Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Evaluating the impacts of current and alternative harvest strategies on salmon populations and fishing… Hawkshaw, Michael Andrew 2018

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

Item Metadata

Download

Media
24-ubc_2019_february_hawkshaw_michael.pdf [ 4.28MB ]
Metadata
JSON: 24-1.0373473.json
JSON-LD: 24-1.0373473-ld.json
RDF/XML (Pretty): 24-1.0373473-rdf.xml
RDF/JSON: 24-1.0373473-rdf.json
Turtle: 24-1.0373473-turtle.txt
N-Triples: 24-1.0373473-rdf-ntriples.txt
Original Record: 24-1.0373473-source.json
Full Text
24-1.0373473-fulltext.txt
Citation
24-1.0373473.ris

Full Text

EVALUATING THE IMPACTS OF CURRENT AND ALTERNATIVE HARVEST STRATEGIES ON SALMON POPULATIONS AND FISHING FLEETS USING THE SKEENA RIVER AS A CASE STUDY by  Michael Andrew Hawkshaw  B.Eng., The University of Victoria, 2002 M.Sc., The University of British Columbia, 2008  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Zoology)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  November 2018 © Michael Andrew Hawkshaw, 2018 ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:  Evaluating the impacts of current and alternative harvest strategies on salmon populations and fishing fleets using the Skeena River as a case study  submitted by Michael Hawkshaw in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Faculty of Graduate and Postdoctoral Studies (Zoology)  Examining Committee: Dr. Carl Walters Supervisor  Dr. Brett van Poorten Supervisory Committee Member Dr. Murdoch McAllister Supervisory Committee Member Dr. Peter Arcese University Examiner  Dr. Scott Hinch University Examiner   Additional Supervisory Committee Members:  Supervisory Committee Member   iii  Abstract Salmon fishery management is complicated, and involves a balancing act between the divergent objectives of stakeholders, requiring decisions with uncertain information while pressured by time constraints.  Unfortunately, the trade-offs between objectives are not always quantitatively evaluated, which means conflicts arising when conservation or harvest objectives are not met cannot be quantitatively balanced.  This thesis addresses several major challenges faced by salmon fisheries managers, including: balancing catch and escapement of multiple stocks in mixed stock fisheries; estimating run timing; and modeling in-season management processes.  Five new models were developed to explore these challenges, using the five species of Pacific salmon and steelhead returning to the Skeena River, as well as their fisheries and management system, as a case study.  First, a new harvest control rule (HCR) was developed using dynamic programming.  Second, an improved run reconstruction method was developed to estimate run timing and catchability in the fisheries of the Skeena River.  Third, a new application of linear programming was used to optimize harvest within the fishing season, and as a fisheries planning model.  Fourth, a Bayesian state-space model was developed to produce an improved in-season run size estimation model.  Finally, these models and outputs were combined into a closed loop simulation to test the outcomes of different HCRs.  The results and models developed in this thesis allow managers to evaluate the likely outcomes of different HCRs, improving their ability to make quantitative trade-offs between different objectives.  The tools developed in this thesis can be directly applied to the Skeena River management system, either piecemeal to improve particular elements of the system or integrated into the existing management process to provide the basis of a management strategy evaluation. More importantly, the tools and lessons learned can be generalized and applied to other salmon and non-salmon fisheries.   iv  Lay Summary Management of salmon fisheries is a complex balancing act between sometimes conflicting objectives of different stakeholders.  Transparency about the trade-offs required to balance different objectives, especially with respect to the cost in terms of harvest in meeting other objectives is an important part of communicating with those stakeholders.  In this thesis five modeling tools were built and used to understand and explain these tradeoffs.  The modeling tools were developed with the Skeena River salmon populations and fisheries as a case study.  The results of this thesis can be applied immediately on the Skeena River system or could be generalized and used in other similar fisheries.  The results of this thesis show the potential for immediate improvements to the management of the Skeena River fisheries by replacing some existing tools, as well as laying the foundation for a Management Strategy Evaluation (MSE), which is a more involved integration of models into the management planning process. v  Preface The work undertaken in this thesis developed from research questions posed by the Canadian Fisheries Research Network (CFRN), funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) with a goal of researching questions that are relevant to Canadian fisheries while simultaneously fostering collaboration between members of industry, government and academia.  The questions examined in this thesis were developed in partnership with representatives from the Skeena River gillnet fishery (UFAWU) and Fisheries and Oceans Canada (DFO): Joy Thorkelson (UFAWU) Steven Cox-Rogers (DFO), and David Peacock (DFO).  A version of Chapter 2 has been published as Hawkshaw, M. and Walters, C., 2015. Harvest control rules for mixed stock fisheries coping with autocorrelated recruitment variation, conservation of weak stocks, and economic well-being. Canadian Journal of Fisheries and Aquatic Sciences, 72(5), pp.759-766a0.  Dr. Walters and I developed the model, Dr. Walters programmed the model in Visual Basic and wrote a first draft of the paper, we both performed analyses and I wrote the final paper.  For chapter 3 Dr. Walters and I developed the model, Dr. Walters programmed the model in Visual Basic, and produced the first draft of the paper; we both performed analyses and edited the paper along with Dr. van Poorten.  A version of Chapter 4 has been submitted for publication (Hawkshaw, M. A. , Walters, C.J. and van Poorten, B.T., Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming).  I developed the model, performed analyses, and wrote the paper. My co-authors helped with editing and provided feedback on analyses. vi  For Chapters 5 and 6 I developed the models, performed the analyses, and wrote the papers.  Dr. Walters and Dr. van Poorten helped with editing and provided feedback on analyses. vii  Table of Contents  Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ........................................................................................................................ vii List of Tables ................................................................................................................................ xi List of Figures ............................................................................................................................. xiii Acknowledgements ....................................................................................................................xxv Dedication ................................................................................................................................. xxvi Chapter 1: Introduction ................................................................................................................1 1.1 Management of Salmon Fisheries ................................................................................... 1 1.2 Skeena River Salmon Fisheries ...................................................................................... 2 1.3 Closed Loop Simulation and Management Strategy Evaluations................................... 4 1.4 Thesis structure ............................................................................................................... 6 1.4.1 Chapter 2: Harvest control rules for mixed stock fisheries coping with autocorrelated recruitment variation, conservation of weak stocks, and economic well-being ..................... 6 1.4.2 Chapter 3: Reconstruction of run timing and harvest rates for Pacific salmon subject to gauntlet fisheries ................................................................................................................. 6 1.4.3 Chapter 4: Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming ............................................................................ 7 1.4.4 Chapter 5: Improved estimates of run timing and size for Skeena River sockeye using a Bayesian state-space model ........................................................................................ 7 viii  1.4.5 Chapter 6: Prediction of harvest management performance for a multispecies salmon fishery under alternative harvest control rules and in-season implementation approaches .... 8 Chapter 2: Harvest control rules for mixed stock fisheries coping with autocorrelated recruitment variation, conservation of weak stocks, and economic well-being .......................9 2.1 Introduction ..................................................................................................................... 9 2.2 Optimization formulation and methods ........................................................................ 12 2.3 Results ........................................................................................................................... 18 2.4 Discussion ..................................................................................................................... 21 Chapter 3: Reconstruction of run timing and harvest rates for Pacific salmon subject to gauntlet fisheries ..........................................................................................................................32 3.1 Introduction ................................................................................................................... 32 3.2 The packet-based run reconstruction method ............................................................... 34 3.3 Sensitivity of reconstructed entry pattern to errors and assumptions ........................... 39 3.4 Application to the Skeena River ................................................................................... 41 3.5 Extending the method to multiple migration routes and stocks .................................... 44 3.6 Discussion ..................................................................................................................... 46 Chapter 4: Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming ...........................................................................................66 4.1 Introduction ................................................................................................................... 67 4.2 Methods......................................................................................................................... 70 4.2.1 Case study: Skeena River salmon fisheries .............................................................. 70 4.2.2 Linear Programming Model ...................................................................................... 71 4.2.3 Retrospective analysis ............................................................................................... 74 ix  4.2.4 Simulation ................................................................................................................. 76 4.3 Results ........................................................................................................................... 78 4.3.1 Retrospective in-season modeling ............................................................................ 78 4.3.2 Simulation testing of in-season management ........................................................... 81 4.4 Discussion ..................................................................................................................... 82 Chapter 5: Improved estimates of run timing and size for Skeena River sockeye using a Bayesian state-space model .......................................................................................................102 5.1 Introduction ................................................................................................................. 102 5.2 Methods....................................................................................................................... 105 5.2.1 Modeling Details ..................................................................................................... 106 5.2.1.1 Area under the curve method (AUC) .............................................................. 106 5.2.1.2 Weighted average method............................................................................... 107 5.2.1.3 Bayesian state-space method .......................................................................... 108 5.2.2 Data ......................................................................................................................... 111 5.2.3 Prior Information .................................................................................................... 112 5.2.4 Retrospective analysis ............................................................................................. 114 5.2.5 Simulation ............................................................................................................... 114 5.3 Results ......................................................................................................................... 114 5.4 Discussion ................................................................................................................... 116 Chapter 6: Prediction of harvest management performance for a multispecies salmon fishery under alternative harvest control rules and in-season implementation approaches ..................................................................................................................................128 6.1 Introduction ................................................................................................................. 129 x  6.2 Methods....................................................................................................................... 133 6.3 Results ......................................................................................................................... 139 6.4 Discussion ................................................................................................................... 144 Chapter 7: Conclusion ...............................................................................................................179 7.1 Research Summary ..................................................................................................... 180 7.1.1 Chapter 2: Harvest control rules for mixed stock fisheries coping with autocorrelated recruitment variation, conservation of weak stocks, and economic well-being ................. 180 7.1.2 Chapter 3: Reconstruction of run timing and harvest rates for Pacific salmon subject to gauntlet fisheries ............................................................................................................. 181 7.1.3 Chapter 4: Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming ........................................................................ 182 7.1.4 Chapter 5: Improved estimates of run timing and size for Skeena River sockeye using a Bayesian state-space model .................................................................................... 183 7.1.5 Chapter 6: Incorporating uncertainty in assessment and management models using closed loop simulations to evaluate harvest control rules ................................................... 184 7.2 Future Directions ........................................................................................................ 185 7.3 Remarks ...................................................................................................................... 187 References ...................................................................................................................................188 Appendices ..................................................................................................................................207 Appendix A Supplementary table for Chapter 4: Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming ............................... 208 Appendix B Preliminary sensitivity analysis of Linear Programming Method ...................... 214  xi  List of Tables  Table 2.1.  Key performance measures for a range of alternative harvest control rules. ............. 25 Table 3.1.  A list of key parameters and variables. ....................................................................... 49 Table 3.2.  A list of key equations and descriptions. .................................................................... 50 Table 3.3.  Estimated parameters for normal distribution approximation to run timings for Skeena River salmon species. Dates are reported in Julian days (e.g. Sept 1st = 245). 95 % CI reported in brackets. ...................................................................................................................... 51 Table 3.4.  Values of the slope and intercept of lines fit to the time series of estimated 50% dates and corresponding p values. .......................................................................................................... 52 Table 4.1.  Summary of values used to parameterize the simulated populations and optimization........................................................................................................................................................ 88 Table 6.1.  Population parameters assumed for simulation models. ........................................... 153 Table 6.2.  Abbreviations used to distinguish between simulated HCRs. The format for abbreviation of HCR names is TARGET SPP[HCR TYPE], Constraint[Constraint type]. This allows the reader to see the main objective and constraints of a HCR. ...................................... 154 Table 6.3a.  Performance measures and outcomes for a suite of Harvest Control Rules (without timing constraint).  Bold values highlight the “best performing” strategy by performance measure. ...................................................................................................................................... 155 Table 6.4.  Mean Sockeye Yield outcomes under different error regimes. ................................ 157 Table 6.5.  Standard Deviation of Sockeye Yield outcomes under different error regimes. ...... 158 Table 6.6.  Chum Escapement outcomes under different error regimes  (% years below SGEN)...................................................................................................................................................... 159 xii  Table 6.7.  Steelhead Escapement outcomes under different error regimes (% years below SGEN). ........................................................................................................................................ 160 Table A.1.  Salmon populations of the Skeen River aggregated to different levels with associated population parameters and data sources. Data sources are: 1) Walters et al. (2008); 2) Korman and English (2013); and 3) Beacham et al. (2014). .................................................................... 208  xiii  List of Figures Figure 2.1.  (a) Optimum escapement targets for Max. Profit objective function with stock size for a range of Wt (from Wt = -2 in the lowest lines to Wt = 2 in the highest lines) and (b) optimum escapement targets (S**(Wt))with the assumptions that the current productivity implied by the last recruitment anomaly (Wt) will persist indefinitely (grey line is Hilborn approximation of optimum escapement, and the black line is the stochastic dynamic optimum escapement showing diverging prediction of optimum escapement as the Wt decreases). ............................................. 26 Figure 2.2.  (a) Simulated and (b) approximated (with eq. 14) optimum harvest rates at different stock size generated using the Max. Utility objective function with varying values for Wt. The highest curve was generated with the highest value of Wt and the less steep curves with lower values of Wt. Notice that even at the lowest Wt values the curve still rapidly climbs from zero exploitation rate to the conservation constraint. ........................................................................... 27 Figure 2.3.  Max. Utility policy (grey line), fixed escapement policy (black line), and current DFO policy (dashed line), shown with historical exploitation rates for Skeena sockeye salmon........................................................................................................................................................ 28 Figure 2.4.  (a) A simulated pattern of recruitment anomalies, (b) exploitation rates (black line) and stock size (dashed line) generated by applying the Max. Profit harvest control rule (HCR), and (c) exploitation rates (black line) and stock size (dashed line) generated by applying the Max. Utility HCR.......................................................................................................................... 29 Figure 2.5.  Changes in income (solid line) and log Utility (dashed line) associated with different maximum allowable exploitation rates. ........................................................................................ 30 Figure 2.6.  Max. Utility optimum policy rule (solid line) and rectilinear rule (dashed line) on a phase plot. ..................................................................................................................................... 31 xiv  Figure 3.1.  Gauntlet fisheries can be represented by entry timing curve (a), spatial fishery pattern with each fishery opening covering a box of times and distances along the migration route (b), and resulting exit timing curve of fish escaping the inshore end of the gauntlet (c).  Migration paths of two simulated packets of fish shown as dotted lines in (b); packet (1) is impacted by fishery opening 3, and packet (2) is not impacted by fishing.  Example entry timing pattern constructed as a normal curve with sinusoidal multiplier that might, for example, represent effects of tidal or wind currents on arrival timing at the gauntlet. ................................ 53 Figure 3.2.  Error pattern in run reconstruction for a simulated population (true timing shown as fine line) with true mean net ground speed 40km/day, when reconstruction method is applied while assuming mean net ground speed 35 km/day.  Note how estimation error is most severe around the time of the long fisheries (boxes labeled 2,3 in Figure 3.1 (b)). ................................. 54 Figure 3.3.  Impact of spatial effort concentration within fishing areas on reconstructed daily run size.  For this simulation, fishing effort declined exponentially from 1.5 times average at the seaward boundary of each fishing area to 0.5 times average at the landward boundary, after the first day of the fisheries in Figure 3.1 lasting longer than 1 day. ................................................. 55 Figure 3.4.  Geographic location and boundaries of the Statistical Area 4 fisheries (from Walters et al. 2008). ................................................................................................................................... 56 Figure 3.5.  Reconstructed Skeena River run timing patterns.  For each species of salmon the distributions of calculated 50% dates (a) and widths of the reconstructed returns (b) are shown as both histograms (bars) and normal approximations of the distribution (red line).   The yearly estimates of the mean return date are presented in (c). ................................................................. 57 Figure 3.6.  Reconstructed Skeena River run timing patterns. ..................................................... 58 xv  Figure 3.7.  Catchability of sockeye salmon in gillnet fisheries, panels show the distributions of the logarithms of the estimated catchabilities for the different fishing areas (see Figure 3.4) over the weeks of the fishing season. .................................................................................................... 59 Figure 3.8.  Catchability of sockeye salmon in seine fisheries, panels show the distributions of the logarithm of estimated catchabilities for the different fishing areas (see Figure 3.4) over the weeks of the fishing season........................................................................................................... 60 Figure 3.9.  Catchability of sockeye salmon by area, panels show the distributions of the logarithm of the catchability by area (see Figure 3.4) for gillnet (upper) and seine net (lower) fisheries. ........................................................................................................................................ 61 Figure 3.10.  Catchability by week, panels show the distributions of the logarithm of the estimates of catchability of sockeye salmon by week for gillnet (upper) and seine net (lower) fisheries. ........................................................................................................................................ 62 Figure 3.11.  Covariation in mean and spread of run timing for the Skeena.  The relationship between the spread of the run (SD) and the 50% date of the return by species. ........................... 63 Figure 3.12.  Annual proportion of total sockeye catch taken after the estimated date of 50% entry to the outside fishing area (there were no fisheries in 1999 and 2005). .............................. 64 Figure 3.13.  Example of a multiple migration route, multiple stock case.  Fish from stock 1 follow two migration routes to a single escapement monitoring destination, are taken in two shared fishing areas  (1, 4) and two route-specific fishing areas (2,3).  Fish of stock 2 are taken in the shared area 1, and in a distinct “terminal” fishing area 5.  Daily escapements E1,t and E2,t are estimated in separate monitoring programs, while only total catches are available for fishery openings in the five areas (route and stock composition are unknown for the shared areas 1 and 4). .................................................................................................................................................. 65 xvi  Figure 4.1.  Distribution of historic peak of return of all species of salmon to the Tyee test fishery (1956-2007)................................................................................................................................... 89 Figure 4.2.  Weekly maximum observed harvest rates (1982-2007).  Boxplots show the distribution of observed weekly harvest rates, the red points are the maximum observed values used as an economic constraint Ueconi. ........................................................................................ 90 Figure 4.3.  Species specific annual recruitment deviates used in retrospective analysis. ........... 91 Figure 4.4.  Boxplots of stock specific Ricker a parameters (upper) and histograms of associated Umsy values (lower) used in the simulations presented by species. ............................................... 92 Figure 4.5.  Patterns of observed and predicted optimal weekly harvest rates for the Skeena River mixed species Pacific salmon fishery. Panel (a) shows observed distribution of weekly harvest rates from 1982-2007. Panels (b-c) show the distributions of optimal weekly harvest rates suggested by retrospective analysis, using Umax for coho, chum, chinook, and pink salmon species as well as Uecon from the weekly maximum observed harvest rates (1982-2007) assuming: (b) no steelhead allocation constraint; and (c) maximum allowable steelhead harvest rate (HR) of 3%.  Panel (d) summarizes the difference in outcome between historical and retrospective fishing patterns under the different scenarios (1 no steelhead allocation constraint, and 2 steelhead constrained to no more than 3% HR). Dark lines represent median values, boxes represent the interquartile range and whiskers represent the full range. ....................................... 93 Figure 4.6.  Pattern of optimum weekly harvest rate from retrospective analysis (a), using Umax as a conservation constraint and Uecon from the weekly maximum observed harvest rates (1982-2007), without an allocation constraint for steelhead.  Panel (b) shows the annual sockeye harvest by brood year with the red line representing the historical harvest and the black the optimized xvii  retrospective harvest.  Panel (c) shows the annual difference between retrospective and optimized harvest, while panel (d) summarizes the overall increase in sockeye harvested. ........ 94 Figure 4.7.  Pattern of optimum weekly harvest rate from retrospective analysis (a), using Umax as a conservation constraint and Uecon from the weekly maximum observed harvest rates (1982-2007), with an allocation constraint of no more than 3% harvest rate for steelhead.  Panel (b) shows the annual sockeye harvest by brood year with the red line representing the historical harvest and the black the optimized retrospective harvest.  Panel (c) shows the annual difference between retrospective and optimized, while panel (d) summarizes the overall decrease in sockeye harvested. ...................................................................................................................................... 95 Figure 4.8.  Impact of different conservation constraints applied to simulated fisheries using retrospective recruitment deviates, and run timing patters (1956-2007).  In both cases Ueconi constraints were applied based upon historic observed maximum weekly HRs. Panel (a) shows the impact of different levels of conservation constraint applied to bycatch species on average sockeye catch where the conservation constraint is expressed as a harvest rate cap of between 0 and 100% allowed on the by-catch species. Panel (b) shows the impact of different levels of conservation constraint on yield where each bycatch stock is constrained to have an escapement greater than or equal to its conservation goal.  In this figure the escapement goal is calculated as a percent of each stock’s Smsy.  (in panel (b) the red line represents the % of years that would have been closed if this constraint had been applied). .................................................................. 96 Figure 4.9.  Average yield in the mixed stock fishery assuming Uecon constraints on weekly harvest, Umsy as conservation constraints on all stocks, and varying the allocation constraint for steelhead between of 0 and 100% allowable harvest rate. ............................................................ 97 xviii  Figure 4.10.  Effect of using different escapement targets as conservation constraints on the non-target stocks on yield at different levels of aggregation.  Each dot represents the average outcome of multiple simulations of many stocks with management controls being applied at different levels of aggregation. (Black dots are aggregated to species level, blue to management unit or conservation unit level, and red to stock level).  The top pane (a) shows the effect on average yield in the fishery of applying conservation constraints based upon escapement targets.  The center pane (b) shows the effect of different escapement targets as conservation constraint on fishing opportunity measured as proportion of seasons closed to fishing, and the bottom pane (c) shows the impact of escapement based conservation constraints on the achieved escapements (here low escapement is considered <10% Smsy). ....................................................................... 98 Figure 4.11.  Trade-off between conservation outcomes and yield for mixed stock fisheries simulated at different levels of aggregation with an escapement based conservation constraint. Each dot represents that average outcome of multiple simulations of many stocks with management controls being applied at different levels of aggregation. (Black dots are aggregated to species level, blue to management unit or conservation unit level, and red to stock level). .... 99 Figure 4.12.  Effect of using different harvest rates as conservation constraints on non-target stocks on yield at different levels of aggregation. Each dot represents the average outcome of multiple simulations of many stocks with management controls being applied at different levels of aggregation. (Black dots are aggregated to species level, blue to management unit or conservation unit level, and red to stock level).  The first pane shows the effect of different harvest rates as conservation constraint on fishing opportunity.  The second panel shows the effect on average yield in the fishery of applying conservation constraints based upon harvest xix  rates, and the final panel shows the impact of harvest rate conservation constraints on the achieved escapements (here low escapement is considered <10% Smsy). ................................ 100 Figure 4.13.  Trade-off between conservation outcomes and yield for mixed stock fisheries simulated at different levels of aggregation with harvest rates applied as conservation constraints. Each dot represents the average outcome of multiple simulations of many stocks with management controls (i.e. constraints) being applied at different levels of aggregation. (Black dots are aggregated to species level, blue to management unit or conservation unit level, and red to stock level). ............................................................................................................................. 101 Figure 5.1.  Distribution of run timing of Skeena River sockeye, a time series of 50% dates (solid points) and duration of the sockeye return (bars show the 95% distribution of the sockeye return in any year) 1982-2007. .............................................................................................................. 121 Figure 5.2.  Skeena River sockeye stock-recruitment relationship.  Ricker parameters and spawner and return estimates presented in Walters et al. 2008. ................................................. 122 Figure 5.3.  Sibling relationship for Skeena River sockeye salmon.  Sibling relationship is calculated as ln(Rt)=a+b*log (Rthree year oldst-1) +εt where a=11.48 and b=0.28. ................... 123 Figure 5.4.  Distribution of run timing of Skeena River sockeye.  Panel (a) shows a histogram of dates by which half of the return has passed the test fishery, panel (b) shows standard deviation of a normal curve fit to sockeye catches at the test fishery (n=51). ........................................... 124 Figure 5.5.  Retrospective performance of the different in-season run size estimation models.  The boxplots show the proportion difference between the reconstructed abundance and in-season run size estimates generated with the different models.  Estimates are generated at 10 different time steps through the 26 fishing seasons for which the models were run.  Panel (a) shows the xx  performance of the Bayesian model, panel (b) shows the Walters-Cunningham model, and panel (c) shows the area under the curve model. .................................................................................. 125 Figure 5.6.  Time series and distribution of Tyee test fishery annual catchability.  Panel (a) shows the time series of Tyee catchability calculated by comparing the total annual catch in the test fishery to the total reconstructed annual return.  Panel (b) shows the histogram of these catchabilities that was used as a prior for the Bayesian model. .................................................. 126 Figure 5.7.  Performance of the three models when confronted with a small early run.  The boxplots show the proportion difference between the simulated abundance and run size estimates generated with the different models.  Estimates are generated at 10 different time steps through 50 fishing seasons for which the models were run.  Data was simulated with a return of 600,000 sockeye arriving 20 days early (the peak of the sockeye run arrived between assessment periods 3 and 4).  Panel (a) shows the performance of the Bayesian state-space model, panel (b) shows the Walters-Cunningham model, and panel (c) shows the area under the curve model with the proportion differences shown on the log scale. .......................................................................... 127 Figure 6.1.  Model structure for evaluating harvest control rules incorporating multiple types of uncertainty. Escapement, in-season abundance, and application of weekly fishery were all modeled with errors. ................................................................................................................... 161 Figure 6.2.  Distributions of observed peak day of migration past Tyee test fishery by species showing migration timing overlap. The box and whisker plots show the distribution of escapement outcomes in every year of the forward simulation, the bar near the center of the box shows the median value, the box shows the interquartile range and the whiskers show the most extreme data point which is no more than 1.5 times the length of the box away from the box. (R Core Team 2013). ....................................................................................................................... 162 xxi  Figure 6.3.  Average sockeye yield for all surveyed HCRs. Green bars correspond to management scenarios where sockeye harvest was not constrained until after the observed peak of the return, blue bars correspond to management scenarios when sockeye harvest was constrained until after the peak of the run has been observed. Table 6.2 has a listing of the HCRs tested corresponding to the codes on the x-axis.......................................................................... 163 Figure 6.4.  Standard deviation of sockeye yield for all surveyed HCRs. Green bars correspond to management scenarios where sockeye harvest was not constrained until after the observed peak of the return, blue bars correspond to management scenarios when sockeye harvest was constrained until after the peak of the run has been observed. Table 6.2 has a listing of the HCRs surveyed corresponding to the codes on the x-axis. ................................................................... 164 Figure 6.5.  Average utility of sockeye yield for all surveyed HCRs. Green bars correspond to management scenarios where sockeye harvest was not constrained until after the observed peak of the return, blue bars correspond to management scenarios when sockeye harvest was constrained until after the peak of the run has been observed. Table 6.2 has a listing of the HCRs surveyed corresponding to the codes on the x-axis. ................................................................... 165 Figure 6.6.  Escapement trajectories for chum salmon for HCRs that initiated harvests before the peak of the sockeye return. The box and whisker plots show the distribution of escapement outcomes in every year of the forward simulation, the bar near the center of the box shows the median value, the box shows the interquartile range and the whiskers show the most extreme data point which is no more than 1.5 times the length of the box away from the box. (R Core Team 2013). The green horizontal line corresponds the SMSY value for chum, while the red horizontal line corresponds to a proxy for SGEN. ........................................................................ 