a)  Figure 2.14 Estimated bias for FMSY resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing six species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  89  d)  1.0  -0.5  -0.5 -1.5  e)  1.5  -1.5  -0.5  0.5  1.5  -1.0  0.0  0.5  b)  f)  0.5  1.0 1.5 -1.5  -0.5  0.5  c)  -1.5  0.5  1.5  Bias in Fmsy (log2)  -1.0  0.0  0.5  a)  Figure 2.15 Estimated bias for FMSY resulting from 100 Monte Carlo simulations where the data were generated with handling time and estimated with the known, true handling time. The simulated data represented a fishery simultaneously capturing 12 species. The data were simulated at three different levels of error a, b) η = 0.1, c, d) η = 0.5, and e, f) η = 1 and generated a, c, e) with and b, d, f) without contrast. The boxes within each figure panel represent one species. Parameter combinations used to simulate the data can be found in Table 2.7.  90  1  (b)  0.0  (c)  -1.0  -0.5  0.0  0.5  1.0  -1.0  -0.5  log2  0.5  1.0  -4  -3  -2  -1  0  (a)  Bo1  Bo  Bo2  κ1  Κ  κ2  q o1  qo  q o2  MSY1  MSY  MSY2  FMSY1  FMSY2  FMSY  Figure 2.16 Estimated bias for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo, MSY, and FMSY. Results are from 100 Monte Carlo simulations. The data were generated for a two species fishery. Data were generated at three different levels of error a) η = 0.1, b) η = 0.5, and c) η = 1and generated without contrast. Data were generated with handling time and parameters were estimated without handling time (i.e. htrue > 0 and hest = 0). Parameter combinations used to simulate the data can be found in Table 2.7.  91  (b)  1.0 0.0  (c)  -1.0  -0.5  0.0  0.5  1.0  -1.0  -0.5  log2  0.5  1.0  -2.0  -1.0  0.0  (a)  Bo1  Bo  Bo2  κ1  Κ  κ2  q o1  qo  q o2  MSY1  MSY2  MSY  FMSY1  F  FMSY MSY2  Figure 2.17 Estimated bias for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo, MSY, and FMSY. Results are from 100 simulation-estimation experiments. The data were generated for a two species fishery. Data were generated without contrast at three different levels of error a) η = 0.1, b) η = 0.5, and c) η = 1. Data were generated with handling time and the parameters were estimated with handling time that was larger than the true handling time (i.e. hest > htrue). Parameter combinations used to simulate the data can be found in Table 2.7.  92  No Contrast  a)  -0.5 0.0 3.0 5  0.0  1.0  2.0  b)  c)  0  1  2  3  4  Bias in Aggregate MSY (log2)  0.5  1.0  1.5  Contrast  η0.01  η0.5  η1  η0.01  η0.5  η1  Figure 2.18 Measured bias between the true aggregate MSY and the estimated aggregate MSY from the status quo approach for a) two-, b) six-, and c) 12-species scenarios when handling time is assumed to be known. Each bar represent the distribution in measured bias for data generated at three levels of error (η = 0.1, η = 0.5, and η = 1).  93  Chapter 3 Assessment of the Hawaiian bottomfish fishery while accounting for non-stationarity in catchability Introduction Multispecies fisheries are often characterized by technical interactions where multiple species can be simultaneously captured by a single fishing gear (Murawski 1984). The multiple target species will generally vary in productivity and population scale; therefore, each species will differ in their tolerance to fishing pressure (Paulik et al. 1967, Hilborn 1976, Christensen and Walters 2004). Ultimately, the goal of stock assessment is to estimate the scale and productivity of a population(s) and use these estimates to better inform decision makers by providing estimates of reference points, stock status, and predictions about how the stock will respond to alternative harvest policies. An important step in estimating the scale and productivity of a population(s) is relating changes in fishery-dependent or fishery-independent observations, generally a relative index of abundance, to changes in population abundance. The component of the stock assessment framework that relates unobserved states such as population size, to observable states such as catch, or catch rates is generally referred to as the observation sub-model. The catchability coefficient, q, is often the one parameter in the observation dynamics sub-model that is used to scale the catch or catch rate observations to population abundance. In many stock assessments, the catchability coefficient is assumed constant and nominal catch rates are assumed proportional to abundance. Many studies have recognized that catchability often varies over time and is density-dependent (see Wilberg et al. 2010 for a review of these studies). Assuming catchability is constant when it is not generally leads to biased abundance and fishing mortality estimates. Another challenge when assessing a multispecies fishery is that the 94  available effort data do not reflect the amount of effort directed at a single species, or if targeting for different species changes over time. Total effort is a coarse measure of fishing effort. Even when species-specific catch is known, total effort does not contain information about targeting and makes it difficult to determine the effective fishing effort towards an individual species. This lack of information makes it difficult to develop indices of abundance for individual species that make up a multispecies fishery. In the absence of scientific surveys, methods used to assess multispecies fisheries have mainly been the same as those used to address single species fisheries. One approach has been to aggregate the catch statistics by summing over species. The summed catch in combination with total effort has been used to develop an aggregated index of abundance. Another approach that follows a prevailing trend in single species assessments is to use covariates that account for changes in targeting (i.e., catch or catch rates of other species) as part of a catch-effort standardization procedure. Another approach has focused on methods to subset multispecies databases using ordination and classification methods to better define directed targeting on individual species. Aggregate CPUE has been used as an index of abundance in several examples to draw conclusions about changes in the abundance of a community of species due to fishing pressure. For example, Ralston and Polovina (1982) and Moffitt et al. (2006) used the catch and effort data for Hawaiian bottomfish fishery to estimate aggregate abundance. Agnew et al. (2000) used the CPUE from a multispecies rajid fishery prosecuted around the Falkland Islands to estimate stock size and sustainable yield for the rajid community. Myers and Worm (2003) conducted a global analysis of shelf and oceanic communities using aggregated CPUE to estimate the depletion of these communities. Aggregating catch and effort statistics over many species effectively treats the multispecies complex as a single species. This approach effectively ignores any differences in the productivity and catchability among species, thereby, ignoring the response of individual 95  species to fishing pressure. The assessment results from an aggregate assessment will largely be determined by the dominant species captured and smaller or less productive stocks may experience overfishing (Paulik et al. 1967, Hilborn 1976, Christensen and Walters 2004). Another approach that has been used is to follow a prevailing trend in single species assessments and use catch-effort standardization methods to develop a relative index of abundance for a single target species (e.g., Punt et al. 2001 and Glazer and Butterworth 2002). In the most common applications, standardization has been mainly done using either generalized linear, generalized additive, or generalized linear mixed models with the main objective being to remove the influence of temporal, spatial, and environmental covariates on catch and effort data (Maunder 2001, Maunder and Punt 2004). The main result of the standardization process is hopefully an index of abundance that reflects proportional changes in abundance so that a single, constant catchability coefficient for a target species of interest can be estimated. The CPUE standardization literature is extensive. There is, however, a paucity of examples incorporating the effects of targeting other species in these standardization models, which would be an expected influential factor. Recognizing that changes in targeting can influence catch rates among species Punt et al. (2001) and Glazer and Butterworth (2002) used the catch and catch rates, respectively, of non-focal species to standardize the catch rate of a target species. More specifically, Punt et al. (2001) used the catch of pink ling (Genypterus blacodes) as an explanatory variable to better explain the variation in blue grenadier (Macruronus novaezelandiae) catch rates in an Australian trawl fishery. Glazer and Butterworth (2002) used the catch rate of all bycatch species as an explanatory variable to standardize aggregate CPUE of west coast hake (Merluccuis capensis and M. paradoxus) in South Africa. Often the change in catch or catch rates among multiple species will be correlated over time. As a result, using the catch or catch rate of non-focal species catch as an explanatory variable will 96  remove the time effects in the standardization procedure and underestimate the variation in CPUE that can be explained by the procedure (Maunder and Punt 2004). Another branch of work that has tried to address the problem of targeting effects on observed catch and effort collected from multispecies fisheries has used a variety of statistical methods (e.g., ordination methods, cluster analysis, and logistic regression) to estimate directed fishing effort for single species and species assemblages from multispecies fisheries data (Murawski et al. 1983, Rogers and Pikitch 1992, Lewy and Vinther 1994, Biseau 1998, Pelletier and Ferraris 2000, Stephens and MacCall 2004, Ulrich and Andersen 2004, Branch et al. 2005). Regardless of the statistical technique or the covariates used to explain the variation among groups, the resulting clusters or subsets from the multispecies database may introduce unintended bias in the resulting relative indices of abundance. For example, if the goal is to separate the data into groups representing one target species the clustering methods will reduce within group variance by selecting high catch trips for a given species. Selecting for high catch trips can inflate the resulting catch rate for the species of interest and may introduce hyperstability (i.e. CPUE remains relatively stable at high abundances) into the index invalidating its use to represent proportional changes in abundance. Another drawback is that the statistical methods ignore potentially important underlying mechanisms that will influence the resulting catch of one species as it relates to another. For example, gear saturation and handling time effects are two mechanisms by which the density of one or more species will influence the catch of another species (Deriso and Parma 1987, Rodgeveller et al. 2008). A high-density species can exclude another from the gear effectively reducing the catch rate of the lower density species. Similarly, the time spent handling one species will reduce the effort spent catching other potentially vulnerable species. Both mechanisms are known to cause hyperstability in relative abundance (Walters and Martell 2004). 97  Fisheries management organizations are increasingly being mandated to reduce overfishing by adopting a precautionary approach to fisheries management (FAO 1996). An important factor in meeting this objective for multispecies fisheries is the ability to make predictions on a per species basis. It has been recognized that new approaches to address multispecies fisheries is needed. To that end, Walters and Bonfil (1999) developed a spatial model that assigned observed catch and effort for individual trawls to 1nmi2 grids. The spatial CPUE estimates and an estimate of the average area swept by the trawl nets were then used to better understand the spatial distribution of vulnerable biomass per species. This study and the previously mentioned studies have data requirements that many fisheries, especially those in the tropics and sub-tropics, do not have. Therefore, not only is there a need to develop models to address multispecies fisheries, but also those that can accommodate data limited situations. As mentioned in Chapter 1: General Introduction, the Hawaiian bottomfish fishery is an example of a data-limited, multispecies fishery. This fishery has been assessed using an aggregate approach ignoring the impact of fishing on the individual species. This chapter represents a step moving away from the aggregate surplus production model used to assess the Hawaiian bottomfish fishery. In this chapter, the mechanistic approach developed in Chapter 2 was applied to the Hawaiian bottomfish fishery data (Main Hawaiian Islands, 1948-2005). This was done to account for technical interactions among species that describe this fishery and account for a mechanism (i.e., handling time effects) that is known to cause hyperstability in fishery-dependent catch and effort data. Using this multispecies assessment framework allows for the estimation of key parameters of interest (i.e., leading parameters) related to the population scale, productivity, and catchability of the individual target species. It also allows for stock status determination and the development of management reference points for the individual target species that are used to determine stock status and fishing mortality rates relative to 98  sustainable levels and develop fishery management policies. The multispecies assessment approach used in this chapter is fitted to species-specific catch. The ability to predict speciesspecific catch using this method is conditional on having an empirical estimate of average handling time. An empirical estimate of average handling time per fish was not available for this assessment. A range of values for the average handling time per fish was developed and the model outcomes across different average handling time per fish values were compared. Lastly, a Bayesian approach was employed to incorporate prior knowledge about productivity, as measured by the recruitment compensation ratio, given the lack of information contained in the catch-effort time series and to quantify uncertainty in the species-specific leading parameters and the species-specific management reference points. Methods Data Commercial catch and effort data were compiled from sales records collected by the Hawaiian Department of Aquatic Resources (HDAR) from 1948 until 2005. Effort and catch data were extracted from the database for the Main Hawaiian Islands only. The data from the Northwest Hawaiian Islands were not included in this analysis given that they are currently closed to fishing and future management actions will only pertain to the Main Hawaiian Islands. The effort and catch data were based on the monthly trip tickets that indicated date fished and the corresponding catch in weight by species (see Figures 1.2b and 1.3 for the effort time-series and Figure 1.4 for the catch data). Each trip was assumed to be equivalent to one day of fishing, the prevailing assumption during previous bottomfish assessments (Moffitt 2006), and was used as the unit of fishing effort used in this assessment. The species included in this analysis accounted for 90 percent of the total catch over the majority of the catch history (Figure 1.5). They include 99  10 of the 13 species, which is made up of all the Deep 7 species (Table 1.1), as well as Seriola dumerili (Kahala), Aprion virescens (Uku), and Caranx ignobilis (White ulua). Analytical methods All parameters, after initial introduction, will be referred to using symbols. The symbols and associated parameter definitions can be found in Table 3.1. Additionally, the system of equations used for this analysis can be found in tabular format. The numbering convention for the equations is as follows: each equation numbers begin with a T followed by the table number and the equation number within the ordered list of equations. State dynamics The analytical method used in this chapter is identical to what was presented in Chapter 2. A brief description and any points of departure will be provided here. The state dynamics of the individual Hawaiian bottomfish species were modeled using the delay-difference model (Deriso, 1980), where recruitment was updated each year according to the Beverton-Holt model. The state dynamic equations can be found in Chapter 2, Table 2.2. The derivations of the growth parameters, the mortality and survival equations, and the equations used to update annual numbers and biomass of the individual Hawaiian bottomfish species are outlined in equations T2.2.2 through T2.2.20. The delay difference model assumes that growth in weight follows the Ford-Brody growth equation, where weight-at-age wa has a linear relationship to the previous weight-at-age wa+1: ‫ݓ‬௔ାଵ = 	ߙ	 + 	ߩ‫ݓ‬௔  (1)  100  for fish that are fully recruited to the fishery. The parameters ρ and α represent the slope (i.e., metabolic rate) and intercept parameters, respectively. Assuming the underlying length-age relationship can be described by the von Bertalanffy growth model, ρ and α can be approximated from the von Bertlanffy growth parameters k and w∞, which represent the metabolic rate coefficient and asymptotic weight (equations T2.2.2 and T2.2.3 in Table 2.2). The asymptotic weight for each species was calculated from known growth coefficients ai and bi for the lengthweight relationship (eq. T2.2.4 in Table 2.2). The von Bertalanffy growth parameters were assumed to be known. The values used for this analysis were gathered from published literature and are summarized in Table 3.2. Observation dynamics The observation dynamics sub-model was used to predict the observed catch for each of the 10 Hawaiian bottomfish species included in this analysis. It was assumed that handling time effects would be an important determinant of catch, given that the Hawaiian bottomfish fishery is a handline fishery. Since these species can be captured simultaneously, handling time effects represent a mechanism that can describe the technical interactions among species (i.e., the handling of one species represents lost fishing time for another species). Additionally, handling time is a known cause of hyperstability in handline fishery catch statistics (Paloheimo and Dickie 1964, Cooke and Beddington 1984, Deriso and Parma 1987), which is an assessment concern for this fishery. Species-specific catch was predicted by way of using Holling’s disc equation. The disc equation was used to predict time varying, species-specific catchability qi (Table 2.2, eq.T2.2.21). The disc equation accounts for changes in catchability via the time budget of the fishing process (time spent searching and time spent handling fish) and relative abundance of each species that competes for hooks within the multispecies fishery. More specifically, total effort is separated into the time spent searching for fish and the time spent handling the gear and 101  landing fish. As was shown in the derivation of the disc equation in Chapter 2, Table 2.3, time varying catchability is a function of species-specific maximum catchability, average handling time per fish, and conspecific and interspecific abundance. Equation T2.2.21 indicates that time varying, species-specific catchability is the species-specific maximum catchability weighted by the proportion of time spent searching (i.e., actively fishing). It was assumed that fishing mortality and natural mortality occurred simultaneously and predicted catch was based on the Baranov catch equation (eq. T2.2.27). Average handling time per fish Average handling time per fish h was assumed to be known and constant over time, whereas maximum catchability qoi was an estimated parameter, but also assumed constant. An empirical estimate of h was not available. A range of values for the average handling time per fish was derived based on the published drop and retrieval times, the depth range of the target species, and the minimum and maximum number of fish that can be captured per line. The Hawaiian bottomfish fleet is a boat-based fishery and currently uses electric handlines configured with a terminal weight, multiple hooks (on average 4 circle hooks) and a chum bag to attract fish. Fishers commonly use twelve volt powered electric reels manufactured by Elec-TraMate. Based on the published gear performance specifications, these reels have drop and retrieval speeds ranging from 257-531feet per minute. Fishing generally happens between 60 and 1200 feet and anywhere from zero to eight fish can be caught per line. Given these statistics, the average handling time per fish could be between three seconds to 10 minutes. ଶ  ℎ=஼  ವ ೑೛೘  ೟೚೟ೌ೗  (2)  102  where D is the depth fished, fpm is the drop or retrieval speed in feet per minute, and Ctotal is total catch. The quotient in the numerator is multiplied by two to account for the drop and retrieval time. The units of the derived average handling time values were minutes per fish. Effort in the HDAR database represent one day of fishing. It was assumed that each trip represented a tenhour fishing day. Average handling time per fish was then converted to days per fish. Table 3.3 summarizes the values for the average handling time per fish explored in this analysis. Estimated leading parameters, likelihood, and priors The estimated parameters of interest (i.e., leading parameters) for each species i were  unfished biomass ‫ܤ‬௢೔ 	and the recruitment compensation ratio Κi, which described the scale and  productivity of the individual populations and the maximum catchability coefficient ‫ݍ‬௢೔ . Other  estimated parameters included annual recruitment anomalies, ωit, and the total standard deviation, ηi, that was apportioned between the observation and process errors for each species. Collectively, the estimated parameters of interest are represented by Θ (eq. T3.4.1). The model was fit to the data using an objective function P(Θ) that contained three components: 1.) the negative log-likelihood of the catch data given the model parameters, 2.) the prior distributions for some model parameters, and 3.) a penalty function to constrain the fishing mortality rate. The negative log-likelihood of the annual catch of species i given the parameters of interest Θ and is given by equation T3.4.2, where n is the number of observations, δCit is the  annual catch residuals (see eq.T2.2.29 for the residual equation), and ߪజ೔ is the standard deviation in the catch residuals. The standard deviation of the catch residuals was calculated as a proportion of the total standard deviation, ηi. Annual recruitment anomalies ωit were assumed to  be lognormally distributed with a mean equal to 0 and standard deviation equal to ߪఠ೔ (T3.4.4). An informative prior for the recruitment compensation ratio Κ was used. The recruitment  103  compensation ratio Κ was transformed to steepness (Myers et al. 1999, Martell et al. 2008) and a beta prior on steepness was used (eq. T3.4.5). The beta distribution can be used to describe random variables that have a range between zero and one (Evans et al. 2000). The steepness parameter has a range between 0.2 and 1 for the Beverton-Holt model (Myers et al. 1999). The first term in equation T3.4.5, was used to scale the steepness parameter between zero and one. Fishing mortality for each species was also constrained using the penalty given by equation T3.4.6. Figure 3.1 provides an example of the penalty used on the fishing mortality rates of the individual Hawaiian bottomfish species. This penalty on the fishing mortality constrained the parameter search from wandering into regions causing unrealistically high fishing mortality rates. The objective function, P(Θ), is given by equation T3.4.7 and is sum of the negative loglikelihoods, the prior on the recruitment compensation ratio, and the penalty on the mean fishing mortality rate. The initial values for the parameters that make up Θ are reported in Table 3.5. The joint posterior of the estimated parameters was numerically approximated using a Markov Chain Monte Carlo (MCMC) procedure implemented in AD Model Builder, which uses a version of the Metropolis-Hastings algorithm (Gelman et al. 2004, ADMB Project 2009). For each hypothesis of average handling time, the MCMC was run for 7 million iterations. The chain was thinned by saving every 5th iteration. A total of 1.4 million iterations were saved. The first 1.2 million saved iterations were discarded as burn-in. Traceplots of the Markov Chain were visually inspected to determine whether the chain had converged (see Figures A.1-A.15, Appendix A). Plots of the marginal and joint posteriors of the estimated leading parameters and management reference points were generated from 20,000 random samples.  104  Management parameters Maximum sustainable yield (MSY), the fishing mortality rate to achieve MSY (FMSY), and the biomass needed to achieve MSY (BMSY) were determined for each species. To obtain these estimates, the average relationship between surplus production, effort, and the delay difference parameters was determined (Hilborn and Walters 1992). All equilibrium calculations can be found in Chapter 2, Table 2.4, except for species-specific BMSY. BMSY was determined using the following equation: ‫ܤ‬ெௌ௒೔ = −  ഥ ೐೔ೕ ା௘ ି௪  షಾ೔ ష	ಷಾೄೊ ೔ ቀఈ೔ ାఘ೔ ௪ ഥ ೐೔ೕ ቁା௪ಲ೔ ௦೚೔ ௪ ഥ ೐೔ೕ  ഥ ೐೔ೕ ା௘ ఉ೔ ቆି௪  షಾ೔ ష	ಷಾೄೊ ೔ ቀఈ೔ ାఘ೔ ௪ ഥ ೐೔ೕ ቁቇ  .  (3)  FMSY and BMSY were used to determine overfishing status and stock status of the individual Hawaiian bottomfish species. Reference points to determine whether a stock was overfished Bstatus and subject to overfishing Fstatus were calculated using the posterior estimates of BMSY and FMSY for each species. Bstatus represents the ratio of current biomass (i.e., for this analysis biomass in year 2005) to equilibrium biomass if the population was fished at FMSY. Fstatus represents the ratio of current fishing mortality (i.e., fishing mortality in year 2005) as compared to FMSY. Four outcomes are possible depending on the combination of Fstatus and Bstatus and are used to determine if a species is overfished and subject to overfishing: 1. Bstatus > 0.7 and Fstatus < 1- neither overfished nor subject to overfishing 2. Bstatus > 0.7 and Fstatus > 1- not overfished, but subject to overfishing 3. Bstatus < 0.7 and Fstatus > 1- overfished and subject to overfishing 4. Bstatus < 0.7 and Fstatus < 1- overfished, but not subject to overfishing.  105  The ratio of current biomass and BMSY is below 0.7, not below 1, indicated overfished status. This is the Bstatus ratio used by the Western Pacific Fishery Management Council for the Hawaiian bottomfish fishery. The rational for using a Bstatus ratio less than one is given by Restrepo and Powers (1999). They indicate that a stock fished at FMSY is expected to fluctuate around BMSY on a scale related to natural mortality, M, and the Bstatus ratio is then 1-M. Using a Bstatus ratio less than 1 avoids determining a stock is overfished when fluctuations are due to swings in natural mortality. Results Trends in predicted biomass, depletion, fishing mortality rate, and catchability Trends in estimated biomass for each species were similar across the alternative average handling time values h, except for Kalekale (Figure 3.2). The biomass trajectory declined rapidly in the beginning of the time series for h values greater than five minutes per fish for Kalekale (Figure 3.2). The greatest similarities in the magnitude of estimated biomass among all h values were shown for Hapu’upu’u, Lehi, Gindai, and White ulua. Average handling time values greater than five minutes per fish resulted in smaller biomass estimates for all other species (Figure 3.2). The trends in and the relative differences in depletion among the h values were similar to those for biomass (Figure 3.3). Estimated depletion was most similar among h values for Hapu’upu’u, Lehi, Gindai, and White ulua. The fishing mortality rates among the h values for these species were also similar (Figure 3.3). In the first two to five years, for all species, except Kalekale, fishing mortality rates were estimated to be higher for h values less than or equal to five minutes per fish than h values greater than five minutes per fish (Figure 3.3). For those species with differences in depletion estimates among the h values, fishing mortality rates were 106  generally higher when the h value was greater than five minutes per fish (Figure 3.3). The depletion of Kalekale was much greater for h values larger than five minutes per fish and was associated with higher fishing mortality rates throughout the time series (Figure 3.3). It should also be noted that the fishing mortality rate for Kahala precipitously declines after 1980 (Figure 3.3). After 1980, Kahala were associated with ciguatera poisoning and the catch of this species declined rapidly (Chapter 1 Figures 1.3, 1.4). During early model runs, the reduction in catch was explained by high fishing mortality rates and low biomass. The results did not agree with anecdotal evidence suggesting that fishermen avoid catching Kahala. To account for this avoidance behaviour, the catchability of this species was set to 10% of its catchability at low stock size starting in 1981 and thereafter, which caused the precipitous decline in fishing mortality rate shown in Figure 3.3. Trends in the ratio of species-specific catchability, qit, and catchability at low stock size, qoi, differed among the average handling time values. The results were presented as the ratio between qit and qoi to show how qit approaches qoi as biomass declined. This ratio remained unchanged and was equal to one indicating that qit and ‫ݍ‬௢೔ were equal regardless of species-  specific depletion when the average handling time hypothesis was equal to zero, as would be expected (Figure 3.4). Larger h values resulted in a non-linear increasing trend in the ratio between qit and qoi as species-specific biomass declined from unfished biomass (Figure 3.4). The rate of increase was dependent on the average handling time hypothesis. The rate of increase was therefore higher for larger average handling time hypotheses (Figure 3.4). The increase in the ratio of species-specific qit and qoi had an increasing stepped pattern as biomass declined from unfished biomass for Hapu’upu’u, Opakapaka, Uku, Ehu, Onaga, Gindai, and White ulua (Figure 3.4). Kahala showed a similar trend until the ratio was fixed at 10 percent. This was done to account for known avoidance behaviour of fishermen that started in the mid-1980s. The 107  trend increased nonlinearly as the biomass of Kalekale declined for average handling time hypotheses greater than five minutes per fish (Figure 3.4, lower left panel). The ratio of speciesspecific catchability and catchability at low stock size increased as the biomass of Lehi declined prior to the early 1960s (Figure 3.4). After the 1960s, biomass increased and the ratio between species-specific catchability and the catchability at low stock size remained stable (Figure 3.4) Figure 3.5 shows the trends in the ratio between qit and qoi relative to the ratio of speciesspecific biomass and total community biomass. The catchability of Kalekale increased towards its qoi for all average handling time values except for h = 0. This increase was non-linear for h values greater than five minutes per fish and as Kalekale made up a smaller proportion of total biomass. The catchability of Ehu and White ulua also increased towards catchability at low stock size and then stabilized for all h values excluding h = 0. Another obvious trend is the decline in the catchability ratio as Opakapaka makes up a smaller proportion of total biomass. The relationship is less obvious for the remaining species. Model fit and maximum likelihood estimates of the leading parameters Improvement in the objective function (i.e. P(Θ) became smaller) was made for h values between zero and 30 minutes per fish (Table 3.3). Improvement in the objective function peaked at 30 minutes per fish, thereafter larger h values led to an increase in the objective function (Table 3.3). The incremental improvement in the objective function resulted in a trade-off in model fit to the observed catch data among species. Figures 3.6 and Table 3.6 summarize the likelihood profiles of the species-specific catch given the estimated leading parameter values. Comparing the likelihood profiles among species across the h values shows that the likelihood values were lowest for Opakapaka, except at h = 60 minutes per fish (Figure 3.5, Table 3.6). This was not a surprise given that Opakapaka has been 108  the dominant species in the catch history (see Figure 1.1 in Chapter 1). The minimum value for Opakpaka was at h = 25 minutes per fish (Figure 3.6). The likelihood values for all other species, except Ehu and Kalekale, were minimized between nine and 60 minutes per fish (Figure 3.6, Table 3.6). The likelihoods for Ehu and Kalekale were minimized at h = 0 (Figure 3.6, Table 3.6). The biggest discrepancy in the model fit to the catch data among the h values occurred within the first two to five years of the time series (Figure 3.8). In these first several years, catch was overestimated for all h values and for Hapu’upu’u, Kalekale, Opakapaka, Onaga, and Gindai (Figures 3.7, 3.8). Catch was overestimate for h < 5 minutes per fish and underestimated for h > 7 minutes per fish for