166 xxii  Figure 6.7.  Escapement trajectories for chum salmon for HCRs constrained to initiate harvests after the peak of the sockeye return. The box and whisker plots show the distribution of escapement outcomes in every year of the forward simulation, the bar near the center of the box shows the median value, the box shows the interquartile range and the whiskers show the most extreme data point which is no more than 1.5 times the length of the box away from the box. (R Core Team 2013). The green horizontal line corresponds the SMSY value for chum, while the red horizontal line corresponds to a proxy for SGEN. ........................................................................ 167 Figure 6.8.  The average yield over the simulation period for the five (5) best performing HCRs...................................................................................................................................................... 168 Figure 6.9.  Median utility of the five (5) best performing HCRs. ............................................. 169 Figure 6.10.  Mean escapement by species for the five (5) best performing HCRs. The green horizontal line corresponds the SMSY value for the species, while the red horizontal line corresponds to a proxy for SGEN. ................................................................................................. 170 Figure 6.11.  Sockeye Yield trade-off figures. Scatter plots show the different sockeye harvests obtained in the years of the forward simulations. Grey dotted lines are the 1:1 lines, points above the line indicate that the HCR on the y-axis had higher yield than the current HCR. The blue lines show contours around 20%, 40%, 60%, and 80% of the data points. ................................ 171 Figure 6.12.  Chum escapement outcomes. Boxplots show chum escapements in the years of the forward simulations. The box and whisker plots show the distribution of escapement outcomes in every year of the forward simulation, the bar near the center of the box shows the median value, the box shows the interquartile range and the whiskers show the most extreme data point which is no more than 1.5 times the length of the box away from the box. (R Core Team 2013). ....... 172 xxiii  Figure 6.13.  Chum escapement trade-off plots showing the different chum escapements in the years of the forward simulations. Grey dotted lines are the 1:1 lines, points above the line indicate that the HCR on has higher escapement than under the current HCR. The blue lines show contours around 20%, 40%, 60%, and 80% of the data points. ........................................ 173 Figure 6.14.  Scatter plots showing sockeye yield and chum escapement in the years of the forward simulations. Labels indicate the harvest control rule where the harvest and escapement outcomes are being compared to one another. ............................................................................ 174 Figure 6.15.  Escapement trajectories for chum salmon for the five (5) best performing HCRs. The box and whisker plots show the distribution of escapement outcomes in terms of % of SEQ in every year of the forward simulation. The grey horizontal line corresponds the SEQ value for Chum.  The text above each plot indicates the HCR being evaluated in each panel. ................. 175 Figure 6.16.  Boxplots showing the distribution of percent errors in recruitment parameter estimates and derived management parameters for each species across all HCRs and error level combinations. Panel (a) shows the Ricker a parameter estimates, panel (b) shows the Ricker b parameter estimates (on a log scale), panel (c) shows the estimates of UMSY, panel (d) shows the estimates of SMSY. ....................................................................................................................... 176 Figure 6.17.  Ricker a parameter estimate error box and whisker plots separated by escapement observation error regime. The red line corresponds to the true Ricker a value. ......................... 177 Figure 6.18.  Ricker b parameter estimate error box and whisker plots separated by escapement observation error regime. The red line corresponds to the true Ricker b value. ......................... 178 Figure B.1.  Distribution of exploitation rates by stock for (a) optimized linear programing algorithm, and (b) application of fixed weekly Ut derived from retrospective analysis.  The red xxiv  dots show UMAX and the green dots show UMSY for each stock.  The difference in total catch by species across all years of the retrospective analysis is shown in panel (c). ......................... 215 Figure B.2.  Changes to the LP solution for weekly Ut due as a result of changing the constraints of linear programing optimization by assuming a 10% CV in Ricker a parameters (a), bars are the retrospective optimum Ut values derived with misidentified Ricker a parameters, the red dots optimum median weekly Ut values.  The stock specific changes in harvest as a result of the changes to optimum weekly Ut are presented in the second panel (b). ...................................... 217 Figure B.3.  Effect of implementation errors on annual catches (all species) assuming a 10% implementation error when applying the optimum Ut targets (a).  The stock specific changes in harvest as a result of the error implementing the optimum weekly Ut are presented in the second panel (b) as number of salmon and in the third panel (c) as the % difference in catch. ............. 219  xxv  Acknowledgements  I offer my thanks to the faculty, and my fellow students at UBC especially Carl and Brett. xxvi  Dedication  For Meghan    1  Chapter 1: Introduction 1.1 Management of Salmon Fisheries Pacific salmon fisheries management is a complicated problem with fisheries catching a mix of species and stocks and a variety of stakeholders with conflicting interests in harvest, conservation, and allocation of catch.  Management processes strive to balance these interests and often fail.  Management processes also involve a mixture of participants and objectives.  Meeting these conflicting objectives is a perennial challenge for management.  International treaties call for the management of fisheries to maximize harvest subject to conservation needs (e.g. Pacific Salmon Treaty 1985), with an emphasis on the precautionary principle (UN General Assembly 1982).  Canadian fisheries are required by law, and policy, to first prioritize conservation, then First Nations’ Food, Social, and Ceremonial (FSC) fisheries, and finally, recreational or commercial harvest (Fisheries Act 1985, R v Sparrow 1999, DFO 2005, Holt and Bradford 2011).  Implementation of fisheries thus becomes a complicated process of balancing desired outcomes and uncertainty. However, the trade-offs between objectives are often neither considered quantitatively, nor adequately communicated.  This leads to either conservation or harvest targets not being met (Deroba and Bence 2008, Walters et al. 2008, Cohen 2012a, Cohen 2012b, Cohen 2012c).  This speaks to a need for quantitative tools that consider and communicate trade-off between conservation and harvest outcomes within and across species and stocks.    Pacific salmon are typically fished in areas where they are concentrated as part of the spawning migration from the ocean to freshwater, these migration corridors are used by different stocks and species.  The fisheries targeting Pacific salmon typically exploit a mix of stocks that have 2  different, but overlapping, return timing and ability to sustain a harvest.  These fisheries are typically managed as aggregate stocks with overall escapement or harvest rate targets (Walters 1975, Hilborn and Walters 1992, Schnute et al. 2000, Walters et al. 2008).  The desire to manage first for conservation has led to the development of stock specific targets (DFO 2005, Holt et al. 2009, Decker and Irving 2013, Korman and English 2013).  Stock specific targets introduce additional complexity to these fisheries.  Managers must not only consider the impact of the fisheries on the aggregate, but also on the component stocks.  Managers need tools to balance the total yield of the mixed stock fishery, given weak-stock constraints.  Managers also need to be able to understand and communicate the trade-offs associated with total yield and conservation impact on the component stocks.  The challenges faced by mixed stock fisheries have been studied worldwide, and different methods have been proposed to meet these challenges (Larkin 1977, Murkowski and Finn 1986 & 1988, Vinther et al. 2004).  Most authors agree that balancing conservation and harvest objectives can be achieved through simple control rules for the single stock fisheries (Allen 1973, Walters 1975, Deriso 1985, Hall et a l. 1988, Walters and Parma 1996).  The challenge is in designing these HCRs to manage the harvest of several different stocks, while optimizing fishery performance against several different objectives.     1.2 Skeena River Salmon Fisheries In order to explore the problems of mixed stock fisheries a case study was needed, and the Skeena River was chosen.  Skeena River salmon fisheries were a major contributor to the regional and provincial economy of British Columbia (BC).  The Skeena River is the second largest in BC and is the second largest producer of salmon.  Recently, the Skeena has become an 3  area of conservation concern.  Historical exploitation of the Skeena salmon stocks has led to a situation where some stocks are at low levels.  While salmon stocks that are at low levels are not necessarily in danger of extinction or extirpation, confusion about this distinction, uncertainty about the application of stock specific escapement goals, and different stakeholder opinions about how to balance the risk of extirpation and the risk to the fisheries has led to conflicts over the conduct of the fisheries.  Commercial fishing interests, advocates for recreational fishing, and environmental groups all have different perspectives on the correct balance.  More recently, continued declines in returns of sockeye salmon (the main commercial catch target), combined with policy changes in the Department of Fisheries and Oceans (DFO), create the need for a re-examination of the Skeena River fisheries.  The current focus on conservation outcomes is being addressed in DFO policies, though not in a manner favorable to continued use of the resource by a commercial fishery (DFO 2017).    The Skeena River has a long history of being used as a case study to test new management techniques and harvest policies. From the 1950s to present, many of the management techniques that are in use today have used the Skeena River as a case study (i.e. use of harvest management “strategies” for coping with natural variability in production, warnings of overharvest of weaker stocks in mixed‐stock fisheries, and systems for in‐season updating and assessment of stock size).  Using the Skeena River as a case study again may lead to new solutions for the problem of competing user groups trying to participate in a mixed stock fishery.  Recent work to verify and collect the catch, effort, and escapement from a long time series of test fishery data has provided a comprehensive data set that enables the development of a suite of models (Walters et al. 2008, Korman and English 2013, DFO 2016a, DFO 2016b).  The Skeena River is host to five species 4  of Pacific salmon and a large population of anadromous rainbow trout (or steelhead (Oncorhynchus mykiss)).  The commercial fisheries target sockeye (O. nerka) and pink salmon (O. gorbuscha). Coho (O. kisutch), chinook (O. tshawytscha), chum (O. keta) salmon and steelhead are also intercepted and are the main targets for recreational anglers (Walters et al. 2008).  The Skeena River is typical of a larger salmon river, as a result the methods and results explored in this thesis can be extended to support fisheries management on other watersheds. 1.3 Closed Loop Simulation and Management Strategy Evaluations Management Strategy Evaluation (MSE) is a considered a state of the art tool in fisheries; it not only looks at the HCR used to determine how to exploit a fishery, but also the methods and types of data collected, the analyses used to manage the harvest control rule (HCR), and the management structure that implements them (Butterworth and Bergh 1993, Punt 2006, Butterworth et al. 2007, Punt et al. 2016).  An MSE is not a prescriptive tool that delivers an “optimal” management decision, but instead one that provides decision makers with the information on which to base a rational decision (Smith 1994).  MSE arises from the application of decision analysis to fisheries assessment and management (Smith et. al. 1999).   Elements of adaptive management (Hilborn and Walters 1992), the development of management procedures (Butterworth and Punt 1999), and risk assessment are incorporated into an MSE (Smith et. al. 1999). According to Smith (1994) MSE involves several key ingredients: • Clear management objectives; • Quantifiable performance measures for each objective; • Identification of alternate management strategies or decision options; and • A way to calculate the performance criteria for each strategy. 5  There are typically three performance measures (or metrics) used when evaluating management strategies: (1) maximizing catch over some time period; (2) minimizing risk to the resource; and (3) maximizing industrial stability (Smith 1994, Butterworth and Punt 1999, Hall and Mainprize 2004, Punt 2006).  An MSE can be used to quantify the likelihood that a HCR or management strategy will meet the management goals (Hall and Mainprize 2004).  There are several examples where an MSE has allowed the development of HCRs and management procedures that are robust to uncertainty (Punt and Donovan 2007, Punt et al. 2016).  In contrast to MSE, a closed loop simulation is a set of sub-models assembled in such a way as to simulate a complete fishing system, including data collection and decision making processes, and is a prerequisite for conducting an MSE.  An MSE is a multi-stakeholder process that needs to be worked through with resource users and the management system for successful development (Punt et al. 2016), but the underlying modeling tools needed for an MSE can be developed outside of this process. A closed loop simulation evaluates the likely performance of a HCR in the context of the management system, the management tools available, and the expected variability in the system.  The management system is modeled over several time-scales relevant to the management system. The Skeena River salmon management system seeks to balance economic, social, and conservation objectives for six species.  Building a closed loop model to represent processes and different sources of error across multiple systems is necessary to understand the cumulative effects of data collection, in-season management tools, HCRs, and natural variability in the populations. (Hilborn and Walters 1992, Walters and Martell 2004, Butterworth 2007, Punt et al. 2016).   6  1.4 Thesis structure The work done in this thesis builds modeling tools to support an MSE process for Skeena River salmon fisheries.  First, by developing a HCR using dynamic programing, second, by characterizing the return timing of the salmon populations of the Skeena River, and finally, by building in-season models to manage the Skeena River fisheries, which are combined into a closed loop simulation, with application to some candidate HCRs and a set of simple performance measures. 1.4.1 Chapter 2: Harvest control rules for mixed stock fisheries coping with autocorrelated recruitment variation, conservation of weak stocks, and economic well-being In the second chapter, dynamic programming was used to construct a HCR.  The HCR was designed to be robust to persistent changes in productivity and was limited by exploitation rate constraints that prevent extinction of non-target weak stocks.  The dynamic programing algorithm seeks an economic objective that recognizes moderate income to be more important to fishermen than maximization of total profit.  This HCR becomes a candidate rule whose performance was tested in the closed loop simulation model developed in Chapter 6.  1.4.2 Chapter 3: Reconstruction of run timing and harvest rates for Pacific salmon subject to gauntlet fisheries  In the third chapter, a novel method for reconstructing entry timing patterns for salmon runs entering gauntlet fisheries was developed.  The method was based on dividing the incoming run into many small packets with variable entry time and net ground speed packets.  The new run reconstruction method was applied to generate run timing patterns for Pacific salmon populations migrating to the Skeena River in northern British Columbia.  The run timing patterns discovered 7  using this method are used to parameterize the linear programming (Chapter 4), run timing (Chapter 5), and closed loop simulations (Chapter 6) in the following chapters. 1.4.3 Chapter 4: Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming  A linear programming (LP) model is a powerful tool for rapidly maximizing an objective function subject to a variety of constraints.  In the fourth chapter, an LP model for in-season management of complex fisheries was developed to maximize the catch in the multi-species, mixed stock Skeena River salmon fisheries.   The model optimizes the weekly opening patterns that maximize the value of fish caught by fishing fleets taking a mixture of fish stocks, while preventing overexploitation of less productive species and stocks.  This analysis shows in-season management tactics developed from retrospective linear programming optimization can result in increased catches on the Skeena River, while restricting exploitation of non-target weak stocks.  This analysis also calculates the costs to the fishery of reductions in fishing opportunity in terms of risk of extirpation of weak co-migrating stocks and allocation priorities quantifying the trade-off between extirpation risk, allocation, and harvest.  The linear programming model is incorporated into the closed loop simulations (Chapter 6) as a sub-model to represent the in-season management process. 1.4.4 Chapter 5: Improved estimates of run timing and size for Skeena River sockeye using a Bayesian state-space model  In the fifth chapter, improved in-season estimates of abundance are made by developing a Bayesian state-space model that quantitatively incorporates prior knowledge about the run timing and stock size from several sources, including historical run timing, stock-recruitment data, and previous year classes.  The model was developed and tested with both simulated and Skeena 8  River data and was shown to be an improvement over the model currently used on the Skeena River.  This modeling work was also used to characterize the bias and precision of the in-season estimation of abundance in the closed loop simulation model of Chapter 6. 1.4.5 Chapter 6: Prediction of harvest management performance for a multispecies salmon fishery under alternative harvest control rules and in-season implementation approaches The sixth chapter of this thesis developed a closed loop simulation model consisting of nested operating models.  This model was built to explore the interaction between fisheries management strategies and the dynamics of several species of Pacific salmon. This model explores the potential impacts of different HCRs, and in-season management practices, on the mixed species Skeena River salmon fishery.  The simulation model was built to be used as part of an MSE process to explore likely outcomes of different HCRs on the Skeena River in terms of escapement and yield in fisheries.  The closed loop simulation model incorporates the HCR developed in Chapter 2, the run timing information developed in Chapter 3, the linear programming model developed in Chapter 4 and the run size models developed in Chapter 5.  The simulation model exposed the non-intuitive and interacting effects of management decisions, HCRs, errors in observations, and management systems on outcomes in a mixed stock salmon fishery.  The current HCR in use on the Skeena River was compared to a set of candidate HCRs and the differences in outcomes explored. Different types of errors were shown to have different impacts on the ability of the management system to maximize yield.   9  Chapter 2: Harvest control rules for mixed stock fisheries coping with autocorrelated recruitment variation, conservation of weak stocks, and economic well-being Dynamic programming is used to construct harvest control rules that account for persistent changes in productivity, exploitation rate constraints that prevent extinction of non-target weak stocks, and an economic objective that recognizes moderate income to be more important to fishermen than maximization of total profit. Persistent productivity changes imply downward adjustment in spawning abundance targets during periods of low productivity, while conservation constraints simply imply upper limits on exploitation rate at high stock sizes. When the economic objective is to maximize the logarithm of net income (diminishing marginal utility or welfare from higher incomes), the optimum control rule shifts from a fixed escapement form to a curve where exploitation rate increases smoothly from zero at the minimum stock size that can be fished profitably to the upper limit set by a conservation constraint. This policy is not the fixed-exploitation rate form that has been historically suggested as a way of stabilizing harvests without major loss in profits. Application of harvest control rules constructed using dynamic programming in a mixed stock salmon fishery in fact results in total profits close to those obtainable with fixed escapement policies but without the frequent low catches or closures implied by fixed escapement policies. 2.1 Introduction In recent years Canada and other jurisdictions have adopted strongly worded policies for conservation and management of fish stocks. Canadian policies for wild Pacific salmon and other species (e.g., DFO 2005; Holt and Bradford 2011) aim to protect habitat and genetic diversity 10  while allowing for sustainable harvesting. Implementation of these policies has involved a “conservation first” principle, with the need to meet spawning abundance objectives placed ahead of objectives for harvesting and allocation among stakeholders. Management staff of Fisheries and Oceans Canada (DFO) have been responding to these policies by using what have historically been called “fixed escapement” harvest policy rules (i.e., rules that allow no harvesting when stock size is below a biological escapement goal and take the surplus above this goal when stock size is larger). This type of harvest control rule (HCR) tends to result in more frequent fisheries closures and can result in economic harm (see review of harvest policy rule options in Deroba and Bence 2008). In a case study on the Skeena River, a recent planning document (DFO 2012) specified a harvest policy rule with a fixed escapement base goal and also specified reduced harvest rates at higher stock sizes to promote recovery of weaker wild stocks taken in the mixed stock river mouth fisheries. A substantial body of harvest policy research indicates that a better balance of conservation and harvest objectives might be achieved by using harvest policy rules (like fixed exploitation rates rather than fixed escapement) that result in less variable harvests over time with little loss in long-term total harvest and essentially no higher risk of stock collapse (e.g., Allen 1973; Walters 1975; Deriso 1985; Hall et al. 1988; Walters and Parma 1996).  There has been much concern over how to adjust harvest policy rules to account for persistent changes in productivity associated with climate change and ecosystem changes associated with other policy initiatives (e.g., protection of marine mammals). In particular, many Pacific salmon stocks have shown worrisome declines in productivity in recent years (e.g. Peterman and Dorner 2012), so that policy parameters (e.g., spawning escapement targets) estimated from long-term 11  data may no longer apply. Walters and Parma (1996) suggested that policy rules based on fixed exploitation rates might be a good way to cope with such changes, but only if it is carrying capacity rather than productivity at low stock size (juvenile survival rate at low stock size) that is changing; unfortunately, at least some productivity declines appear to be associated with density-independent declines in juvenile survival rates. Spencer (1997) used stochastic dynamic programming in a similar manner to investigate optimal harvest policies for populations subject to variable predation and environmental conditions. Collie et al. (2012) developed Kalman filter-based time-varying harvest policies to cope with time-varying productivity. Stochastic dynamic programming has been used for optimal harvest policy study in fisheries for some time now (Walters 1975, 1986). Our analysis and the analysis of others (Spencer 1997; Collie et al. 2012) show that derived optimum policy rules bear little relationship to the rectilinear policy rules (do not fish at low stock sizes, then increase fishing rates linearly to a maximum for larger stock sizes; e.g., Mace and Sissenwine 2002) that have become popular in fisheries management in recent years.  This paper uses stochastic dynamic programming to estimate optimum harvest policy rules that account for (i) constraints on harvest rates to prevent loss of small, weak stocks that are not targeted for economic management but are taken as bycatch in mixed stock fisheries; (ii) persistent productivity changes as represented by autocorrelation in deviations from long-term production or stock–recruitment relationships; and (iii) diminishing marginal utility from higher net incomes (i.e., the notion that having at least some income is much more important to fishermen than to increase income when it is already large). 12  2.2 Optimization formulation and methods To specify an “optimum” harvest policy rule for long-term management over decision periods (years or generations) t = 1, 2,…, it is necessary to assume two main things: (i) a production function that relates abundance left after harvest at time t to stock size available for harvest at t + 1 and (ii) a value or utility function that defines the contribution vt to long-term cumulative value Vt of the harvest taken at time t (harvest at time t is dependent on stock size at time t). For the analysis presented here, it is assumed that the optimum policy is the one that maximizes the expected value of    (1)  where the sum is open-ended over time (no fixed planning horizon) and does not include discounting, so as to reflect a basic fisheries objective of long-term sustainability. Discounting is only an issue for very unproductive stocks. Dynamic programming computational method results in a policy rule that is independent of t (i.e., depends only on the system state at time t provided the production function is stationary over time).  For this analysis, a Ricker production function is assumed for convenience in relating the model to field data on stocks such as Pacific salmon:       (2)  Nt+1 is the stock size (numbers or biomass) available for harvest at time t +1, St is the “spawning” stock size left after harvest in decision period t, r is the intrinsic growth rate of the population when St is low, b is a density-dependent parameter specifying how rapidly productivity (R/S) declines as stock size increases, and Wt+1 is a stochastic environmental effect. For Pacific salmon, in the senior author’s experience, estimated r values from historical data are 13  most often in the range 0.3–1.9 (see Walters et al. 2008). Wt is represented as an autoregressive or moving average process of the form: 𝑊𝑡 = 𝜌𝑊𝑡−1 + 𝑊𝑡∗√(1 − 𝜌2   (3) Here, ρ is a first-order autocorrelation coefficient (where -1≤ ρ≤ 1, and ρ = 1 represents a moving average process), and 𝑊𝑡∗ is a normally distributed effect with mean zero and standard deviation σv (Morris and Doak 2002). ρ values on order 0.2–0.6 are common for salmon data sets, and σv is typically in the range 0.3–0.8 (Mertz and Myers 1996; Myers 2001). There are good empirical and theoretical reasons for assuming log-normality in recruitment variation (Peterman 1978), but see Fogarty (1993) for a review of concerns related to small stock sizes. It should be noted that the optimum policy is not at all sensitive to the form of the density-dependent effect in eq. 2, provided the effect is monotonic increasing in St (no depensatory effects at low stock size; e.g., essentially the same optimum policy rule is obtained when e-bSt in eq. 2 is replaced by 1/(1 + bSt) (Beverton–Holt) or 1 – bSt (logistic)). Note that the standard deviation of Wt is given by σw = σv/(1 – ρ2)1/2.  To avoid unnecessary complication in the optimization calculations, it will be assumed that the basic decision variable for harvest management is the spawning stock size St and that preseason or in-season assessments allow accurate estimation of the state variables Nt and Wt by the time in decision period t that St is “chosen” as a function of these two quantities (i.e., the optimum decision rule specifies St as a function of Nt and Wt). This assumption can break down in situations where Nt is assessed with high inaccuracy and (or) is much smaller than expected at the start of period t. Knowledge of Wt at the time of decision simply means being able to use Nt, St–1, and estimates of r and b in eq. 2 to calculate the recruitment anomaly that most likely led to 14  Nt. The framework of dynamic programming constructed for this analysis does not assess needed adjustments to optimum policies so as to correct for “implementation errors” associated with estimating Nt and Wt and actually achieving St goals. A more complex management strategy evaluation simulation model could be constructed to determine such needs (Collie et al. 2012 demonstrate this with closed loop simulations).  Prediction of the value or utility components vt in eq. 1 for each possible abundance state Nt and decision choice St should involve at least some consideration of the immediate net economic income It for the choice. That net income can be predicted as catch (Nt – St) times price minus cost of the effort needed to take the catch, i.e.:      (4)  Here, P is price per fish or per biomass, c is cost per unit effort, and E(Nt,St) is the fishing effort needed to drive abundance down during the fishing season of period t from Nt to St. Assuming that the duration of the fishing season is relatively short (where time in the fishing season is represented by T, and T is much less than the decision period), natural mortality and growth of fish during the season can be ignored, and changes in N during the season can be predicted from the rate equation       (5)  where CPUE is instantaneous catch per effort, and f is the fishing fleet size (total effort E = fT). For most fisheries, it is reasonable to assume that CPUE varies as a power function of N, implying        (6)  15  Here, α is a scaling parameter that depends on the units of effort, and β is a power parameter that can imply hyperstability (β < 1.0) or hyperdepletion (β > 1.0) in CPUE as N decreases over the season. For boundary condition N = Nt at the start of a season and season length T, the solution of eq. 6 for St at the end of the season is      (7)  From this solution, the effort needed to reach any particular St decision choice can be calculated simply by solving eq. 7 for E = fT:     (8)  (For the special case β = 1 (i.e., constant catchability α = q, where q is the proportion of the stock taken per unit of fishing effort), eq. 7 reduces to St = Nt e−qE, and eq. 8 reduces to E(Nt,St) = ln(Nt/St)/q). Further, the seasonal depletion process implied by eq. 6 exposes a potentially important constraint on St, namely that fishermen will be unwilling to continue fishing beyond the point where they stop earning more than their fishing cost (i.e., they will not drive St down to lower than the point where price times CPUE is equal to c). At this point, the economic minimum Secon is given by        (9)  Secon can be interpreted as an abundance level below which effort falls to zero independent of regulation (it can be calculated by combining eqs. 4 and 8); this abundance can often be estimated by examining empirical relationships between abundance and fishing effort without involving complex assessments of prices, CPUE, and costs c.  16  There are at least two reasonable options for linking per-period utility vt to net income It. The first, as used in most past optimization studies, is to assume constant utility for income, implying       (10a)  The second is to assume that the marginal utility of increasing income is a decreasing function of income, i.e.:      (10b)  The argument for using a logarithmic utility function is quite simple; if a fisherman is offered an additional income of say $10 000 on top of a base income of $30 000, that additional amount makes a very big difference to his welfare. But if he is offered the same $10 000 on top of a base income of $100 000, the additional income means much less. For the logarithmic utility function of eq. 10b, the added utility of each increment like $10 000 is assumed inversely proportional to the base income (another utility function can be used in place of eq. 10b to achieve the same results as long as there is a diminishing value of increased income and a penalty for zero income).  Combining the various equations above, the stochastic dynamic programming problem can be represented as the following maximization to be carried out for each possible Nt,Wt that can be reached as of time t:  (11)  This equation says that the maximum value Vt that can be obtained from time t forward is the sum of an immediate value vt (computed from eq. 10a or 10b) and an expected value over Vt+1 17  where each possible Wt+1 is weighted by the probabilities p(Wt+1|Wt) of alternative recruitment anomalies over the next period and where Nt+1 for each possible Vt+1 is determined by the decision choice St and the next anomaly Wt+1 through eq. 2. Smin is the minimum of three possible limits on St choice:   (12)  That is, (i) S cannot exceed Nt; (ii) for higher Nt, S cannot be less than the economic minimum Secon; and (iii) S cannot be low enough to cause a higher exploitation rate than Umax. Here, Umax represents the “conservation constraint” imposed on exploitation rate by concerns about bycatch impact on weaker stocks or non-target species. Umax corresponds to the maximum harvest rate that can be applied to a fish stock before it begins to trend towards extinction. Umax can be calculated from the stock–recruitment relationship of a fish stock and is discussed in Hilborn and Walters (1992). For a mixed stock fishery, the Umax of the weakest stock is used to limit fishing on the aggregate stock to prevent any component stock’s extinction.  Numerical solution of the optimization eq. 11 requires calculation of V(N,W) over a discrete grid of N,W values. For the results below, N was discretized at unit values 1,2, …, 600 and W at 0.2 standard deviation (σW) units from –2.0 to 2.0 standard deviations (21 discrete levels). A scaling factor can be used to link the discrete levels of N (1–600) to population sizes. The first step in the optimization is to calculate and store the closest integer values Nt+1(S,W) for every possible S,W on the grid. These integer values are used to look up Vt+1 values for each possible choice St and next anomaly Wt+1. Then for each possible Nt, Wt, the St that maximizes eq. 11 is found by simply calculating Vt for each feasible St value, and Vt is stored for the best S. Repeating this over 18  time, each time using the Vt from the last iteration as Vt+1 (value iteration) leads to a table of optimum S values S*(N,W) that stops changing from iteration to iteration (so-called stationary optimum policy). It is this time-independent stationary policy table that represents the optimum policy rule for long-term management.  For the results presented below, we used Skeena River sockeye salmon (Oncorhynchus nerka) as a case example, as in Walters (1975). For this case, long-term stock–recruit data indicate r ≈ 1.2, r/b ≈ 2.3 million fish, σv ≈ 0.6, and ρ ≈ 0.5. Extensive analysis of stock–recruit data for the various species and substocks that are intercepted in the Skeena sockeye fishery has indicated that exploitation rate needs to be constrained to a harvest rate Umax ≈ 0.6 to prevent high risk of extinction for any bycatch species or small sockeye substock (Walters et al. 2008). Management of the Skeena system has been complicated by development of spawning channels (Fulton River and Pinkut Creek) that now produce a high proportion (70%) of the total sockeye catch. The high r value (1.8–2.1) for these enhanced substocks creates surplus production that fortunately can be harvested at terminal locations near the enhancement facilities without causing over-exploitation of the larger wild substocks that have historically supported the fishery. The extra economic value of that terminal harvest is not considered in the calculations below. 2.3 Results For the simple additive Max. Profit objective (eq. 10a), the computed optimum escapement policy S*(Nt,Wt) using eq. 11 is the simple “fixed escapement” form (i.e., do not harvest for Nt less than some optimum S**(Wt) and harvest the surplus Nt – S**(Wt) whenever Nt is large). When Nt is large enough to imply exploitation rate U = (N – S)/N greater than the conservation constraint UMAX, limit the harvest rate to Umax (S** = (1 – Umax)Nt when Nt is high). Increasing 19  fishing costs (higher c or Secon) result in modest increase in S**(Wt). If we set the conditions of the stochastic model to those that approximate the deterministic, we can compare our results with those previously calculated and then examine how moving away from the deterministic assumptions changes our optimum policy prescriptions. For ρ = 0 or Wt near 0.0, S** is well approximated by Hilborn’s approximation (Hilborn and Walters 1992) for the deterministic maximum sustainable yield (MSY) for S (SMSY) for the Ricker model      (13)  For high ρ values (persistent “regime shifts”), S** varies more strongly with Wt, with lower optimum escapements when Wt is very negative (during poor production regimes). For intermediate Wt, S** can again be reasonably approximated by Hilborn’s equation, but with r replaced by r + Wt (Figure 2.1); that is, set S** by assuming that the current productivity implied by Wt will persist indefinitely. For the Max. Utility objective (eq. 10b), the form of the optimum policy S*(Nt,Wt) changes dramatically so as to allow at least some fishing whenever abundance Nt exceeds the economic minimum for fishing Secon. For all Wt, the optimum exploitation rate (N – S**)/N increases smoothly toward the conservation constraint Umax, with relatively weak dependence on Wt even for high ρ values (Figure 2.2). The optimum exploitation rate Uopt for Nt > Secon and Uopt < Umax can be well approximated by a logarithmic function of the form   (14) where UMSY is the Hilborn approximation of the optimum harvest rate for MSY (UMSY= 0.5r – 0.07r2), NMSY is predicted mean stock size for S equal to Hilborn’s SMSY, and κ is an “empirical” constant that varies with Wt and is obtained simply by fitting this function to the dynamic programming estimates of optimum U (Uopt) = [Nt – S*(Nt,Wt)]/Nt. For low Secon, κ varies from a low of around 0.09 for low r (<0.5) to a high of around 0.15 for higher r (>1.0). Equation 14 20  underestimates Uopt for very high stock sizes (Nt > 2r/b), but such large stock sizes are too uncommon to be a serious concern in policy implementation.  