Kahala, Uku, Ehu, Lehi, and White ulua (Figure 3.7). A notable pattern in the catch residuals of Lehi is apparent; catch was consistently overestimated in the early years (1948 to the early-1970s) and underestimated from the mid-1970s to the end of the time series (Figure 3.7, 3.8). There was strong auto-correlation in the catch residuals and the recruitment anomalies for Lehi (Figures 3.8, 3.9). Negative recruitment anomalies were estimated early in the time series (i.e., 1948 ~1970) and positive recruitment anomalies were estimated for years after 1970 (Figure 3.8, 3.9). The correlation between the catch residuals and predicted recruitment anomalies was not surprising given the parameterization of the observation and process error terms. Auto-correlation in the estimated recruitment anomalies was also strong for all other species regardless of the average handling time hypothesis (Figure 3.9) and may be an indication of model misspecification (e.g., qo are not constant over time).. Posterior density estimates and correlation in the estimated parameters The marginal posterior densities of the leading parameters, Bo, Κ, and qo, and the corresponding pair plots of the joint posteriors for these parameters and each species are plotted 109  in Figures 3.10 through 3.19 (see Tables in Appendix A for MLE estimates). The speciesspecific marginal posteriors of Bo were similar among the h values for all species (Figures 3.103.19, top left panel). The marginal posterior densities of Κ for Ehu, Hapu’upu’u, Kahala, Uku, and White ulua reflect the prior information and were insensitive to the handling time (h) values (Figures 3.10, 3.12, 3.13, 3.18, 3.19). The marginal posterior densities of Κ for the remaining species deviate from the prior density indicating that the dataset may contain information about the productivity of these individual species. The marginal posterior densities of Κ for Gindai, Lehi, Onaga, and Opakapaka were insensitive to the h values and the median estimate was larger than the prior (Figures 3.11, 3.15, 3.16, 3.17). This indicates that these species may have higher productivity than what was specified by the prior. The median posterior estimates of Κ for Kalekale also deviated from the prior and were sensitive to the assumed h value (Figure 3.14). The posterior estimates were smaller for larger h values; the precision in the posterior distribution also increased for larger h values (Figure 3.14). Some instability was seen in the posterior estimates of Κ for Kalekale (Figure 3.14). This instability shows up as high autocorrelation in the traceplots of Κ for Kalekale (see Appendix A, Figures A.2, A.5, A.8, A.11, A.14). The marginal posterior density of qo for all species was sensitive to the assumed value of h (Figures 3.8-3.18, lower right panel). Larger h values resulted in larger median estimates of qo. The joint posterior between Bo and qo for all species and values of h showed strong negative correlation (Figures 3.10-3.19, lower left panel). Strong negative correlation between Bo and qo makes it difficult to resolve whether a stock is large with low catchability or small with high catchability. The joint posterior between Bo and Κ were also negatively correlated for all values of h and all species (Figures 3.10-3.19, middle panel). There was little contrast in the catch and effort data to resolve confounding between Bo and Κ, and an informative prior on Κ was necessary to resolve strong parameter correlation (Figures 3.10-3.19). The joint posterior 110  estimates of Κ and qo for all species and values of h showed some positive correlation. A strong lower bound was evident in this relationship and reflects the informative prior density on Κ (Figures 3.10-3.19). Posterior density estimates and correlation in management parameters The species-specific marginal posterior densities for MSY, FMSY, and BMSY, the corresponding pair plots of the joint posterior densities, and the joint posterior density for Fstatus and Bstatus are plotted in Figures 3.20-3.29. The species-specific marginal posterior for MSY and BMSY were insensitive to the value of h (Figures 3.20-3.29, top left and bottom right panels). The species-specific marginal posterior densities for FMSY were also relatively insensitive to the assumed value of h for all species. The joint posterior density for BMSY and MSY for all species showed strong positive correlation; this pattern was insensitive to the h values (Figures 3.20-3.29). The joint posterior density for BMSY and FMSY was negatively correlated for all species (Figures 3.20-3.29). Some positive correlation between FMSY and MSY was evident for most species. The correlation between FMSY and MSY had an interesting pattern for Kalekale (Figure 3.24). A portion of the joint posterior was positively correlates and at the lower end of the MSY estimates, FMSY and MSY were negatively correlated (Figure 3.24). This may be due to the instability in the Κ estimates for Kalekale (Figures A.2, A.5, A.8, A.11, A.14, Appendix A). FMSY and MSY were positively correlated for Uku, several outliers obscured this relationship (Figure 3.28). The top, right panel of Figures 3.20-3.29 shows the joint posterior of Fstatus and Bstatus. Table 3.8 corresponds to Figures 3.20-3.29 and summarizes the probability of a species experiencing overfishing, being overfished, a combination of the two, or neither outcome for each average handling time hypothesis. The probability of an outcome x was calculated as: 111  ܲ(‫ 	 = )ݔ‬, ௫  ௡  (5)  where x is the number of points from the Fstatus - Bstatus joint posterior associated with one of the four outcomes and n is the total number of samples. Table 3.7 summarizes the percentage of the MCMC samples associated with the four Bstatus – Fstatus combinations. Opakapaka, Onaga, Uku, Gindai, Lehi, and Kahala have a high probability of not being overfished and not being subject to overfishing (average probability: 99.32, 98.75, 98.44, 98.10, 97.09, and 90.47 percent, respectively; Table 3.7a). This outcome was not sensitive to the assumed value of average handling time for these five species; there was an approximate 1% difference between the highest and lowest percent probability for these species, except Kahala. The difference between the highest and lowest percent probability for Kahala is approximately nine percent. The relationship between the probability of not being overfished and not subject to overfishing and the assumed h value was negatively correlated , where the highest probability for Kahala is 94.21 percent and is associated with a h value of zero minutes per fish and the lowest probability (~85.1 percent) is associated with h = 9 minutes per fish (Table 3.7a). The average probability of not being overfished and not being subject to overfishing is highest for Hapu’upu’u, Kalekale, Ehu, and White ulua. White ulua has the lowest probability of not being overfished and not being subject to overfishing among the species. This probability was sensitive to and negatively correlated with the h value for Hapu’upu’u, Kalekale, Ehu, and White ulua (Table 3.7a). The probability of being subject to overfishing without being overfished was less than one percent for all species and was not sensitive to the assumed value of average handling time (Table 3.7b). This was also true for the percent probability of being overfished while experiencing overfishing, except for Hapu’upu’u. Ehu, and White ulua (Table 3.7c). The 112  probability of being overfished and experiencing overfishing ranged between 1.21-3.16 percent for Hapu’upu’u (Table 3.7c). The probability of Ehu being overfished while experiencing overfishing ranged from 1.92 to approximately 7.49 percent and for White ulua the range was between 10.24 and 18.10 percent (Table 3.7c). This probability was also sensitive to and positively correlated with the h value for these three species. The probability of being overfished without being subject to overfishing is, on average, less than 10 percent for Opakapaka, Onaga, Uku, Gindai, Lehi, and Kahala (Table 3.7d). The average percent probability of this scenario for Kalekale, Hapu’upu’u, Ehu, and White ulua is 41.80, 30.5, 36.6, and 66.93, respectively (Table 3.7d). The probability of being overfished without experiencing overfishing was insensitive to the h values for Opakapaka, Onaga, Uku, Gindai, Lehi, and White ulua. This probability was sensitive to the h value for Kahala, Kalekale, Hapu’upu’u, and Ehu, where the probability was positively correlated with the assumed value of h (Table 3.7d). The difference in the highest and lowest probability is 9.11, 33.78, 10.27, and 16.01 percent for Kahala, Kalekale, Hapu’upu’u, and Ehu, respectively. Discussion The analysis presented in this chapter represents the first application of this multispecies assessment model to the Hawaiian bottomfish fishery data. The assessment model was run for alternative assumptions about hyperstability and technical interactions, by way of handling time effects, to determine whether stock status information and management reference points for the individual bottomfish species could be disentangled from the existing fishery-dependent timeseries (i.e., species-specific catch and total effort). An empirical estimate of average handling time per fish, h, was not available, therefore, alternative values of h were derived from published gear performance statistics and the depth distribution of the Hawaiian bottomfish species. The 113  lower bound of the evaluated range was equal to zero. This was included in the analysis because it simplifies to the joint estimation of the leading parameters for the multiple species while assuming constant catchability and in turn fishing mortality per species is proportional to total effort. Additionally, when h = 0, technical interactions among species are assumed to be noninfluential on catchability (i.e., the denominator of T2.3.7 is equal to 1, Chapter 2, Table 2.3). The comparison of the non-zero h values and h = 0 was done to determine whether accounting for hyperstability in the observation model better explains the catch observations than without. Non-zero average handling time hypotheses were expected to better describe the data than h = 0 given the combination of gear type and depths fished. The results indicate that handling time effects help to describe the data. For example, an improvement in the minimized objective function was obtained up to a considerably high value of h, 30 minutes per fish. Additionally, evaluation of the negative log likelihood of speciesspecific catch indicated that the catch of most species was better described by a non-zero value of h. Although handling time effects may help to better describe the data, inspection of the marginal posterior densities of the leading parameters indicated that these estimates were relatively insensitive to the assumed value of h, except for catchability at low stock size qo. An increase in h led to an increase in qo, therefore, h and qo are positively correlated. An increase in h leads to a loss in active fishing time, therefore, to minimize the difference between the observed and predicted catch the estimate of qo had to be increased to compensate for lost fishing time. Comparing the marginal posterior densities of the management reference points, MSY, BMSY, and FMSY, indicate that they were also insensitive to the assumed value of h. The ultimate use of stock assessment results is to provide management advice via estimated management reference points. The results presented in this chapter indicate that the management advice on a per species basis among average handling time hypotheses was similar. 114  A number of simplifying assumptions were made pertaining to the population and observation dynamics models used to carry out this analysis. The assumptions made about the population dynamics of the Hawaiian bottomfish species and the expected bias as a result of violating these assumptions were discussed in Chapter 2. Rather than reiterate this discussion, the reader is referred to the Assumptions and expected bias section in Chapter 2. The discussion of this chapter will focus on the assumptions pertaining to the observation dynamics model which likely caused the trade-off in the model fit to the catch observations among species, as well as potentially obscured the influence of handling time effects. This analysis like many others in the fisheries literature was also reliant on fishery dependent data (i.e., nominal commercial catch and effort data). Fishery dependent time series data often lack the necessary contrasting information to resolve confounding between population parameters (e.g., unfished biomass and productivity) that is needed to make inferences about populations responses to fishing and fisheries management policies. The implications of using non-informative fishery dependent data on the results from this analysis will also be discussed. Assumptions pertaining to observation dynamics Key assumptions of the observation dynamics model were 1) h was known and timeinvariant, 2) h was the same for all species, 3) catchability at low stock size qoi was timeinvariant, and 4) search (i.e., fishing) was random. Walters and Martell (2004) call assumed stationary parameters “the parameters that aren’t” because the assumption is likely violated and can cause unintended bias. The intention of using the disc equation was to derive time-varying catchability for the individual target species making up the Hawaiian bottomfish fishery, thereby accounting for non-stationarity in catchability due to handling time effects and changing conspecific and interspecific abundance. 115  The assumption that h is time-invariant may be easily violated. Changes in skill, gear efficiency, and fishing depths would cause h to change over time. A known change in gear efficiency occurred in the 1970s when the bottomfish fishing fleet transitioned from using Samoan reels (i.e., hand cranked reels) to using electric reels. Electric reels are a more efficient gear type in terms of drop and retrieval times than Samoan reels and have most likely led to a reduction in the average handling time per fish. This may help explain why larger h values better predicted the catch observations in the earlier years of the fishery for most species. The expected directional bias of violating the assumption of a stationary average handling time is dependent on the direction average handling time changes. For example, if technological advances increased gear efficiency or fishers learn over time to better operate the existing gear and become more efficient operators, it would be expected that h would decline. In equation T3.3.21, time-varying catchability is the catchability at low stock size weighted by the proportion of total time spent fishing (i.e., 1/(1+hƩqoiNit)). A decrease in h would shrink the denominator causing time-varying catchability to increase. If h is assumed constant when in fact it has declined, over the time period of declining h the proportion of time spent fishing will be underestimated and in turn time-varying catchability and fishing mortality would be underestimated. The converse would be expected if technological advances led to fishers to move offshore and fish in deeper waters. Fishing at greater depths could lead to an increase in average handling time per fish. Over the time period of increasing h, if h is assumed constant, the proportion of time spent fishing would be overestimated and in turn catchability and fishing mortality would be overestimated. One way to overcome this assumption violation and account for changes in efficiency would be to allow for h to vary over time. One approach to obtain time-varying h estimates would be to interview fishers that have fished with both gear types used in the Hawaiian bottomfish fishery and apply the different h values to the periods of perceived 116  changed in gear efficiency. An alternative and less costly approach would be to try and model h as a random walk process; subtle contrasts in the catch rates of different species over time may inform change in h over time. The assumption that h is the same for all species may also be overly simplistic. The depth range at which the Hawaiian bottomfish are found is quite large. All species can be captured throughout the depth range. Some species, however, are more commonly fished for at certain depths. Ralston and Polovina (1982) conducted a cluster analysis and defined three species groupings of the Hawaiian bottomfish according to depth. The depth ranges of the species groupings overlapped substantially, however, it would not be unreasonable to assume, that on average, h for fish found at deeper depths would be greater than those found at shallower depths. For example, incorrectly assuming h is larger than the true h for a species found in shallower waters would inflate the denominator of equation T3.3.7. The proportion of time spent fishing, time-varying catchability, and fishing mortality are then underestimated. The converse could be said for species that inhabit deeper waters. If the assumed value of h is less than true h the denominator of equation T3.3.7 will be smaller and lead to an overestimate of the proportion of time spent fishing, time-varying catchability, and fishing mortality and underestimate biomass. Another assumption of the disc equation is that search (i.e., fishing) is a random process. Violating this assumption would be expected to have important ramifications on the assumed stationarity of catchability at low stock size, qoi. Fishers generally exhibit some form of targeting behaviour, which is often dictated by the potential cost and profits earned by fishing for a particular species, the perception of resource abundance at a given location, experience catching a particular species, and management policies. Therefore, fishing is generally not a random process. Quirijns et al. (2008) and Branch and Hilborn (2008) demonstrated fishers will alter 117  their targeting behaviour in response to changing individual quotas for the Dutch beam trawl fishery and the British Columbia groundfish trawl fishery, respectively. For example, catch and CPUE declined for shortraker, rougheye, and yelloweye rockfish corresponding to an annual decline in the individual total allowable catch between 1997 and 2001 for each of these species (Branch and Hilborn 2008). Fishermen actively avoided these species because if the quotas were reached, then the entire multispecies fishery would be shut down. There is some evidence that targeting takes place in the Hawaiian bottomfish fishery. In the 1980s, kahala was implicated as a source of ciguatera poisoning and observed catch of this species declined dramatically indicating potential avoidance behaviour or simply discarding kahala (Figure 1.3). Targeting behaviour directly influences a species’ vulnerability to fishing (i.e., increased targeting would lead to increased vulnerability and avoidance behaviour would lead to a decline in vulnerability). Non-random targeting behaviours not only result in time varying catchability, but also non-stationary catchability at low stock size. For example, qoi for a more profitable species would increase over time as fishers focus their fishing activity on this species and become adept at targeting through better gear configuration. In this situation, assuming catchability at low stock size is constant rather than time-varying would lead to an under-estimation of fishing mortality and overestimate of biomass. Although the disc equation accounts for time varying catchability due to handling time effects, as well as relative changes in abundance among species, making simplifying assumptions such as constant qoi and h may bias the estimated change in catchability over time. The predicted recruitment anomalies (ωit) exhibited patterns of auto-correlation, representing predicted persistent change, for most species and all hypotheses of the average handling time per fish. A lack of discernible differences in the leading parameters and management reference points under  118  different average handling time hypotheses may be due to the predicted recruitment anomalies better capturing persistent change in the system. The period between 1970 and 1990 marked a time of fishery expansion, the number of licenses and effort increased during this time and then declined after 1990 (Figure 1.2). This period of expansion corresponds to declining overall and species-specific (for almost all species) catch rates (Figure 1.2). Declining catch rates during periods of fishery expansion may indicate stock depletion or interference among fishers (Hilborn and Walters 1992). Competitive interference between fishers generally leads to a negative correlation between catch rates and effort (Gillis et al. 1993, Swain and Wade 2003). A spatial evaluation of catch and effort data from the snow crab fishery in the Gulf of St. Lawrence showed catch rates were suppressed in areas of high effort indicating interference competition has operated in this fishery (Swain and Wade 2003). Unintentional interference among fishers is likely given the number of new licenses that entered the Hawaiian bottomfish fishery. Inexperienced fishers may try to imitate others to find the best fishing locations in an attempt to increase their individual fishing power (Hilborn and Ledbetter 1985), but at the same time lead to overcrowding and depressing catch rates in those fishing area. Interference competition leads to catch rates declining more quickly than abundance and time varying catchability declines exponentially as abundance declines (i.e., hyperdepletion). The multispecies disc equation only accounts for the influence of handling time effects and conspecific and interspecific abundance on catch rates, and contradicts the prediction of interference competition. If the dominant mechanism influencing catch rates changed over time this may help to explain why there was no discernible difference in the model fit to the observations across hypotheses in the later years of the time series. A number of studies have considered the effects of search time (Mangel and Clark 1983, Mangel and Beder 1985,) and handling time (Cooke and Beddington 1984, Deriso and Parma 119  1987, Walters and Martell 2004 chapter 9) on the interpretation of catch rates (generally for a single species) as a relative index of abundance. All have demonstrated that assuming a linear relationship between catch rates and abundance is generally erroneous if search or handling time greatly influences catch. Deriso and Parma (1987) investigated the influence of handling time on the catch rates of three snapper species observed during a depletion experiment on a reef in the Northern Marianas. They demonstrated that species-specific catch rates were not proportional to abundance due to handling time effects and that predicted abundance for each of the three species was overestimated when assuming catch rates were proportional to abundance. Although the method to predict catch in this chapter is similar to Deriso and Parma (1987), a couple of differences are worth mentioning. The data used for their analysis was part of a depletion experiment and represents repeated sampling over 13 days in the same fishing locations. Repeated sampling was made around a 0.8nmi reef, whereas the data used for the analysis in this chapter represents catch observations throughout the Main Hawaiian Islands. Spatial aggregation of catch data may dampen the influence of handling time. Average handling time per fish is correlated with skill, gear efficiency, and depth of fishing, where average handling time is positively correlated with depth and negatively correlated with skill and gear efficiency. Total fishing effort, therefore, represents a complex relationship between these factors among fishers and across space. Walters (2003) argued that spatially aggregated catch and effort observations are weighted towards those areas with higher catch and effort. Assuming all else is equal, areas with lower average handling time per fish will generally result in higher catch rates. If spatially aggregated catch rates are weighted towards those areas with higher catch rates and presumably lower handling times (i.e., areas targeted by highly skilled fishers with efficient gear), this could effectively reduce the influence of average handling time on the predictions in this analysis. 120  Information contained in fishery-dependent data Another possible reason for the similarities in the leading and management parameter estimates among the h values may be due to the lack of information contained within the fishery dependent data. There are numerous examples of one-way trip datasets, where there is a declining trend in CPUE as effort increases (Hilborn and Walters 1992). One-way trip data are generally considered to be uninformative about scale and productivity parameters because of the negative correlation between unfished biomass and the recruitment compensation ratio, Κ. Using one-way trip data can lead to an infinite number of parameter combinations that explain the data equally well; the stock is either large and unproductive or small and productive (Hilborn and Walters 1992). Hilborn (1979) demonstrated that informative data about population scale, productivity, and catchability is generally produced when a fishery undergoes a period of heavy exploitation, followed by recovery and then lighter exploitation. Species-specific and total CPUE from the Hawaiian bottomfish fishery represent one-way trip data (Figures 1.1). The lack of information contained in the data led to confounding among the leading parameters making it difficult to resolve whether a species was from a large, unproductive, and less catchable stock or the converse. Estimates of Κ and qoi, for most species, commonly reached the lower or upper bound potentially indicating a lack of information about these parameters in the data and that the model may be over-parameterized. Informative priors on Κ and the average fishing mortality rate were used to provide information about population productivity and catchability. The posterior estimates of Κ were nearly identical to the prior probability density function (Figure 3.10 – 3.19), indicating the lack information in the data about population productivity. This was true for all h values, which explains why estimates of Κ did not differ among hypotheses and why management related parameters were the same. 121  A lack of informative data generally limits the number of latent variables that can be estimated due to strong confounding among estimated parameters. Recruitment compensation was negatively correlated with unfished biomass and positively correlated with qoi, whereas unfished biomass and qoi were negatively correlated. Using an informative prior on Κ resolved some of this confounding, however, it was still apparent. Given the level of confounding between Κ and unfished biomass, the informative prior on Κ also implies information on unfished biomass. This would help explain the similarity in the posterior density functions for unfished biomass among hypotheses. The informative prior on recruitment compensation did not seem influential on maximum catchability. The marginal posterior estimates of maximum catchability were larger under hypotheses with larger values of average handling time per fish (Figure 3.10 - 3.19). All else being equal, larger values of h will suppress catch rates. Given that marginal posterior estimates of Κ and unfished biomass were relatively unchanged among hypotheses of average handling time per fish, under hypotheses with larger values a shift towards larger values of qoi was needed to explain the observed data or they would have been grossly underestimated. The ability to estimate the leading parameters in Chapter 2 was not hindered by the lack of contrast in the observations, likely because the observation and process errors were independent and identically distributed. The one-way trip data generated in Chapter 2 resulted in the population being reduced to approximately 20% of unfished biomass, whereas data generated with contrast were also reduced to 20% of unfished biomass before effort was removed to allow for recovery. Unfished biomass, recruitment compensation, and maximum catchability were accurately estimated when data were generated with and without contrast. There was a tendency to overestimate recruitment compensation when process and observation errors were large, this is similar to the results obtained by Magnusson and Hilborn (2007) when estimating steepness 122  using scenarios with and without contrast. Magnusson and Hilborn (2007) also found that when using catch and a relative index of abundance that is described as a one-way trip can perform as well as data with contrast. Data that can be described as one-way trips, but also lead to severe declines in the population are probably informative because they lead to a well-defined stockrecruitment curve and allows for better estimation of productivity parameters such as recruitment compensation (Myers and Barrowman, 1996). Three (Hapu’upu’u, Ehu, and White ulua) of the ten species were predicted to be at less than 50% of unfished biomass and therefore the majority of the data contains little information about recruitment compensation for the individual species. Historically this fishery has been assessed as a single aggregate species. In other words, the catch and effort statistics were aggregated to develop a total relative index of abundance and unfished biomass, a productivity term, catchability, as well as error terms were estimated for the community as a whole. Comparing the number of parameters between previous assessments and this analysis, one-tenth the number of parameters were estimated in previous assessments. For example, Martell et al. (2006) used a semi-implicit Schaefer model to assess the aggregate bottomfish community in the Main Hawaiian Islands. Their results indicate that estimates of the productivity parameter were highly sensitive to the variance of the prior density for this parameter indicating that the data were not informative about the productivity of the community. This exemplifies the non-informative nature of the raw catch and effort statistics collected from Hawaiian bottomfish fishery and used for assessments, regardless of the number of parameters being estimated. It cannot be expected that the same data will provide any more information about a greater number of parameters. The benefit of using the multispecies approach, however, is that by explicitly modeling per species catch information about per species abundance is provided. In other words, per species abundance must be at least as large as the observed catch.  123  Using an aggregate approach that fits the model to total catch or overall catch rates loses this ability. Another problem with the aggregate approach is the implicit assumption that all species are the same in terms of productivity and catchability. It is highly unlikely that the aggregate statistics can represent all individual species unless they were identical in terms of scale, productivity and catchability (Kleiber and Maunder 2008). More importantly, ignoring the relative differences in productivity can lead to the overfishing of the weaker stocks (Paulik et al. 1967, Hilborn, 1976). The Magnuson-Stevens Fishery Conservation and Management Reauthorization Act 2006 “mandates the use of annual catch limits and accountability measures for all stocks”. The ability to achieve this mandate lies in the ability to develop quantitative models to make predictions about how a stock responds to fishing and management policies, which in turn are reliant on reliable, informative data sources. For many fisheries, including the Hawaiian bottomfish fishery, the only data available for input into stock assessment models are fishery dependent catch and effort statistics. The results in this chapter indicate that even when the observation dynamics sub-model represents a reasonable hypothesis of the underlying fishing process, without informative data it is difficult to obtain estimates of population scale and productivity, important parameters needed to derived management reference points. This points to the need for data collection programs that move beyond fishery-dependent catch and effort statistics that provide the required information. To this end, potential data collection programs pertaining to multispecies fisheries will be evaluated as part of a management procedure evaluation in the next chapter.  124  Model comparison and future research The value used for average handling time changes the structure of the catchability equation. A non-zero average handling time represents a more complex model that has one additional parameter. An average handling time that is equal to zero results in a reduced, less complex model. More complex models generally fit data better than reduced models because the extra parameters help to explain more variation in the data. Although the fit to the data is important, another goal of any modeling exercise is to strive for parsimony (i.e., simplicity). Formal statistical methods can be used to determine whether additional complexity is warranted. Model comparison can be conducted using methods such as, likelihood ratio tests for nested models and Akaike’s information criterion (AIC)and Bayesian information criterion (BIC) for non-nested models. Formal model comparison was not conducted in this chapter due to concerns about model misspecification. The predicted recruitment anomalies show strong autocorrelation indicating that assuming average handling time and catchability at low stock size were constant over time may be incorrect. The catch likelihoods indicate that average handling time may be an estimable parameter. One way to address this issue in the future would be to develop a Bayesian prior density for average handling time based on the estimates derived from the published gear statistics and treat it as an estimable parameter. Changes in average handling time or catchability at low stock size over time could also be estimated as random walk processes. Modeling these parameters as a random walk process allows them to gradually change over time. Factors that would cause these parameters to change gradually over time include changes in gear efficiency and fisher experience (i.e., fishers gradually become more proficient). This approach should be investigated in future studies  125  Final remarks An important step in evaluating the usefulness of this approach in relation to others is to evaluate the performance of the resulting management advice when admitting uncertainties in the system. A simulation method that has been advocated to address this issue is management procedure evaluation (Butterworth and Punt 1999). Uncertainty about changes in catchability and the influence of the technical interactions among the bottomfish species on the observed catch and in turn the management outputs are of major concern. The performance of the modeling approach used in this chapter will be compared to the status quo approach and will be evaluated while admitting uncertainty about the observation dynamics of this fisheries system using management procedure evaluation.  126  Tables Table 3.1 Parameter symbols and descriptions used to describe the state and observation dynamic models for the Hawaiian bottomfish fishery. Notation  Description  Subscript i  Species  t  Year  Estimated Parameters ‫ܤ‬௢೔  Unfished biomass  kg  Recruitment compensation ratio  -  ߈௜  ‫ݍ‬௢೔ Growth Parameters ‫ܮ‬ஶ೔  Units  days-1  Maximum catchability  Asymptotic length  cm  von Bertalanffy growth coefficient  -  Length-weight scalar  cm/kg  Length-weight power parameter  -  Mean weight at age of recruitment  kg  Observed States h  Handling time  days  Et  Annual fishing effort  days  Observed landings  kg  ݇௜  ܽ௜ ܾ௜  ܹ஺ ௜  ‫ܥ‬௜௧  Continued on next page  127  Table 3.1 Continued Notation  Description  Units  Unobserved States Bit  ܰ௢೔ , Nit ܴ௢೔ , Rit  -  Unfished numbers, Numbers  number of recruits  Unfished recruits, Recruits  qit  Catchability  Fit  Fishing mortality  Zit  Total mortality  sit  Total survival  ‫ܥ‬෢ ప௧  kg  Biomass  days-1 kg  Predicted landings  Derived parameters Slope of the Ford-Brody growth ρi  function (metabolic rate parameter)  -  Intercept of the Ford-Brody growth αi  function  ‫∞ݓ‬೔  Asymptotic weight  Mi  Natural mortality  Si  Natural survival  ‫ܣ‬௜  ‫ݓ‬௜  ‫ݏ‬௢೔ βi  Age at recruitment Average weight Maximum juvenile survival rate Recruitment scalar  kg kg years kg recruit/spawner recruit/spawner Continued on the next page  128  Table 3.1 Continued Notation  Description  Units  Error terms ωit  Process error  number of recruits  ηi  Total standard deviation  -  ξi  -  ߪఠ೔  Proportion of ηi associated with observation error Standard deviation in νit  kg  Standard deviation in ωit  number of recruits  Residuals ߜ஼೔೟  Catch residuals  kg  Likelihood and priors P(Κ)  Prior on recruitment compensation  -  Ω  Steepness  -  L(Ci | θi) L(ωi |θωi)  Likelihood of the observed catch of species i given the parameters of all species j -  Ψ  Objective function to be minimized  ߪజ೔  -  129  Table 3.2 Species-specific growth parameter values used and the sources from which they came. L∞ is the asymptotic length, k is the von Bertalanffy growth coefficient, a and b parameters describing the length-weight relationship, and WAi is the mean weight-at-recruitment. Symbols next to the values refer to footnotes below the table Species L∞ k a b WAi Hapu’upu’u  122*  0.13*  0.018+  3+  2  Kahala  149¦  0.314¦  0.022+  2.94+  3  Kalekale  44ↄ  0.351ↄ  0.007+  3.258+  0.6  Opakapaka  78†  0.146†  0.029+  2.825+  1.5  Uku  85.2  0.244  0.005+  3.264+  3  Ehu  71.8‡  0.163‡  0.018+  2.984+  0.7  Onaga  109ↄ  0.123ↄ  0.017+  2.961+  2.2  Lehi  123ↄ  0.163ↄ  0.015+  2.961+  2.5  Gindai  44 ↄ  0.234 ↄ  0.021+  2.995+  2  White ulua  184§  0.111§  0.022+  2.913+  3  +  Froese and Pauly (2011)  ¦  Humphreys (1986)  ↄ  Ralston and Williams (1988)  †  Ralston and Miyomoto (1983)  ‡  Smith and Kostlan (1991)  §  Sudekum et al. (1991)  130  Table 3.3 The joint posterior probability of the estimated leading parameters across the different average handling time hypotheses. Average handling time Average handling time (day/fish) (minute/fish) P(Θ) 0  0  -201.472  0.0033  2  -203.708  0.0076  5  -206.962  0.012  7  -222.684  0.015  9  -225.522  0.025  15  -252.779  0.033  20  -260.932  0.042  25  -267.991  0.047  28  -270.216  0.05  30  -270.717  0.055  33  -270.006  0.07  42  -258.974  0.1  60  -169.094  131  Table 3.4 State and observation dynamic models used to assess the Hawaiian bottomfish. The state dynamics were modeled using a delay difference model (Deriso, 1980), recruitment was described by the Beverton-Holt stock-recruitment model, and the observation model was derived from Holling’s disc equation. Equation number  Description  Subscripts i  Species  t  Time  a  Age  Estimated parameters T3.4.1  Θi = (Boi, Ei, qoi, ηi, ωit)  Residuals T3.4.2  ߜ஼೔೟ = 	 ln ‫ܥ‬௜௧ − 	 ln ‫ܥ‬෢ ప௧  Likelihood and priors T3.4.3  ∑௧ ߜ஼೔೟ ଶ ݊ ଶ ‫ܥ(ܮ‬௜ |Θ) = 	 ln ߪఔ೔ + 2 2ߪజ೔ ଶ  T3.4.4  T3.4.5 T3.4.6 T3.4.7  ∑௧ ߱௜௧ ଶ ݊ ‫ܮ‬൫߱௜௧ |ߪఠ೔ ൯ = 	 ln ߪఠ೔ ଶ + 2 2ߪఠ೔ ଶ P(Κi) ~ߚ ቀ  ఆ೔ ି଴.ଶ ଴.଼  , 12,9ቁ, where ߗ௜ =  P(‫ܨ‬ത ) = ܿሾln ‫ܨ‬ത − 	 ln 0.2ሿଶ  ௷೔  ସା௷೔  ܲ(Θ) = 	 ෍ ‫ܥ(ܮ‬௜௧ |Θ) + ෍ ‫ܮ‬൫߱௜௧ |σఠ೔೟ ൯ + 	ܲ(߈௜ ) + ܲ(‫ܨ‬ത ) ௜  ௜  132  Table 3.5 Initial values and the upper and lower bounds for the estimated parameters. * indicates value was fixed and not estimated. Parameter Lower bound Upper bound Initial value Boi Hapu’upu’u  -  -  250000 kg  Kahala  -  -  400000 kg  Kalekale  -  -  13000000 kg  Opakapaka  -  -  250000 kg  Uku  -  Ehu  -  -  380000 kg  Onaga  -  -  1000000 kg  Lehi  -  -  425000 kg  Gindai  -  -  10000 kg  White ulua  -  -  400000 kg  Κi  1  100  5  qoi  1.125352e-07  1.01  0.05  ξi  -  -  0.5*  ηi  0  3  0.7  ωit  -5  5  0  1000000 kg  133  Table 3.6 The likelihood of the catch given the estimated model parameters L(Ci | Θ) for hypotheses of h. The values in bold are the lowest value of L(Ci | Θ) for each species.  h (day/fish)  0  h (min/fish)  0  0.0033 0.0076 0.012 2  5  7  0.015  0.025  0.033  0.042  0.047  0.05  0.055  0.07  0.1  9  15  20  25  28  30  33  42  60  Opakapaka  -15.81 -16.00 -16.39 -22.53 -22.75 -27.91 -28.96 -29.81 -29.61 -29.12 -27.61 -19.67  6.68  Ehu  -12.26 -12.21 -12.11 -10.57 -10.35 -12.17 -11.75 -11.17 -10.81 -10.59 -10.18  -7.98  -7.06  Uku  -6.37  -6.46  -6.63  -9.93  -10.14 -12.56 -12.88 -13.16 -13.16 -13.05 -12.64  -8.66  -5.04  Kalekale  -5.39  -5.35  -5.22  -0.95  -0.32  20.81  14.76  5.28  17.52  Hapu'upu'u  -3.99  -4.15  -4.41  -7.60  -7.85  -11.69 -11.57 -11.35 -11.18 -11.05 -10.75  -8.43  -8.57  White ulua  -1.84  -1.93  -2.07  -2.29  -2.38  -5.07  -5.36  -5.66  -5.75  -5.75  -5.65  -4.86  -5.27  Onaga  1.10  0.95  0.68  -3.32  -3.54  -10.22  -9.81  -9.04  -8.46  -8.05  -7.21  -3.01  -2.99  Kahala  2.84  2.84  2.84  2.60  2.52  -5.36  -5.35  -5.28  -5.19  -5.11  -4.89  -3.32  0.02  Lehi  11.73  11.48  11.11  9.98  9.68  8.47  7.94  7.21  6.83  6.64  6.36  5.50  5.68  Gindai  20.59  20.36  19.97  15.35  14.92  10.69  10.68  10.93  11.24  11.49  12.00  14.14  14.69  20.27  19.04  17.74  16.73  134  Figure 3.7 Percentage of MCMC samples associated with four Bstatus and Fstatus combinations: a.) Bstatus > 0.7 and Fstatus < 1 (not overfished and no overfishing), b.) Bstatus > 0.7 and Fstatus > 1 (not overfishing, but overfishing), c.) Bstatus < 0.7 and Fstatus > 1 (overfished and overfishing), and d.) Bstatus < 0.7 and Fstatus < 1 (overfished, but not overfishing). A total of 2500 random samples were taken. Tables correspond to the top right corner of Figures 3.16-3.25.  a.)  Average handling time hypotheses (minutes/fish) 0  2  Species  5  7  9  Mean  Bstatus > 0.7, Fstatus < 1  Opakapaka  99.82  99.79  99.27  98.94  98.78  99.32  Onaga  99.1  98.95  98.54  98.58  98.6  98.75  Uku  98.86  98.77  98.72  98.35  97.49  98.44  Gindai  98.62  98.02  97.31  98.58  97.99  98.1  Lehi  97.75  96.93  96.99  96.96  96.82  97.09  Kahala  94.21  93.31  91.35  88.41  85.1  90.47  Kalekale  76.48  70.91  57.07  43.67  42.39  58.1  Hapu'upu'u  72.61  69.01  71.15  63.15  60.61  67.3  Ehu  68.26  65.01  57.93  55.23  46.54  58.59  White ulua  24.19  22.63  17.02  17.69  14.65  19.24  b.)  Bstatus > 0.7, Fstatus > 1  Opakapaka  0  0  0  0  0.02  0.01  Onaga  0  0  0.02  0  0  0.01  Uku  0  0  0  0  0  0  Gindai  0  0  0  0  0  0  Lehi  0  0.01  0  0  0  0  Kahala  0  0  0  0  0  0  Kalekale  0  0  0  0  0  0  Hapu'upu'u  0.02  0.03  0.06  0.08  0.06  0.05  Ehu  0.08  0.12  0.14  0.16  0.22  0.15  White ulua  0.02  0.01  0.01  0.02  0  0.01  Continued on next page 135  Table 3.7 Continued  c.)  Average handling time hypotheses (minutes/fish) 0  2  Species  5  7  9  Mean  Bstatus < 0.7, Fstatus > 1  Opakapaka  0  0  0  0.01  0.01  0  Onaga  0  0  0.01  0  0  0.01  Uku  0  0.01  0  0.02  0  0.01  Gindai  0  0  0  0  0  0  Lehi  0  0  0  0  0.02  0.01  Kahala  0  0  0  0  0  0  Kalekale  0  0  0.06  0.12  0.31  0.1  Hapu'upu'u  1.21  1.59  1.84  3.16  2.9  2.14  Ehu  1.92  3.15  4.79  5.94  7.49  4.66  White ulua  10.24  11.15  15.34  14.27  18.1  13.82  d.)  Bstatus < 0.7, Fstatus < 1  Opakapaka  0.18  0.21  0.73  1.05  1.18  0.67  Onaga  0.89  1.05  1.43  1.42  1.39  1.24  Uku  1.14  1.22  1.28  1.63  2.51  1.56  Gindai  1.38  1.98  2.69  1.42  2.01  1.9  Lehi  2.25  3.06  3  3.03  3.15  2.9  Kahala  5.79  6.69  8.65  11.59  14.9  9.53  Kalekale  23.52  29.09  42.87  56.21  57.3  41.8  Hapu'upu'u  26.16  29.37  26.95  33.61  36.43  30.5  Ehu  29.73  31.72  37.14  38.67  45.74  36.6  White ulua  65.55  66.21  67.62  68.01  67.24  66.93  136  6 0  2  4  Penalty  8  10  12  Figures  0  2  4  6  8  10  F Figure 3.1 Example of the penalty used to constrain the fishing mortality rate of the individual Hawaiian bottomfish fishery.  137  1950  200 1950  1970 1990  50 0 1950  1970 1990 Ehu  300  1970 1990 Gindai  1950 1970  1990  0  0  0  5  20  100  10  200  100  1950 15 20 25  Kalekale  60  1990  h=0min h=2min h=5min h=7min h=9min  100  400 200 1990  1950 1970  Lehi 150  Uku  0  200 1950 1970  600  1200  1970 1990  White Ulua  0  0  0  500  400  100 50 0 400  600  1990  Kahala  0  Bit (metric tons)  1950 1970  Onaga  400  1500  Opakapaka  800  200 150  Hapu'upu'u  1950  1970 1990  1950  1970 1990  Years  Figure 3.2 Annual predicted biomass measured in metric tons for each species for five hypotheses of average handling time per fish h.  138  1950  1980  0.20  1.2  0.10  0.4 0.0  0.00  0.12 0.08 0.04 0.00  0.8  1980  Fit  0.02 0.04 0.06 0.08 0.00  h=0min h=2min h=5min h=7min h=9min  1980  0.05  0.8  0.00  0.3 0.2  1980  0.4  0.1 0.0  1950  0.10  0.4  1.2  Gindai  0.15  0.12  1.2 0.8 0.4 0.0  0.08 0.04 0.00 0.4  1950  1.2 0.8 0.4 0.0  0  0.0  2  0.4  4  6  0.8  8  1.2  1980  Ehu 10  Kalekale  0.4  0.1 0.0  1950  1950  Lehi  0.2  1980  White Ulua  1980  0.0  0.4 0.0  0.1 0.0  1950  1950  0.3  0.8 0.2  0.8 0.4 0.0  Bit / Boi  0.3  1.2  Uku  1.2  Kahala  1980 1.2  1950  0.8  0.4 0.0  0.8  0.10  1980  Onaga  0.0  1950  0.00  0.0  0.4  0.8  0.20  1.2  Opakapaka  1.2  Hapu'upu'u  1950  1980  Years  Figure 3.3 Annual estimated depletion (Bit/Boi; solid lines, primary axis) and fishing mortality (Fit, dashed lines, secondary axis) from the MLEs of the leading parameters for each species for five hypotheses of average handling time per fish h.  139  0.0  0.4  0.8  0.8 0.0 0.8  0.0  0.4  0.8  0.8  h=0min h=2min h=5min h=7min h=9min  0.0 0.4  0.8  0.0  0.4  0.8  0.0  0.4  0.8  Gindai  0.8  Ehu  0.0 0.8  0.4  0.4  0.8 0.0  0.4  0.8 0.4 0.0  0.4  0.0  Lehi  0.0 0.8  Kalekale  0.0  0.4  0.8 0.8  0.4  0.8 0.4  qit / qoi  0.4 Uku  0.0  0.4  White Ulua  0.4 0.0  Kahala  0.0  Onaga  0.0  0.4  0.8  Opakapaka  0.0  0.0  0.4  0.8  Hapu'upu'u  0.0  0.4  0.8  0.0  0.4  0.8  Bit / Boi  Figure 3.4 The relationship between the ratio of species-specific catchability and catchability at low stock size (qit /qoi) and depletion (Bit/Boi) for each species and five hypotheses of average handling time per fish h.  140  0.030  0.40  0.46  0.8 0.0 0.240  0.04  0.08  0.8  h=0min h=2min h=5min h=7min h=9min  0.0  0.4  0.8 0.0 0.080  0.095  0.02  0.8 0.4 0.0  0.0 0.020  0.04 Gindai  0.8  Ehu  0.4  0.8 0.4 0.0  0.015  0.225 Lehi  0.4  0.8 0.4  0.12  Kalekale  0.005  0.210  Uku  0.0  0.09  0.4  0.8 0.4 0.34  Kahala  0.06  White Ulua  0.0  0.4 0.0  0.4 0.0 0.020  qit / qoi  Onaga  0.8  Opakapaka  0.8  Hapu'upu'u  0.035  0.050  0.004  0.006  0.008  Bit /Btotal  Figure 3.5 The relationship between species-specific catchability and catchability at low stock size (qit/qoi) and the ratio of species-specific biomass and total biomass for five average handling time hypotheses. Stars indicate the starting point  141  20 0 -10 -30  -20  Likelihood  10  Opakapaka Ehu Uku Kalekale Hapu'upu'u White ulua Onaga Kahala Lehi Gindai  0  20  40  60  80  h  Figure 3.6 Profile of the negative log-likelihoods of species-specific catch, L(Ci | Θi), against the average handling time per fish values h (minutes per fish). Values plotted in this figure are presented in Table 3.7.  142  40 20  40 0 1950  1970 1990  1970 1990  20 10 5 0 1970 1990  50  Ehu  Gindai  1.5 0.5 0.0  10 0 1990  1970 1990  1.0  30 20  40 20 0 1950 1970  1950 2.0  1950  40  Kalekale  1990  h=0min h=2min h=5min h=7min h=9min Observed  50 0  20 0  1990  60  80  1950 1970  1950 1970  Lehi  15  100  100 60  1950  Uku 150  Kahala  0  20  50 0 1990  White Ulua  60  80 60  100  15 10 5 0 1950 1970  Cit (metric tons)  Onaga  80  150  Opakapaka  20  Hapu'upu'u  1950  1970 1990  1950  1970 1990  Years  Figure 3.7 Observed and predicted (solid lines) catch for each species and five hypotheses of average handling time per fish (h).  143  Figure 3.8 Catch residuals (ln ‫ܥ‬௜௧ − 	 ln ‫ܥ‬መ௜௧ ) on a natural logarithmic scale for each species and five hypotheses of average handling time per fish h.  144  Figure 3.9 Estimated, annual recruitment anomalies (ωit) for each species and five hypotheses of average handling time per fish h.  145  Figure 3.10 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Ehu. Posteriors were generated from 20,000 random samples.  146  Figure 3.11 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Gindai. Posteriors were generated from 20,000 random samples.  147  Figure 3.12 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Hapu’upu’u. Posteriors were generated from 20,000 random samples.  148  Figure 3.13 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Kahala. Posteriors were generated from 20,000 random samples.  149  Figure 3.14 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Kalekale. Posteriors were generated from 20,000 random samples.  150  Figure 3.15 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Lehi. Posteriors were generated from 20,000 random samples.  151  Figure 3.16 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Onaga. Posteriors were generated from 20,000 random samples.  152  Figure 3.17 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Opakapaka. Posteriors were generated from 20,000 random samples.  153  Figure 3.18 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for Uku. Posteriors were generated from 20,000 random samples.  154  Figure 3.19 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for unfished biomass Bo, the recruitment compensation ratio Κ, and catchability at low stock size qo estimated for five hypotheses of average handling time per fish h for White ulua. Posteriors were generated from 20,000 random samples.  155  Figure 3.20 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Ehu. Posteriors were generated from 20,000 random samples.  156  Figure 3.21 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Gindai. Posteriors were generated from 20,000 random samples.  157  Figure 3.22 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Hapu’upu’u. Posteriors were generated from 20,000 random samples.  158  Figure 3.23 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Kahala. Posteriors were generated from 20,000 random samples.  159  Figure 3.24 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Kalekale. Posteriors were generated from 20,000 random samples.  160  Figure 3.25 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Lehi. Posteriors were generated from 20,000 random samples.  161  Figure 3.26 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Onaga. Posteriors were generated from 20,000 random samples.  162  Figure 3.27 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Opakapaka. Posteriors were generated from 20,000 random samples.  163  Figure 3.28 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for Uku. Posteriors were generated from 20,000 random samples.  164  Figure 3.29 Joint posterior densities (lower triangle) and marginal posterior densities (diagonal) for MSY, FMSY, and BMSY and the joint posterior density for Fstatus and Bstatus (upper diagonal) estimated for five hypotheses of average handling time per fish h for White ulua. Posteriors were generated from 20,000 random samples.  165  Chapter 4 Management procedure evaluation for the Hawaiian bottomfish fishery Introduction Increasing concerns about overfishing, especially in the face of uncertainty about the population dynamics of target species, the observation dynamics of a fishery, the assumptions made in stock assessment models, environmental variability, information contained within data, etc., has led fisheries management organizations to adopt a precautionary approach to fisheries management. Precautionary fishery management should consider and avoid unacceptable outcomes, which include inter alia, over-exploitation of a resource and the loss of biodiversity (FAO 1996). Precautionary management should also consider and account for uncertainty and decision makers should develop a conservative course of action when available information is limited or non-informative (FAO 1996, Garcia 1996). The precautionary approach has generally been presented as management objectives, policies, and decision rules meant to prevent overfishing and rebuild overfished stocks (Essington 2006, New Zealand Ministry of Fisheries 2007, Fisheries and Oceans Canada 2009). This is the case in the United States where the main goal of fisheries management, as outlined by the national standards of the Magnuson-Stevens Reauthorization Act (MSA), is to avoid overfishing while achieving optimal yield on a continual basis. Additionally, rebuilding plans must be implemented for all fisheries that are considered overfished. The MSA mandates fishery management councils to develop fishery management plans in accordance to the national standards. National standard guidelines translate the broad management objectives of the MSA into explicit concepts such as catch, fishing mortality, and biomass targets and limits to define stock status, as well as harvest control rules to develop policy in relation to perceived stock 166  status (Darcy and Matlock 1999, Restrepo and Powers 1999). For example, as of 2011 domestic fisheries must be managed using annual catch limits (ACLs), which are determined as part of a hierarchical system based on overfishing limits as specified in fishery management plans. Additionally, a harvest control rule must be defined to provide a framework for adjusting management parameters (e.g., catch, fishing mortality, or effort) in relation to changing stock status. Although these definitions provide a framework for stock status evaluation and designation of management policy, they do not guarantee that management objectives will be met. Formal evaluation of the entire management system (data collection, stock assessment, and harvest strategies and control rules) aids in determining whether well intentioned legislative measures will meet management objectives given inherent uncertainties in the management system (Punt 2006). Management procedure evaluation is a method that has been used to evaluate management procedures in relation to management objectives given underlying uncertainties about the system in question (Butterworth and Bergh 1993, Geromont et al. 1999, Kell et al. 1999). An evaluation of this type represents an adaptive process where simulated management actions lead to learning about a system (Walters and Hilborn 1978, Walters 1986). Adaptive processes can be described as either active or passive. Active adaptive processes include deliberate perturbations (i.e., experimental management policies) to a system and are intended to provide an informative response to resolve uncertainty (Walters and Hilborn 1978, Walters 1986). Passive adaptive processes are more common in resource management and are not deliberate experiments that are designed resolve uncertainty. They represent a system where management actions are taken, stock assessments (state and parameter estimates) are updated with additional data, and the future policy is updated (when there is no parameter updating, only re-estimation of the stock size each year and policy adjustment to the new estimates, the policy is 167  simply a non-adaptive feedback policy, Walters 1986). Passive adaptive management may lead to improvements in parameter estimates; as management policies are updated and varied, this variation is assumed to lead to some learning about the system. An example of an analytical tool that represents this adaptive process in a simulation framework is management procedure evaluation (Sainsbury et al. 2000). Management procedure evaluation (also referred to as management strategy evaluation) is a Monte Carlo simulation tool that has been promoted and used to evaluate the entire fishery management system (Butterworth et al 1997, Smith et al. 1999, Sainsbury et al. 2000, Punt et al. 2001). The main goals of MPE are to clearly define the management objectives for a fishery, evaluate whether these management objectives can be met using various management procedures, and identify the trade-offs among the management objectives across different management procedures (Butterworth et al. 1997, Smith et al. 1999, Punt et al. 2001). A management procedure represents the entire process from collecting data, conducting an assessment and forecast, and applying a harvest control rule to determine an annual catch limit (ACL). Management procedure evaluation is used to test alternative management procedures or a specific component of the management procedure including existing and alternative data collection programs, and is used to evaluate how they perform with respect to pre-determined management objectives (performance measures). The basic structure of a MPE consists of an operating model, a stock assessment model, a harvest control rule, a harvest decision model, and a harvest implementation model (McAllister et al. 1999). The operating model represents a reasonable possibility about the “true” system dynamics, incorporates any uncertainties that may influence management outcomes, and is used to simulate the population and observation dynamics of the system. The simulated observations then become the data that are used in a stock assessment model to determine stock status and 168  management decisions made based on the estimates of stock status and the application of the harvest control rule. The simulated management decision is implemented on the operating model (true states) and its effects on the “true” population are projected forward in time, generally. For some pre-specified time-step (e.g., annually or once every few years or once every several years), the assessment and management decisions are updated. Performance of the management decisions are evaluated using performance measures, which help to clearly identify the trade-offs among the potentially conflicting management objectives. The performance of management procedures relative to pre-specified management objectives and the realized trade-offs among the conflicting management objectives will be influenced by the perspective taken to develop policies and the harvest control rules used to relate the management variable to stock status. For example, the MSA mandates that all US domestic fisheries be managed by annual catch limits (ACLs) a type of catch quota system. An ACL policy applied to a single species fishery is straightforward; this is not the situation for multispecies fisheries. How should the management variable and the stock status variable that are used as part of the harvest control rule be represented on an aggregate or species specific basis, and what should be done when fishing effort prescriptions from the species control rules are widely divergent (e.g., prescribe high catch for one species but none for another)? The primary management objectives of the MSA are to ensure optimal yield, avoid overfishing targeted stock(s), and conserve target and non-target species. If aggregate control rules are used, all else being equal, relative differences in productivity will cause some species to be more resilient to fishing than others and may lead to overfishing less productive species (Paulik et al. 1967, Hilborn 1976, Hilborn 1985). Conversely, managing for the less productive species (i.e., weak stock management) can potentially lead to tremendous loss due to foregone catch of more productive species (Hilborn et al. 2004, Christensen and Walters 2004). Using 169  MPE, the management trade-offs under these differing management systems can be identified and evaluated and the expected benefits or losses of implementing a particular form of an ACL policy or harvest control rule can be compared. These trade-offs are not uncommon when managing multispecies fisheries and will be addressed for the Hawaiian bottomfish fishery in this chapter. An additional factor that may influence the performance of a management procedure in closed-loop policy simulations is the type of data that are used for assessments. Fisheryindependent data are not always collected given the cost relative to the value of the fishery. Fishery-dependent catch and effort statistics from industrial fisheries, however, are more readily available for assessments, but are highly suspect. These data are often uninformative due to a lack of trend information (i.e., no long-term changes in CPUE), involve catch and effort patterns that are not likely to be proportional to abundance, or represent one-way trip data as is the case for the Hawaiian bottomfish fishery. The ability to jointly estimate population scale and productivity from such uninformative data are minimal (Hilborn 1979). The development of catch quotas, such as ACLs, is reliant on stock assessment models to accurately estimate population scale. Investments in fishery-independent data collection programs, therefore, may become of great importance in the future. As such, it is important to evaluate future data collection programs as part of the feedback loop to determine if the information will inform management decision rules. In the following section, I describe the MPE framework I developed for the Hawaiian bottomfish fishery. An important objective of this chapter was to develop a tool that can be used and build upon to evaluate management procedures for the Hawaiian bottomfish fishery. Three additional objectives were addressed using this MPE framework: (1) how does the status quo (i.e., aggregate ACL) policy perform compared to a species-specific ACL policy in terms of 170  meeting management objectives, (2) compare different decision rules and evaluate the potential benefits and costs of their implementation, and (3) evaluate alternative data collection programs in terms of information quality about decision rule and corresponding ACL. Two alternative decision rules were evaluated: a precautionary harvest control rule, and a weak stock harvest control rule. These two harvest control rules were initially chosen ad hoc, and it was not my intention to determine an optimal harvest control rule, as this would require my own personal choice of balancing trade-offs between conservation, stability of the fishery in terms of catch and economic performance. I am merely trying to propose a method in which trade-offs can be addressed in a quantitative manner. In light of some of the results obtained in this chapter, I also explored a third alternative decision rule, and present the results of this rule in the Appendix B. Three alternative data collection programs were considered, the resulting data classes from these programs are as follows: (1) the status-quo fishery-dependent catch and effort data, (2) speciesspecific fishery-independent relative index of abundance, and (3) species-specific fisheryindependent monitoring of annual fishing mortality rates through a tagging program. Lastly, three performance measures were used to evaluate the performance of the MPs with respect to the management objectives over the short-term and long-term perspectives: (1) average annual variation in total catch (AAV), (2) average total catch, and (3) average total depletion. Methods Overview of the management procedure evaluation Management procedure evaluation is a simulation tool that models the entire decision making process as a closed-loop system and is used to quantitatively compare alternative management procedures using performance measures. The MPE framework presented here has four components, (1) an operating model that represents alternative scenarios of the underlying 171  “true” system dynamics, (2) two alternative stock assessment models, (3) two alternative harvest control rules to determine an annual catch limit (ACL), and 4) the performance measures used to evaluate how well each management procedure achieves pre-specified management objectives. The different combinations of stock assessment models, data types, and harvest control rules constitute the suite of management procedures tested (i.e., these are considered the tools that are required to provide annual catch advice for fisheries management). The first step of MPE is to construct an operating model that is capable of generating data from several scenarios about the underlying true dynamics of the resource. The use of alternative operating model scenarios is intended to represent alternative hypotheses that span key model uncertainties and test the robustness of the alternative management procedures. Operating models are usually constructed by fitting age-structured models to the available historical data; this fitting process is often referred to as conditioning the operating model to available data. Key parameter and structural uncertainties are identified at this stage. To test candidate management procedures, MPE proceeds in an iterative process where the population is projected forward in time. In each projection year, the following sequence of events happens: (i) the population status is determined using a stock assessment model, (ii) future catch or effort is determined using the harvest control rule, (iii) the harvest is implemented (with or without error) in the operating model, and (iv) the operating model is then used to generate new data for the process to start over again in the next time step. MPE represents a closed-loop feedback system where the dynamics, stock status, and management policy are updated each year. In the following sections I detail the individual components of the MPE framework used in this chapter, but I first identify the candidate management procedures.  172  Management procedures Each of the management procedures outlined in Table 4.1 were defined according to a combination of harvest control rule (i.e., precautionary or weak stock harvest control rule), the types and quality of the data available for use in an assessment model, the assumed value of average handling time in the assessment model (h =0 or 7 minutes per fish), and two alternative assessment models. The data types include: 1) catch by species and total effort from the multispecies fishery, 2) catch by species, total effort, and species-specific relative abundance information from a fishery-independent survey (two levels of observation error representing different levels of investment in the monitoring program), and 3) catch by species, total effort, and a mark-recapture program (two levels with either 250 or 2000 tags). The catch by species and total effort data spans the entire time series (i.e., historical and projection periods), whereas, the fishery-independent data were simulated only over the projection years. A total of twentyone alternative management procedures were evaluated across two operating model scenarios (handling time effects on catch and effort). A perfect-information management procedure P1 was also evaluated as part of this MPE. The perfect-information management procedure represents that of an “omniscient manager”, who is able to anticipate future uncertainty. In the perfect-information management procedure all uncertainties are known and biomass is equal to the true biomass simulated in the operating model. A harvest control rule is not associated with the perfect-information procedure; rather, future catch is determined from the true EMSY. The performance measures obtained from the perfect information scenario serves as a comparison in which to evaluate all other management procedures.  