For the Skeena River sockeye case, the dynamic programming Uopt for Wt = 0 is surprisingly close to the exploitation rates achieved for most years since 1970, except that very low exploitation rates have occurred in a few recent years when an “escapement first” fixed exploitation rate rule (Figure 2.3) has been followed. The DFO control rule introduced in 2012 (DFO 2012) results in a radical decrease in harvests compared with the alternative control rules implied by dynamic programming or a fixed harvest rate policy.  The two objective functions imply radically different patterns of variation in exploitation rates over time, as illustrated by simulations of the Skeena sockeye fishery using the stochastic Ricker model (eqs. 1–2) with ρ = 0.5 (Figure 2.4). Stock–recruitment analyses of the Skeena River sockeye stocks show an autocorrelation of 0.5 in recruitment deviations. Increasing autocorrelation increases the frequency of productivity regimes even though there is a lot of high-frequency variability (ρ = 0.5), enough to generate strong regimes.  Spencer (1997) simulated productivity regimes using ρ = 0.6, while Decker et al. (2014) estimated a ρ of 0.4 for interior Fraser River coho stocks which demonstrate a strong regime shift (Decker and Irvine 2013). The time-varying fixed escapement policy for this case implies complete closure of the fishery in about 14% of years (estimated by simulating 100 000 years of management), while the Max. Utility policy would almost never (0.4% of years) result in complete closure.  21  Comparison of simulated mean annual incomes (It) and utilities for the policies resulting from the two objective functions, and for simpler policies computed using Hilborn’s approximations, indicate relatively small loss in mean income (or total yield) from using the Max. Utility policy for the Skeena case (Table 2.1). Interestingly, the fixed exploitation rate policy (as recommended in various previous studies) results in a more substantial loss in yield, mainly owing to overfishing during unproductive regime periods when Wt < 0. The alternative optimum policy rules mainly differ in their ability to deliver relatively stable fishing opportunity, as measured by the proportion of years when no fishing is allowed.  Not surprisingly, policy performance as measured by mean income It or ln(It + 1) is extremely sensitive to the conservation limit Umax, for Umax values near or below UMSY estimated using Hilborn’s approximation (Figure 2.5). Fortunately, situations where Umax is much lower than the UMSY for larger stocks are not common; over a century of intense mixed stock fishing has already driven most of the smaller, less productive (Umax ≪ UMSY) stocks extinct so that such stocks are no longer included in assessments of weak stock conservation requirements. However, low Umax values would still result in practice, if Umax were set low enough to avoid economic overfishing (U > UMSY) even for weaker stocks. 2.4 Discussion A shift from rectilinear or fixed escapement policy rules for management of productive stocks to rules that involve smooth increase in target fishing mortality rates with increasing stock size as implied by the Max. Utility objective appears to offer better outcomes for fish harvesters. In fact, such changes should not even be controversial, given that the welfare of fishermen and fishing communities is a central concern of fisheries management in general and ecosystem-based 22  management in particular (Pikitch et al. 2004, DFO 2005). A policy such as that derived here using stochastic dynamic programming promises nearly the same net incomes as a fixed escapement policy, still protects escapement when stock sizes are low, and avoids the no-harvesting years that can cause severe economic hardship for fishers while being responsive to fluctuations in productivity. The stochastic dynamic programming method we present can be applied to any mixed stock salmon fishery. Using the results of a stock–recruit analysis, it should be straightforward to use the Ricker a and b values for the stock complex and characterize the recruitment variation in terms of σv and ρ. Given these inputs, it is possible to generate Max. Utility HCRs and then evaluate the performance of these new rules against the currently applied HCRs. Martell et al. (2008), for example, summarize the parameter values required to generate a Max. Utility HCR for the Bristol Bay and Fraser sockeye runs. However, it is not a simple matter at all to deal with the issue of how high Umax should be, given that higher values imply progressively greater extinction risk for weak and bycatch stocks.  It is important that Umax values be set as real conservation constraints (i.e., harvest rates aimed at preserving future management options by avoiding irreversible loss of stock structure through local extinctions). Improper selection of Umax can lead to economic losses that are not required for the preservation of biodiversity in mixed stock fisheries (when set too low) or can lead to overexploitation of weak stocks leading to collapses or extinctions (when set too high) (Holt and Peterman 2008, Holt and Bradford 2011). Stochastic dynamic programming suggests that low or no harvest situations can easily be avoided simply by presenting managers with estimates of extinction Umax exploitation rates (1 – e−r) for the stocks of concern, allowing a policy choice that implies less economic harm than a fixed escapement or escapement first policy.  This type of 23  management should not be controversial as a similar approach is taken in the mixed stock sockeye fisheries the Fraser River (Cass et al. 2004, Pestel et al. 2008).  Even for situations where there is no severe conservation constraint, Max. Utility optimum policy rules differ dramatically from the popular rectilinear rules (Hilborn and Walters 1992), when shown on a phase plot where U:UMSY is plotted against N:NMSY (Figure 2.6). As indicated by the approximation in eq. 14, the Max. Utility policy implies smoothly decreasing fishing mortality rates for stock sizes below optimum and allows for fishing rates to exceed UMSY when stock sizes are large (fishery not yet fully developed or after strong recruitment events and periods).  We have not attempted to evaluate Max. Utility policy rules in terms of their impact on implementation problems and errors (Eggers 1993; Holt and Peterman 2008). Errors in stock size (Nt) estimation and tactics used to achieve target exploitation rates or escapements can certainly be expected to lead to reduced average economic performance (lower mean income It) and to increased risk of overfishing (St ≪ SMSY) (), but we see no reason to expect larger losses from the Max. Utility rules than can be expected from fixed escapement, fixed exploitation rate, or rectilinear policy rules. It should certainly be possible to achieve considerably better performance for policy rules besides fixed escapement than Eggers (1993) estimated for Bristol Bay salmon; he estimated extremely large errors for implementation of fixed exploitation rate policies when he assumed simple effort regulation and high variability in the relationship between effort and exploitation rate. But such errors could be reduced considerably by utilizing in-season assessment and correction procedures where there are multiple fishery openings and 24  hence opportunities to make corrections for effects of variation around the average relationship between exploitation rate and effort.  We have also not attempted to address the distributional or equity problem of optimum fleet size (f), assuming only that f is large enough to generate whatever exploitation rate is implied by the E(N,S) relationship. This ignores the overall profitability of fishing, which includes costs related to fleet size but not simply proportional to fishing effort, and the more fundamental social question of whether to regulate fleet size so as to be “efficient” (make a few people wealthy) or to provide more modest employment and life style opportunity for a larger collection of license holders. But it should certainly help to address those larger issues to know that there are reasonable harvest control rules that ensure near maximum average yield without the high variability and frequent closures that can result from using fixed escapement (or even rectilinear) policy rules.  25  Table 2.1.  Key performance measures for a range of alternative harvest control rules.    Control Rule Mean Income (It)Mean Utility (ln(It+1))Prop. Years no fishingMax Profit 56.3 3.23 0.15Max Utility 54.9 3.48 0.005Fixed Escapement SMSY 56.1 3.14 0.19Fixed Exploitation UMSY 42.7 3.23 026    Figure 2.1.  (a) Optimum escapement targets for Max. Profit objective function with stock size for a range of Wt (from Wt = -2 in the lowest lines to Wt = 2 in the highest lines) and (b) optimum escapement targets (S**(Wt))with the assumptions that the current productivity implied by the last recruitment anomaly (Wt) will persist indefinitely (grey line is Hilborn approximation of optimum escapement, and the black line is the stochastic dynamic optimum escapement showing diverging prediction of optimum escapement as the Wt decreases).   Last Recruitment anomaly (Wt) Optimum escapement (S**(Wt)) Optimum escapement (St) Stock size (Nt) 27   Figure 2.2.  (a) Simulated and (b) approximated (with eq. 14) optimum harvest rates at different stock size generated using the Max. Utility objective function with varying values for Wt. The highest curve was generated with the highest value of Wt and the less steep curves with lower values of Wt. Notice that even at the lowest Wt values the curve still rapidly climbs from zero exploitation rate to the conservation constraint.   Stock size (Nt) Stock size (Nt) Approximate Optimum (Ut) Optimum exploitation rate (Ut) 28   Figure 2.3.  Max. Utility policy (grey line), fixed escapement policy (black line), and current DFO policy (dashed line), shown with historical exploitation rates for Skeena sockeye salmon.   Exploitation rate (Ut) Run Size (1000 fish) 29   Figure 2.4.  (a) A simulated pattern of recruitment anomalies, (b) exploitation rates (black line) and stock size (dashed line) generated by applying the Max. Profit harvest control rule (HCR), and (c) exploitation rates (black line) and stock size (dashed line) generated by applying the Max. Utility HCR.   Anomaly (Wt) Stock Size (Nt) Stock Size (Nt) Year Year Year 30   Figure 2.5.  Changes in income (solid line) and log Utility (dashed line) associated with different maximum allowable exploitation rates.   Umax Median Income (It) 31   Figure 2.6.  Max. Utility optimum policy rule (solid line) and rectilinear rule (dashed line) on a phase plot.  N/Nmsy U/Umsy 32  Chapter 3: Reconstruction of run timing and harvest rates for Pacific salmon subject to gauntlet fisheries A key component of in-season salmon management is an accurate historical record of salmon arrival patterns.  Current run reconstruction techniques often introduce artificial spikes or bumps in the reconstructed arrival patterns, which are caused by assigning catches to incorrect entry days.  A method is demonstrated for reconstructing entry timing patterns for salmon runs entering gauntlet fisheries, based on dividing the incoming run into many small entry time-net ground speed packets.   Simulating removals of fish from these packets forward and backward over time as they pass through fisheries leads to reconstructed entry patterns that are not contaminated by spikes of fish.  The method is not particularly sensitive to measurement errors in daily escapement measurements near the inside boundary of the gauntlet, but it is sensitive to errors in assessing the variation in fish net ground speeds and to uneven distribution of fishing effort within each area-time fishery opening.   The new run reconstruction method is applied to generate run timing patterns for Pacific salmon populations migrating to the Skeena River in northern British Columbia.   3.1 Introduction Pacific salmon fisheries typically occur along the migration routes followed by maturing fish.  These fisheries are managed as gauntlets of area-time fishery openings that have the potential to generate very high exploitation rates on the proportion (or segments) of the salmon runs exposed to harvest during each opening.  Management of such gauntlet fisheries often involves an in-season adaptive process.  In these in-season processes, available catch and escapement index information (as of each day or week as the fishing season progresses) are used to update run size 33  and exploitation rate estimates with the aim of reaching some seasonal management target (typically a total spawning escapement or an exploitation rate target).  Success of in-season updating procedures is critically dependent on use of historical information on the arrival timing pattern at the offshore end of the gauntlet.  The estimation or “run reconstruction” of such arrival timing patterns requires use of escapement timing data along with catch removals.  Models for run timing reconstruction have typically involved some type of virtual population estimation (see review in Branch and Hilborn 2010), where incoming run numbers are estimated backward in time by adding catch components to estimates of escapement, after discretizing the run into one-day or half-day “boxcars” (Cave and Gazey 1994) or “groups” (Branch and Hilborn 2010) of fish.   There are two major structural problems with most models that lead to errors in the run reconstruction prediction of entry timing patterns.  First, reconstruction models going back to the early 1980s (e.g., Gilhousen 1980, Gatto and Rinaldi 1980) have pointed out that discretization can cause severe artifacts in the estimates of daily entry numbers, due to incomplete or partial exposure to fishing mortality of fish entering the fisheries at different times of day and/or being present at different locations in the fishing areas at the times of opening for openings large enough to have more than one migration-days of fish contributing to the catch.  Failure to account for partial exposure patterns typically leads to reconstructed entry timing patterns that have large, artificial “bumps” for days during and before high fishery catches.  Secondly, individual variation in fish net ground speeds can cause the “holes” cut in the runs by intense fisheries to “fill” over time.  Escapement patterns consist of mixtures of fish that migrated at different net ground speeds; when these fish are assigned to rigid boxcars or packets, the catches 34  added to them in back-calculation of entry abundance will be inflated.  This is a result of fish from other entry days being included in the escapement component of the virtual abundance back-calculation because they swim faster or slower than the boxcar or group model time step (Cave and Gazey 1994, Cox-Rogers 1994, Branch and Hilborn 2010).  This paper shows a simple solution to the bumpy entry timing patterns caused by discretization and net ground speed variation in salmon populations that have plagued past run reconstruction methods.  The basis of this solution involves two components: (1) discretize the stock into much, much finer entry “packets” of fish, representing fish entering over very short (0.01-0.03 day) time steps; and (2) assign variable net ground speeds to the packets, representing the likely distribution of individual net ground speeds.  The solution requires both forward and backward time simulations of the fates of the packets.  The forward simulations are used first to assess relative contributions of packets subject to different fishery exposures to daily escapements.  Then, backward simulations (virtual population estimation) are used to reconstruct abundances over time for each packet.  The entry numbers for each day are then the sums over the packets entering the fishing area that day.  While the solution may seem computationally burdensome, tracking tens of thousands of different entry time and net ground speed packets forward and backward over several movement days (at very fine space-time steps) is quickly performed by modern personal computers. 3.2 The packet-based run reconstruction method To avoid unnecessary complication in equations and indices, the packet-based method is presented for a single species (or stock) following a single migration route; the calculations can be readily generalized to multiple stocks following multiple migration routes, as in Branch and 35  Hilborn (2010).  Table 3.1 and Table 3.2 summarize the key parameters and equations described in this section.  The general approach is to envision packets of fish moving along a one-dimensional line from the ocean to the inshore or river point where daily escapements are monitored, with fishery openings represented as blocks of time and space (Figure 3.1).  Time is represented in two ways, as integer days d (d=1 at the start of the run) and as continuous time t in days (so that d=int(t), i.e., d is the integer component of t).  Then at any moment t in time, each packet “p” has position xp(t) along the movement line, and over the next discrete time step Δt (where Δt<<1.0 days) moves to position  xp(t+Δt)=xp(t)+spt      (1) where sp is the average net ground speed (e.g., km/day) of the packet.  In the terminology of numerical analysis, movement of the packet over x,t represents a Lagrangian approach to integration of abundances over the x,t space-time field.  Positions xp can be updated either forward or backward in time, simply by adding or subtracting distance increments spΔt in eq. (1).  Each packet is defined as having a set of key and possibly unique attributes, including:  sp—packet’s net ground speed (km/day)  top—time when the packet enters the system at position x=0  tep—time when the packet exits the system at x=xexit (tep=xexit/sp)  Np—number of fish in the packet at entry to the system  Ep—number of fish in the packet when it passes exit/monitoring position xexit. Note that the first three parameters (sp, top, tep) need to be specified in advance of the analysis, i.e., net ground speeds are not likely to be estimable from data gathered on catches and escapements.  Note further that Np is a component of a daily entry number Nd, where d=int(top), 36  and Ep is a component of an (observed or assumed) daily exit number Ed where d=int(tep).  A critical point that makes the method work is that if the daily entry number Nd is uniformly distributed over t within the day (packets are assigned the same Np for every t in day d), then the contributions of the packets to daily escapement Ed cannot be uniformly distributed over the exit day for any day where packets that have been fished are exiting, since every packet exiting on day d has been subject to a possibly unique and different exploitation history (exposure to fisheries).  For simulations of harvest impact, packet numbers Np must be initialized as proportions pinp of assumed daily entry numbers Nd for forward simulations, and escapement numbers Ep must be initialized as proportions 𝑝𝑑𝑜𝑢𝑡 of observed daily escapements Ed.  If time within each day is discretized into nt time steps (so Δt=1/nt) and net ground speeds are discretized into ns speeds sp (k=1…ns) with assumed proportions of fish p swimming at each net ground speed, then the simulation is constructed with ntns packets of fish entering the system each day.   