173  Operating model The operating model represents a “true” system and represents the key hypotheses about the dynamics of fish populations and fisheries impacts (Butterworth and Punt 1999). The operating model is made up of four sub-models: 1) the dynamics of the populations in this multispecies fishery, 2) the observation dynamics of the fishery, 3) the impacts of harvest, and 4) the implementation of resulting policy (McAllister et al. 1999). It covers two distinct time periods, historic and future. The historic time period includes the years 1948-2005 and the future includes the years 2006-2031 (i.e., 25 projection years). The operating model was conditioned on the fisheries dependent data, species-specific catch and total effort, collected by the State of Hawaii for the historical time period. The process of conditioning the operating model is identical to the assessment model used in Chapter 3 and developed in Chapter 2 (see Table 2.2 for system of equations) and provides the initial starting states for the projection period. Therefore, the forward projections over future years were populated by the stock size and leading parameter estimates from the assessment model. This was done to ensure consistency with the historical data (Cox and Kronlund 2008). Hyperstability of the aggregated catch per unit effort data in the Hawaiian bottomfish fishery has been a major concern in recent stock assessments. Moffitt et al. (2006) indicate that advances in fishing technology over time have led to an increase in catchability, which would in turn lead to hyperstability. Factors such as changes in handling time and targeting behaviour can also lead to a non-stationary catchability (e.g., see Chapter 2). Handling time and targeting behaviour were included as the two alternative structural assumptions in the operating model that would cause non-stationarity in catchability. Two alternative operating model scenarios were considered to account for the uncertainty in catchability in the operating model. The first operating model scenario assumes that average handling time is negligible for all species (i.e., 174  catchability is constant over time) and the second operating model scenario assumes that average handling time is equivalent to seven minutes per fish (i.e., catchability for each species is timevarying). Other sources of error that were included in the operating model were of a more typical form, random and uncorrelated process errors via stochastic recruitment and observation errors via measurement errors in catch rates. Additionally, the commercial catch statistics for the Hawaiian bottomfish fishery were not originally collected for use in stock assessments; i.e., they were not collected to develop relative indices of abundance. In an attempt to resolve uncertainty in the multispecies assessment model and possibly allow for the estimation of handling time (i.e., hyperstability in the commercial catch statistics), a fisheries independent data collection program for each species was simulated where it is assumed that the relative abundance data from the survey is directly proportional to the true abundance. The new fishery-independent data start in the first projection year of the closed-loop simulation and was not forecasted backward to 1948, which is the beginning of the historical time series. Multispecies population dynamics Before describing the sub-models making up the operating model, the reader is referred to Table 4.2. Table 4.2 summarizes the definitions of the parameter and variable symbols used throughout the remainder of this chapter. The state dynamics of the ten Hawaiian bottomfish species included in the analysis were simulated using the delay-difference model as outlined in Chapters 2 and 3 (see Table 2.2). The key assumptions of the delay-difference model are: 1) growth in weight for age Ai and older fish is described by the Ford-Brody growth model, 2) fish age Ai and older are fully vulnerable to the fishery, 3) natural mortality Mi is the same for fish age Ai and older and is constant, and 4) all fish age Ai and older are sexually mature. Recruitment was simulated according to the Beverton175  Holt recruitment model and annual recruitment anomalies ωit (process error) were log normally distributed. Lognormal recruitment anomalies represented the sole source of stochastic variation in the state dynamics. Observation dynamics of the fishery: Fishery dependent data and targeting behaviour Table 4.3 summarizes the observation dynamics sub-models used to simulate fisherydependent and fishery-independent data. The equation numbering convention for Table 4.3 and all others is as follows: T followed by the table number and the ordered list value within the table. It was assumed that fishery-dependent catch and total effort data were the minimum available information for future stock assessments. Annual catch for each species Cit (where t > 2005) was simulated using the Baranov catch equation and was calculated as a function of species specific, annual fishing mortality rates Fit, total mortality Zit, and biomass Bit (eq. T4.3.1). Prior and up to 2005, Cit was set to the landed observed catch Lit. Total mortality was calculated as the sum of natural and fishing mortality (eq. T4.3.2). Fishing mortality rates were calculated as a function of total effort and species specific catchability (eq. T4.3.3). Total effort for t >2005 was dependent on the stock status and was determined by one of the two harvest control rules (explained later in this section). A key uncertainty that is of concern for most catch series is non-stationarity in catchability, specifically if it leads to hyperstable indices of relative abundance. A known cause of hyperstability is handling time, which is a plausible factor influencing catch in the Hawaiian bottomfish fishery given the gear type (i.e., handlines). To account for handling time effects, catchability was simulated using the disc equation (eq. T4.3.4, excluding the targeting parameter term (etg) which is explained below). Another plausible factor causing non-stationarity in  176  catchability is a change in targeting different species over time, which potentially masked handling time effects on catchability. Given the broad depth distribution of the Hawaiian bottomfish species, it was assumed that the species composition of the catch reflects the depth of fishing. Species groups were classified into two general depth classes using a hierarchical clustering analysis method in the stats package of R (R Development Core Team 2011). Beginning and ending fishing depths for 214 out of 16457 trips from 2002 to 2005 were reported in the Hawaiian bottomfish fishery dependent database. Depth data were not recorded for trips before 2002. Average depth for each trip was calculated and Ward’s minimum variance method was used to find species groups that were most similar in terms of the observed average depth in which they were caught. Groupings were similar to those found by Ralston and Polovina (1982) and are shown in Figure 4.1. The dendrogram presented in Figure 4.1 has two main branches. One branch is defined by Uku and White ulua, which represent species found at shallow depths, The second main branch is separated into two sub-groupings; 1.) Lehi, Hapu’upu’u, Gindai, and Opakapaka represent intermediate depth species, and 2.) Kahala, Kalekale, Ehu, and Onaga represent species found at the deepest depths. For the purposes of this analysis, species were defined by the two main branches. The species were either considered to be “shallow” or “deep” species and will be referred as such throughout the rest of this chapter. The catchability equation was modified to account for targeting behaviour by depth (eq. T4.3.4). The targeting parameter tg was derived as a function of a sine transformed random uniform deviate x (eq.T4.3.5). This stochasticity caused the targeting on one depth group to be the reciprocal of the other and was reflected in allocation of fishing mortality for each species (eq. T4.3.3).  177  Fishery independent data Currently, fishery dependent data are the only available data for the Hawaiian bottomfish fishery. It was therefore of interest to evaluate management procedures with a combination of fishery-dependent and fishery-independent data to evaluate the performance of management procedures when the addition of fishery-independent data compared to when only fisherydependent data are available. Two fisheries independent programs were evaluated: (1) a research survey to provide species-specific indices of relative abundance that are proportional to stock size, and (2) a mark-recapture program to directly monitor fishing mortality rates through recovery rates of tagged fish on an annual basis. The depth range of the waters where Hawaiian bottomfish are commonly found precludes the implementation of a conventional mark-recapture program where fish must be caught, brought to the boat deck, tagged, and then released. A genetic tagging technology, a biopsy hook, has been designed to collect tissue samples in situ (Buckworth et al. 2006, Hague 2006). In situ tagging avoids the problem of increased mortality due to barometric trauma. The tagging program evaluated in this thesis was done with a genetic tagging program in mind. The tagging program was classified as a fisheries-independent source of information to avoid potential biases that may arise via unknown tag reporting rates in a fishery-dependent mark-recapture program. A fisheries-independent program would somehow overcome major assumptions of typical mark-recapture programs (see Martell and Walters 2002). For example, Martell and Walters (2002) suggest that designing a tagging program so that tag collection is not apparent to fishers (i.e., when the fish have already been sold to fish houses or dealers) would reduce the chance of violating the assumption that all recaptured tags are reported. A relative index of abundance for each species Yit was simulated using equation T4.3.6. It was assumed that the survey catch per unit effort was proportional on average to true 178  abundance of the individual species. The survey index was simulated with log-normal observation errors, where φi are random normal deviates with a mean equal to zero and known varianceσଶ஦೔ . Two levels of observation error were considered to reflect levels of investment in the survey. The associated CVs for the surveys were 0.2 and 0.4, where a lower CV reflects greater investment. Mark-recapture data were simulated as a Poisson process. The number of tag recoveries  nit for each species was simulated as a Poisson sample from the total number of released tags ܰሶ௜௧ (T4.3.7) and the expected number of recaptures was the product of released tags and the  probability of recapture ܰሶitPit. The probability of recapture Pit was calculated as the product of the annual exploitation rate and the reporting rate (eq. T4.3.8). Assumptions of the markrecapture model are: i) the annual reporting rate τit was assumed to be known and 100 percent, ii) the probability of capturing marked and unmarked fish is the same, and iii) there is no additional mortality associated with marking fish. Assessment models Two assessment models were used, an aggregate surplus production model and the multispecies delay-difference assessment model presented in Chapters 2 and 3. The aggregate surplus production model represents the current assessment method that is used to estimate aggregate abundance, aggregate stock status, and the aggregate ACL for the Hawaiian bottomfish fishery. Aggregate assessment A deterministic, semi-implicit version of the aggregate surplus production model that has been used to assess the Hawaiian bottomfish fishery was applied to the historical and simulated 179  data. A semi-implicit version of the Schaefer surplus production model was used for numerical stability (ADMB Project 2009). The estimated leading parameters θ are unfished biomass Bo, the catchability coefficient q, the intrinsic rate of growth r, and the variance in the catch observations σ2 (eq. T4.4.1). The semi-implicit form of the Schaefer model, where biomass (bt) was initialized as Bo is represented by equation T4.4.2. The variable ∆ is the implicit time step and represents six months (eq. T.4.4.3). The model was conditioned on effort (days fished) through the annual fishing mortality equation, which was a function of a single estimated catchability coefficient q and annual effort Et (eq. T4.4.4). Predicted catch over the period (t) is given by equation T4.4.5 and is the product of the fishing mortality rate and total biomass. The model was fitted to observed total catch and the residuals were calculated as the log difference between observed and predicted catch (eq. T4.4.6). The residuals were assumed to be log normally distributed with a mean equal to zero and variance σ2. Four parameters of interest were estimated by the aggregate surplus production model, Bo, q, r, and σ2. It is important to note the absence of the species subscript i. This assessment approach, which represents the status quo for Hawaiian bottomfish, ignores any differences among species and it is assumed that q and r are the same for all species. The negative loglikelihood that was minimized is given by equation T4.4.7 and represents the likelihood of total catch data given the estimated parameters θ, where n is the number of observations. This minimization was done for each simulation year to provide adaptive updating of parameter estimates during each MPE realization. The management reference points, MSY, BMSY, and EMSY, developed from the aggregate surplus production model are given by equations T4.4.8, T4.4.9, and T4.4.10, respectively. 180  Multispecies assessment The multispecies assessment model is the same as that was evaluated in Chapter 2 and used Chapter 3 (see Table 2.2 for system of equations). Modifications made to the assessment model pertain to the inclusion of additional data sources. Differences in the estimated parameters of interest (eq. T4.5.1), predicted observation dynamics, and likelihoods can be found in Table 4.5. All MPs that were evaluated at a minimum had fishery-dependent commercial catch and effort data available for assessment. Species-specific catchability and catch were predicted using equation T4.5.2 and T4.5.3 and the associated log-transformed residuals between observed and predicted catch were calculated using equation T4.5.4. The standard deviation of the catch observations was calculated as a proportion of total standard deviation (eq. T4.5.5). The speciesspecific relative indices of abundance were predicted as T4.5.6, where ‫ݍ‬௦೔ is the survey  catchability coefficient for species i. It was assumed that ‫ݍ‬௦೔ was constant and the species-  specific relative index of abundance ܻ෠௜௧ was proportional to abundance. The log transformed residuals between the observed and predicted indices were calculated from equation T4.5.7. When mark-recapture data were available for assessment, the number of expected recaptures was predicted using equation T4.5.8, where ܰሶ௜௧ is the total number of released tags and Pit is the probability of recapture. The probability of recapture was calculated as function of annual fishing mortality and the reporting rate τit which was assumed to be known and be 100 percent (eq. T4.5.9). The negative log likelihood of the catch given the parameters of interest Θi for species i is given by equation T4.5.10, where n is the number of observations. Annual recruitment anomalies ωit were assumed to be log normally distributed with a mean equal to 0 and standard 181  deviation equal to ߪఠ೔೟ (eq. T4.5.11). An informative prior for the recruitment compensation ratio Κ was used. The recruitment compensation ratio Κ was transformed to steepness (Myers et al. 1999, Martell et al. 2008) and a beta prior on steepness was used (eq. T4.5.12). The beta distribution can be used to describe random variables that have a range between zero and one (Evans et al. 2000). The steepness parameter has a range between 0.2 and 1 for the BevertonHolt model (Myers et al. 1999). The first term in equation T4.5.12, was used to scale the steepness parameter between 0 and 1. The prior for steepness remained unchanged as more data were accumulated over time in the projection time period of the model. Fishing mortality for each species was also constrained using the penalty given by equation T4.5.13. The objective function that was minimized when fishery-dependent data were the only source of data for assessment is given by equation T4.5.14. The likelihood of the species specific survey index is given by equation T4.5.15, where nsurv is the number of survey observations and ߪ௒ଶ೔ is the variance in the survey observations. Observation errors in the survey were assumed to be  lognormally distributed and the resulting likelihood of the catch and survey index given ‫ݍ‬௦೔ 	and  ߪ௒ଶ೔ is given by equation T4.5.15. The objective function that was minimized when fishery-  dependent data and fishery-independent species-specific relative indices of abundance were available for assessment is given by T4.5.16. It was assumed that the number of tag-recaptures was an outcome of a Poisson process, so that the resulting negative log likelihood can be expressed as equation T4.5.17. The objective function that was minimized given the estimated parameters is given by equation T4.5.18. Table 4.6 summarizes the equilibrium equations used to obtain species-specific and community based management reference points, MSY, BMSY, and EMSY, from the multispecies delay difference model. This will not be explained in detail since it was previously explained in Chapter 3. 182  Harvest control rules Harvest control rules represent a pre-agreed upon plan to adjust catch, fishing effort, or fishing mortality with updated stock-assessments (Hilborn and Walters 1992). Two stock-size dependent harvest control rules were evaluated in this chapter, where management advice was specified as total effort given the aggregate stock size. For ease of comparison, the rules will be referred to as precautionary and weak-stock harvest control. The harvest control rules limit the fishing mortality rate via setting effort limits, where fishing effort was adjusted based on the current status of the stock. The precautionary harvest control rule is shown in Figure 4.2. For the precautionary harvest control rule, if the current biomass was greater than 80% of BMSY, then the total annual fishing effort was set to 80% of the fishing effort that would achieve MSY (EMSY). If the current biomass was less than 80% of BMSY and greater than 40% of BMSY, the fishing effort was adjusted downwards (linearly) and was dependent on the ratio between current biomass and BMSY. If the current status of the stock was less than 40% of BMSY, the fishery was closed and fishing effort was set to zero. The weak-stock harvest control rule was more conservative than the precautionary harvest control rule. Fishing was prohibited (i.e., effort = 0) when the estimated biomass of any one species fell below its estimated BMSY. Effort was otherwise set to 80% of BMSY. The weak-stock harvest control rule was not used with the aggregate assessment approach since MSY-derivatives were only estimated for the community of species using the aggregate assessment model. The way in which EMSY and BMSY were determined was dependent on the assessment model that was used. Equations T4.4.9 and T4.4.10 were used to determine EMSY and BMSY from the aggregate assessment model and equations T4.6.12 and T4.6.13 were used from the multispecies assessment model. It is important to note that EMSY and BMSY from the aggregate 183  assessment approach represents a mean relationship between surplus production and overall stock biomass across species and therefore ignores any differences among species. Speciesspecific management reference points were determined from the multispecies delay difference model. Ideally, the ACL for each species would be developed in relation to the species-specific EMSY and BMSY, which were developed from the multispecies assessment model. EMSY will differ among species and the technical interactions of the Hawaiian bottomfish fishery make it difficult manage using individual harvest control rules. EMSY and BMSY were determined from the summed relationship between surplus production and effort or biomass across species for the management procedures that employed the multispecies assessment approach (see Table 4.6 for equilibrium calculations). The resulting recommended ACL represented the summed yield across species associated with the given effort level. Effort from the harvest control rule was translated into realized catch for each species through the fishing mortality and catch equations (eq. T4.3.1, eq. T4.3.3). In the event that biomass was overestimated (i.e., estimated biomass and ACL are greater than the “true” biomass), catch is set to 90% of the true biomass. This ensures that the catch can never be greater than the true biomass and represents a situation where an unrealistic ACL has been set and the catch cannot be achieved due to unavailable biomass. Evaluating performance The performance of management procedures must be evaluated with respect to specified management objectives. The goals of most management systems are to maximize catch, maximize the stability of catch, and avoid overfishing or causing a stock to be overfished (Butterworth et al. 1997, Kirkwood 1997, De la Mare 1998). Performance measures are used as part of a MPE to quantify how well a management procedure performs in relationship to the 184  specified management objectives, as well as evaluate the trade-offs among the competing management objectives. Three performance measures, average annual variation in total catch (AAV), average total catch, and average total depletion, were chosen to represent the management objectives of maintaining a productive fishery and preventing overfishing. AAV and average catch are performance measures that are of particular importance to the stakeholders (i.e., the fishers) as they measure the stability of catch/economics and the potential productivity of the fishery. Average depletion was used to evaluate how well conservation goals were met by the management procedures. Performance measures were calculated in terms of total catch and biomass summed across species, as well as on a species-specific level (Table 4.7). Measuring performance on the aggregate level provides for easier comparison between management procedures. Measuring performance on the species level is also important to fully evaluate the impact of the management procedure on the individual species. AAV was only measured on the aggregate level (eq. T4.7.1). Aggregate and species-specific average catch were calculated using equations T4.7.2 and T4.7.3, respectively. Lastly, aggregate and species-specific average depletion were calculated using equations T4.7.4 and T4.7.5, respectively. The performance measures were compared on short- and long-term projection scales. Short-term projections represented the MP performance within the first five projection years (i.e., 2006-2011) and long-term projections represented performance for all years after 2011. Evaluating the performance of management policies over different temporal scales helps to evaluate the short-term losses in relation to long-term gains or vice versa. The simulation results are presented in plots that show the trade-offs among the performance measures.  185  Results Figures 4.3 and 4.4 present the short-term and the long-term performance measures, respectively, and are referred to frequently throughout this section. The separate presentation of the short-term and long-term results was done for ease of interpretation. In the presentation below, shorthand notation is frequently used to refer to the MPs. The notation for the management procedures is summarized in Table 4.1; this table will be helpful in interpreting the results that follow. Short-term performance measures Average annual variation in total catch, precautionary harvest control rule The range in the AAV estimates across the MPs associated with the precautionary harvest control rule was between 0.15 and ~1.5 and was similar between the operating model scenarios (Figure 4.3 a, b). The AAV estimates within an MP were also similar among the two operating model scenarios (Figure 4.3 a, b). In general, high values of AAV are undesirable for the fishing industry; high values of AAV imply high volatility in annual catches and therefore annual income. The data used in the stock assessment model was the most important factor with respect to the observed differences in the AAV estimates among the management procedures. Median short-term AAV was greatest for MPs, T3 and T4, which were both described by the availability of tagging data in addition to species-specific catch and total effort for assessment (Figure 4.3 a, b). In addition, these MPs also assume that the catch and effort data were hyperstable in the assessment model (hassess=7 minutes per fish). The median estimate of short-term AAV was also high for A1, which was described by the availability of aggregate catch and effort data for stock 186  assessment and T1 and T2, as compared to all other MPs. Median short-term AAV for A1, T1, and T2 was greater than when species-specific catch and total effort were available alone (C1 and C2) or in addition to species-specific relative indices of abundance (S1 through S4) for assessment (Figure 4.3 a, b). Within data class comparisons of median AAV estimates indicate that assuming that catch and effort data are proportional to abundance (hassess=0; C1, S1, S2) or hyperstable (hassess=7 min/fish; C2, S3, S4) in the assessment model did not influence the estimates of AAV. The assumption made about the relationship between the fishery-dependent data and abundance did influence the median estimate of AAV when tagging data were available for assessment. More specifically, T1 and T2 (hassess =0) had lower AAV than T3 and T4 (hassess = 7 min/fish). The estimated AAV was similar among the precautionary management procedures described by species-specific catch and effort data alone (C1 and C2) or in addition to speciesspecific relative indices of abundance (S1 through S4) and the management procedure described by perfect information (P1) for both operating model scenarios (Figure 4.3 a, b, e, f). AAV was greater for the management procedure described by aggregate catch and effort data (A1) and the MPs described by the availability of tagging data (T1-4) than when having perfect information (P1; Figure 4.3 a, b, e, f). Average annual variation in total catch, weak stock harvest control rule Median estimates of short-term AAV and the variation in the estimates among the simulations were similar among all MPs, except for C3 (Figure 4.3 c, d). Management procedure C3 was described by the availability of species-specific catch and effort data for assessment and an assumed average handling time equal to zero (i.e., catch and effort are assumed to be proportional to abundance) in the assessment model. The estimates among the 100 MPE 187  realizations for C3 ranged between 0.12 and 1 and were similar between the scenarios. AAV was similar, ~0.25, among the management procedures using the weak-stock harvest control rule, except C3, and the management procedure described by perfect information were similar, regardless of the operating model scenarios (Figure 4.3 c, d, e, f). Average total catch, precautionary harvest control rule The performance of the management procedures with regard to short-term average catch was influenced by the data available for assessment, as well as the assumed relationship between the data and abundance in the assessment model. The estimates of short-term average catch for a given MP were also similar between the operating model scenarios. The short-term average catch estimates across the MPs ranged between 100,000kg and ~700,000kg for the operating model scenario that simulated catch and effort data without handling time effects (i.e., h=0; Figure 4.3 g). The range of short term average catch across the MPs was similar for the operating model scenario that simulated catch data with handling time (i.e., h=7min/fish); the upper bound is 600,000kg (Figure 4.3h). Among the MPs described by different data classes, median estimates of short-term average catch was higher when species-specific catch and effort data (C1-2, S1-4, T1-2) were available than when aggregate catch and effort data (A1) were available for assessment (Figure 4.3 g, h). The MPs described by tagging data and the assumption that catch and effort data were hyperstable in the assessment model (hassess=7min/fish; T3 and T4) also had lower short-term average catch than C1, C2, S1 through S4, and T1 and T2. The median estimate of short-term average catch was similar among A1, T3, and T4 and less than the other MPs (Figure 4.3 g, h). A comparison of the MPs described by the same data class (e.g., C1 and C2) indicates that differences in the median estimates of short-term average catch are due to the assumed value of 188  average handling time in the assessment model, which is directly related to the relationship between the data and abundance. Within the data types, the MPs that assume that the catch and effort data were proportional to abundance (hassess=0; C1, S1, S2, T1, T2) have higher median estimates of short-term average catch than those that assume hyperstability (hassess = 7 min/fish) in the assessment model (C2, S3, S4, T3, T4; Figure 4.3 g, h). The amount of variation in the species-specific relative abundance indices did not influence the estimate of average catch given the similarity in the estimates (e.g., S1 and S3 have a lower CV than S2 and S4). The number of released tags influences median estimates of average catch, with higher median estimates associated with a larger number of tags (T1<T2 and T3<T4; Figure 4.3 g, h) presumably due to greater precision in the estimates of stock status.. Table 4.8 summarizes the percent difference in realized catch between each of the precautionary MPs and the management procedure with perfect information (P1). Management procedures S1, S2, and T2, under the operating model scenario generating proportional data (h=0) are the only management procedures that have median values indicating a gain in average catch relative to the management procedure with perfect information (Figure 4.3g,k). The similarities among these MPs are that the data are assumed to be proportional to abundance in the assessment model and input data include species-specific catch data and total effort in addition to species-specific relative indices of abundance (S1 and S2) or tagging data (T2). A gain in catch was also shown for these management procedures, as well as C1 (species-specific catch and total effort and hassess=0) for the operating model scenario generating hyperstable data (Figure 4.3h, l). Average total catch, weak stock harvest control rule The estimates of short-term average catch were similar among all MPs, except for C3. A comparison of short-term average catch estimates, within the MPs, indicates that the estimates 189  were extremely stable among the 100 MPE realizations in the short-term; this outcome was the same for both operating model scenarios (figure 4.3i, j). Table 4.8 summarizes the percent difference in realized catch between each of the weakstock MPs and the management procedure with perfect-information (P1). A substantial loss in catch would be expected under the weak-stock MPs as compared to the MP with perfect information, between 80 and 100 percent on average depending on the MP. This is also shown in Figure 4.3 when comparing panels i and k, as well as j and l. Depletion level of total biomass, precautionary harvest control rule The performance among the precautionary management procedures with regard to shortterm average depletion was similar; subtle differences were due to the data available for assessment and the assumed relationship between the data and abundance in the assessment model (Figure 4.3 m, n). Short-term average depletion of the population was greater when species-specific catch and effort (C1-2, S1-4, T1-2, T4) were available than when aggregate catch and effort (A1) were the data available for assessment (Figure 4.3 m, n). The median estimate of short-term average depletion of the population for T3, which is described by species-specific catch and total effort data and an assessment model that assumes data are hyperstable, and A1 were similar and less than the other MPs, but minimally. Short-term average depletion estimates were similar among the managements procedures described by perfect information (P1) and by species-specific catch and total effort data alone (C1 and C2) and species-specific relative indices of abundance (S1-4) or tagging data (T1, T2; Figure 4.3 m, n, q, r). Short-term average depletion of the population was less for the management procedure described by aggregate catch and effort data (A1) than that described by perfect information (P1), regardless of the operating model scenario (Figure 4.3m, n, q, r). Similarly, 190  short-term average depletion of the population was less under T3 and T4 (species-specific catch and total effort data and hassess=7min/fish) than when perfect information was available (P1; Figure 4.3m, n, q, r). The operating model scenario also influenced the estimates of short-term average depletion. The estimates of short-term average depletion ranged between 47% and 63% of unfished biomass across the MPs under the operating model scenario that generated the catch data without handling time (h=0; Figure 4.3m). The range in the estimates of short-term average depletion for the operating model that generated catch data with handling time (h=7min/fish) was 40% and 55% of unfished biomass, indicating a greater reduction in biomass than under the other operating model scenario (Figure 4.3n). Depletion level of total biomass, weak stock harvest control rule The weak-stock MPs led to stable estimates of short-term average depletion and did not vary greatly among the trials (Figure 4.3 o, p). The estimates between the scenarios did differ. The estimates of short-term average depletion of the population ranged between 64% and 66% of unfished biomass across the MPs under the operating model scenario that generated proportional catch data (Figure 4.3o). The range in the estimates of short-term average depletion for the operating model that generated hyperstable data were 56% and 60% of unfished biomass, indicating a greater reduction in biomass than under the other scenario (Figure 4.3p). Assuming that the biomass required to achieve MSY is 50% of unfished biomass, the projected average short-term depletion is above BMSY. The estimates of short-term average depletion of the population among the management procedures were similar. The median estimate of depletion was less for the MPs described by only species-specific catch and effort data (C3 and C4) than all other MPs (Figure 4.3 o, p). 