Assuming fish enter the fishery evenly over time, entry numbers Np(top) for packets with net ground speed sp are given by assuming 𝑝𝑝𝑖𝑛 =p*sp/nt.  Np(top)=p*spNd/nt      (2a) and exit numbers Np(tep)=Ep are given by  Ep=𝑝𝑑𝑜𝑢𝑡Ed       (2b) Estimation of 𝑝𝑑𝑜𝑢𝑡is more complex, since as noted above, the output packet contributions to daily Ed cannot be evenly distributed over time for packets that suffer fishing mortality, even if the entry time distribution is flat.  A simple estimate of 𝑝𝑝𝑜𝑢𝑡can be obtained by simulating forward over time with fishery impacts as indicated below, while accumulating predicted values 37  Ed over packets that exit on day d, then taking 𝑝𝑝𝑜𝑢𝑡=Ep/Ed, where Ep is simulated surviving numbers of packet p and Ed is simulated total escapement for day d.  In fact, a quite good estimate of 𝑝𝑝𝑜𝑢𝑡can generally be obtained simply by simulating forward over time using Np=p*sp for all packets, i.e., ignoring variation in entry numbers Nd entirely along with scaling by 1/nt (since the ratio Ep/Ed does not depend on the scaling of E).  For simulation of fishery impacts, it is necessary to specify a space-time field of “elementary” exploitation rates u(x,t), where u is the proportion of fish that start time step t at position x that are harvested over the interval t to t+Δt.  Given the u(x,t) field, forward simulations are performed simply by updating Np and xp using eq. (1) for xp and a survival equation for Np:  Np(t+Δt)=Np(t)(1-u(xp(t),t))     (3a) Backward (virtual reconstruction) simulations are performed for each packet using eq. (1) with negative x increment (xp(t)=xp(t+Δt)-sp Δt), and  Np(t)=Np(t+Δt)/(1-u(xp(t),t))     (3b) It is possible to simulate packet numbers over time, either forward or backward, if the u(x,t) field can be well estimated.  In order to estimate the u(x,t) exploitation rate field, a reasonable strategy is to define a set or list f=1…nf of fishery openings, where the following information is available for each opening f: x1,f—seaward position of the start of fishery open area f (i.e., where fish enter the fishing area) x2,f—landward position of the end of fishery open area f (i.e., where fish exit the fishing area) t1f—starting time (days from start of modeled season, need not be integer) of fishery f t2f—ending time (days, again need not be integer) of fishery f 38  Vf—number of fishing vessels operating during fishery f qf—daily fishing mortality rate caused by each vessel during fishery f Cf—total catch taken during fishery f (summed over all migration packets)  This implies that each fishery is represented as a “box” in the x,t plane, with the x limits of the box defined by x1f,x2f, and the t limits of the box defined by t1f and t2f (Figure 3.1). For any x,t position within this box, the elementary exploitation rate is then predicted by the exponential removal model  u(x,t)=1-exp{-qfVfΔt}      (4) Note that the right hand side of this equation is the same for all x in the interval x1t to x2t and t in the interval t1t to t2t, i.e., we do not presume to know how fishing effort was distributed spatially within area f or over time during the opening.  Known concentration structures, (e.g., concentration of vessels near the entry x1t) should be modeled in this framework by dividing the opening into two spatial fisheries, each with known effort V; likewise, known causes of catchability variation over time (e.g., tides) could also be modeled as variation in q over the interval t to t+ Δt.  Note also that it is computationally very inefficient when solving the dynamic equations (3a-3b) to look up the u(x,t) for each time step by checking which (if any) fishery operated (or is planned to operate) at position x,t.  This inefficiency can be avoided by creating a (very large) “fishery incidence” lookup table, called e.g., FisheryNo(ix,it), which stores the fishery code number f for very fine integer space-time increments ix=xmax/Δx, it=tmax/Δt (with Δx small like Δt, e.g., Δx=1 km).  Then, as eqs. 3a,3b are being solved, ix and it are calculated for each time step and the fishery number looked up from the FisheryNo table.  39  It is almost impossible to initially choose fishery catchability coefficients qf that predict observed catches Cf (i.e., are consistent with all observed Cf), given that number of fish exposed to harvest (Nd pattern) is not initially known.  Fortunately, a simple iterative calculation allows estimation of q.  Beginning with reasonable initial estimates q(0)f,  1. simulate forward over time using eq. (3a) for all packets to obtain 𝑝𝑝𝑜𝑢𝑡 estimates by packet,  2. use these along with daily escapements Ed to initialize the backward simulations, and  3. run the backward equations (3b) for all packets while accumulating predicted catch contributions of each packet to each fishery that it passes (each contribution is just u(x,t)Np(x,t).   This results in predicted catches Cf̂ for each fishery.  Then, update the estimated catchability coefficients by fishery using the relaxation equation  q(1)f=(1-W)q(0)f+Wq(0)fCf/Cf̂     (5) That is, take the improved estimate q(1)f to be a weighted average (with relaxation weight W0.1 to 0.5, lower for high q cases) of q(0)f and a new estimate that is corrected downward if predicted catch exceeds true catch, and upward if the predicted catch is lower than observed.  Then repeat the above steps (1)-(3), each time using the most recent result from eq. (5) as the starting qf.  This iteration typically converges in 5-10 iterations to qf estimates that almost exactly predict the observed catches, i.e., backward reconstructions that account almost exactly for both escapements Ed and observed catches Cf.  3.3 Sensitivity of reconstructed entry pattern to errors and assumptions The reconstruction method outlined above can generate run reconstructions for complex entry patterns like the example in Figure 3.1, provided three conditions are met: daily escapements (Ed) and the distribution of net ground speeds (sp) are known exactly, and fishing effort (Vf) is 40  evenly distributed over time and space within each fishery opening.  The method is not at all sensitive to fine time-scale stochastic variation in net ground speeds and/or fine space-time scale variation in fishing effort; such fine scale effects are averaged out over observations of many packets reaching the escapement monitoring point.  Daily escapements are typically measured with considerable random error, due to operation of test fishing gear (nets, acoustic counting systems).  Random observations errors in Ed are back-propagated over time (eq. 3b) into larger errors in the entry numbers Nd estimates.  Fortunately, there is a simple approach to removing much of the effect of such errors.  That is, first conduct a backward simulation (eq. 3b) using the raw escapement data and reasonable qf (fishery impact) estimates, then smooth the resulting Nd estimates using a simple 3-point moving average, then simulate forward with the smoothed N estimates to give a correspondingly smoothed time series of Ed estimates for which fishery effects have not been artificially removed (as would be the case if the Ed data were directly smoothed using a moving-average calculation).  In simulation tests, this approach removes almost all the observation error effects, except for those associated with a few wildly large positive errors (as would be predicted to occur if the observation errors are log-normally distributed).  It is not so simple to deal with reconstruction errors caused by incorrect specification of the net ground speed distribution.  If fishery openings are short in both time and space relative to net ground speeds (e.g., fishing areas 40 km long open for one day per week for fish that move around 40km/day), neither the assumed mean net ground speed or variability in assumed net ground speed have large effects on reconstructed abundance.  But if fishing areas are large (e.g., 41  2x daily swimming distance) and openings are long (e.g., 3-4 days each week), even 10% errors in assumed mean net ground speed can cause large artifacts (spikes) in reconstructed abundances (Figure 3.2).  In fact, the spike pattern caused by incorrect net ground speed specification is so striking in simulated data that occurrence of the pattern in reconstructions for actual data might be used as evidence about how to adjust the assumed net ground speeds (adjust the assumed mean net ground speed to see if there is a speed such that spiky patterns disappear from the reconstructed Nd).  Likewise, concentration of fishing vessels near the entry or exit boundaries of fisheries is likely to cause spiky patterns in reconstructions that do not split the fishing areas into distinct openings.  Such concentrations typically develop on the second and later days of long openings (vessels are likely to shift toward the entry boundary during periods of increasing daily entry, and toward the exit boundary for late openings when entry numbers are falling). Using a simple exponential model for relative effort over distance within each fishing area can demonstrate the problems that arise with concentration of fishing vessels.  Assuming 1.5x average effort at the entry boundary and roughly 0.5x average effort near the exit boundary on the second and later days of each fishery generates simulated reconstruction errors that have a spiky pattern that looks quite similar to the pattern caused by incorrect net ground speed specification (Figure 3.3). 3.4 Application to the Skeena River The method presented above was used to reconstruct return patterns for five species of Pacific salmon (sockeye, pink, chinook, chum, and coho) and steelhead trout migrating through the gauntlet fisheries of the Skeena River.  The Skeena River was used to demonstrate the results of this run reconstruction method for two reasons.  First, there are good time series of escapement 42  index, catch, and effort data by species for recent years.  These data include daily catch and effort data for the years 1982-2012 reported by statistical sub area (Figure 3.4) and by fleet (gill and seine fleet); daily catches from May 29th to October 1st by species in the Tyee test fishery for the years 1956-2007; and ratios of aggregate Tyee test fishery catches to aggregate escapement for the years 1982-2007 (allowing yearly estimates of the test fishery catchability coefficient).  Secondly, the Skeena River was used because Skeena River salmon follow a single migration route through the commercial fisheries that impact them, allowing us to use the simple equations and methods presented above.  The data available can be used to construct the fishery incidence table and to generate Ep; this can then be used with the reconstruction equations to reconstruct the return entry patterns for 26 years of the time series.    Distributions of the 50% date to the fishery and spread of the return as well as estimated entry patterns show (Figure 3.5, Figure 3.6) that the reconstruction method does indeed give reasonable entry timing patterns apparently uncontaminated by spikes associated with misallocation of catches to entry times.  It is standard practice to assume that a normal distribution can be used to represent the time pattern of migrating salmon past a fixed point (e.g., fishing area or test fishery), (Mundy 1979, Cave and Gazey 1994, Gazey and Palermo 2000) though other forms are certainly possible (e.g. Chasco et al. 2007 use a Richards form).  The reconstructed entry numbers to the fishery show that entry patterns for Skeena River salmon can indeed be well represented by normal curves, for most species and years; only steelhead show substantial deviations from normal curve patterns, and this is not surprising considering that the steelhead run consists of several large stocks with different run timing and relative abundance 43  patterns over the years.  Summary statistics listed in Table 3.3 describe the variability of the parameters of the normal curves fit to the reconstructed entry numbers.  This reconstruction has also identified the spatial and temporal patterns in catchability of the commercial fisheries.  The reconstructed patterns of catchability for both the gillnet and seine fleets show a distinct increase in catchability both as the season goes on, and as the fisheries move from the ocean towards the river (Error! Reference source not found. to Error! Reference source not found.).  The increase in catchability from seaward to river fisheries is not unexpected as the fish migration corridor narrows as it moves inshore.  The increased catchability over the course of the season may be a result of fisher behavior, fish behavior, or river conditions (Hilborn and Walters 1992).  There is no significant pattern of correlation between the 50% date of the return and the spread of the run (Error! Reference source not found.) for any species except coho salmon (Pearson's product-moment correlation of 0.84 with a p value of 3.398e-07).  In addition to this pattern in catchability, “tail-end loading” of the fishery can be diagnosed when examining the reconstructed return.  Tail-end loading of the fishery occurs when more catch is taken from the second half of the return than from the first half.  On the Skeena River the gillnet fishery has more effort the second half of the sockeye return, while the seine fishery has almost all of its effort in the second half of the sockeye return.  When this pattern of effort is combined with the time trend in catchability you see a distinct pattern of more catch taken after the peak of the run than before (Error! Reference source not found.). The estimated sockeye return timing does not show temporal trends indicative of selection for changes in run timing, or an impact of 44  tail-end loading on the standard deviation of the run timing distribution (Figure 3.5).  In order to test for directional movement in 50% date of return, associated with tail end loading, lines were fit to the estimated 50% date time series (Table 3.4) and the p value of the slope calculated.  Pink salmon was the only species where there a significant slope to a line fit to the time series of 50% dates.   3.5 Extending the method to multiple migration routes and stocks It is common for fish to follow multiple migration routes before reaching escapement monitoring sites, and for catches in particular fishing areas to consist of mixtures of fish from different stocks (Error! Reference source not found.).  This section describes the three relatively simple changes needed for the method to deal with these more complex situations.  In the more general case, each packet of fish is assigned two additional attributes, a packet-specific migration route code rp, and a stock code sp, and the total number of modeled packets is increased by the factor rpsp.  First, daily escapement estimates Est need to be provided for each distinct stock. These may come either from stock composition monitoring at a single location, or from escapement monitoring on approaches to multiple spawning locations.  Note that for multiple stock cases, the critical escapement contribution proportions 𝑝𝑝𝑜𝑢𝑡then need to be estimated (by forward simulations using eq. 3) or used to initialize backward simulations (eq. 4) as proportions of the escapements of each stock s, using the sp assigned to each packet.  Second, it is necessary to provide an independent estimate 𝑝𝑟𝑟𝑜𝑢𝑡𝑒 of the proportion of fish (of each stock) that follow each migration route r.  The only evidence that will appear in the 45  reconstruction results if bad 𝑝𝑟𝑟𝑜𝑢𝑡𝑒 estimates are used is suspiciously high or low estimates of fishery-specific catchability coefficients qf.  Suppose, for example, that 𝑝1𝑟𝑜𝑢𝑡𝑒 in Figure 3.5 is set very low, but high catches are observed in fishing area 2 (where only fish migrating along route 1 are taken).  The q estimation procedure (eq. 5) will simply compensate for low numbers of fish back-calculated (eq. 4) to escape area 2 by increasing catchability coefficients for area 2 fisheries, so as to ensure enough fish enter area 2 to account for the observed catches from it; the overall back-calculated estimates for numbers of stock 1 fish entering the gauntlet will still be correct (except for possible errors due to mis-assignment of catch in area 1), i.e., will include area 2,3,4 observed catches.  One way that has been used to get around this problem for Fraser River sockeye, which follow two basic migration routes around Vancouver Island, has been to assume similar catchability coefficients scaled by swept area for fisheries along route 1 (through the Juan de Fuca Strait) and route 2 (through the Johnstone Strait), in which case 𝑝𝑟𝑟𝑜𝑢𝑡𝑒 can be roughly estimated by using corrected ratios of observed catches along the two migration routes (Putman et al. 2014).  Third, it is necessary to account for differences between migration routes and stocks in the travel distances to each fishery location.  This means that the fishery entry and exit positions X1,f and X2,f , and the distances to escapement monitoring point(s) xexit, can be different for each migration route-stock combination.  If the fisheries incidence table approach (FisheryNo table) is used to keep track of which fishery is open at discrete x,t steps, it is necessary to construct and store a separate FisheryNo table for each r-s combination.   46  3.6 Discussion The method presented provides a structural improvement to current run reconstruction methods by allowing for more realistic representation of fish migration through gauntlet fishing areas.  Fixed net ground speeds and large migration groups (or boxcars) introduce a known structural problem into reconstructed abundances (Cave and Gazey 1994, Branch and Hilborn 2010). By allowing for variation in net ground speed within migrating salmon populations the major problem with discretizing salmon runs into “boxcars” or groups is corrected.   A typical use of normal approximations of run timing derived from run reconstructions is to estimate run size within-season in order to guide management actions.  Management of the Skeena River salmon fishery (as well as many other fisheries) is driven by a goal of meeting a fixed escapement target for the aggregate stock (DFO 2017), and in-season decisions about harvest are driven by weekly estimates of run size which are used to calculate allowable catches.  Adkison and Cunningham (2015) demonstrate how the main cause of in-season estimation errors is uncertainty (or misspecification) of the proportion of the run estimated to have passed by the date of estimation.  Removing known artifacts from reconstructed abundances means that run timing curves generated from the reconstructed abundances are more likely to better represent the underlying population, hence reducing errors in the weekly abundance estimates.    Application of this method to the Skeena River gauntlet fisheries shows that the pattern of entry of fish to the fishing areas is normally distributed consistent with expectation.  However, these reconstructions of the Skeena River returns could be compromised by two possible effects.  First, spatial resolutions of fishing areas could be too coarse.  The statistical areas in which catch and 47  effort are reported are large, and the fishing effort is not always evenly distributed in them.  Larger fishing areas could lead to concentration of effort with expected errors in reconstructing return patterns (i.e., “spiky” patterns in the reconstruction).  Secondly, hyperstability in catches at the test fishery could lead to underestimates of the numbers of fish passing the test fishing gear when abundances are high.  Gillnet fishing gear has a well-documented problem of saturation at high abundance (Hansen et al. 1998, Šmejkalet al. 2013).  The effect of saturation in the test fishery is to underrepresent the daily passage of fish (i.e., underestimating the Ed numbers).  