191  Short-term average depletion of the population was less for all weak-stock management procedures compared to the management procedure with perfect information, regardless of the operating model scenario (Figure 4.3 o, p, q, r). Long-term performance measures Average annual variation in total catch, precautionary harvest control rule The performance of the precautionary management procedures with regard to AAV in the long-term was similar among the management procedures described by the availability of aggregate catch and effort data (A1), species-specific catch data alone (C1 and C2) and in addition to species-specific relative indices of abundance (S1-4), regardless of the operating model scenario (Figure 4.4 a, b). The management procedures described by the availability of tagging data (T1-4) were associated with considerably higher AAV than the other MPs, regardless of the operating model scenario. Within data type comparisons indicate that the assumed relationship between the data and abundance in the assessment model did not lead to differences in performance with respect to long-term AAV among the management procedures described by species-specific catch and effort data alone, C1 (hassess =0) and C2 (hassess = 7 min/fish), or species-specific relative abundance indices, S1-2 (hassess =0) and S3-4 (hassess = 7 min/fish; Figure 4.4a, b). An interaction between the number of released tags and the assumed relationship between the data and abundance in the assessment model was apparent for MPs T1-4. For example, the median estimate of AAV for T1 (250 released tags, h = 0 minutes) was less than T2 (2500 released tags, h = 0 minutes), whereas the median estimate for T3 (250 released tags, h = 7 minutes/fish) was greater than T4 (2500 released tags, h = 7 minutes/fish, Figure 4.4a, b).  192  The AAV associated with a given precautionary MP was similar between the operating model scenarios (Figure 4.4 a, b). This was also shown for the management procedure described by perfect information (P1, Figure 4.4 e, f). Performance of the precautionary management procedures and the management procedure described by perfect information was similar, except for the management procedures described by the availability of tagging data. The AAV associated with T1-4 was much greater than when prefect information was available for stock assessment (Figure 4.4a, b, e, f). Average annual variation in total catch, weak stock harvest control rule The performance of the weak-stock management procedures with regard to long-term AAV was similar among the management procedures described by the availability of speciesspecific catch data alone(C3 and C4) and in addition to species-specific relative indices of abundance (S5 through S8), regardless of the operating model scenario (Figure 4.4 c, d). The range of long-term AAV was between 0.45 and ~1.25. The management procedures described by the availability of tagging data (T5 through T8) were associated with considerably higher AAV than the other MPs and ranged between 1.25 and 2 (Figure 4.4 c, d). Comparing MPs within the same data type indicates that the assumed relationship between the catch and effort data and abundance in the assessment model influenced the estimate of long-term AAV for the operating model scenario simulating catch data with handling time (h = 7 min/fish; Figure 4.4d). Management procedures making the incorrect assumption about proportionality (hassess = 0; C3, S5, S6, T5,T6) were associated with higher long-term AAV than those making the correct assumption (hassess = 7 min/fish, C4, S7, S8, T7,T8; Figure 4.4d) The long-term AAV associated with all weak stock management procedures was greater than that associated with perfect information (Figure 4.4 c, d, e, f). 193  Average total catch, precautionary harvest control rule The performance of the precautionary management procedures with respect to long-term average catch was influenced by the data type available for assessment and the operating model scenario. Long-term average catch was similar among the management procedures described by the availability of species-specific catch data alone (C1 and C2) and this in addition to speciesspecific relative indices of abundance (S1 through S4) under the operating model scenario simulating catch data without handling time (Figure 4.4g). This performance metric was also similar between the management procedure described by aggregate catch and effort data (A1) and those described by the availability of tagging data (T1 through T4) for the same operating model (Figure 4.4g). The median estimate of long-term average catch for A1 was ~250,000kg, ~350,000kg for C1 and C2 and S1-4, ~300,000kg for T1, T2, and T4, and 200,000kg for T3. For the scenario simulating catch data without handling time the MPs described by species-specific catch and effort data alone (C1 and C2) and the MPs described by the addition of species-specific relative abundance indices are similar to the management procedure described by perfect information (P1; Figure 4.4g, k). All other MPs under this scenario are shown to have lower long-term average catch than under the perfect-information MP. Under the operating model scenario that simulated catch data with handling time (h = 7 min/fish), clear distinctions in the estimates of long-term average catch among data types were not obvious (Figure 4.4h). For example, the median estimate of long-term average catch for A1 was ~250,000kg, ~300,000kg for C1, ~275,000kg for C2 and S1-3, ~250,000kg for S4, T1, T2, and T4, and 175,000kg for T3. The assumed relationship between the fishery-dependent data and abundance in the assessment model was shown to influence the estimates of long-term average catch between the management procedures described by species-specific catch and total effort 194  data. More specifically, long-term average catch was greater for C1 (hassess=0) than C2 (hassess = 7min/fish; Figure 4.4h). A comparison of the MPs under the scenario simulating hyperstable data indicates that all MPs, except C1 and S3 fall below what would be expected if perfect information was available (Figure 4.4h, l). Average total catch, weak stock harvest control rule The performance of the weak-stock management procedures with respect to long-term average catch were influenced by the data type available for assessment, the assumed relationship between the catch and effort data and abundance in the assessment model and the operating model scenario. Within a data type, the long-term average catch was greater when it was assumed that the catch and effort data were proportional to abundance in the assessment model for both operating model scenarios; e.g., C3 (h=0) > C4 (h=7min/fish; Figure 4.4i, j). Comparing the MPS associated with different data types but that make the same assumption about the relationship between abundance and fishery-dependent data indicates that long-term average catch is greatest when only species-specific data are available for assessment followed by the MPs associated with species-specific relative abundance indices, and the MPs associated with tagging data. For example, long-term average catch for C3 is greater than S5 and S6, which is greater than T5 and T6 and all assume proportionality between the fishery-dependent data and abundance (Figure 4.4i, j). This pattern is evident for both operating model scenarios (compare panels i and j in Figure 4.4). Long-term average catch was less for the weak stock MPs when the fishery-dependent data simulated with handling time (Figure 4.4j) than when the data are not simulated with handling time (Figure 4.4i). This is also shown for the management procedure described by having perfect information (Figure 4.4k, l). The long-term average catch associated with all 195  weak-stock management procedures was less than what would be realized if a stock assessment scientist had perfect information (Figure 4.4 i, j, k, l). The assumed value of average handling time in the assessment model influenced the median estimates of long-term average catch, within MP groups. Under the weak-stock harvest control rule, median estimates of long-term average catch were smaller when it was assumed that average handling time per fish was 7 minutes (C4, S7-8 and T7-8) rather than 0 minutes (C3, S5-6 and T5-6, Figure 4.4i, j)). Median estimates of long-term average catch were similar among C3, S5-6 and T5-6, the same was also true for C3, S5-6 and T5-6 (Figure 4.4i, j). The level of observation and the number of released tags did not influence the median estimates of long-term average catch. Depletion level of total biomass, precautionary harvest control rule All MPs resulted in long-term average depletion estimates that were above 0.2Bo, a common proxy used to determine whether a population is overfished (Figure 4.4m, n). The data available for assessment and the assumed relationship between the fishery-dependent data and abundance were influential on the performance of the MPs with respect to long-term average depletion (Figure 4.4 m, n). Long-term average depletion was greater for the MPs associated with species-specific catch and effort data (C1 and C2), as well as species-specific relative indices of abundance (S1 through S4) and tagging data (T1 and T2) than when aggregate catch and effort data were available (A1). The estimate for this performance measure for A1 was more similar to T3 and T4, which were described by tagging data and an assumed hyperstable relationship between the fishery-dependent data and abundance in the assessment model (Figure 4.4 m, n). The assumed relationship between the fishery-dependent data and abundance in the assessment was also influential. Comparing MPs described by the same data type, long-term 196  average depletion was greater when the relationship between the data and abundance in the assessment model was proportional (C1, S1, S2, T1, T2) than hyperstable (C2, S3, S4, T3, T4); this pattern was shown for both operating model scenarios (Figure 4.4 m, n). The number of released tags also influenced the performance of those MPs associated with tagging data. More specifically, long-term average depletion was greater for the MPs associated with a larger number of released tags (T2 and T4) than a smaller number of released tags (T1, T3; Figure 4.4 m, n). Long-term average depletion was similar among the MPs described by the availability of perfect information P1, C1 and C2 (species-specific catch and total effort), S1-4 (species-specific catch and total effort, and species-specific relative abundance indices) and T1 and T2 (speciesspecific catch and total effort, and species-specific tagging data). Long-term average depletion was greater for P1 than the MP described by aggregate catch and effort data or MPs described by tagging data and an assumed hyperstable relationship between the fishery-dependent data and abundance in the assessment model (T3 and T4). Depletion level of total biomass, weak stock harvest control rule Long-term average depletion was well above 0.2Bofor all weak-stock MPs and both operating model scenarios (Figure 4.4 o, p). Performance with respect to long-term average depletion was influenced by the assumed relationship between the fishery-dependent data and abundance in the assessment model. The MPs assuming proportionality in the assessment model (hassess = 0; C3, S5, S6, T5, T6) had greater long-term average-depletion than those assuming hyperstability (hassess = 7 min/fish; C4, S7, S8, T7, T8) regardless of the operating model scenario. Long-term average depletion was greater under a management procedure with perfect information than any of the weak-stock MPs (Figure 4.4 o, p, q, r). The median estimate of long197  term average depletion when perfect information was available was ~35% or ~30% of unfished biomass (100% greater depletion than the weak-stock MPs) depending on the operating model (Figure 4.4 o, p). Total biomass and total catch projections Perfect information Figure 4.5 shows the total catch and total biomass projections for the perfect information MP and both operating model scenarios. The catch projections shown indicate that when perfect information was available total catch exhibited considerable inter-annual variability, which was also shown in Figures 4.3 k, l and 4.4 k, l). For ease of interpretation the results will be summarized in terms of overall trends. Total catch initially increased from 2005 catch levels when perfect information was available for assessment for both operating models scenarios (Figure 4.5, top panels). The range in the initial increase in total catch was between 400,000 kg and 1 million kilograms when the fishery-dependent data were simulated without handling time (h = 0; Figure 4.5; top, left panel). When the fishery-dependent data were simulated with handling time the initial increase in total catch was between 300,000kg and 700,000 kg (Figure 4.5 top right panel). Regardless of the operating scenario, the initial increase in total catch was followed by a gradual decline to a point of relative stability. Total biomass declined over time to a point of relative stability by 2020 (Figure 4.5, bottom panels). The trends in catch and biomass for the management procedures under the precautionary harvest control rule, except those described by tagging data, were more similar to the perfect information management procedure than those employed under the weakstock harvest control rule (Figures 4.5, 4.6, 4.7).  198  Precautionary harvest control rule Projections of total catch were highly variable inter-annually for all MPs under the precautionary harvest control rule, similar to the management procedure described by perfect information. Total catch initially increased from 2005 levels for all management procedures under the precautionary harvest control rule (Figure 4.6). The initial increase was followed by a reduction, and then an increase to a level of stability for the management procedure described by the availability of aggregate catch and effort data (A1; Figure 4.6, first row). This pattern in projected catch was similar between the operating model scenarios and was associated with total biomass that remained near 2005 levels (Figure 4.7, first row). Total catch gradually declined after the initial increase for the management procedures described by species-specific catch and total effort that was assumed to be proportional to abundance in the assessment model C1 and those that were associated with species-specific relative abundance indices (S1 and S2;Figure 4.6, second and third rows). Biomass gradually declined over the projection years for these management procedures (Figure 4.7, second and third rows). Total catch also declined after the initial increase, but stabilized for management procedures described by species-specific catch and total effort that was assumed to be hyperstable in the assessment model alone C2 and in addition to species-specific relative abundance indices S3 and S4. Biomass also declined and then stabilized for these management procedures (Figure 4.6, second and third rows). The trends in catch and biomass were similar between the operating model scenarios (Figures 4.6 and 4.7, second row). The trend in projected total catch for T1 through T4 increased in the first projection year, then declined to a point of relatively stability (Figure 4.6). The 95% confidence region for T1 through T4 was wider than for the other MPs due to variability in annual catch between zero and 199  non-zero catch policies in later years (Figure 4.6). The trend in total catch was projected to decline over the first 10-15 years for the MPs T1 and T2 regardless of the operating model scenario (Figure 4.6). Trends in the total catch projection after these 10-15 years resembled a pulse fishing pattern with the lower 95% confidence interval dropping to zero (Figure 4.6). The associated trend in total biomass for T1 and T2 indicate that total biomass was projected to decline and then stabilize (Figure 4.7). The total catch projections resemble a pattern of pulse fishing after an initial increase for the management procedures described by species-specific catch and total effort data that were assumed to be hyperstable in the assessment model and species-specific tagging data (T3 and T4; Figure 4.6, fourth row). Although T3 and T4 have similar total catch projections, the trends in biomass differ. Total biomass was projected to increase after a subtle decline for T3 (Figure 4.6, fourth row). The trend differs for T4 in that total biomass was projected to decline within the first three to five years, increase for several years and then decline (Figure 4.7, fourth row). Weak stock harvest control rule All MPs under the weak stock harvest control rule resulted in zero catch over the initial projection years (Figure 4.8). The projected length of time when there was no catch varied among the MPs and was due to the stock size of at least one species that was lower than its BMSY. The median projection for the weak stock MPs was highly variable over the remaining projection years. The 95% confidence intervals also demonstrated this variability (Figure 4.8). It should be noted that the weak-stock harvest control was quite conservative compared to the precautionary harvest control rule and is the cause of this variability. Total catch was projected to increase initially, which was was associated with the years of no catch; it then declined, and then stabilized (Figure 4.8). 200  Total biomass initially increased for all weak-stock MPs due to the absence of catch (Figure 4.9). When it was assumed the fishery-dependent data were proportional to biomass in the assessment model, biomass declined and then stabilized for all MPs (C3, S5, S6, T5, T6). When the fishery-dependent data were assumed to be hyperstable (h = 7minutes per fish) in the assessment model, the initial increase was followed by a decline in projected biomass (C4, S7, S8, T7, T8). . The lower bound of the confidence interval was at or above the biomass estimate in 2005 for all MPs (Figure 4.9). Average catch and depletion per species Short-term projections Short-term average catch for the MPs under the precautionary harvest control rule was greater than the weak-stock harvest control rule (Figure 4.10). Average short-term catch was dominated by Opakapaka, Uku, and Onaga for all precautionary MPs (Figure 4.10 d, e, g). All other species had significantly smaller average catches in the short term, which reflects relative differences in catchability among the species. Median estimates of short-term average depletion for the precautionary MPs was greatest or species such as, Hapu’upu’u, Kalekale, Ehu, and White ulua (Figure 4.11a, c, f, j). Regardless, short-term average depletion was greater under the precautionary MPs than the weak-stock MPs for all species in the short-term (Figure 4.11). Median estimates of short-term average catch was zero for eight MPs under the operating model scenario simulating fishery-dependent data without handling time and 9 MPs for the scenario simulating the data with handling time (Figure 4.10). Under the weak-stock harvest control rule, catch was prohibited when at least one species fell below its BMSY. Figure 4.11 shows short-term average depletion for each species. The prohibition of catch in the short-term under the weak-stock MPs was to allow for the recovery of species, such as Kalekale, Ehu, and 201  White ulua (Figure 4.11c, f, j). When perfect information (P1) was available, the depletion of Hapu’upu’u, Kalekale, Ehu, and White ulua was projected to be below 0.2Bo (Figure 4.10 a, c, f, j). Long-term projections When comparing the precautionary and weak-stock management procedures for longterm average total catch, this metric was greater for the precautionary management procedures than the weak-stock management procedures. This was true for Kahala, Opakapaka, Uku, Onaga, Lehi, and Gindai (Figure 4.12 b, d, e, g, h, i). Long-term average catch under a particular precautionary management procedure of the same data type and assessment assumptions was smaller for Hapu’upu’u, Kalekale, Ehu, and White ulua than for the corresponding weak-stock management procedure (Figure 4.12 a, c, f, j). Long-term average depletion from the individual species perspective indicates that under a management procedure with perfect information depleting Hapu’upu’u, Kalekale, Ehu, and White ulua to below 0.2Bo would be expected, which was also seen under the precautionary management procedures (Figure 4.13 a, c, f, j). Although long-term average depletion for the management procedures under the weak-stock harvest control rule was above 0.2Bo for all species, depletion was greatest for Hapu’upu’u, Kalekale, Ehu, and White ulua (Figure 4.13 a, c, f, j). Fundamental trade-offs A fundamental trade-off that is often evaluated for any set of MPE options is between catch and stock depletion. Figure 4.14 summarizes the trade-off between median long-term catch and median long-term depletion for the aggregated results. The trade-off curve between 202  catch and stock depletion is convex (as defined by Walters and Martell 2004, pg. 23) so that an increase in one measure does not lead to an accelerated decline in the other measure. A convex trade-off curve allows for a balance between the two measures to be achieved. The management procedures were separated along the trade-off curve by harvest control rule type, which was especially true when the operating model simulated fishery-dependent data that were proportional to abundance (h = 0; Figure 4.14a). In general, the management procedures under the precautionary harvest control rule resulted in higher catch and greater depletion than the management procedures under the weak-stock harvest control rule, as it should. Within this region of the trade-off curve, the management procedures resulting in the greatest catch and depletion were described by species-specific catch and effort data (C1 and C2), species-specific relative abundance indices (S1-4), and perfect information (P1; Figure 4.14a). One management procedure under the precautionary harvest control rule, T3, which was described by speciesspecific catch and total effort data that were assumed proportional to abundance (hassess=0) and species-specific tagging data (250 released tags per species) were within the same region as the management procedures under the weak-stock harvest control rule. The management procedure that represents the status quo approach, A1, falls between the management procedures under the precautionary and weak-stock harvest control rules and represents a balance between gains in median long-term catch and median long-term depletion (Figure 4.14a). The trade-off curve for the operating model scenario that simulated hyperstable fishery-dependent data was similar to the curve for the other operating model scenario (Figure 4.14b). One difference was that the separation between the precautionary and weak-stock management procedures was more distinct (Figure 4.14b). Figure 4.15 separates the catch-depletion trade-off curve into regions of high catch and depletion and low catch and depletion. This figure also clearly demarcates the management 203  procedures that assume that the fishery-dependent data are proportional to abundance in the assessment model from those that do not. The separation of MPs along the trade-off curve did not seem to be influenced by the assumed value of average handling time in the assessment model within the region of high catch and depletion (Figure 4.15a, b; compare MPs associated with orange filled circles and those without). Within the region of low catch and depletion, when the fishery-dependent data were assumed to be proportional to abundance in the assessment model, catch and depletion were higher than when the data were assumed hyperstable in the assessment model (Figure 4.15 c, d). Figures 4.14 and 4.15 ignore the multispecies nature of the Hawaiian bottomfish fishery. The fundamental trade-off between the precautionary and weak-stock management procedures from a individual species perspective is the potential of forgone catch and the potential loss of individual species. Figure 4.16 shows the trade-off between long-term catch and the number of overfished species in the long-term. The biomass of all species remained above 0.2Bo for the management procedures under the weak-stock harvest control rule, regardless of scenario (Figure 4.16 a, b). All of the management procedures associated with the precautionary harvest control rule, except T3, resulted in a loss of at least one species (Figure 4.16a). The reduction of biomass to below 0.2Bo for at least one species was shown for the all management procedures associated with the precautionary management procedure when the data were with handling time effects (Figure 4.16b). When perfect information was available so that the catch limit was set to the community based MSY, median catch was the highest among the management procedures and at least four out of ten species would expected to be overfished (Figure 4.16 a, b).  204  Discussion One of the primary goals of management procedure evaluation is to identify trade-offs between management objectives resulting from the implementation of alternative management procedures on short and long-term scales (Butterworth and Punt 1999, Smith et al. 1999). It also represents an objective framework used to compare alternative decision rules and their ability to meet management objectives (Punt et al. 2001) and to find a management procedure or multiple management procedures that are robust to underlying uncertainties in a system (Kirkwood 1997). A key uncertainty for the Hawaiian bottomfish fishery is the relationship between catchability and abundance, the factors that influence this relationship, and the interpretation of relative indices of abundance. Fisher targeting behaviour and handling time effects were two factors considered in this analysis. Two operating model scenarios were evaluated: 1) the data were generated without handling time effects and 2) with handling time effects thereby accounting for technical interactions among species. Fisher targeting behaviour was another source of uncertainty in the operating model and was included in both operating model scenarios. Three performance statistics, short- and long-term average catch, average depletion, and average annual variation, were used to reflect the following management objectives: 1) maximization of catch, 2) minimization of the risk of overexploitation, and 3) maximization of fishery stability (Butterworth and Punt 1999). Trade-offs were compared at the community level and individual species level to evaluate management performance. Management performance and harvest control rules The different harvest control rules used to determine the annual effort allocated to the fishery, which was translated into an ACL, led to the most obvious management trade-off among the management procedures. At the aggregate level, the management procedures associated with 205  the precautionary harvest control rule resulted in higher catch and greater depletion of the population than the management procedures associated with the weak-stock harvest control rule. Although all precautionary management procedures resulted in long-term average depletion above 20% of aggregate unfished biomass, the higher long-term average aggregate catch levels were achieved by over-exploiting several individual species. The management procedures associated with the weak-stock rule outperformed the management procedures associated with the precautionary rule with respect to the conservation oriented management objective at the aggregate level, as well as the species level. The long-term average depletion of the aggregate and for each species was above 20% unfished biomass for all management procedures associated with the weak-stock management procedure. Over-exploitation risk was better minimized by the weak stock management procedures by greatly reducing the long-term average catch. Previous studies examining the management of mixed-stock and multispecies fisheries have shown that while reducing the risk of over-exploitation weak stock management generally leads to substantial foregone catch of more productive species (Hilborn 1976, Hilborn et al. 2004, Christensen and Walters 2004). Hilborn et al. (2004) demonstrated that weak stock management of the west coast groundfish fishery (a multispecies fishery described by technical interactions) would lead to a 90 percent loss in potential yield. This was also shown in this chapter; implementing the weak-stock rule led to a considerable loss in catch (24%-62%) as compared to implementing the perfect-information and precautionary MPs. The trade-off between yield and the risk of over-exploiting species may be mitigated by selective fishing practices or targeting (Branch and Hilborn 2008, Ainsworth and Pitcher 2010). A targeting behaviour model was included as part of the observation dynamics of the operating model. Very simply, it was assumed that fishers could target species by depth. Species were separated into depth categories, shallow (i.e., Kahala and Uku) and deep species (i.e., all other 206  species). The targeting model adjusted species catchability so that catch increased or decreased in a reciprocal pattern according to depth category. As such, all species within a depth category experienced the same proportional increase or decrease in annual catchability. In the event of an increase in targeting, this in combination with the input control (EMSY) determined from overall abundance estimates can potentially cause unsustainable catch of less productive species. This is unlike the observations made by Branch and Hilborn (2008) for the British Columbia multispecies groundfish fishery. Their analysis of the BC groundfish CPUE data, which has 100% observer coverage and no discarding, showed that fishers adjusted their catch rates in accordance with shifts in quota regulations. In other words, fishers reduced their catch rates on species with lower quotas and increased their catch rates on those species with higher catch rates. Targeting and its influence on catch composition has been a consistent source of uncertainty for the Hawaiian bottomfish fishery. The targeting model used as part of the operating model is rather simplistic. It will be important in the future to explore different models describing the targeting behaviour of Hawaiian bottomfish fishers and evaluate management procedure performance for procedures that encourage more selective targeting at least by fishing depth. The relative economic stability of the fishery, another management objective that was evaluated, was measured as the average annual variation in catch. AAV was considerable for all management procedures and in general was higher for the management procedures associated with the weak-stock harvest control rule than the management procedures associated with precautionary harvest control rule. The weak-stock rule was more conservative than the precautionary rule and the considerable AAV associated with the management procedures described by the weak-stock harvest control rule is an artefact of closing the fishery due to the over-exploitation of at least one species when fishing is still viable for the other species. Appendix B explores a modified weak-stock harvest control rule. Briefly, management followed 207  the precautionary control rule until at least one species was fished below its BMSY. When the estimated biomass of at least one species fell below its BMSY, the modified weak-stock harvest control rule continued to specify effort similarly to the precautionary rule, except the scale of the effort axis (i.e., the ratio between current effort and EMSY) was halved. Therefore, when the estimated aggregate biomass was at 80% of BMSY, rather than setting effort to 80% of EMSY, effort was set to 40% of EMSY (Figure B.1). Effort was reduced linearly from 40% of EMSY to zero when aggregate biomass was between 80% and 40% of BMSY. This alternative harvest control rule was evaluated to show the sensitivity of AAV to the harvest control rule used for decision making. Although AAV was still high for the modified weak-stock rule, its management performance was intermediary to the precautionary and weak-stock rules. AAV for the modified weak-stock rule was less than the stricter weak-stock rule and more similar to, but less than, the precautionary rule. Additionally, the modified weak-stock rule better achieved catch objectives than the weak-stock rule while better achieving conservation objectives on the aggregate and species levels than the precautionary rule. Management procedures resulting in high AAV represent economic instability to the fishing community and could lead to ineffective management (Cox and Kronlund 2008). In general, stock-size dependent harvest control rules similar to the ones evaluated in this chapter and Appendix B would be expected to result in higher AAV than constant catch or constant exploitation rate strategies, while the latter generally provide reasonable catch levels similar to stock-size dependent rules while minimizing the risk of over-exploitation (Hilborn and Walters 1992, Walters and Parma 1996, Hjerne and Hannson 2001). Constant catch strategies obviously reduce inter-annual variation in catch and this reduction will be greater than that from a constant exploitation rate strategy. The disadvantage of a constant catch strategy is that it generally results in lower catch than a constant exploitation strategy to achieve the same conservation 208  objectives. This was shown for the South African anchovy fishery and the northwestern Hawaiian Islands lobster fishery (Butterworth and Bergh 1993, DiNardo and Wetherall 1999). Constant exploitation rate strategies have also been shown to track environmental variation resulting in reasonable annual catch, while minimizing risk to the resource and minimizing interannual variation (Walters and Parma 1996). Lobster fishers in Hawaii were more amenable to a constant exploitation rate strategy even though inter-annual variation was higher than would be expected from a constant catch strategy given the potential for greater catch over the long-term (DiNardo and Wetherall 1999). Given the high AAV resulting from the stock-size dependent harvest control rules presented in this chapter, future evaluations should consider constant catch and constant exploitation rate strategies to determine whether their implementation would reduce inter-annual variation in catch for a multispecies fishery as has been shown for single species fisheries. Management procedures can also be designed to explicitly constrain AAV (Bergh and Butterworth 1987, Kell et al. 2005). Stability in catch may provide economic stability from year to year, but it will also lead to an overall reduction in long-term average catch that could be achieved by implementing management procedures with greater AAV (Bergh and Butterworth 1987, Kell et al. 2005, Kell et al. 2006). Bergh and Butterworth (1987) evaluated the management performance of constant catch, constant harvest rate, and constant escapement policies assuming a range of AAV constraints for the South African anchovy fishery. They found that relaxing the constraint led to greater average annual catch without additional risk to the stock. An evaluation of management strategies employing a harvest control rule constraining inter-annual variation in the catch of North Atlantic flatfish and roundfish stocks suggests that the constraint can lead to either delayed management or foregone yield, which is in turn dependent on starting biomass levels and the biology of the species (Kell et al. 2005, Kell et al. 209  2006). Therefore artificially constraining inter-annual variation is not always an adequate method to ensure management objectives are achieved. The work of Kell et al. (2005, 2006) was done at the request of managers to evaluate an existing management procedure employed by the International Council for the Exploration of the Sea (ICES). Their work indicates that adopting a single type of harvest control rule to base management decisions for all fisheries may result in unintended management trade-offs and ineffectual management. An important continued avenue of research will be to evaluate the expected management performance of existing harvest control rules with application to multiple fisheries, as well as developing and evaluating new candidate rules that balance management trade-offs. Data, assessment model assumptions, and performance The management procedures that were evaluated in this chapter were defined, in part, by the data used in the assessment model. The data types considered were: total catch (i.e., catch was summed across all species) and effort, per species catch and total effort, species-specific fishery independent indices of abundance, and species-specific mark-recapture data to monitor exploitation rates of each species. The status quo management procedure A1 was used to compare the alternative management procedures to a procedure similar to what is currently being used in Hawaii. The management trade-offs resulting from the status quo management procedure could only be evaluated for the precautionary rule, given that the aggregate surplus production model could not determine stock status by species. The catch-depletion trade-off curves presented in Figure 4.14, show that A1 represents a compromise between gains in catch while maintaining biomass above over-exploitation levels on the aggregate level. It also leads to the over-exploitation of minimal species as compared to the majority of precautionary management procedures. The way in which aggregate MSY and associated reference points (EMSY and BMSY) were determined differed between the status quo and multispecies assessment 210  models and help to explain this result. The total equilibrium yield curve estimated by the multispecies assessment model was simply the summed species-specific equilibrium yield curves. This total yield curve was heavily weighted by more productive species (Paulik et al 1967, Adams 1980). The aggregate assessment approach assumes a single production relationship for the community of Hawaiian bottomfish species and the resulting yield curve ignores the differences in species. A1 better achieved the conservation objectives through either derived EMSY or BMSY values that were lower than those derived by the multispecies assessment model or the proportion of EMSY allocated to the fishery was smaller due to the assessment model estimating lower biomass of the community than the multispecies assessment model. The EMSY estimate, and in turn the effort allocated to the fishery, would be smaller than that derived by the multispecies assessment model if the single productivity parameter estimated by the status quo assessment model indicated the lower productivity for the aggregate than the combined influence of the species-specific estimates from the multispecies model. Although A1 performed relatively well, the main drawback of the status quo approach is that is not equipped to provide speciesspecific stock status information, which is a requirement of the Magnusson-Stevens Act.  The addition of auxiliary data (i.e., data other than fishery-dependent catch and effort) in the assessment model was expected to improve management procedure performance given that the statistical performance of stock assessment models has been shown to improve when using fishery-independent relative indices of abundance and tag-recapture data. The interpretation of management performance among the management procedures was dependent on how the results were presented (i.e., for the aggregated community or viewed from the species level). The aggregated performance measures indicate that catch objectives were better met by the management procedures described by catch and effort data and survey data. Greater realized catch led to greater long-term average aggregate depletion for these management procedures and 211  was achieved at the expense of over-exploiting several species of small population size or lesser productivity. Conversely, management procedures described by tag-recapture data resulted in less long-term average aggregate catch, less long-term average aggregate depletion, and fewer, over-exploited individual species. In comparison to the other management procedures, those described by tag-recapture data performed well and were more conservative at the species level. An undesirable management trade-off associated with management procedures described by tag-recapture data was that they were associated with the considerably higher AAV than the other management procedures evaluated.  The considerable AAV associated with the management procedures described by tagrecapture data may seem unexpected given that studies have indicated better statistical performance (i.e., greater accuracy and precision in estimates of fishing mortality and biomass) when tag-recapture data are used in stock assessment models (Martell and Walters 2002, Hulson et al. 2011). Martell and Walters (2002) used a closed-loop simulation model to evaluate management performance when using tagging data to monitor fishing mortality rates, but did not use AAV as a performance measure. Their results indicate that the average 20-year fishing mortality rates of three separately assessed species were accurately estimated when tagging data was available. Although tagging data afforded greater accuracy in fishing mortality estimates, catch between years could have varied greatly given annual fluctuations in biomass and fishing mortality. Additionally, the interaction between stock status and harvest control rules can also lead to unintended or unexpected management results. MPEs conducted by Kell et al. (2005, 2006) for North Atlantic flatfish and roundfish stocks implemented a harvest control rule formulated to constrain inter-annual variation in catch and to move the populations towards target biomass levels and fishing mortality rates. Constraining inter-annual variation in catch delayed achieving management goals and resulted in cyclic oscillations in biomass for some 212  flatfish and roundfish species (Kell et al. 2005, 2006). The authors appropriately point out that although the harvest control rule constrained inter-annual variation, over the long-term the range in realized catch was quite large due to fluctuating biomass. The considerably high AAV (i.e., two to three times higher than the other management procedures) associated with tag-recapture management procedures in this chapter can be explained by these management procedures having a higher probability of detecting reductions in abundance and levels equivalent to overexploitation. Figures 4.6 and 4.8 (bottom row), show frequent fishery closures due to overexploitation, which then allowed the more vulnerable species to recover, overall population size to build, and subsequent larger catches. Given that the inclusion of tag-recapture data in the assessment model corrects for biases due to changes in catchability the variability in biomass is in response to not only changes in effort but also environmental variation. For example, following poor recruitment years the fishery would be shut down to allow for recovery, which would induce high inter-annual variation in catch. The biomass trajectories for management procedures described by catch and effort data and those described by species-specific survey data continually decline in response to effort; given the relative minimal variability in the biomass trajectories over the projection years, AAV was relatively low.  Assessment model assumptions The assumptions in the assessment model presented in this chapter are the same as those discussed in Chapters 2 and 3. Any differences in the assumptions made in the observation dynamics sub-model pertain to how the survey or tag-recapture observations were predicted. The assumptions made in the assessment model were: i) the growth parameters were known and constant over time, ii) fish reaching the age-at-recruitment and older were fully vulnerable to the fishery, fully mature, and have the same natural mortality, and iii) average handling time h was  213  known, the same for all species, and constant over time. Assumptions unique to this chapter are: iv) fishery-independent survey was proportional to species-specific biomass through a speciesspecific catchability coefficient, and v) the reporting rates of tag recaptures were equal to 100%. Although assumptions i-iii were previously addressed in Chapter 2, it is important to reiterate how violating these assumptions would influence expected management performance. Bias in the fishing mortality and biomass estimates from the assessment model would be expected by making incorrect assumptions about the growth parameters. Theoretical work by Adams (1980) and Beddington and Kirkwood (2005) have shown that the von Bertalanffy growth coefficient and the size at which fish recruit to a fishery are positively correlated with long-term fishing mortality. All else being equal, incorrectly assuming a larger value of the von Bertalanffy growth coefficient or a larger size-at-recruitment would lead to an overestimate longterm fishing mortality and underestimate biomass. Violating these assumptions would be expected to lead to optimistic performance in relation to catch objectives. Performance with regard to conservation objectives would be expected to be pessimistic if the true von Bertalanffy growth coefficient or size-at-recruitment were less than what was assumed in the assessment model. The assumption that fish become fully vulnerable to the fishery and fully mature at the same age also has important ramifications on the fishing mortality that a population can withstand (Myers and Mertz 1998). The theoretical work of Myers and Mertz (1998) suggests that implementing regulations that modify fishery selectivity to allow fish to mature before being selected by a fishery increased the long-term fishing mortality a population can tolerate without being over-exploited. Incorrectly assuming that the age-at selectivity and maturity are the same when the true-age-at maturity is older would lead to an overestimate of long-term fishing  214  mortality. This could lead to depensatory fishing and would be reflected in poor performance of conservation objectives. An important assumption made in the observation dynamics sub-model, when speciesspecific fishery-independent indices of abundance were simulated, was that the indices were proportional to biomass through a constant species-specific catchability coefficient. This represents a best case scenario. The intent of a fishery-independent survey is to provide an index of abundance that is proportional to abundance. The reality is that hook competition and handling time effects may lead to non-proportionality between the index and biomass (Deriso and Parma 1987, Rodgveller et al. 2008). Rodgveller et al. (2008) evaluated 25 years of longline survey data collected throughout Alaskan waters and found that sablefish catch rates were negatively correlated with both grenadier and rockfish catch rates. Deriso and Parma (1987) also showed a negative relationship in catch rates between three snapper species caught in the Mariana Islands during a depletion study. Simulating survey data that are proportional to abundance and correctly making this assumption in the assessment model did not greatly improve management performance as compared to the MPs described by only species-specific catch and total effort data. Given this result and the time required to carry out the MPEs, it did not seem appropriate to evaluate a management procedure that included a fishery-independent data collection program that was biased due to a non-linear relationship between survey catchability and abundance. An important assumption made in the tag-recapture model was that tag-reporting rates were equal to100%. A violation of this assumption would negatively bias fishing mortality estimates. For example, a lower reporting rate than what was assumed would result in fewer reported recaptures. The combination of fewer observed recaptures and a higher assumed reporting rate would underestimate fishing mortality and overestimate abundance. Given the 215  depth range of Hawaiian bottomfish species, the tag-recapture program evaluated in this MPE pertains to genetic tagging. Reporting rates would be influenced by identifying points of sale and buyer cooperation to sample sold fish. Violating the reporting rate assumption could be minimized by tagging samples using a stratified, random sampling design over the distribution of the species of interest and conducting a power analysis to determine the optimal number of samples that would need to be collected to detect an effect. Uncertainty An integral component of MPE is to account for plausible uncertainties in the operating model. The uncertainties considered as part of MPE include process, observation, model, estimation, decision, and implementation uncertainties (Hilborn and Peterman 1996, Francis and Shotton 1997, Butterworth and Punt 1999). Incorporating all plausible uncertainties will lead to a better understanding of how well management procedures perform in relation to management objectives under realistic uncertainty. For the purposes of this analysis, the operating model included process and observation uncertainties. Process uncertainty was simulated as random, log-normally distributed recruitment anomalies without auto-correlation. One source of observation uncertainty was explored using two different operating model scenarios. The operating model scenarios that were considered either simulated catch with or without handling time, which is a potential source of non-stationarity in the catchability of the individual Hawaiian bottomfish species. Anecdotal evidence suggests that targeting is a very real aspect of the Hawaiian bottomfish fishery, contributes to the species composition of the observed catch, and is another source of non-stationarity in catchability. A simple model was used to simulate changes in targeting between depth groups in the operating model.  216  The realized catch simulated by the operating model was partially determined by the targeting model. Due to these targeting effects, the recommended catch levels based on the effort decision from the harvest control rule would not necessarily be achieved annually. Rosenberg and Brault (1993) make the valuable point that if the objectives between managers and fishers differed greatly the ability to effectively implement any management procedure could be a great source of uncertainty. The ability to implement a management procedure is greatly influenced by the compliance of fishers to regulation and proper monitoring of the fishery and enforcement of regulation. Examples of fisher behaviour that can lead relatively high levels of implementation uncertainty include non-reporting or under-reporting of catch and at-sea discarding. High grading is an example of discarding and is done to adjust catch composition to optimize total catch value and is a potential source of substantial implementation uncertainty for multispecies fisheries. Gillis et al. (1995) used optimal foraging models to simulate fisher behaviour and evaluate the influence of effort limit and catch limit management policies on highgrading in a multispecies fishery. High-grading was greatest when catch-limits were low and effort limits were high. Although their simulations were based on trip limits, the results indicate that catch-quotas (especially those perceived as small or sub-optimal in terms of economic gain by fishers) in combination with unregulated effort may lead to increased high-grading to optimize economic gain. Punt et al. (2002) demonstrated that market demands can lead to highgrading. More specifically they showed that the recovery of highly valued species can be compromised when TACs of less valuable species increase and are associated with high discard rates to ensure catch composition favours more valuable species. This, as with non-reporting and under-reporting catch, leads to an inaccurate representation of fishing mortality, which in turn leads to inaccurate estimates of productivity.  217  The ability to accurately estimate productivity has implications on the ability to predict and forecast the recovery potential of a population and the risk of overfishing a population under different management scenarios. Formal management of the Hawaiian bottomfish fishery through a quota system is still relatively new and with increasing management mandates through the MSA changes to the current management system may occur. Currently an aggregate ACL policy is in place, but with future management demands species-specific ACLs may be implemented. As these quota policies are enforced management should consider formally structuring incentives to discourage high-grading and mis-reporting (Branch and Hilborn 2008). Depending on the attitudes of fishers in the face of changing management and the incentives that are put in place to improve compliance, a better characterization of implementation uncertainty should be included in future MPEs for this fishery. Ignoring harvest-decision, estimation, and model uncertainty, as well as auto-correlation within a given uncertainty category will lead to overly optimistic projected outcomes (i.e., uncertainty in the projected outcomes will be underestimated, Hilborn and Peterman 1996, Punt 1997, Punt et al. 2008). For example, Punt (1997) demonstrated that the ability of a management procedure to meet management objectives, in terms of the probability of a population falling below 0.2Bo, degraded with more admitted uncertainty and auto-correlation in recruitment anomalies. Punt et al. (2008) also demonstrated that the distribution of depletion estimates widened when uncertainties such as, implementation and estimation error, as well as associated auto-correlation were included as part of an MPE to evaluate threshold management strategies for west coast groundfish. It is, therefore, recognized that the results from this analysis are rather precise and potentially optimistic given the level of uncertainty assumed in the operating model. As the first MPE carried out for the Hawaiian bottomfish fishery, the operating model presented  218  here will serve as a reasonable basis for future MPE developments and future work should include other plausible uncertainties. Conclusions A crucial component of MPE is to explicitly specify the management objectives for a fishery. Vague definitions will only lead to debate among stakeholders, scientists, and managers. Kirkwood (1997) reviewed the evolution of the MPE conducted by the International Whaling Commission, IWC, and noted that ultimately the commission had to develop a hierarchy of clearly prioritized management objectives. Once the IWC specified that the top management priority was to promote conservation goals this eliminated any management procedure that only marginally achieved these goals (Kirkwood 1997). The National Standards of the MSA provide a list of mandatory and discretionary components for fishery management plans. Although the National Standards provide an outline for fisheries management, discretion is given to managers to determine the most effective course of action to achieve each standard. For example, NS 3 indicates that stocks should be managed as a unit, but discretion is given to define the management unit depending on management objectives, biological, economical, technical, and social issues. This definition is crucial to how multispecies fisheries are managed. Given stakeholder and scientific input, this can lead to some debate about the fishery management priorities for any US multispecies fishery. It is therefore suggested that before conducting future MPEs for the Hawaiian bottomfish fishery, the management priorities in terms of catch or conservation should be specified. It will also be important to identify and define the management unit (i.e., the aggregate, individual species, or smaller species groups) for which management decisions will be made. As the results have shown, this influences the interpretation of management performance.  219  The similarities in the results between the operating model scenarios indicates that handling time effects may be a less influential determinant of observed catch than fisher targeting behaviour. The operating model included a crude mechanism to implement a targeting behaviour model, which was used for both operating model scenarios. The operating model could be expanded to better evaluate management performance for different targeting behaviour hypotheses. The operating model could be expanded to simulate spatially explicit targeting with respect to depth strata in future management procedure evaluations for the Hawaiian bottomfish fishery. Additionally, targeting is generally driven by economic motivations. The operating model could also be extended to incorporate the bio-economic considerations that would influence the species composition of catch for this multispecies fishery and the species-specific catchability. The results presented in this chapter, similar to other studies evaluating the trade-offs among the management objectives for multispecies fisheries, make apparent the difficulty of simultaneously or co-managing fish populations where technological interactions dominate (Punt et al. 2002, De Oliveira et al. 2004, Dichmont et al. 2006). Managing a multispecies fishery characterized by technological interactions with a blanket TAC policy determined by total effort led to the over-utilization of some species, while under-utilizing others given relative differences in productivity and hence resilience to fishing. This was the case for the management procedure described by perfect-information as well as some of the precautionary rule management procedures. Dichmont et al. (2006) demonstrated the difficulty of simultaneously managing two tiger prawn species caught as part of Australia’s Northern prawn fishery (NPF) using a total effort input control. One management objective of the NPF is to maintain each prawn species at the spawning stock size required to achieve MSY, which was an unobtainable goal when the two tiger prawn species were fished at EMSY (i.e., total effort to achieve aggregate MSY). The results 220  presented in Dichmont et al. (2006) also showed that seasonal closures in addition to effort limitations more closely reached the management objectives of the NPF than effort limitations alone. Their results indicate coupled management procedures may be required to adequately protect all target species while reducing the potential for foregone catch. Future MPEs for the Hawaiian bottomfish fishery should evaluate the mandated management strategy, annual catch limits, in combination with other management strategies such as seasonal and spatial closures to determine whether management objectives are better met under coupled management.  221  Tables Table 4.1 Management procedure descriptions. Management procedures were defined by the harvest control rule, data used as part of the assessment in projection years, observation error levels, and the average handling time per fished used in the assessment model hassess. C & E refers to annual catch by species (measured in kg) and total, annual effort (measured in trips). MSDD is short-hand for multispecies delay-difference model. Survey q or Number tags CV  MP Harvest control notation rule  Assessment Model  hassess (min/fish)  Data  A1  Precautionary  Surplus Production  Annual catch and effort  0  C1  Precautionary  MSDD  C&E  0  C2  Precautionary  MSDD  C&E  7  C3  Weakest stock  MSDD  C&E  0  C4  Weakest stock  MSDD  C&E  7  S1  Precautionary  MSDD  C & E + survey index  0.1  0.2  0  S2  Precautionary  MSDD  C & E + survey index  0.1  0.4  0  S3  Precautionary  MSDD  C & E + survey index  0.1  0.2  7  S4  Precautionary  MSDD  C & E + survey index  0.1  0.4  7  S5  Weak-stock  MSDD  C & E + survey index  0.1  0.2  0  S6  Weak-stock  MSDD  C & E + survey index  0.1  0.4  0  Continued on next page  222  Table 4.1 continued Survey q or Number tags  CV  hassess (min/fish)  MP notation  Harvest control rule  Assessment Model Data  S7  Weak-stock  MSDD  C&E+ survey index  0.1  0.2  7  S8  Weak-stock  MSDD  C&E+ survey index  0.1  0.4  7  T1  Precautionary  MSDD  C&E+ tagging  250  1.0001  0  T2  Precautionary  MSDD  C&E+ tagging  2000  1.0001  0  T3  Precautionary  MSDD  C&E+ tagging  250  1.0001  7  T4  Precautionary  MSDD  C&E+ tagging  2000  1.0001  7  T5  Weak-stock  MSDD  C&E+ tagging  250  1.0001  0  T6  Weak-stock  MSDD  C&E+ tagging  2000  1.0001  0  T7  Weak-stock  MSDD  C&E+ tagging  250  1.0001  7  T8  Weak-stock  MSDD  C&E+ tagging  2000  1.0001  7  223  Table 4.2 Model parameter symbols and descriptions used in this chapter. Notation  Description  Subscripts i  Species  t  Time, number of projection years  ∆  Change in time step  g  Depth group  s  Survey  Estimated parameters by multispecies assessment model ‫ܤ‬௢೔ Κ௜  ‫ݍ‬௢೔ ߟ௜  ߱௜௧ ‫ݍ‬௦೔  ߪ௒ଶ೔  Unfished biomass of species i Recruitment compensation ratio of species i Maximum catchability of species i Total variance for species i Annual process error for species i Survey catchability coefficient for species i Variance in the survey observations for species i  Estimated parameters by aggregate assessment model  ‫ܤ‬௢  Unfished total biomass  r  Intrinsic rate of growth  q  catchability coefficient Continued on next page  224  Table 4.2 continued Notation  Description  Estimated parameters by aggregate assessment model σ2  observation error variance  Observed states h  ‫ܧ‬௧  ‫ܮ‬௜௧ , ‫ܮ‬௧  Average handling time per fish in the operating model Observed total effort Observed landings of species i in year t and total landings  Simulated observation parameters  ‫ݐ‬௚  ‫ݍ‬௜௧  ‫ܥ‬௜௧ , ‫ܥ‬௧ ‫ܨ‬௜௧ ܻ௜௧  Ṅ௜௧ ṅ௜௧ ܲ௜௧ ߬௜௧  Targeting on depth group g Time varying catchability of species i Annual catch of species i and annual total catch Annual fishing mortality for species i Annual survey index of abundance for species i Annual number of tags released for species i Annual number of tags recaptured for species i Annual probability of recapturing a tagged fish of species i Annual reporting rate for species i  Derived observation parameters  ‫ݍ‬ො௜௧  Predicted time varying catchability of species i Continued on next page  225  Table 4.2 continued Notation  Description  Derived observation parameters ‫ܥ‬መ௜௧ , ‫ܥ‬መ௧ ܻ෠௜௧  ‫ܨ‬෠௜௧  ܲ෠௜௧ Ṙit  Predicted annual catch of species i and total catch Predicted annual survey index of abundance for species i Predicted annual fishing mortality for species i Predicted probability of capturing a tagged fish of species i Predicted number of recaptures of species i in year t  Known growth parameters ‫ܮ‬ஶ೔ ݇௜ ܾ௜  ܽ௜  Asymptotic length of species i von Bertalanffy growth coefficient of species i Length-weight power parameter Length-weight scalar  Derived growth parameters  ‫ݓ‬ஶ೔ ߩ௜  ߙ௜  ‫ݓ‬ ഥ௜  ‫ݓ‬஺೔  Asymptotic length of species i Slope of the Ford-Brody growth function (metabolic rate parameter) Intercept of the Ford-Brody growth equation Mean weight of the unfished population Mean weight at the age of recruitment  Derived state parameters  	‫ܤ‬௜௧ ,  Annual biomass for species i Continued on next page  226  Table 4.2 continued Notation  Description  Derived state parameters ܾ௧  ܴ௢೔ ܴ௜௧  ܰ௢೔ ܰ௜௧ ‫ܣ‬௜  ‫ݏ‬௢೔ ߚ௜  ‫ܯ‬௜  ܼ௜௧ ܵ௜  ‫ݏ‬௜௧ Ω௜  Annual total biomass Unfished recruits for species i Annual recruits for species i Unfished numbers for species i Annual numbers for species i Age of recruitment for species i Maximum juvenile survival rate for species i Recruitment scalar for species i Natural mortality for species i Total mortality for species i Natural survival for species i Annual survival for species i Steepness for species i  Residuals and error terms  ߥ୧୲  ߜ௒೔೟ ߪజ ௜  ߪఠ೔  Log transformed catch residuals for species i Log transformed survey index residuals for species i Standard deviation in catch observations for species i Annual standard deviation in process error for species i Continued on next page  227  Table 4.2 continued Notation  Description  Residuals and error terms ߦ௜  ߥ୲  Proportion of total variance associated with observation error for species i Log transformed total catch residuals  Likelihood and priors ‫ܥ(ܮ‬, ‫)ߠ	|	ܧ‬ ‫ܥ(ܮ‬௜ |	ߠ௜ )  ‫߱(ܮ‬௜௧ |	ߟ௜ ) ܲ(Ω௜ ) ܲ(‫ܨ‬ത )  ‫ܮ‬൫ܻ௜ |	‫ݍ‬௦ ௜ ߪ௒ଶ೔ ൯ ‫݊	(ܮ‬ሶ ௜௧ ) ܲ(ߠ)  Log normal likelihood for total catch and effort Log normal likelihood for species-specific catch Log normal likelihood for process errors Prior probability density on steepness for species i Penalty on mean fishing mortality rate Log normal likelihood for survey index of abundance Log likelihood of Poisson distribution for tag recaptures Objective function , joint posterior probability density of estimated parameters  Equilibrium parameters aggregate surplus production assessment model  ‫ܤ‬ெௌ௒೟ ‫ܧ‬ெௌ௒೟  Biomass to achieve total maximum sustainable yield in year t Total effort to achieve maximum sustainable yield in year t  Equilibrium parameters multispecies assessment model  ‫ܤ‬௘೔ೕ೟  ܰ௘೔ೕ೟ ‫ݏ‬௘೔ೕ೟  Equilibrium biomass of species i, effort hypothesis j, in year t Equilibrium numbers of species i, effort hypothesis j, in year t Equilibrium total survival of species i, effort hypothesis j, in year t Continued on next page  228  Table 4.2 continued Notation  Description  Equilibrium parameters multispecies assessment model ‫ݍ‬௘೔ೕ೟  ‫ݓ‬ ഥ௘೔ೕ೟ ‫ܨ‬௘೔ೕ೟  ܼ௘೔ೕ೟ ‫ܥ‬௘೔ೕ೟ ‫ܥ‬௘೟  Ẏெௌ௒೔೟ Ẏெௌ௒೟  Ḃெௌ௒೔೟ Ḃெௌ௒೟ Ėெௌ௒೟  Equilibrium catchability of species i, effort hypothesis j, in year t Equilibrium mean weight of species i, effort hypothesis j, in year t Equilibrium fishing mortality of species i, effort hypothesis j, in year t Equilibrium total mortality of species i, effort hypothesis j, in year t Equilibrium catch of species i, effort hypothesis j, in year t Equilibrium total catch of species i, effort hypothesis j, in year t Maximum sustainable yield for species i, in year t Maximum sustainable yield total yield Biomass to achieve maximum sustainable yield for species i, in year t Biomass to achieve total maximum sustainable yield in year t Total effort to achieve maximum sustainable yield in year t  Performance measures AAVt  ‫ܥ‬௧̅  ̅ ‫ܥ‬௜௧ ഥ௧ ‫ܦ‬  ഥ௜௧ ‫ܦ‬  Average annual variation in total catch over time period t Average total catch over time period t Average catch of species i over time period t Average total depletion over time period t Average depletion of species i over time period t  229  Table 4.3 The observation dynamics sub-model used to simulate species-specific catch, speciesspecific relative indices of abundance from a research survey, and the numbers of recaptured tags per species for forward projections. Equation Number  Equation  Subscripts i  Species  t  Time  g  Depth group  s  Survey  Observation dynamics  T4.3.1 T4.3.2 T4.3.3  T4.3.4  T4.3.5 T4.3.6 T4.3.7 T4.3.8  ‫ܮ‬௜௧ 	, ‫ ≤ ݐ‬2005 ‫ܨ‬ ‫ܥ‬௜௧ = ቐ ௜௧ (1 − ݁ ି௓೔೟ )‫ܤ‬௜௧ ݁ ఔ೔೟ 	, ‫ > ݐ‬2005 ܼ௜௧ ܼ௜௧ = ‫ܨ‬௜௧ + Mi  ‫ܨ‬௜௧ = 	 ‫ݍ‬௜௧ Ėெௌ௒೟ ‫ݍ‬௜௧ =  ‫ݐ‬௚ = ൜  ‫ݍ‬௢ ௜ 	݁ ௧೒ 1 + ℎ ∑௜ ‫ݍ‬௢ ௜ ܰ௜௧  ‫ ݔ ݊݅ݏ‬, ݃ = ‫ݏ‬ℎ݈݈ܽ‫ݓ݋‬ 1 − ‫ ݔ ݊݅ݏ‬, ݃ = ݀݁݁‫݌‬  ܻ௜௧ = 	 ‫ݍ‬௜௦ ‫ܤ‬௜௧ ݁ ఝ೔ ṅ௜௧ 	~ܲ‫(ݏ݅݋‬Ṅ௜௧ )  ܲ௜௧ = ߬௜௧ (1 − ݁ ିி೔೟ )  230  Table 4.4 Aggregate surplus production model to represent the status quo assessment method. Equation number  Description  Subscripts t Estimated parameters T4.4.1  Year ߠ = 	 (‫ܤ‬௢ , ‫	ݍ‬, ‫ݎ‬, ߪ ଶ )  State dynamics  T4.4.2  T4.4.3 Observation dynamics T4.4.4 T4.4.5 T4.4.6 Likelihood and priors T4.4.7 Reference points T4.4.8 T4.4.9 T4.4.10  ܾ௧ା୼ =  ܾ௧ (1	 + 	‫ݎ‬Δ) ܾ 1 + ‫ܤ ݎ‬௧ Δ + 	 ‫ܨ‬௧ Δ ௢  ∆ = ½ (i.e., 6 months) ‫ܨ‬௧ = ‫ܧݍ‬௧  ‫ܥ‬መ௧ା୼ = ‫ܨ‬௧ ܾ௧ା୼ Δ  ߥ௧ 	 = 	݈݊ ‫ܥ‬௧ − 	 ݈݊ ‫ܥ‬መ௧ା୼ ∑ ߥ௧ ଶ ݊ ‫ ߪ ݈݊ 	 = )ߠ	|	ܥ(ܮ‬+ + 	ܲ(‫)ݎ‬ 2 2ߪ ଶ ‫= ܻܵܯ‬  ‫ܤݎ‬௢ 4  ‫ܤ‬ெௌ௒ = ‫ܧ‬ெௌ௒ =  ‫ܤ‬௢ 2  ‫ݎ‬ 2‫ݍ‬  231  Table 4.5 Estimated parameters of interest, the observation dynamics sub-models, and the likelihoods used as part of the multispecies delay difference assessment model. Equation number  Description  Subscripts i  Species  t  Projection year  d  1 = 	ܿܽ‫ܿݐ‬ℎ	ܽ݊݀	‫ݐ‬o‫ݐݎ݋݂݂݁	݈ܽݐ‬ Data type = ቐ 2 = 	ܿܽ‫ܿݐ‬ℎ, ‫ݐݎ݋݂݁	݈ܽݐ݋ݐ‬, ܽ݊݀	‫	 ݕ݁ݒݎݑݏ‬ 3 = 		ܿܽ‫ܿݐ‬ℎ, ‫ݐݎ݋݂݂݁	݈ܽݐ݋ݐ‬, ܽ݊݀	‫݃݊݅݃݃ܽݐ‬  Estimated parameters  T4.5.1  ߠௗ௜  θଵ୧ = 	 B୭౟ , Κ ୧ , q ୭౟ , η୧ , ω୧୲ = 	 ቐ ߠଶ୧ = 	 ߠଵ୧ , q ୱ౟ , ߪ௒ଶ೔ ߠଷ୧ = 	 ߠଵ୧  Observation dynamics T4.5.2  T4.5.3 T4.5.4 T4.5.5 T4.5.6 T4.5.7 T4.5.8 T4.5.9  ‫ݍ‬ො௜௧ =  ‫ܥ‬෢ ప௧ =  ‫ݍ‬௢ ௜ 1 + ℎ௔௦௦௘௦௦ ∑௜ ‫ݍ‬௢ ௜ ܰ௜௧ ‫ܨ‬௜௧ (1 − ݁ ି௓೔೟ )‫ܤ‬௜௧ ܼ௜௧  ߥ୧୲ = 	 ݈݊ ‫ܥ‬௜௧ − 	 ݈݊ ‫ܥ‬෢ ప௧ ߪజ ௜௧ = 	 ߦ௜ ߟ௜  ܻ෠௜௧ = 	 ‫ݍ‬௦೔ ‫ܤ‬௜௧  ෢ ߜ௒೔೟ = 	 ݈݊ ܻ௜௧ − 	 ݈݊ ܻ ప௧ ܴሶ௜௧ = 	 ܲ෠௜௧ ܰሶ௜௧  ܲ෠௜௧ = 1 − ݁ ିி෠೔೟  Continued on next page  232  Table 4.5 continued Equation number Likelihood and priors T4.5.10  T4.5.11  T4.5.12  T4.5.13  T4.5.14  T4.5.15  T4.5.16 T4.5.17 T4.5.18  Description ∑௧ ߜ஼೔೟ ଶ ݊ ‫ܥ(ܮ‬௜ |ߠ௜ ) = 	 ݈݊ ߪఔ೔ + 2 2ߪజ೔ ଶ  ∑௧ ߱௜௧ ଶ ݊ ‫ܮ‬൫߱௜ |ߪఠ೔ ൯ = 	 ݈݊ ߪఠ೔ + 2 2ߪఠ೔ ଶ P(ߗ௜ ) ~ܾ݁‫ ܽݐ‬ቀ  ఆ೔ ି଴.ଶ ଴.଼  , 12,9ቁ, where ߗ௜ =  ‫ܨ‬ത ܲ(‫ܨ‬ത ) = ܿ ൭log	ቆ ቇ൱ 0.2  ଶ  ௷೔  ସା௷೔  ܲ(ߠଵ ) = 	 ෍ ‫ܥ(ܮ‬௜ |߆௜ ) + ෍ ‫ܮ‬൫߱௜ |ߪఠ೔ ൯ + 	 ෍ ܲ(Ω௜ ) + 	ܲ(‫ܨ‬ത ) ௜  ‫ܮ‬൫ܻ௜ |	‫ݍ‬௦೔ , ߪ௒ଶ೔ ൯  ௜  ∑௧ ߜ௒೔೟ ݊௦௨௥௩ = ݈݊ ߪ௒೔ + 2 2ߪ௒೔ ଶ  ଶ  ௜  ܲ(ߠଶ ) = ܲ(ߠଵ ) + 	 ෍ ‫ܮ‬൫ܻ௜ 	|‫ݍ‬௦೔ , ߪ௒ଶ೔ ൯ ௜  L(ṅ௜௧ |ߠଷ ) = −ܴሶ௜௧ + ݊ሶ ௜௧ ln ܴሶ௜௧ − ln ݊ሶ ௜௧ ܲ(ߠଷ ) = 	ܲ(ߠଵ ) + 	 ∑௜௧ L(ṅ௜௧ |ߠଷ )  233  Table 4.6 Equilibrium analysis to obtain an estimate of the total effort to obtain total maximum sustainable yield ‫ܧ‬ெௌ௒೟ for each projection year (2006-2030) that is applied to the harvest control rule within the management procedure evaluation. Equation number  Description  Subscripts i  Species  t  Projection year  j  Effort hypothesis  Equilibrium equations  T4.6.1  ‫ܤ‬௘೔ೕ೟ = −  T4.6.2  ‫ݓ‬ ഥ௘೔ೕ೟ =  T4.6.3 T4.6.4  T4.6.5  T4.6.6 T4.6.7 T4.6.8  ‫ۓ‬ ۖ  ߚ௜ ൬−‫ݓ‬ ഥ௘೔ೕ೟ + ‫ݏ‬௘೔ೕ೟ ቀߙ௜ + ߩ௜ ‫ݓ‬ ഥ௘೔ೕ೟ ቁ൰  ‫ݏ‬௘೔ೕ೟ ߙ௜ + ‫ݓ‬஺೔ ቀ1 − ‫ݏ‬௘೔ೕ೟ ቁ  ‫ݏ‬௘೔ೕ೟ = 	 ݁ ܰ௘೔ೕ೟ =  −‫ݓ‬ ഥ௘೔ೕ೟ + ‫ݏ‬௘೔ೕ೟ ቀߙ௜ + ߩ௜ ‫ݓ‬ ഥ௘೔ೕ೟ ቁ + ‫ݓ‬஺೔ ‫ݏ‬௢೔ ‫ݓ‬ ഥ௘೔ೕ೟  1 − ߩ௜ ‫ݏ‬௘೔ೕ೟  ିெ೔ ି	ாೕ ௤೐೔ೕ೟    ‫ܤ‬௘೔ೕ೟  ‫ݓ‬ ഥ௘೔ೕ೟  ‫ݍ‬௢೔   1 + ℎ௔௦௦௘௦௦ ∑ ‫ݍ‬௢೔ ܰ௢೔ ‫ݍ‬௘೔ೕ೟ୀ ‫ݍ‬௢೔ ‫(۔‬1 − ‫ݍ)ݎ݋ݏ‬௘ + 	‫ݎ݋ݏ‬ ೔ೕ೟ ۖ 1 + ℎ ∑ ‫ݍ‬௢೔ ܰ௘೔ೕ೟ ‫ە‬ ‫ܨ‬௘೔ೕ೟ = 	 ‫ܧ‬௝ ‫ݍ‬௘೔ೕ೟  ܼ௘೔ೕ೟ = ‫ܨ‬௘೔ೕ೟ + ‫ܯ‬௜ ‫ܥ‬௘೔ೕ೟ =  F௘೔ೕ೟  ܼ௘೔ೕ೟  ቀ1 − ݁  ି௓೐೔ೕ೟  ቁ ‫ܤ‬௘೔ೕ೟ Continued on next page  234  Table 4.6 continued Equation number Reference points T4.6.9 T4.6.10 T4.6.11 T4.6.12 T4.6.13  Description ‫ܻܵܯ‬௜௧ = max	൫‫ܥ‬௘೔೟ ൯ ‫ܥ‬௘೟ = 	 ෍ ‫ܥ‬௘೔ೕ೟ ௜  ‫ܻܵܯ‬௧ = max	൫‫ܥ‬௘೟ ൯  ‫ܧ‬ெௌ௒೟ = 	 ‫ܧ‬௝ 	ቀmax	൫‫ܥ‬௘೟ ൯ቁ ‫ܤ‬ெௌ௒೟ = 	B ቀmax	൫‫ܥ‬௘೟ ൯ቁ  235  Table 4.7 Performance measures used to evaluate the relative performance of each management procedure over short- and long-term projections Equation number Subscripts t Performance measures T4.7.1  T4.7.2  T4.7.3  T4.7.4  T4.7.5  Description 2005 < ‫ ≤ ݐ‬2011 Projection	period = 	 ቄ ‫ ≥ 	ݐ‬2012 ‫ܸܣܣ‬௧ =  ‫ܥ‬ഥ௧ =  തതതത ‫ܥ‬ప௧ = തതത ‫ܦ‬௧ =  ∑௧ห‫ܥ‬௧௢௧೟శభ − 	 ‫ܥ‬௧௢௧೟ ห ∑௧ ‫ܥ‬௧௢௧೟  ∑௜௧ ‫ܥ‬௜௧ ݊ ∑௧ ‫ܥ‬௜௧ ݊  ‫ܤ‬௜௧ ‫ܤ‬௜ଵ  ݊  ∑௜௧  ഥ௜௧ = ‫ܦ‬  ‫ܤ‬௜௧ ‫ܤ‬௜ଵ  ݊  ∑௧  236  Table 4.8 The interquartile range, median, and mean for the percent difference in average projected short-term catch for all management procedures relative to the perfect information management procedure. Results are shown for operating model scenario one (h = 0 minutes) and operating model scenario two (h = 7 minutes). Negative values represent a loss and positive values represent a gain in catch relative to the perfect information management procedure. Operating model scenario 2 (h= 7 min/fish)  Operating model scenario 1 (h=0) HCR  MP  LB  Median  UB  Mean  LB  Median  UB  Mean  Precautionary  A1  -60.3  -46.0  -20.7  -43.7  -52.3  -37.7  -12.6  -36.3  Precautionary  C1  -26.3  -8.3  19.7  -6.4  -18.9  2.4  34.7  4.8  Precautionary  C2  -35.3  -18.6  6.0  -17.3  -28.7  -10.4  16.9  -8.8  Precautionary  S1  -15.2  1.5  8.2  0.3  -2.6  12.8  19.2  12.2  Precautionary  S2  -9.2  2.1  8.2  1.6  4.3  14.0  20.3  13.4  Precautionary  S3  -32.5  -20.6  -7.9  -20.4  -32.8  -12.0  -1.3  -13.5  Precautionary  S4  -39.2  -23.3  -10.2  -23.7  -36.9  -18.1  -1.2  -18.8  Precautionary  T1  -26.7  -12.4  4.4  -12.6  -22.3  -11.5  8.0  -9.9  Precautionary  T2  -8.6  3.9  9.8  2.8  -14.7  6.3  20.6  6.0  Precautionary  T3  -69.0  -57.4  -16.7  -54.2  -69.3  -57.3  -40.1  -56.3  Precautionary  T4  -71.2  -33.9  -7.6  -38.9  -71.0  -25.3  16.0  -26.2  Weak-stock  C3  -100  -78.2  -50.3  -80.9  -100  -100  -52.7  -86.2  Weak-stock  C4  -100  -100  -79.6  -98.9  -100  -100  -100  -100  Weak-stock  S5  -100  -100  -68.1  -93.7  -100  -100  -63.1  -96.6  Weak-stock  S6  -100  -100  -69.9  -95.2  -100  -100  -69.1  -97.1  Weak-stock  S7  -100  -100  -79.5  -99.0  -100  -100  -100  -99.5  Weak-stock  S8  -100  -100  -100  -99.9  -100  -100  -100  -100  Weak-stock  T5  -100  -100  -71.3  -95.3  -100  -100  -73.0  -97.9  Weak-stock  T6  -100  -100  -71.3  -95.3  -100  -100  -73.0  -97.9  Weak-stock  T7  -100  -100  -100  -99.9  -100  -100  -100  -100  Weak-stock  T8  -100  -100  -100  -99.9  -100  -100  -100  -100  237  Table 4.9 The interquartile range, median, and mean for the percent difference in average projected long-term total catch for all management procedures relative to the perfect information management procedure. Results are shown for operating model scenario one (h = 0 minutes) and operating model scenario two (h = 7 minutes). Negative values represent a loss and positive values represent a gain in catch relative to the perfect information management procedure. Operating model scenario 2 (h= 7 min/fish)  Operating model scenario 1 (h=0) HCR  MP  LB  Median  UB  Mean  LB  Median  UB  Mean  Precautionary  A1  -32.5  -23.1  -12.8  -23.0  -23.7  -14.8  11.2  -13.4  Precautionary  C1  -6.1  8.2  19.7  7.9  -6.3  6.1  18.1  6.1  Precautionary  C2  -15.8  6.8  19.4  5.7  -19.2  -7.9  10.1  -6.5  Precautionary  S1  -3.7  2.1  8.4  2.2  -9.7  -4.2  2.8  -4.1  Precautionary  S2  -3.2  2.3  6.5  2.3  -8.9  -4.1  2.3  -3.9  Precautionary  S3  -6.5  5.0  11.8  4.2  -13.8  -0.2  8.3  -0.4  Precautionary  S4  -17.0  5.2  11.8  3.9  -25.6  -10.7  7.0  -9.0  Precautionary  T1  -36.5  -14.1  1.2  -15.4  -36.8  -11.9  3.0  -14.2  Precautionary  T2  -39.5  -7.9  0.0  -9.3  -40.8  -8.0  4.6  -9.4  Precautionary  T3  -50.3  -38.5  -2.5  -35.1  -52.9  -40.9  -24.3  -40.4  Precautionary  T4  -41.3  -13.4  6.5  -13.3  -29.0  -12.0  5.3  -11.6  Weak-stock  C3  -39.0  -22.9  -4.6  -22.8  -42.8  -23.8  -4.1  -24.2  Weak-stock  C4  -62.6  -33.5  -15.2  -35.8  -57.2  -47.4  -34.3  -46.4  Weak-stock  S5  -44.6  -29.4  -13.5  -29.2  -57.1  -35.6  -17.6  -35.9  Weak-stock  S6  -42.4  -26.3  -13.0  -26.8  -59.0  -34.3  -15.5  -34.7  Weak-stock  S7  -62.4  -38.3  -23.9  -40.9  -67.7  -54.5  -44.2  -55.3  Weak-stock  S8  -68.1  -51.9  -26.5  -50.4  -68.1  -55.4  -43.7  -55.7  Weak-stock  T5  -44.2  -32.6  -19.5  -32.1  -59.2  -38.9  -20.4  -39.1  Weak-stock  T6  -44.2  -32.6  -19.5  -32.1  -59.2  -38.9  -20.4  -39.1  Weak-stock  T7  -75.1  -66.0  -54.1  -65.5  -69.9  -61.9  -54.3  -62.0  Weak-stock  T8  -72.2  -59.6  -34.4  -58.2  -71.8  -56.5  -38.5  -56.0  238  Onaga  Ehu  Kalekale  Opakapaka  Gindai  Hapuupuu  Lehi  White Ulua  Uku  Kahala  50 0  Height  100  150  Figures  Species  Figure 4.1 Species groupings based on the reported average beginning and end catch depths.  239  1.0  Precautionary rule  Effort ratio  0.8  0.6  0.4  0.2  0.0 0.0  0.5  1.0 Biomass ratio  1.5  2.0  Figure 4.2 Plot of the precautionary harvest control rule. The effort ratio is E/EMSY and the biomass ratio is B/BMSY.  240  Short Term Projections h=7min  h=0  Weak Stock Control Rule  h=7min  Perfect Information h=0  h=7min  a)  b)  c)  d)  e)  f)  g)  h)  i)  j)  k)  l)  m)  n)  o)  p)  q)  r)  1.0  Data types: Aggregated C&E C&E C&E + survey C&E + tag Perfect information  h=0  5 4 3 2 0.6 0.0  0.2  0.4  Dt  0.8  1.0  1.2 0  1  Ct (100000 kgs)  6  0.0  0.5  AAV  1.5  2.0  OM Scenarios:  Precautionary Control Rule  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  P1  P1  Management Procedure  ഥ௧ for 21 management procedures (see Table 4.1 for shorthand notation) that fall under Figure 4.3 Short term projections for AAV, ‫ܥ‬௧̅ , and ‫ܦ‬ two harvest control rules (precautionary and weak-stock) and two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). Each box summarizes the performance measures estimates resulting from 100 MPE realizations. 241  Long Term Projections OM Scenarios: 2.0  AAV  1.5  Data types: Aggregated C&E C&E C&E + survey C&E + tag Perfect information  h=0  Precautionary Control Rule  h=7min  h=0  Weak Stock Control Rule  h=7min  Perfect Information h=0  h=7min  a)  b)  c)  d)  e)  f)  g)  h)  i)  j)  k)  l)  m)  n)  o)  p)  q)  r)  1.0  0.5  4.0  Ct (100000 kgs)  3.5 3.0 2.5 2.0 1.5 1.0 0.5 1.2 1.0  Dt  0.8 0.6 0.4 0.2 0.0  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  P1  P1  Management Procedure  ഥ௧ for 21 management procedures (see Table 4.1 for shorthand notation) that fall under Figure 4.4 Long-term projections for AAV, ‫ܥ‬௧̅ , and ‫ܦ‬ two harvest control rules (precautionary and weak-stock) and two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels).  242  MSY (Perfect information) OM scenarios  h=0  h = 7min/fish  1000  P1  P1  Total catch(1000s kg)  800  600  400  200  0  Total biomass (1000s kg)  5000  4000  3000  2000  1000  0 1960  1980  2000  2020  1960  1980  2000  2020  Years  Figure 4.5 Total catch (top panels) and biomass (bottom panels) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030 for the two operating model (OM) scenarios. The projected trajectories represent years in which catch was set to MSY under the perfect information management procedure. The solid lines represent three individual trajectories and the shaded region represents the 95 percent confidence region. 243  Precautionary Harvest Control Rule Scenario 1 1200  Scenario 2  A1  A1  1000 800 600 400 200 0 1200  C1  C2  C1  C2  1000  Total catch (1000s kg)  800 600 400 200 0 1200  S1  S2  S3  S4  S1  S2  S3  S4  T1  T2  T3  T4  T1  T2  T3  T4  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1000 800 600 400 200 0 1200 1000 800 600 400 200 0  Years  Figure 4.6 Total catch (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the precautionary harvest control rule was implemented. The solid lines represent three individual trajectories and the shaded region represents the 95 percent confidence region. Each panel represents a different management procedure. 244  Precautionary Harvest Control Rule Scenario 1 6000  Scenario 2  A1  A1  5000 4000 3000 2000 1000 0 6000  C1  C2  C1  C2  5000  Total biomass (1000s kg)  4000 3000 2000 1000 0 6000  S1  S2  S3  S4  S1  S2  S3  S4  T1  T2  T3  T4  T1  T2  T3  T4  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  5000 4000 3000 2000 1000 0 6000 5000 4000 3000 2000 1000 0  Years  Figure 4.7 Total biomass (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the precautionary harvest control rule was implemented and for two scenarios (hsim = 0 minutes and hsim = 7 minutes). The solid lines represent three individual trajectories and the shaded area represents the 95 percent confidence region. Each panel represents a different management procedure. 245  Weak Stock Harvest Control Rule Scenario 1 C3  Scenario 2 C4  C3  C4  1500  1000  500  Total catch (1000s kg)  0  S5  S6  S7  S8  S5  S6  S7  S8  T5  T6  T7  T8  T5  T6  T7  T8  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1500  1000  500  0  1500  1000  500  0  Years  Figure 4.8 Total catch (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the weak stock harvest control rule was implemented. The solid lines represent three individual trajectories and the shaded region represents the 95 percent confidence region. Each panel represents a different management procedure. 246  Weak Stock Harvest Control Rule Scenario 1 6000  C3  Scenario 2 C4  C3  C4  5000 4000 3000 2000 1000  Total biomass (1000s kg)  0 6000  S5  S6  S7  S8  S5  S6  S7  S8  T5  T6  T7  T8  T5  T6  T7  T8  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  1960 1980 2000 2020  5000 4000 3000 2000 1000 0 6000 5000 4000 3000 2000 1000 0  Years  Figure 4.9 Total biomass (1000s kg) trajectories over the historic time period, 1948-2005, and the projected time period, 2006-2030. The projected trajectories represent years in which the weak stock harvest control rule was implemented. The solid lines represent three individual trajectories and the shaded area represents the 95 percent confidence region. Each panel represents a different management procedure 247  Short Term Projections 0.2  OM Scenarios: a)  h=0  Precautionary Control Rule  h=7min  h=0  W eak Stock Control Rule  h=7min  Perfect Information h=0  h=7min  0.1 0.67  b)  0.34 0.22  c)  0.11 2.5  d)  1.25  Ct (100000 kgs)  1.26  e)  0.63 0.35  f)  0.18 1.91  g)  0.96 0.25  h)  0.12  i) 0.03 0.45  j)  0.23  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  P1  P1  Management Procedure  Figure 4.10 Short-term species-specific average catch for 21 management procedures falling under two harvest control rules (precautionary and weak-stock) and two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). Each row represents one species: a) Hapu’upu’u, b) Kahala, c) Kalekale, d) Opakapaka, e) Uku, f) Ehu, g) Onaga, h) Lehi, i) Gindai, and j) White ulua. 248  Short Term Projections 1.2  OM Scenarios: a)  0.6 0.2 1.2  b)  0.6 0.2 1.2  c)  h=0  Precautionary Control Rule  h=7min  h=0  W eak Stock Control Rule  h=7min  Perfect Information h=0  h=7min  Dt  0.6 0.2 1.2  d)  0.6 0.2 1.2  e)  0.6 0.2 1.2  f)  0.6 0.2 1.2  g)  0.6 0.2 1.2  h)  0.6 0.2 1.2  i)  0.6 0.2 1.2  j)  0.6 0.2  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  P1  P1  Management Procedure  Figure 4.11 Short-term species-specific mean depletion for 21 management procedures falling under two harvest control rules (precautionary and weak-stock) and two operating model scenarios (h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). Each row represents one species: a) Hapu’upu’u, b) Kahala, c) Kalekale, d) Opakapaka, e) Uku, f) Ehu, g) Onaga, h) Lehi, i) Gindai, and j) White ulua. The dashed line represents overfishing (i.e., Bcurrent/Bo = 0.2). 249  Long Term Projections 0.13  OM Scenarios: a)  h=0  Precautionary Control Rule  h=7min  h=0  W eak Stock Control Rule  h=7min  Perfect Information h=0  h=7min  0.06 0.48  b)  0.24 0.16  c)  0.07 1.76  d)  0.8  Ct (100000 kgs)  0.85  e)  0.38 0.25  f)  0.11 0.97  g)  0.44 0.18  h)  0.09 0.04  i)  0.02 0.32  j)  0.14  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  P1  P1  Management Procedure  Figure 4.12 Long-term projections for species-specific average catch for two harvest control rules (precautionary and the weak stock) and two scenarios (hsim = 0 minutes and hsim = 7 minutes). Each row represents one species: a) Hapu’upu’u, b) Kahala, c) Kalekale, d) Opakapaka, e) Uku, f) Ehu, g) Onaga, h) Lehi, i) Gindai, and j) White ulua.  250  Long Term Projections 1.2  OM Scenarios: a)  0.6 0.2 1.2  b)  0.6 0.2 1.2  c)  h=0  Precautionary Control Rule  h=7min  h=0  W eak Stock Control Rule  h=7min  Perfect Information h=0  h=7min  Dt  0.6 0.2 1.2  d)  0.6 0.2 1.2  e)  0.6 0.2 1.2  f)  0.6 0.2 1.2  g)  0.6 0.2 1.2  h)  0.6 0.2 1.2  i)  0.6 0.2 1.2  j)  0.6 0.2  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  A1 C1 C2 S1 S2 S3 S4 T1 T2 T3 T4  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  C3 C4 S5 S6 S7 S8 T5 T6 T7 T8  P1  P1  Management Procedure  Figure 4.13 Long-term species-specific mean depletion for 21 management procedures falling under two harvest control rules (i.e., precautionary and weak-stock) and two operating model scenarios (i.e., h = 0 minutes per fish and 7 minutes per fish). Also presented are two perfect information management procedures (far right panels). Each row represents one species: a) Hapu’upu’u, b) Kahala, c) Kalekale, d) Opakapaka, e) Uku, f) Ehu, g) Onaga, h) Lehi, i) Gindai, and j) White ulua. The dashed line represents overfishing (i.e., B = 0.2 Bo). 251  OM scenario: h=7 min/fish 4  a)  black: Precautionary HCR blue: Weak-stock HCR red: Perfect information  C1 C2 S4 S3 S1P1 S2  b)  3  Long-term median catch (100,000 kgs) 1 2 3  T2 T1  C1  T4  P1 S3  S2 S1 T2 C2 S4 T1 T4 A1 C3  2  A1 C3 S6 S5 T6 T5C4 T3  S7 S6 S5 T6 T3 T5  S8  C4  T8  S7 S8 T8 T7  0  0  T7  1  4  OM scenario: h=0  0.0  0.2  0.4  0.6  0.8 1.0 0.0 0.2 Long-term median depletion  0.4  0.6  0.8  1.0  Figure 4.14 Trade-off curve between long-term catch and stock size for the two operating model scenarios; a) the fishery-dependent data were simulated to be proportional to abundance and b) the fishery-dependent data were simulated to be hyperstable. Refer to Table 4.1 for management procedure short-hand, which is used to indicate where the individual management procedures lie on the trade-off curve. 252  c) black: Precautionary HCR blue: Weak-stock HCR P1: Perfect information hassess = 0  3  4  a) C1 P1  S1 S2  C2 S3S4 T2  T4  T1  T4 C3  2  S6 S5  T6 T5  T3  C4 S7 S8  1  T8 T7  0 0.0 0.5 1.0 1.5 2.0 2.5 3.0  Long-term median catch (100,000 kgs)  A1  b)  d) C1  P1 S3  S2S1  C2 S4 T1  T2  T4  A1  A1 C3  T3  S6 S5  T6 T5 C4 S7 S8 T8 T7  0.15  0.20  0.25  0.30  0.35  0.40  0.45  0.50 0.50  0.55  0.60  0.65  0.70  0.75  0.80  0.85  Long-term median depletion  Figure 4.15 Trade-off curves separated into regions of high catch and depletion (a, b) and low catch and depletion (c, d) for the operating model scenarios: fishery-dependent data were simulated to be proportional to abundance (a, c) and fishery-dependent data were simulated to be hyperstable (b, d). The cut-off represents the balanced trade-off A1. Refer to Table 4.1 for management procedure short-hand, which is used to indicate where the individual management procedures are along the trade-off curve. 253  OM scenario: h=7 min/fish 4  a)  black: Precautionary HCR blue: Weak-stock HCR red: Perfect information  b)  3  C1 C2 S4 S3 P1 S1 S2  T4  T2  C1 P1 S3  T1  S2 S1 A1  C2 T2 S4 T4 T1  3  4  A1  2  C3 S6 S5 C4 T6 T5  C3  T3 S7 S6 S5 T6 T5 S8  T3  C4  T8  S7 S8 T8 T7  0  1  T7  0  Long-term median catch (100,000 kgs) 1 2 3  4  OM scenario: h=0  0  1  2  3  4 5 0 1 2 Median number of overfished species (B<0.2Bo)  5  Figure 4.16 Trade-off between long-term total catch and the number of overfished species (B<0.2Bo) for two operating model scenarios a) the fishery-dependent data were simulated to be proportional to abundance and b) the fishery-dependent data were simulated to be hyperstable. Refer to Table 4.1 for management procedure short-hand, which is used to indicate where the individual management procedures along the trade-off curve. A total of ten species were considered for analysis. 254  Chapter 5 Summary Legislative mandates are increasingly calling for the end of overfishing. In the United States the Magnusson-Stevens Reauthorized Fisheries Conservation and Management Act (MSA) is the main regulatory legislation that outlines and defines fisheries management objectives and requirements. Under the re-authorized act all fisheries must be managed by annual catch limits (ACLs). ACLs can be developed for individual species or groups of species depending on the definition of stock. The development of ACLs is reliant on quantitative predictions using stock assessment models. Therefore, there is now an increased demand to conduct quantitative assessments to determine stock status and link the results to management policies that will avoid over-exploitation. This is a seemingly straightforward task, unfortunately, there is usually a disconnect between available assessment models, the data available for assessment, management goals, and legislative requirements. Multispecies fisheries present additional challenges within this fishery management framework. One complicating factor is the data available for assessments and the lack of information about catch rates on individual species. At the most basic level catch by species is needed to develop relative indices of abundance on a per species basis. Many fisheries in the US Caribbean report catch as species groups that can contain several different species (personal observation). This precludes conducting assessments to determine stock status on a per species basis. When species-specific catch is available, as has been shown for the Hawaiian bottomfish fishe ry in this thesis, the corresponding effort data most likely does not contain information about targeting. This is especially true for fisheries characterized by strong technical interaction s where species can be simultaneously caught and where fishing may be fairly indiscriminate. Without information about targeting, effective fishing effort for any one species is unknown and  255  it is difficult to develop unbiased, species-specific relative indices of abundance and management advice. In the absence of informative data about changes in the relative abundance of individual species, managers and assessment scientists can decide to ignore the multispecies aspect of a fishery and predict stock status and develop management advice for the aggregated community. Although a relatively productive fishery could be maintained using an aggregate approach a management trade-off is the over-exploitation of individual species that are les resilient to fishing pressure. Given the management need to estimate the stock status of individual species, a stochastic multispecies model to reconstruct historical abundance from species-specific catch and total effort data were presented and applied to the Hawaiian bottomfish fishery data in Chapters 2 and 3. A delay-difference model was used to describe the population dynamics of the individual species within a larger multispecies model (Deriso 1980). Holling’s disc equation, which partitions total effort into two components, the time spent actively fishing and the time spent handling the gear and processing the captured fish, was used to model the observation dynamics. Handling time represents loss of effective fishing time for one or more species and limits the catch rates of all species. The advantage of modifying the disc equation to account for multiple species is that: 1) it accounts for the technical interactions between species and 2) it accounts for a mechanism, handling time, which is a known cause of hyperstability in catch and effort data (Paloheimo and Dickie 1964, Cooke and Beddington 1984). Monte Carlo simulation experiments (Chapter 2) showed that estimates of the leading parameters and management reference points were relatively unbiased. Given this result, the model developed in Chapter 2 was applied to the Hawaiian bottomfish fishery-dependent data. The application of the multispecies model to the Hawaiian bottomfish fishery data was dependent on the assumption that average handling time per fish was known. An empirical 256  estimate of average handling time per fish was not available for this analysis. Using published gear performance statistics, a range of reasonable handling estimates were derived from these statistics and used for this analysis. A sensitivity analysis was done using the derived range of average handling time estimates to evaluate how sensitive the assessment results were to the assumed value of average handling time. The lowest bound of the average handling time range was zero. This is equivalent to assuming that species-specific catchability is time-invariant and species-specific catch rates are proportional to abundance. This is also analogous to simultaneously conducting 10 stock assessments where species do not interact biologically or through the fishing process and therefore all species experience the same fishing effort which is the same as total effort.  The posterior estimates of the leading parameters and the derived  management reference parameters were relatively insensitive to the assumed value of average handing time. The negative log likelihood of the species-specific catch observations did indicate that for some species a non-zero handling time better described the data than assuming handling time was negligible. Chapters 2 and 3 represent an important first step in moving away from an aggregate assessment approach to obtain abundance and management reference point estimates for individual target species. Developing assessment methods that can adequately accommodate available data and at the same time provide needed management advice is an integral step towards meeting multispecies management objectives. This, however, does not ensure that multispecies management objectives will be met or that new assessment methods will provide better management advice than the status quo approaches. Management procedure evaluation (MPE) is a Monte Carlo simulation method that has been promoted to evaluate the entire management system. MPE simulates the entire management system, from collecting data, conducting stock assessments, and making and implementing management decisions. An MPE 257  was conducted in Chapter 4 to evaluate the management performance of the aggregate approach and the multispecies model presented in this thesis. MPE was also conducted to evaluate management performance for two different harvest control rules and additional data sources such as fishery-independent, species-specific relative indices of abundance and mark-recapture data to monitor fishing mortality. The interpretation of management performance was dependent on the perspective (i.e., aggregate or by species) at which the results were evaluated. For example, from the aggregate perspective the management procedures associated with the precautionary harvest control rule in the long-term met conservation objectives; i.e., long-term average depletion was above the overexploitation proxy. At the species level, the management procedures associated with the precautionary harvest control rule led to the over-exploitation of one or more species. The tradeoffs between management objectives were also determined by the harvest control employed by a particular management procedure. For example, the management procedures associated with the weak-stock harvest control rule prevented over-exploitation of all species, as the rule is intended to do. This conservation oriented management objective when employing the weak-stock harvest control rule was achieved by considerably limiting catch as compared to the management procedures associated with the precautionary harvest control rule. The MPE results also demonstrate the difficulty in managing a multispecies fishery to avoid the over-exploitation of all target species when using community-based metrics to develop management policies. The annual catch limits developed as part of the MPE were derived from the total effort required to achieve MSY of the overall community of species. Even with the availability of perfectinformation, more than one species was over-exploited using this aggregate effort metric to develop ACLs.  258  Future avenues of research Handling time effects helped disentangle species-specific abundance information from the Hawaiian bottomfish fishery data in Chapter 3. However, the recruitment anomalies showed patterns of autocorrelation possibly pointing to model mis-specification. This result combined with the MPE results of Chapter 4 suggest that mechanisms other than handling time effects may be the cause of non-stationary catchability. In recent stock assessments of the Hawaiian bottomfish fishery, catchability has been treated as a step-function, where catchability has increased over four arbitrary time-periods associated with increased gear and fishing efficiency. A random walk approach could be used to estimate species-specific catchability. It may be more appropriate to model species-specific catchability as a random walk process to account for gradual changes over time that would be due to changes in gear efficiency or changes in the target species guild. The advantage of treating species-specific catchability as random walk processes would be that it may help to account for some of the autocorrelation that was estimated as process error in the recruitment anomalies. An important step in determining whether using a random walk approach to estimate species-specific catchability is appropriate given the available data will be to conduct simulation experiments as was done in Chapter 2. Simulation experiments can also be used to identify additional data types that may be needed to accurately estimate catchability estimated as a random walk process. Evaluating the management performance of the advice provided by the modified model will remain important. The MPE framework developed in Chapter 4 can be used to accommodate and evaluate alternative assessment models. A limitation of all the management procedures evaluated in Chapter 4 was the considerable average annual variation in catch. Much of the average annual variation (AAV) in catch can be attributed to the harvest control rules that were used to make management decisions. Both the precautionary and weak-stock harvest 259  control rules made steep reductions in effort when biomass fell below a pre-determined threshold. It is recommended that harvest rules known to reliably reduce AAV in catch, constant harvest rate and constant catch policies, should be evaluated to determine if their performance in  a multispecies situation is better than what was presented in Chapter 4. Future work should also develop and evaluate novel alternative harvest control rules that jointly account for changes in the stock status of multiple species. The development of these harvest control rules will require participation of all stakeholders to precisely define and prioritize the management objectives for the overall multispecies fishery and the individual species themselves. Lastly, it will be valuable to evaluate the ACL management strategy coupled with season and spatial closures to determine if management objectives at the species level can be better achieved while still allowing for a productive fishery.  260  References Adams, P.A. 1980. Life history patterns in marine fishes and their consequences for fisheries management. Fishery Bulletin 78 (1): 1-12. ADMB Project. 2009. AD Model Builder: automatic differentiation model builder. Developed by David Fournier and freely available from admb-project.org Agnew, D.J., Nolan, C.P., Beddington, J.R., and Baranowski, R. 2000. Approaches to the assessment and management of multispecies skate and ray fisheries using the Falkland Islands fishery as an example. Canadian Journal of Fisheries and Aquatic Sciences 57: 429-440. Ainsworth, C.H., and Pitcher, T.J. 2010. A bioeconomic optimization approach for rebuilding marine communities: British Columbia case study. Environmental Conservation 36(04): 301311. Bannerot, S.P., and Austin, C.B. 1983. Using frequency distributions of catch per unit effort to measure fish-stock abundance. Transactions of the American Fisheries Society 112: 608-617. Beddington, J.R., and Kirkwood, G.P. 2005. The estimation of potential yield and stock status using life-history parameters. Philosophical Transactions of the Royal Society Biological Sciences 360: 163-170. Bergh, M.O., and Butterworth, D.S. 1987. Towards rational harvesting of the South African anchovy considering survey imprecision and recruitment variability. South African Journal of Marine Science 5: 937-951. Beverton, R.J.H., and Holt, S.J. 1959. A review of the life-spans and mortality rates of fish in nature and their relationship to growth and other physiological characteristics. Ciba Foundation Colloquia on Aging 5: 142-180. Biseau, A. 1998. Definition of a directed fishing effort in a mixed-species trawl fishery, and its impact on stock assessments. Aquatic Living Resources 11(3): 119-136. Branch, T.A., and Hilborn, R. 2008. Matching catches to quotas in a multispecies trawl fishery: targeting and avoidance behavior under individual transferable quotas. Canadian Journal of Fisheries and Aquatic Sciences 65(7): 1435-1446. Branch, T.A., Hilborn, R., and Bogazzi, E. 2005. Escaping the tyranny of the grid: a more realistic way of defining fishing opportunities. Canadian Journal of Fisheries and Aquatic Sciences 62(3): 631-642. Branch, T.A., Hilborn, R., Haynie, A.C., Fay, G., Flynn, L., Griffiths, J., Marshall, K.N., Randall, J.K., Scheuerell, J.M., Ward, E.J., and Young, M. 2006. Fleet dynamics and fishermen behavior: lessons for fisheries managers. Canadian Journal of Fisheries and Aquatic Sciences 63(7): 1647-1668. 261  Buckworth, R.C., Bryce, C.R., and Donati, A.C. Fish biopsy device. US 2006/0106324 A1. May 18, 2006. Butterworth, D.S., and Bergh, M.O. 1993. The development of a management procedure for the South African anchovy resource. African Journal of Marine Science Butterworth, D.S., Cochrane, K.L., De Oliviera, J.A.A. 1997. Management procedures: A better way to manage fisheries? The South African experience. In Global trends: Fisheries management. Ed. Pikitch, E.K., Huppert, D.D, and M.P Sissenwine. pp. 83-90. Butterworth, D.S., and Punt, A.E. 1999. Experiences in the evaluation and implementation of management procedures. ICES Journal of Marine Science 56: 985-998. Butterworth, D.S. and Rademeyer, R.A. 2008. Statistical catch-at-age analysis vs. ADAPT-VPA: the case of Gulf of Maine Cod. ICES Journal of Marine Science 65: 1717-1732. Cheung, W.L., and Sadovy, Y. 2004. Retrospective evaluation of data-limited fisheries: a case from Hong Kong. Reviews in Fish Biology and Fisheries 14: 181-206. Cheung, W., and Sumaila, U. 2008. Trade-offs between conservation and socio-economic objectives in managing a tropical marine ecosystem. Ecological Economics 66(1): 193-210. Christensen, V., and Walters, C.J. 2004. Trade-offs in ecosystem-scale optimization of fisheries management policies. Bulletin of Marine Science 74(3): 549-562. Cobb, J.N. 1905. The commercial fisheries of the Hawaiian Islands 1903. US Bureau of Fisheries. Washington, DC. pp. 453-512. Cooke, J.G., and Beddington, J.R. 1984. The relationship between catch rates and abundance in fisheries. IMA Journal of Mathematics Applied in Medicine & Biology 1: 391-405. Cox, S.P., and Kronlund, A.R. Practical stakeholder-driven harvest policies for groundfish fisheries in British Columbia, Canada Fisheries Research 94: 224-237. Crecco, V., and Overholtz, W.J. 1990. Causes of density-dependent catchability for Georges Bank haddock Melanogrammus aeglefinus. Canadian Journal of Fisheries and Aquatic Sciences 47: 385-394. Dankel, D.J., Jacobson, N., Georgianna, D., and Cadrin, S.X. 2009. Can we increase haddock yield within the constraints of the Magnuson–Stevens Act? Fisheries Research 100(3): 240-247. Darcy, G.H., Matlock, G.C. 1999. Application of the precautionary approach in the national standard guidelines for conservation and management of fisheries in the United States. ICES Journal of Marine Science 56: 853-859. De la Mare, W.K. 1998. Tidier fisheries management requires a new MOP (managementoriented paradigm). Reviews in Fish Biology and Fisheries 8: 349-356. 262  De Oliveira, J.A.A., and Butterworth, D. 2004. Developing and refining a joint management procedure for the multispecies South African pelagic fishery. ICES Journal of Marine Science 61(8): 1432-1442. Deriso, R.B. 1980. Harvesting strategies and parameter estimation for an age-structured model. Canadian Journal of Fisheries and Aquatic Sciences 37: 268-282. Deriso, R.B., and Parma, A.M. 1987. On the odds of catching fish with angling gear. Transactions of the American Fisheries Society 116: 244-256. Dichmont, C.M., Deng, A., Punt, A.E., Venables, W., and Haddon, M. 2006. Management strategies for short lived species: The case of Australia's Northern Prawn Fishery 2. Choosing appropriate management strategies using input controls. Fisheries Research 82(1-3): 221-234. DiCosimo, J., Methot, R.D., Ormseth, O.A. 2010. Use of annual catch limits to avoid stock depletion in Bering Sea and Aleutian Islands management area (Northeast Pacific). ICES Journal of Marine Science 67:1861-1865. DiNardo, G.T. and Wetherall, J.A. 1999. Accounting for uncertainty in the development of harvest strategies for the Northwestern Hawaiian Islands lobster trap fishery. ICES Journal of Marine Science 56:943-951. Essington, T.E. 2006. The precautionary approach in fisheries management: the devil is in the details. Trends in Ecology and Evolution 16(3): 121-122. Evans, M., Hastings, N., and Peacock, B. 2000. Statistical distributions, 3rd Edition. John Wiley & Sons, Inc. FAO. 1996. FAO technical guidelines for responsible fisheries – Precautionary approach to capture fisheries and species introduction. FAO, Rome. 41pp. Fisheries and Oceans Canada. 2009. Sustainable Fisheries Framework. Francis, R.I.C.C., and Shotton, R. 1997. “Risk” in fisheries management: a review. Canadian Journal of Fisheries and Aquatic Sciences 54: 1699-1715. Froese, R. and D. Pauly, Editors. 2000. FishBase 2000: concepts, design and data sources. ICLARM, Los Baños, Laguna, Philippines. 344 p. Fu, C. and Quinn II, T.J. 2000. Estimability of natural mortality and other population parameters in a length-based model: Pandalus borealis in Kachemak Bay, Alaska. Canadian Journal of Fisheries and Aquatic Sciences 57: 2420-2432. Garcia, S.M. 1996. The precautionary approach to fisheries and its implications for fishery research, technology, and management: An updated review. FAO Fisheries Technical Paper 350(2). Rome, 210pp.  263  Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B. 2004. Bayesian data analysis, second edition. Chapman & Hall. Boca Raton, Florida. 668pp. Geromont, H.F., De Oliveira, J.A.A., Johnston, S.J., Cunningham, C.L. 1999. Development and application of management procedures for fisheries in southern Africa. ICES Journal of Marine Science 56: 952-966. Gillis, D.M., Peterman, R.M., and Pikitch, E.K. 1995. Implications of trip regulations for highgrading: a model of the behavior of fishermen. Canadian Journal of Fisheries and Aquatic Sciences 52: 402-415. Gillis, D.M., Peterman, R.M., and Tyler, A.V. 1993. Movement dynamics in a fishery: application of the ideal free distribution to spatial allocation of effort. Canadian Journal of Fisheries and Aquatic Sciences 50:323-333. Glazer, J.P., and Butterworth, D.S. 2002. GLM-based standardization of the catch per unit effort series for South African west coast hake, focusing on adjustments for targeting other species. South African Journal of Marine Science 24: 323-339. Haight, W.R., Kobayashi, D.R., and Kawamoto, K.E. 1993. Biology and management of deepwater snappers of the Hawaiian archipelago. Marine Fisheries Review 55(2): 20-27. Hampton, J., Sibert, J.R., Kleiber, P., Maunder, M.N., and Harley, S.J. 2005. Decline of Pacific tuna populations exaggerated? Nature 434: E1-E2. Harley, S.J., Myers, R.A., and Dunn, A. 2001. Is catch-per-unit-effort proportional to abundance? Canadian Journal of Fisheries and Aquatic Sciences 58(9): 1760-1772. Hague, M.J. 2006. The use of genetic tagging to assess inshore rockfish populations within a marine conservation area in the Strait of Georgia. MS thesis Simon Fraser University. 129pp. He, X., Bigelow, K.A., Boggs, C.H. 1997. Cluster analysis of longline sets and fishing strategies within the Hawaii-based fishery. Fisheries Research 31: 147-158. Hilborn, R. 1976. Optimal exploitation of multiple stocks by a common fishery: A new methodology. Canadian Journal of Fisheries and Aquatic Sciences 33(1): 1-5. Hilborn, R. 1979. Comparison of fisheries control systems that utilize catch and effort data. Canadian Journal of Fisheries and Aquatic Sciences 36: 1477-1489. Hilborn, R. 1985. Apparent stock recruitment relationships in mixed stock fisheries. Canadian Journal of Fisheries and Aquatic Sciences 42: 718-723. Hilborn, R. and Ledbetter, M. 1985. Determinants of catching power in the British Columbia salmon purse seine fleet. Canadian Journal of Fisheries and Aquatic Sciences 42: 51-56.  264  Hilborn, R. and Peterman, R.M. 1996. The development of scientific advice with incomplete information in the context of the precautionary approach. FAO Fisheries Technical Paper 350(2). Rome, 210pp. Hilborn, R., Punt, A.E., and Orensanz, J. 2004. Beyond band-aids in fisheries management: Fixing world fisheries. Bulletin of Marine Science 74(3): 493-507. Hilborn, R., and Walters, C.J. 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics, & Uncertainty. Kluwer Academic Publishers. Norwell, Massachusetts. 570pp. Hjerne, O., Hansson, S. 2001. Constant catch or constant harvest rate? The Baltic Sea cod (Gadus morhua L.) fishery as a modeling example. Fisheries Research 53: 57-70. Holling, C.S. 1959a. The components of predation as revealed by a study of small mammal predation of the European pine sawfly. The Canadian Entomologist 91:293-320. Holling, C.S. 1959b. Some characteristics of simple types of predation and parasitism. The Canadian Entomologist 91(7): 385-398. Holt, R.D. 1977. Predation, apparent competition, and the structure of prey communities. Theoretical Population Biology 12(2): 197-229. Hulson, P-J.F., Miller, S.E., Ianelli, J.N., and Quinn III, T.J. 2011. Including mark-recapture data into a spatial age-structured model: walleye Pollock (Theragra chalcogramma) in the eastern Bering Sea. Canadian Journal of Fisheries and Aquatic Sciences 68: 1625-1634. Humphreys, R. 1986. Carangidae. In Fishery Atlas of the Northwestern Hawaiian Islands: Carangidae. Editors Uchida, R.N. and Uchiyama, J.H. NOAA Tech. Rep. NMFS 38. Impact Assessment, Inc. 2007. Hawaii's pelagic handline fisheries: History, trends, and current status. Western Pacific Regional Fishery Management Council. 84 pp. Jensen, A.L. 1996. Beverton and Holt life history invariants result from optimal trade-off of reproduction and survival. Canadian Journal of Fisheries and Aquatic Sciences 53: 820-822. Johannes, R.E. 1998. The case for data-less marine resource management: examples from tropical nearshore fin fisheries. Trends in Ecology and Evolution 13(6): 243-246. Kell, L.T, O’Brien, C.M., Smith, M.T., Stokes, and T.K., Rackham, B.D. 1999. An evaluation of management procedures for implementing a precautionary approach in the ICES context for North Sea plaice (Plueronectes platessa L.). ICES Journal of Marine Science 56: 834-845. Kell, L.T., Pastoors, M.A., Scott, R.D., Smith, M.T., Van beek, F.A., O’Brien, C.M., Pilling, G.M. 2005. Evaluation of multiple management objectives for Northeast Atlantic flatfish stocks: sustainability vs. stability of yield. ICES Journal of Marine Science 62: 1104-1117. Kell, L. T., Pilling, G. M., Kirkwood, G. P., Pastoors, M. A., Mesnil, B., Korsbrekke, K., 265  Abaunza, P., Aps, R., Biseau, A., Kunzlik, P., Needle, C. L., Roel, B. A., and Ulrich, C. 2006. An evaluation of multi-annual management strategies for ICES roundfish stocks. ICES Journal of Marine Science, 63: 12-24. Ketchen, K.S. 1964. Measures of abundance from fisheries with more than one species. ICES Journal of Marine Science 155: 113-116. Kimura, D. 1981. Standardized measures of relative abundance based on modeling log(c.p.u.e.) and their application to Pacific ocean perch (Sebastes alutus). ICES Journal of Marine Science 39( ): 211-218. Kirkwood, G.P. 1997. Management procedures: The revised management procedure of the International Whaling Commission. In Global trends: Fisheries management. Ed. Pikitch, E.K., Huppert, D.D, and M.P Sissenwine. pp. 91-99. Kleiber, P., and Maunder, M. 2008. Inherent bias in using aggregate CPUE to characterize abundance of fish species assemblages. Fisheries Research 93(1-2): 140-145. Lewy, P., and Vinther, M. 1994. Identification of Danish North Sea trawl fisheries. ICES Journal of Marine Science 51: 263-272. Linnane, A. and Crosthwaite, K. 2009. Spatial dynamics of the South Australian rock lobster (Jasus edwardsii) fishery under a quota-based system. New Zealand Journal of Marine and Freshwater Research 43: 475-484. MacCall, A. 1976. Density dependence of catchability coefficient in the California Pacific sardine, Sardinops sagax caerulea, purse seine fishery, California Department of Fish and Game. Mackinson, S., Deas, B., Beveridge, D., and Casey, J. 2009. Mixed-fishery or ecosystem conundrum? Multispecies considerations inform thinking on long-term management of North Sea demersal stocks. Canadian Journal of Fisheries and Aquatic Sciences 66(7): 1107-1129. Magnusson, A., and Hilborn, R. 2007. What makes fisheries data informative? Fish and Fisheries 8: 337-358. Mangel, M., and Beder, J.H. 1985. Search and stock depletion: Theory and applications. Canadian Journal of Fisheries and Aquatic Sciences 42: 150-163. Mangel, M., Clark, C.W. 1983. Uncertainty, search, and information in fisheries. ICES Journal of Marine Science 41: 93-103. Manooch III, C. 1987. Age and growth of snappers and groupers. In Tropical Snappers and Groupers: Biology and Fisheries Management. Editors Polovina, J.J. and Ralston, S. Westview Press, Boulder, CO. Manooch III, C. and Potts, J. 1997. Age, growth, and mortality of greater amberjack, Seriola dumerili, from the U.S. Gulf of Mexico headboat. Fishery Bulletin of Marine Science, 61(3):671-683. 266  Martell, S.J.D., and Walters, C.J. 2002. Implementing harvest rate objectives by directly monitoring exploitation rates and estimating changes in catchability. Bulletin of Marine Science 70(2): 695-713. Martell, S.J.D., Korman, J., Darcy, M. Christensen, L.B., Zeller, D. 2006. Status trends of the Hawaiian bottomfish stocks: 1948-2004. University of British Columbia. Contractors report to NMFS. Martell, S.J.D., Pine, W.E., and Walters, C.J. 2008. Parameterizing age-structured models from a fisheries management perspective. Canadian Journal of Fisheries and Aquatic Sciences 65(8): 1586-1600. Maunder, M.N. 2001. A general framework for integrating the standardization of catch per unit of effort into stock assessment models. Canadian Journal of Fisheries and Aquatic Sciences 58(4): 795-803. Maunder, M., and Punt, A. 2004. Standardizing catch and effort data: a review of recent approaches. Fisheries Research 70(2-3): 141-159. Maunder, M., Sibert, J., Fonteneau, A., Hampton, J., Kleiber, P., and Harley, S. 2006. Interpreting catch per unit effort data to assess the status of individual stocks and communities. ICES Journal of Marine Science 63(8): 1373-1385. McAllister, M.K., and Pikitch, E.K. 1997. A Bayesian approach to choosing a design for surveying fishery resources: application to the eastern Bering Sea trawl survey. Canadian Journal of Fisheries and Aquatic Sciences 54: 301-311. McAllister, M.K., Starr, P.J., Restrepo, V.R., and Kirkwood, G.P. 1999. Formulating quantitative methods to evaluate fishery-management systems: what fishery processes should be modeled and what trade-offs should be made? ICES Journal of Marine Science 56: 900–916. Meyer, R. and Millar, R.B. 1999. Bayesian stock assessment using a state-space implementation of the delay-difference model. Canadian Journal of Fisheries and Aquatic Sciences 56: 37-52. Michielsen, C.G.J, McAllister, M.K., Kuikka, S., Pakarinen, T., Karlsson, L., Romakkaniemi, A., Perä, I., and Mäntyniemi, S. A Bayesian state-space mark-recapture model to estimate exploitation rates in mixed-stock fisheries. Canadian Journal of Fisheries and Aquatic Sciences 63: 321-334. Moffitt, R.B., Kobayashi, D.R., and DiNardo, G.T. 2006. Status of the Hawaiian bottomfish stocks, 2004. Administrative Report H-06-01, NOAA PIFSC, Honolulu. 50pp. Moffitt, R.B., Parrish, F.A., Polovina, J.J. 1989. Community structure, biomass, and productivity of deepwater artificial reefs in Hawaii. Bulletin of Marine Science 44(2): 616-630. Morales-Nin, B. and Ralston, S. 1990. Age and growth of Lutjanus kasmira (forksal) in 267  Hawaiian waters. Journal of Fish Biology, 36:191-203. Murawski, S.A. 1984. Mixed-species yield-per-recruitment analyses accounting for technological interactions. Canadian Journal of Fisheries and Aquatic Sciences 41: 897-916. Murawski, S.A., Lange, A.M., Sissenwine, M.P., and Mayo, R.K. 1983. Definition and analysis of multispecies otter-trawl fisheries off the northeast coast of the United States. ICES Journal of Marine Science 41: 13-27. Myers, R.A., and Barrowman, N.J. 1996. Is fish recruitment related to spawner abundance? Fishery Bulletin 94: 707-724. Myers, R.A., Bowen, K.G., and Barrowman, N.J. 1999. Maximum reproductive rate at low population sizes. Canadian Journal of Fisheries and Aquatic Sciences 56: 2404-2419. Myers, R.A., Mertz, G. 1998. The limits of exploitation: A precautionary approach. Ecological Applications 8(1): S165-S169. Myers, R.A., and Worm, B. 2003. Rapid worldwide depletion of predatory fish communities. Nature 423: 280-283. New Zealand Ministry of Fisheries. 2007. Harvest strategy for New Zealand Fisheries. Wellington, New Zealand. 20pp. Paloheimo, J.E., and Dickie, L.M. 1964. Abundance and fishing success. ICES Journal of Marine Science 155: 152-163. Polacheck, T. 2006. Tuna longline catch rates in the Indian Ocean: Did industrial fishing result in a 90% rapid decline in the abundance of large predatory species? Marine Policy 30(5): 470-482. Paulik, G.J, Hourston, A.S., and Larkin, P.A. 1967. Exploitation of multiple stocks by a common fishery. Canadian Journal of Fisheries and Aquatic Sciences 24(12): 2527-2537. Pauly, D. 1982. Studying single-species dynamics in a tropical multispecies context. In Theory and Management of tropical Fisheries. Eds. D. Pauly & G.I. Murphy. ICLARM. 39-69. Pelletier, D., and Ferraris, J. 2000. A multivariate approach for defining fishing tactics from commercial catch and effort data. Canadian Journal of Fisheries and Aquatic Sciences 57: 51-65. Peterman, R.M., Steer, G.J. 1981. Relation between sport-fishing catchability coefficients and salmon abundance. Punt, A.E. 1997. The performance of VPA-based management. Fisheries Research 29: 217-243. Punt, A., Dorn, M., and Haltuch, M. 2008. Evaluation of threshold management strategies for groundfish off the U.S. West Coast. Fisheries Research 94(3): 251-266.  268  Punt, A.E. 2006. The FAO precautionary approach after almost 10 years: Have we progressed towards implementing simulation-tested feedback-control management systems for fisheries management. Natural Resource Modeling 19(4): 441-464. Punt, A.E., and Smith, A.D.M. 1999. Harvest strategy evaluation for the eastern stock of gemfish (Rexea solandri). ICES Journal of Marine Science 56: 860-875. Punt, A.E., Smith, A.D., and Cui, G. 2001. Review of progress in the introduction of management strategy evaluation (MSE) approaches in Australia’s South East Fishery. Marine and Freshwater Research 52: 719-726. Punt, A.E., Smith, D.C., Thomson, R.B., Haddon, M., He, X., and Lyle, J.M. 2001. Stock assessment of the blue grenadier Macruronus novaezelandiae resource off south-eastern Australia. Marine and Freshwater Research 52: 701-717. Punt, A.E., Smith, A.D.M., and Cui, G. 2002. Evaluation of management tools for Australia's South East Fishery 1. Modelling the South East Fishery taking account of technical interactions. Marine and Freshwater Research 53: 615-629. Quinn, T.J. and Deriso, R.B. 1999. Quantitative Fish Dynamics. Oxford University Press, New York. 542pp. Quirijns, F.J., Poos, J.J., and Rijnsdorp, A.D. 2008. Standardizing commercial CPUE data in monitoring stock dynamics: Accounting for targeting behavior in mixed fisheries. Fisheries Research 89: 1-8. R Development Core Team (2011). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org/. Rademeyer, R.A., Plaga´nyi, E.E., and Butterworth, D.S. 2007. Tips and tricks in designing management procedures. ICES Journal of Marine Science 64: 618-625. Ralston, S. 1987. Mortality rates of snappers and groupers. In Polovina, J.J., R. S., editor, Tropical Snappers and Groupers: Biology and Fisheries Management. Westview Press, Boulder, CO. Ralston, S. Miyamoto, G.T. 1983. Analyzing the width of daily otolith increments to age the Hawaiian snapper, Pristipomoides filamentosus. Fishery Bulletin 81(3): 523-535. Ralston, S., and Polovina, J.J. 1982. A multispecies analysis of the commercial deep-sea handline fishery in Hawaii. Fishery Bulletin 80(3): 435-448. Ralston, S.V. and Williams, H.A. 1988. Depth distributions, growth, and mortality of deep slope fishes from the Mariana archipelago. NOAA Technical Memo: NOAA-TM-NMFS-SWFC-113. 53pp. Restrepo, V.R., and Powers, J.E. 1999. Precautionary control rules in US fisheries management: specification and performance. ICES Journal of Marine Science 56: 846–852. 269  Rijnsdorp, A.D., Daan, N., and Decker, W. 2006. Partial fishing mortality per fishing trip: a useful indicator of effective fishing effort in mixed demersal fisheries. ICES Journal of Marine Science 63: 556-566. Rodgveller, C.J., Lunsford, C.R., Fujioka, J.T. 2008. Evidence of hook competition in longline surveys. Fishery Bulletin 106: 364-374. Rogers, J.B., and Pikitch, E.K. 1992. Numerical definition of groundfish assemblages caught off the coasts of Oregon and Washington using commercial fishing strategies. Canadian Journal of Fisheries and Aquatic Sciences 49: 2648-2656. Roff, D.A. 1984. The evolution of life history parameters in teleosts. Canadian Journal of Fisheries and Aquatic Sciences 41: 989-1000. Rose, G.A., and Leggett, W.C. 1991. Effects of biomass-range interactions on catchability of migratory demersal fish by mobile fisheries: An example of Atlantic cod (Gadus morhua). Canadian Journal of Fisheries and Aquatic Sciences 48: 843-848. Rosenberg, A.A. and S. Brault. 1993. Choosing a management strategy for stock rebuilding when control is uncertain. In Risk evaluation and biological reference points for fisheries management. Eds. Smith, S.J. , Hunt, J.J. and Rivard, D. Can. Spec. Pub. Fish. Aquat. Sci. 120. Rothchild, B.J. 1967. Competition for gear in a multiple-species fishery. ICES Journal of Marine Science 31(1) 102-110. Sadovy, Y. 2005. Trouble on the reef: the imperative for managing vulnerable and valuable fisheries. Fish and Fisheries 6: 167-185. Sainsbury, K. J., Punt, A. E., and Smith, A. D. M. 2000. Design of operational management strategies for achieving fishery ecosystem objectives. ICES Journal of Marine Science, 57: 731– 741. Schnute, J. 1987. A general fishery model for a size-structured fish population. Canadian Journal of Fisheries and Aquatic Sciences 44: 924-940. Schnute, J. and Richards, L.J. 1995. The influence of error on population estimates from catchage models. Canadian Journal of Fisheries and Aquatic Sciences 52: 2063-2077. Schnute, J., Kronlund, A.R. 2002. Estimating salmon stock-recruitment relationships from catch and escapement data. Canadian Journal of Fisheries and Aquatic Sciences 59: 433-449. Sinoda, M. 1981. Competition for baited hook in a multispecies fishery. Bulletin of Japanese Society of Scientific Fisheries 47(7): 843-848. Smith, M.K. and Kostlan, E. 1991. Estimates of age and growth of Ehu Etelis carbunculus in four regions of the Pacific from density of daily increments in otoliths. Fishery Bulletin 89: 461472. 270  Smith, A.D.M., Sainsbury, K.J., and Stevens, R.A. 1999. Implementing effective fisheriesmanagement systems –management strategy evaluation and the Australian partnership approach. ICES Journal of Marine Science 56: 967-979. Somerton, D.A., Kikkawa, B.S. A stock survey technique using the time to capture individual fish on longlines. Canadian Journal of Fisheries and Aquatic Sciences 52: 260-267. Stephens, A., and MacCall, A. 2004. A multispecies approach to subsetting logbook data for purposes of estimating CPUE. Fisheries Research 70(2-3): 299-310. Sudekum, A.E., Parrish, J.D., Radtke, R.L., and Ralston, S. 1991. Life history and ecology of large jacks in undisturbed, shallow, oceanic communities. Fishery Bulletin 89: 493-513. Swain, D.P., and Sinclair, A.F. 1994. Fish Distribution and Catchability: What Is the Appropriate Measure of Distribution? Canadian Journal of Fisheries and Aquatic Sciences 51: 1046-1054. Swain, D.P, and Wade, E.J. 2003. Spatial distribution of catch and effort in a fishery for snow crab (Chionoecetes opilio): tests of predictions of the ideal free distribution. Canadian Journal of Fisheries and Aquatic Sciences 60: 897-909. Ulrich, C., and Andersen, B.S. 2004. Dynamics of fisheries, and the flexibility of vessel activity in Denmark between 1989 and 2001. ICES Journal of Marine Science 61(3): 308-322. Walters, C. 1986. Adaptive management of renewable resources. The Blackburn Press, New Jersey. 374pp. Walters, C. 2003. Folly and fantasy in the analysis of spatial catch rate data. Canadian Journal of Fisheries and Aquatic Sciences 60(12): 1433-1436. Walters, C.J., and Bonfil, R. 1999. Multispecies spatial assessment models for the British Columbia groundfish trawl fishery. Canadian Journal of Fisheries and Aquatic Sciences 56: 601628. Walters, C.J., and Hilborn, R. 1978. Ecological optimization and adaptive management. Annual Review of Ecology and Systematics 9: 157-188. Walters, C.J., Hilborn, R. and Parrish, R. 2007. An equilibrium model for predicting the efficacy of marine protected areas in coastal environments. Canadian Journal of Fisheries and Aquatic Sciences 64: 1009-1018. Walters, C.J., and Martell, S.J.D. 2004. Fisheries Ecology and Management. Princeton University Press. Princeton, New Jersey. 399pp. Walters, C.J. and Parma, A.M. 1996. Fixed exploitation rate strategies for coping with effects of climate change. Canadian Journal of Fisheries and Aquatic Sciences 53: 148–158. Walters, C.J., and Pearse, P. 1996. Stock information requirements for management systems in commercial quota fisheries. Reviews in Fish Biology and Fisheries 6: 21-42. 271  Wilberg, M., Thorson, J.T., Linton, B., and Berkson, J. 2010. Incorporating Time-Varying Catchability into Population Dynamic Stock Assessment Models. Reviews in Fisheries Science 18(1): 7-24. Worm, B., Hilborn, R., Baum, J.K., Branch, T.A., Collie, J.S., Costello, C., Fogarty, M.J., Fulton, E.A., Hutchings, J.A., Jennings, S., Jensen, O.P., Lotze, H.K., Mace, P.M., McClanahan, T.R., Minto, C., Palumbi, S.R., Parma, A.M., Ricard, D. Rosenberg, A.A., Watson, R., and Zeller, D. 2010. Rebuilding Global Fisheries. Science 325: 578-585.  272  Appendix A: Supplementary information for Chapter 3 Tables Table A.1 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the average handling time per fish h = 0. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.21  5.17  -10.85  0.62  Kahala  13.27  6.16  -10.18  0.91  Kalekale  11.65  2.65  -9.90  0.83  Opakapaka  14.60  5.86  -11.70  0.46  Uku  13.23  6.12  -10.60  0.61  Ehu  12.70  3.71  -10.58  0.57  Onaga  14.06  6.31  -11.66  0.70  Lehi  11.88  6.31  -11.73  1.03  Gindai  10.12  6.54  -11.21  1.07  White ulua  13.33  3.56  -10.95  0.67  Table A.2 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 2 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.21  5.13  -10.80  0.62  Kahala  13.28  5.95  -10.15  0.91  Kalekale  11.65  2.63  -9.75  0.84  Opakapaka  14.58  5.80  -11.62  0.46  Uku  13.22  6.06  -10.52  0.61  Ehu  12.70  3.74  -10.51  0.58  Onaga  14.05  6.28  -11.59  0.70  Lehi  11.89  6.30  -11.70  1.02  Gindai  10.13  6.52  -11.17  1.07  White ulua  13.33  3.53  -10.90  0.67  273  Table A.3 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 5 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.21  5.08  -10.72  0.61  Kahala  13.29  5.62  -10.11  0.91  Kalekale  11.62  2.70  -9.48  0.84  Opakapaka  14.54  5.70  -11.50  0.45  Uku  13.20  5.96  -10.42  0.61  Ehu  12.69  3.81  -10.41  0.58  Onaga  14.03  6.24  -11.50  0.70  Lehi  11.91  6.27  -11.65  1.02  Gindai  10.13  6.49  -11.11  1.06  White ulua  13.33  3.50  -10.83  0.67  Table A.4 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 7 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.19  4.93  -10.40  0.57  Kahala  13.31  3.94  -9.81  0.93  Kalekale  11.44  5.08  -6.66  0.82  Opakapaka  14.40  5.20  -11.05  0.40  Uku  13.16  5.31  -10.06  0.57  Ehu  12.58  5.00  -9.89  0.63  Onaga  13.93  6.12  -11.11  0.66  Lehi  11.97  6.23  -11.46  1.01  Gindai  10.15  6.19  -10.90  0.99  White ulua  13.34  3.52  -10.54  0.67  274  Table A.5 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 9 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.10  6.84  -10.20  0.58  Kahala  13.17  6.37  -9.68  0.95  Kalekale  11.43  5.24  -6.76  0.85  Opakapaka  14.30  7.96  -10.86  0.40  Uku  13.03  8.10  -9.83  0.57  Ehu  12.45  7.34  -9.62  0.64  Onaga  13.85  9.08  -10.93  0.66  Lehi  11.94  9.02  -11.36  1.01  Gindai  10.09  9.08  -10.77  0.99  White ulua  13.22  5.20  -10.30  0.69  Table A.6 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 15 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.07  6.96  -7.95  0.53  Kahala  13.09  4.10  -6.86  0.70  Kalekale  10.93  10.17  -3.81  1.18  Opakapaka  14.09  4.41  -8.40  0.35  Uku  13.03  4.68  -7.60  0.54  Ehu  12.53  6.23  -7.58  0.62  Onaga  13.71  5.97  -8.62  0.56  Lehi  11.89  6.09  -9.22  0.98  Gindai  10.06  5.86  -8.68  0.91  White ulua  13.30  3.83  -8.24  0.62  275  Table A.7 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 20 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.08  6.97  -7.93  0.53  Kahala  13.08  4.16  -6.84  0.70  Kalekale  11.03  9.57  -4.30  1.19  Opakapaka  14.08  4.26  -8.36  0.34  Uku  13.03  4.61  -7.58  0.54  Ehu  12.53  6.22  -7.57  0.62  Onaga  13.71  5.93  -8.58  0.57  Lehi  11.89  6.03  -9.20  0.97  Gindai  10.05  5.82  -8.64  0.91  White ulua  13.31  3.82  -8.22  0.62  Table A.8 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 25 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.08  6.97  -7.88  0.53  Kahala  13.08  4.26  -6.80  0.71  Kalekale  11.14  8.60  -4.80  1.21  Opakapaka  14.08  4.05  -8.29  0.33  Uku  13.04  4.50  -7.52  0.54  Ehu  12.55  6.04  -7.55  0.63  Onaga  13.70  5.84  -8.51  0.58  Lehi  11.88  5.94  -9.14  0.95  Gindai  10.03  5.76  -8.56  0.91  White ulua  13.31  3.80  -8.17  0.61  276  Table A.9 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 30 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.09  6.87  -7.79  0.54  Kahala  13.08  4.42  -6.75  0.71  Kalekale  11.21  7.46  -5.19  1.22  Opakapaka  14.08  3.85  -8.19  0.34  Uku  13.05  4.35  -7.44  0.54  Ehu  12.58  5.63  -7.52  0.63  Onaga  13.70  5.71  -8.40  0.59  Lehi  11.87  5.85  -9.04  0.94  Gindai  10.02  5.71  -8.44  0.92  White ulua  13.32  3.78  -8.07  0.61  Table A.10 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 42 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.14  6.41  -7.56  0.57  Kahala  13.11  4.85  -6.63  0.76  Kalekale  12.03  2.40  -7.06  1.03  Opakapaka  14.09  3.84  -7.92  0.44  Uku  13.09  4.23  -7.20  0.59  Ehu  12.70  4.61  -7.42  0.68  Onaga  13.73  5.42  -8.14  0.67  Lehi  11.88  5.57  -8.78  0.90  Gindai  10.01  5.62  -8.11  0.98  White ulua  13.35  3.75  -7.81  0.63  277  Table A.11 Leading parameter estimates for each species from the multispecies assessment model from Chapter 3when the assumed h = 60 minutes per fish. Species  ln Bo  Κ  ln qo  Total stdev  Hapu'upu'u  12.15  5.85  -6.83  0.57  Kahala  13.22  6.13  -6.37  0.86  Kalekale  12.27  2.66  -7.20  1.28  Opakapaka  14.34  4.34  -7.93  0.91  Uku  13.35  3.04  -6.96  0.65  Ehu  12.97  2.63  -7.17  0.70  Onaga  13.83  4.55  -7.61  0.68  Lehi  11.92  5.67  -8.06  0.91  Gindai  10.05  5.73  -7.40  0.98  White ulua  13.36  3.40  -7.09  0.62  278  Figures  Figure A1 Traceplots of 20,000 random samples for per species unfished biomass, Boi, when it was assumed average handling time per fish, h, was equal to zero.  279  \  Figure A.2 Traceplots of 20,000 random samples for the per species recruitment compensation ratio, Κi, when it was assumed average handling time per fish, h, was equal to zero.  280  \  Figure A.3 Traceplots of 20,000 random samples for the per species catchability at low stock size, qoi, when it was assumed average handling time per fish, h, was equal to zero.  281  Figure A.4 Traceplots of 20,000 random samples for per species unfished biomass, Boi, when it was assumed average handling time per fish, h, was equal to two minutes per fish.  282  Opakapaka  Onaga  White Ulua  0  5000  10000  15000 20000  40  0  0  10  10  10  20  20  30  20  20  40  40  30  50  30  60  60  40  70  80  Hapu'upu'u  0  5000  10000  15000  20000  0  5000  Uku  20000  0  5000  10000 15000  20000  40 10  10  10  20  20  20  Κ  30  30  30  40  40  10000 15000  Lehi  50  50  Kahala  0  5000  10000  15000 20000  0  5000