Underestimating the Ed when abundances are high will result in an underestimate of the kurtosis of the true normal curve describing the return, which will tend to give the impression of a wider migration distribution than is actually the case.    Errors in estimating the normal curve that represents the return timing can lead to several types of management errors (depending on the management system).  Adkison and Cunningham (2015) demonstrate that differences between expected and actual return patterns can lead to over escapement when the run is later and larger than expected, or over harvest when the return is smaller and earlier than usual, for systems managed to an escapement target.  The Skeena River sockeye run is managed to an escapement goal for sockeye, and incorrect expectation about the duration or timing of the return could lead to these same errors.  Tail-end loading of fisheries targeting Skeena River sockeye (Error! Reference source not found.) can lead to selection pressure for earlier run timing (Quinn et al. 2007), and though this is not currently evident on the Skeena (Figure 3.5), it needs to be taken into consideration when managing the system, because of the potential impacts on genetic diversity. (Adkison and Cunningham 2015, Carney and Adkison 2014, Quinn et al. 2007, Schindler et al. 2010).  Given the importance of the historical 48  information about salmon return patterns to management decision making, the use of this new run reconstruction method that removes known artifacts in reconstructed seaward abundance of salmon species should be adopted when generating the run timing curves that will be used for in-season management.    Historical management planning and analysis for the Skeena has mainly utilized weekly rather than daily run reconstructions (Cox Rogers 1994, Ward et al. 1993), and those weekly estimates generally agree closely with our daily estimates when summed to weekly time scales.  Perhaps the weekly estimates are adequate for most planning purposes, but it is quite possible that the more detailed daily reconstructions can be used to evaluate alternative management approaches that do not operate on a rigid weekly fishing schedule (e.g. having fishery openings every 4 days or 10 days).  49  Table 3.1.  A list of key parameters and variables.    Parameter DescriptionPre-specified parameterss p packet’s ground speed (km/day)to p time when the packet enters the system at position x=0te p time when the packet exits the system at x=x exit  (te p =x exit /s p )Modeled variables, counters, and derived parametersd time (discrete days)t time (continuous)p  packetΔt  time stepx p (t) position of a packetN p number of fish in the packet at entry to the systemE p number of fish in the packet when it passes exit/monitoring position  x exit .N d daily entry numberE d daily exit number (observed or assumed)proportions of assumed daily entry numbersproportions of daily escapements E dn t number of time steps per dayu(x,t) elementary exploitation ratesn f number of fishery openingsx 1,f position of the start of fishery open area fx 2,f position of the end of fishery open area ft 1f starting time of fishery ft 2f ending time  of fishery fV f number of fishing vessels operating during fishery fq f daily fishing mortality rate caused by each vessel during fishery  fC f total catch taken during fishery f  (summed over all migration packets)FisheryNo(ix,it) fishery incidence lookup tableΔx space incrementTable 1: A list of key parameters and variables50  Table 3.2.  A list of key equations and descriptions.    Equation Number Purposex p (t+Δt)=x p (t)+s p Δt (1) calculation of position of packetsN p (to p )=p*s p N d /n t (2a) calculation of entry numbers in a packetE p =            E d (2b) calculation of exit numbers in a packetN p (t+Δt)=N p (t)(1-u(x p (t),t)) (3a) calculation of numbers in a packet (forwards)N p (t)=N p (t+Δt)/(1-u(x p (t),t))(3b) calculation of numbers in a packet (backwards)u(x,t)=1-exp{-q f V f Δt} (4) calculation of elementary exploitation rate q (1) f =(1-W)q(0)f +Wq(0)f C f / (5) iterative calculation of q51  Table 3.3.  Estimated parameters for normal distribution approximation to run timings for Skeena River salmon species. Dates are reported in Julian days (e.g. Sept 1st = 245). 95 % CI reported in brackets.    Species Mean Date Standard DevaiationSockeye 203.5 (197.8-209.2) 13.7 (10.7-16.7)Pink 217.5 (210.0-225.0) 9.5 (6.9-12.1)Chinook 185.7 (181.9-189.5) 14.7 (11.8-17.6)Chum 223.6 (216.3-230.9) 10.6 (7.3-13.8)Coho 225.3 (210.7-239.9) 12.7 (5.5-20.0)Steelhead 217.3 (207.0-227.7) 13.6 (9.2-17.9)52  Table 3.4.  Values of the slope and intercept of lines fit to the time series of estimated 50% dates and corresponding p values.    Species Slope Intercept p value significanceSteelhead 0.21 210.41 0.124 no Sockeye -0.01 199.51 0.933 no Pink -0.20 217.07 0.039 yesCoho 0.21 219.41 0.292 no Chinook -0.04 182.13 0.446 no Chum 0.05 218.81 0.605 no 53   Figure 3.1.  Gauntlet fisheries can be represented by entry timing curve (a), spatial fishery pattern with each fishery opening covering a box of times and distances along the migration route (b), and resulting exit timing curve of fish escaping the inshore end of the gauntlet (c).  Migration paths of two simulated packets of fish shown as dotted lines in (b); packet (1) is impacted by fishery opening 3, and packet (2) is not impacted by fishing.  Example entry timing pattern constructed as a normal curve with sinusoidal multiplier that might, for example, represent effects of tidal or wind currents on arrival timing at the gauntlet.   54   Figure 3.2.  Error pattern in run reconstruction for a simulated population (true timing shown as fine line) with true mean net ground speed 40km/day, when reconstruction method is applied while assuming mean net ground speed 35 km/day.  Note how estimation error is most severe around the time of the long fisheries (boxes labeled 2,3 in Figure 3.1 (b)).   55   Figure 3.3.  Impact of spatial effort concentration within fishing areas on reconstructed daily run size.  For this simulation, fishing effort declined exponentially from 1.5 times average at the seaward boundary of each fishing area to 0.5 times average at the landward boundary, after the first day of the fisheries in Figure 3.1 lasting longer than 1 day.   56   Figure 3.4.  Geographic location and boundaries of the Statistical Area 4 fisheries (from Walters et al. 2008).   57   Figure 3.5.  Reconstructed Skeena River run timing patterns.  For each species of salmon the distributions of calculated 50% dates (a) and widths of the reconstructed returns (b) are shown as both histograms (bars) and normal approximations of the distribution (red line).   The yearly estimates of the mean return date are presented in (c).    Year 50% date (Julian days) proportion      proportion           50% dates (Julian days, n=26) Spread (days, n=26) 58     Figure 3.6.  Reconstructed Skeena River run timing patterns.    Week of year   Proportion of return entering fishing area 59     Figure 3.7.  Catchability of sockeye salmon in gillnet fisheries, panels show the distributions of the logarithms of the estimated catchabilities for the different fishing areas (see Figure 3.4) over the weeks of the fishing season.   Week of year log(qGN) 60   Figure 3.8.  Catchability of sockeye salmon in seine fisheries, panels show the distributions of the logarithm of estimated catchabilities for the different fishing areas (see Figure 3.4) over the weeks of the fishing season.   log(qSN) Week of year 61   Figure 3.9.  Catchability of sockeye salmon by area, panels show the distributions of the logarithm of the catchability by area (see Figure 3.4) for gillnet (upper) and seine net (lower) fisheries. log(qSN) log(qGN) Fishing area 62    Figure 3.10.  Catchability by week, panels show the distributions of the logarithm of the estimates of catchability of sockeye salmon by week for gillnet (upper) and seine net (lower) fisheries. log(qGN) log(qSN) Week 63    Figure 3.11.  Covariation in mean and spread of run timing for the Skeena.  The relationship between the spread of the run (SD) and the 50% date of the return by species. Spread of distribution (days) Spread of distribution (days) Spread of distribution (days) Spread of distribution (days) Spread of distribution (days) Spread of distribution (days) 50% date (Julian day)  50% date (Julian day)  50% date (Julian day)  50% date (Julian day)  50% date (Julian day)  50% date (Julian day)  64    Figure 3.12.  Annual proportion of total sockeye catch taken after the estimated date of 50% entry to the outside fishing area (there were no fisheries in 1999 and 2005).  Proportion of sockeye catch after 50% date Year 65    Figure 3.13.  Example of a multiple migration route, multiple stock case.  Fish from stock 1 follow two migration routes to a single escapement monitoring destination, are taken in two shared fishing areas  (1, 4) and two route-specific fishing areas (2,3).  Fish of stock 2 are taken in the shared area 1, and in a distinct “terminal” fishing area 5.  Daily escapements E1,t and E2,t are estimated in separate monitoring programs, while only total catches are available for fishery openings in the five areas (route and stock composition are unknown for the shared areas 1 and 4).  66  Chapter 4: Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming A linear program model for management of seasonally complex fisheries is developed to address in-season management challenges using the multi-species, mixed stock Skeen River salmon fisheries as a case study.   The model aims to find weekly opening patterns and exploitation rates that maximize the value of fish caught by fishing fleets taking a mixture of fish stocks, while preventing overexploitation of less productive species and stocks.  The management problem is cast as a set of decisions about weekly exploitation rates over any season where stocks pass through the fishing area with different arrival timing (weekly numbers vulnerable) patterns. The optimization is driven by the landed value of different stocks, but value is maximized only within a domain constrained by conservation limits for each stock and economic limits for each fleet.  As well as maximizing harvest available within the Skeena River system in any year, the in-season model is used in other ways: management performance that might be achieved over multiple years with different stock abundances and timing patterns is evaluated through simulations and retrospective analysis; the value of information from different types of fishery monitoring is calculated; and conservation constraints that limit fishery operations are identified.  This analysis shows in-season management tactics developed from retrospective linear-programming optimization can result in increased catches on the Skeena River, while restricting exploitation of non-target weak stocks.  This analysis also calculates the costs to the fishery of reductions in fishing opportunity aimed at reducing the risk of extirpation of weak co-migrating stocks and allocation priorities. 67  4.1 Introduction Management of mixed stock or multi-species fisheries presents fisheries managers with a number of challenging questions.  For example: is it possible to manage each stock and/or species separately or should the aggregate complex be managed as a unit?  How should a mixed stock fishery targeting stocks with different productivities balance total yield given weak-stock constraints?  Should management allow unproductive stocks to be depressed or extirpated by management strategies that take advantage of larger and more productive stocks?  These questions have been prominent in mixed stock fisheries around the world, and they still persist although various approaches have been taken to address them (Ricker 1958, Larkin 1977, Murkowski and Finn 1986 & 1988, Vinther et al. 2004, Hilborn et al. 2012).    Pacific salmon are mainly exploited in mixed stock fisheries and are typically managed as aggregate stocks with overall escapement or harvest rate targets (Walters 1975, Hilborn and Walters 1992, Schnute  et al. 2000, Walters et al. 2008).   Recent adoption of precautionary policies, that require setting specific targets for the different species and spawning stocks, means that new tools are needed to manage these aggregate fisheries so as to respect stock or species constraints.  In Canada, the Policy for Conservation of Wild Salmon (commonly referred to as the Wild Salmon Policy, WSP) aims to manage salmon for sustainable use, with a goal of preventing irreversible harm to any single wild salmon stock (DFO, 2005).  This policy has led to setting specific escapement, or harvest, targets for each salmon population within the various aggregate fishing areas (DFO 2006, Holt et al. 2009, Holt and Bradford 2011).  Under a new precautionary regime individual stocks are being assigned their own targets, but they are still being captured in overlapping, aggregate fisheries, making management strategies much more 68  complex when attempting to optimize yield.  Harvest control rules developed for aggregate stocks are not designed to simultaneously manage every stock to its optimum level. Current approaches tend to manage the aggregate to a specific escapement target, adjusted in an ad hoc manner to address specific stocks of concern as they pass through the fishery (e.g. time-area closures to avoid catching specific weak stocks, weak stock escapement targets, or species specific harvest rate caps).  There is clearly a need for formal optimization analysis to show whether ad hoc approaches are leading to poor decisions about how to implement the WSP policy and to unnecessary losses in fishing opportunity.    Managing fisheries is a complex decision analysis problem with a large number of policy options to be evaluated across a range of spatial and temporal scales.  When attempting to optimize the number and length of openings in a salmon fishing season, the number of control variables and constraints becomes very large, therefore, even small changes in openings may greatly affect the total harvest taken.  Management problems that require trading off many variables in a constrained solution space are an ideal application for a linear programming approach.  Linear programming (LP) models were designed in the 1950s (Danzig 1951) to rapidly converge on optimum solutions for problems involving multiple bounded linear inequalities. Linear programming models can be used to optimize harvest in a mixed stock fishery while meeting stock specific escapement, exploitation rate (or fishing mortality rate) targets or constraints (Murkowski and Finn 1986 & 1988). Optimizing the linear system permits evaluation of different management constraints and allocation decisions on the value of a fishery and costs to each fishery (Mӓntyniemi et al. 2009). Additionally, it is possible to explore various patterns of management and types of information that maximize value of the fishery (Pike 1986, Dorfman 69  and Solow 1987, Mӓntyniemi et al. 2009). LP models are not unknown to fisheries management and have been applied to a number of different problems (Larson et al. 1996, Ahmed 1991, Spencer et al. 2002), but application in recent years has waned while these complex problems persist. Probably the first published application of linear programming in fisheries was in fact for in-season salmon management (Rothschild and Balsiger 1971), with the aim of finding the best allocation of harvesting over the daily run timing of a salmon run entering coastal fishing areas (similar to the approach taken in this study).  An LP approach allows estimation of the optimum fishing pattern for a fleet (or group of fleets) given an economic goal, such as total value of fish landed by the fleet(s). The fisheries problem is expressed as a weighted sum of decision variables (e.g. weekly exploitation rates to be allowed) and constraints.  More broadly, by varying the value associated with the harvest by fleet and constraints placed upon the optimization, it is possible to explore how short-term patterns of in-season fisheries management can affect achievement of long-term (multi-year) decision rules (harvest control rules) or allocation plans.  When constraints applied within the shorter time period (e.g. a year or a fishing season) are derived from the objectives used in development of long-term decision rules, the LP model can expose how application of within-year constraints interact with long-term objectives.    This study applied an LP model in a retrospective manner to evaluate yields that could have occurred for Skeena River (British Columbia) salmon fisheries if managed under different sets of constraints. This model can simulate and optimize an in-season management approach using information on stock composition in a mixed stock fishery to maximize value of landed salmon.  70  The model was also used to evaluate the value of information associated with knowledge of run size and timing of stocks at different levels of aggregation, from individual stock to coarse species-level aggregation. Finally, results were used to generate a “shadow price” for each constraint, i.e. the change in overall value expected through conservation or increased harvest of any particular stock. 4.2 Methods 4.2.1 Case study: Skeena River salmon fisheries The Skeena River is the second largest coastal river in British Columbia and it has active commercial, recreational and First Nations fisheries.  The main commercial target species of salmon are sockeye (Oncorhynchus nerka) and pink salmon (O. gorbuscha). Coho (O. kisutch), Chinook (O. tshawytscha), chum (O. keta) and steelhead (O. mykiss) are intercepted in commercial fisheries and are the main target species for recreational anglers (Walters et al. 2008).  Fisheries and Oceans Canada (DFO) has identified 32 sockeye Conservation Units (CU) for the Skeena River, 12 chinook CUs, four coho CUs, four chum CUs, and five pink CUs (skeenasalmonproject.org). Between June and August, maturing adults of these species all migrate through the main commercial fishing areas outside the river mouth on their way to upstream spawning areas (Figure 4.1), where they are further divided into different populations by stream or lake, management unit, or the Wild Salmon Policy CU framework (Appendix A,  Table A.1).    The Skeena River salmon fisheries were used as a case study for several reasons.  First, the fisheries are dominated by two large commercial fleets (gillnet and seine), which operate in sequence without overlap.  Second, there is a long running test fishery and extensive escapement 71  monitoring provided by Fisheries and Oceans Canada (DFO 2016a, DFO 2016b).  The combination of sequential fisheries and detailed monitoring provides for run timing, escapement, and catch data that can be used to parameterize a realistic simulation model and to perform historical reconstructions.   Third, there is a serious tradeoff problem for at least one of the species caught in the fishery, steelhead, for which target exploitation rates are very low in order to provide fish for upstream recreational fisheries and avoid conservation concern. Such low target rates can potentially prevent the multi-species commercial fishery from achieving expected harvest values that come mainly from sockeye salmon.    4.2.2 Linear Programming Model Structuring a decision problem as a system of linear inequalities makes it possible to quickly find an optimal solution, even when the number of possible solutions is very large (Dantzig 1951).  The in-season management problem for salmon can be represented as an optimization whose goal is to maximize the total value V of the commercial harvest given a set of constraints, where total value is calculated as: V=∑ ∑ 𝑃𝑗 ∗ 𝐹𝑖,𝑗 ∗ 𝑥𝑖𝑛𝑗=1𝑚𝑖=1 .     (eq. 1) Here m is the number of decision periods (e.g. weeks or days) in the fishing season, and n is the number of species and stocks contributing to value over the season.  Pj  is the landed value of fish of stock or species j, and Ni,j is the number of fish of stock j that are at risk to capture by a fishery opening in time period i.  The decision variables xi in this equation are period-specific exploitation rates (proportion of Ni,j caught, constrained between 0 and 1),  assuming all stocks j will be subject to the same rate in each period (i.e. are equally vulnerable to the gears).  The assumption of equal vulnerability of stocks is made as precautionary assumption.  Gillnet 72  fisheries targeting salmon returning to the Skeena are fished with a combination of mesh sizes and hang ratios that varies with opening and target species (Les Jantz, DFO resource management personal communication).  Records of the mesh and hang ratio utilized in each fishery are not available, and even when employing a specific hang ratio and mesh size there is individual variation in the method of fishing that can lead to capture of all lengths of Pacific salmon in gill net fisheries (Karen Burnett, DFO catch monitoring personal communication), while seine fisheries are not size selective.  Maximizing equation (1) will maximize the commercial landed value of the fish caught over the whole fishery season, operating on the mixed set of fish stocks.  To maximize profit of the fishery it is also necessary to account for costs associated with fishing.  Fishermen must assume fixed costs, such as mortgage and license fees, before the fishing season begins; these costs should not affect profitability of an opening within the fishing season. Variable costs associated with fishing can be incorporated into the model using constraints on the weekly harvest rate and/or by expressing Pj as a cost-corrected fraction of the landed fish price.     There is typically a rapid depletion of fish in any spatial salmon fishery opening, therefore the profit maximizing harvest rate (Ueconi) that fishermen would be willing to exert in that opening, absent any regulatory restrictions, can be calculated and used as a constraint on the linear programming solution.  Where there is rapid localized depletion, the number of fish (Ni,j) within the fishing area can be treated as a closed population that is subject to exponential depletion during any opening, i.e. abundance declines rapidly with accumulating effort E at a rate 𝑒−𝑞𝑗𝐸.  Assuming that fishermen stop fishing when price multiplied by the catch per unit effort no longer exceeds the cost of fishing (i.e. when the sum of the value of the fishery in any decision period i 73  reaches ∑ 𝑃𝑗𝐹𝑖,𝑗𝑞𝑗𝑛𝑗=1 = 𝑐𝑜𝑠𝑡), fishermen will not exert effort E beyond the point where ∑ 𝐹𝑖,𝑗 =𝑐𝑜𝑠𝑡∑ 𝑃𝑗𝑞𝑗𝑛𝑗=1 .  This gives an upper bound for effort:      𝐸∗ = −𝑙𝑛(𝑐𝑜𝑠𝑡∑ 𝑃𝑗𝐹0,𝑗𝑞𝑗𝑗)𝑞𝑗         (eq. 2) Which is an economic upper bound for harvest rate for each specific salmon fishery opening:  𝑈𝑒𝑐𝑜𝑛𝑖 = 1 − 𝑒−𝑞𝑗𝐸∗= 1 − (𝑐𝑜𝑠𝑡∑ 𝑃𝑗𝐹0,𝑗𝑞𝑗𝑗)                           (eq. 3) Here, Fo,j is the abundance of stock j at the start of the week. When operating and opportunity costs (or reasonable estimates) are available, the Ueconi constraints in area or time i can be introduced as inequalities:    ∑ 𝐹𝑖,𝑗𝑥𝑖𝑛𝑗∑ 𝐹𝑖,𝑗𝑛𝑗≤ 𝑈𝑒𝑐𝑜𝑛𝑖.   (eq. 4)  Conservation constraints, for each stock or species, aiming to cap annual exploitation rates (or achieve target annual exploitation rates) for each species or stock j can be expressed as:    ∑𝐹𝑖,𝑗∗𝑥𝑖𝑁𝑗𝑚𝑖 ≤ 𝑈𝑚𝑎𝑥𝑗   (eq. 5)   Here Umaxj is the maximum allowable total exploitation rate (for the year) on species or stock j, and 𝑁𝑗𝑡𝑜𝑡 is its total run size (sum of Fij over weeks), this results in n total constraints, one for each stock or species. Note that the exploitation rate target (Umaxj) for each species may vary from year to year in longer term management if Umaxj is specified from a stock-size dependent control rule (e.g., Umaxj varies strongly with stock size if a fixed escapement control rule is used Umaxj=max(0,( 𝑁𝑗𝑡𝑜𝑡-Escj)/ 𝑁𝑗𝑡𝑜𝑡 )) where Escj is the escapement target for stock j and not at all if a fixed exploitation rate rule is used; see Hawkshaw and Walters 2015 for an analysis of optimum control rule choices).  74  The constraining equations (eq. 2 and 3, 5, and the 0<xi<1 bounds for Ueconi and Umaxj) are assembled into a matrix and the resulting system of equations can be solved for the xi that maximize eq. 1 by using the SIMPLEX algorithm developed for linear programming (Dantzig 1951).  For this study, the algorithm was implemented in the R statistical programming language (R Core Team 2014) using the lpSolver package (Berkelaar et al. 2014).     4.2.3 Retrospective analysis The goal of the retrospective analysis was to: 1) show the optimum pattern of weekly fisheries historically, given historical run timings and abundances, in order to contrast that with the fisheries that actually took place; and 2) examine the yields that could have been possible given the observed pattern of recruitment variability and perfect knowledge about run timing and abundance at the start of each fishing season (a subsequent paper uses closed loop modeling to explicitly consider uncertainties in abundance and run timing within each fishing season).    Weekly abundances (Ni,j) were estimated from historical run timing, abundances and fishery openings by species (and for some CUs) reported by DFO scientists (Cox-Rogers 1994, Beacham et al. 2014) and the Tyee test fishery (http://www.pac.dfo-mpo.gc.ca/fm-gp/northcoast-cotenord/skeenatyee-eng.html), along with run reconstructions (chapter 3) that used the Tyee escapement index along with historical catch data.  Ni,j was estimated as 𝑁𝑗𝑡𝑜𝑡*ri,j, where 𝑁𝑗𝑡𝑜𝑡 is total  annual run size of stock j and ri,j is the proportion of the run occurring in week i. Run reconstruction methods provide normal approximations that can be used to characterize ri,j, even for stocks where 𝑁𝑗𝑡𝑜𝑡 is uncertain.  Data on inter-annual variation in 𝑁𝑗𝑡𝑜𝑡 and ri,j were used to 75  realistically characterize the behavior of the different populations for simulation evaluation and to evaluate the historical in-season performance of management (Figure 4.1).  Historical cost information was not available for most years; however the weekly maximum observed harvest rates were available for many years. They show consistent patterns between years, with relatively low maximum exploitation rates observed in weeks near the start and end of the fishery when abundances are low, indicating strong impact of marginal cost on willingness of fishers to exert effort (Figure 4.2).  In this analysis, these historical maximum exploitation rates were assumed to approximate Ueconi for each year’s LP. In parameterizing the linear optimization system of inequalities, historic maximum weekly harvest rates (Figure 4.2; Walters et al. 2008) were used to approximate cost, by setting weekly maximum harvest rate to the observed maximum, over all years.  In-season and inter-annual variation in landed value of the fisheries was not modeled; prices Pj were assumed to be constant over time, as the landed value of salmon has remained constant or declined slightly since the 1980s (G.S. Gislason and Associates Ltd. 2011).  Historical run timing patterns and Ricker stock-recruitment parameters (Hilborn and Walters 1992) were used to generate a reconstruction of the fishery while accounting for changes in recruitment that likely would have occurred if exploitation rates had been different, e.g. if different harvest control rules had been followed (Martell et al. 2008).  Complete time series of stock-recruitment deviations, run timing and run spread information were available at the species aggregate level for 1956-2007 (Walters et al. 2008, Figure 4.3).    The goal of this retrospective analysis was to evaluate the potential relative performance of management with in-season optimization using the LP model. Performance was evaluated by 76  examining total yield and species-specific targets, and comparisons were made between historical outcomes and estimated optimal outcomes using the LP model given perfect information for in-season management. The analysis ignored in-season decision making and possible “implementation errors” that arise in trying to achieve fixed harvest rates (Holt and Peterman 2006, 2008, Hilborn et al. 2009, Collie and Peterman 2012).  Population parameter estimates for the Skeena River salmon stocks, in particular the Ricker a (stock productivity) parameter (Walters et al. 2008, Figure 4.4), were used to set conservation constraints for the linear programming optimization (i.e. using the relationships betsween Ricker parameters and management reference points presented in Hilborn and Walters 1992).  Different conservation constraints for the in-season linear programming were applied in the retrospective analysis to explore differences in yield as the stock or species specific annual exploitation rate constraints were varied relative to the Umaxj values implied by stock-recruitment analysis.  As noted above, the observed weekly maximum harvest rate was used to set an upper bound for harvest rate within any decision period (i.e. Ueconi is used as a cost constraint for the optimization, in addition to the conservation constraints).    4.2.4 Simulation Linear programming optimization of weekly fisheries was used in multi-year simulations to explore: 1) how application of species or stock-based constraints (in-season tactics) should affect the long-term harvest and conservation outcomes, with a goal of achieving different long-term harvest control rules (strategies); and 2) what improvements to yield or conservation outcomes might be possible with species or stock-specific goals applied in the context of mixed stock fishing.  77   Simulations were conducted while examining three typical levels of stock aggregation, which represent achievable management outcomes with different amounts of information about run size and timing.  The highest level of aggregation simulated was the species. In most cases, test fishery and catch data are available at the species level. Many fisheries are currently managed with one target species and by-catch of other species controlled at the species level.  The next level of aggregation simulated was the CU or management unit (MU) for sockeye salmon, while the five other species of salmon remained aggregated.  This type of management is typical of many salmon fisheries in British Columbia (Ann-Marie Huang DFO personal communication).  The lowest aggregated level simulated was individual stock management for all the species except steelhead.    Run timing and run size were assumed to be known without error in the management simulation models (both in-season and aggregate) and no implementation error was applied in calculating the weekly exploitation rates (xi).  The simulation model for each year generated weekly salmon abundances Fij from a run size (𝑁𝑗𝑡𝑜𝑡), a run timing (rij) pattern over weeks, and target escapements and harvest rates.  Run timing of the different stocks was set assuming a normal distribution pattern for rij each year, with inter-annual variability in mean arrival time (timing of the peak of the run), and standard deviation (run spread over weeks), consistent with variability observed in historical analysis of the Skeena fisheries and from the Tyee test fishery (Cox Rogers personal communication, Walters et al. 2008; chapter 3).  Populations were assumed to have Ricker stock-recruitment relationships with parameters typical of Pacific salmon (Myers et 78  al. 1995, 1997, 1999, Hilborn and Walters 1992), including inter-annual variation represented by recruitment deviates wd~N(0,0.6) with an autocorrelation of 0.5 (Hawkshaw and Walters 2015).      In applying an in-season model to the Skeena River fisheries, the decision variable x was the exploitation rate ERi to allow in the commercial fishery for each week i of the commercial fishing season, which extends from late June to September each year.  This decision variable was chosen because historically the Skeena River fishery has been managed to weekly target exploitation rates (Cox-Rogers personal communication, Walters et al. 2008).   Simulation parameters are summarized in Table 4.1. 4.3 Results 4.3.1 Retrospective in-season modeling Retrospective use of the linear programming model with perfect knowledge of future recruitment anomalies gave predictions of annual patterns of openings and closings that would have maximized long-term yield while meeting conservation constraints. Harvest rate based conservation constraints used in a retrospective analysis showed that the optimum pattern of salmon harvest management for the Skeena is to begin early in the season with high effort (Figure 4.5) and then, depending on the exploitation rate constraint applied for steelhead, reduce weekly effort and harvest rate as early as weeks 9, 10, and 11 of the fishing season (Figure 4.5, Figure 4.6, and Figure 4.7 illustrate the impacts under different steelhead exploitation rate constraints).  As the constraint on steelhead harvest is applied in addition to the conservation constraints, the optimum pattern of fisheries openings is to fish earlier to maximize sockeye harvest before the steelhead constraint becomes binding (Figure 4.7).  The current management practice has shifted from the historic pattern and does not match the optimum pattern (Figure 79  4.5); the new practice is to delay opening the fisheries, concentrate effort in the middle or near the end of the season and end fishing early (well before the end of the sockeye runs) because of steelhead allocation decisions.   This analysis shows that the current management pattern of late openings and earlier closures could be changed to improve yield in mixed stock fisheries by beginning fishing earlier and allowing limited fishing when steelhead are co-migrating (Figure 4.5c).  Using different conservation constraints for the in-season optimized linear programming in a retrospective analysis showed dramatically different yield depending on the severity of the constraints (Figure 4.8).  The pattern of average yields over the retrospective period showed that for a large range of harvest rate targets based upon conservation constraints the average yield is unaffected (Figure 4.8a), though the exact point of diminishing return differed for each combination of stocks and run timing.  When a weaker co-migrating species is exploited to its conservation limit harvest rate (i.e. Umaxj for the simulation), the yield of the stronger co-migrating species is much less constrained. Although average yield is reduced when applying more stringent harvest rate constraints (i.e. constraint << Umax), there are no years in which the fisheries are fully closed (Figure 4.8).   Using escapement targets as conservation constraints (i.e. Umaxj varying from year to year with 𝑁𝑗𝑡𝑜𝑡) resulted in more dramatic reductions in yield than using fixed harvest rate constraints.  Additionally, when increasingly restrictive escapement targets were used as conservation constraints, fisheries were closed more often (Figure 4.8b). When a stock is close to or below an escapement target, the harvest of the more abundant co-migrating stocks is very strongly 80  constrained.  There is a pattern of strongly diminishing returns when conservation escapement targets are brought up to levels usually associated with conservation limits (i.e. when fixed escapement targets range from a low proportion of Smsy (e.g. the 40% Smsy suggested by Holt et al. 2014) up to Smsy (recommended by Johnston 2013)).  As the fixed escapements targets for all stocks are increased, the number of years without fishery openings increases as well (Figure 4.8b).    When examining the outcomes of using harvest rate conservation constraints, two major factors constrained yield.  These factors were expressed as binding constraints in the linear program solution and can be evaluated in terms of either lost value (dollars) to the fishery or forgone yield (numbers of sockeye).  In the retrospective evaluation, economic constraints on the weekly maximum harvest Ueconi and allocation constraints on steelhead stocks were the primary binding constraints (Figure 4.9).  Binding constraints arose because maximum weekly harvest rates due to economic, and steelhead allocation, which limited yield in the early and late parts of the fishing season.  These economic constraints (based upon observed historic maximum weekly harvest rate) limited fishing in both the beginning and the end of the fishing season, while the overlap in run timing between the steelhead return and the larger, more productive sockeye return meant allocation constraints applied to the steelhead limit harvest rates at the end of the fishing season.  Applying allocation constraints to the steelhead return significantly reduced sockeye fishery yield when allowable steelhead exploitation rates were constrained to 26% or less (Figure 4.9).  When the steelhead constraint was increased to allow harvest rates above 26% the weekly Ueconi constraint became the most binding constraint. 81  4.3.2 Simulation testing of in-season management Using escapement targets for multiple stocks generally resulted in reduced yield and fishing opportunities.  Yield decreased both as the number of constraints increased because of finer scale management (moving from species to CU to individual stock constraints), and across a range of fixed escapement constraints.  Yield was maximized only when conservation constraints were set to be in a specific range of escapement targets for most levels of aggregation.  There was a pattern of diminishing yields that occurred when escapement targets were set too high, but there was also a reduction in yield when escapements were set too low.  The yield when fisheries were opened increased as the escapement constraints moved from a very low number for each stock and approached Smsy.  However, as the constraint increased towards Smsy there was a larger fraction of years of simulation for which the constraints severely restricted fishing opportunity (Figure 4.10).  This pattern of diminishing opportunity was exacerbated as the number of modeled constraints increased (as management is done on a finer scale).  The variability in the yield (measured as the standard deviation of yields over time) over the simulations showed a similar pattern to the average yield, peaking at an intermediate value.  Conservation outcomes (measured as the percentage of stocks returning at a less that 10% of Smsy) were poor when low escapement targets were used, but improved as the escapement targets approach Smsy.  This resulted in a tradeoff between yield and conservation outcome (Figure 4.11), leading to a curved relationship between conservation outcome and average yield for a range of conservation constraints (Figure 4.11).  Conservation outcomes can be maximized for any level of aggregation, but average yields corresponding to those conservation outcomes are dramatically reduced as stocks are managed at a finer level (because protection of just a few very small stocks led to severe reductions in harvest of larger, more productive stocks). 82   Using fixed harvest rates (not varying from year to year with stock size) as constraints on co-migrating stocks enabled high levels of yield for the mixed stock fishery across a wide range of conservation constraints, and results were nearly the same across levels of aggregation.  Average yield over the simulations was maximized at approximately Umsy of the most abundant stock, when constraints were applied in a highly aggregated fashion (species), but yield was high across all levels of aggregation for basically the same range of harvest rate constraints (Figure 4.12b). As in the retrospective analysis, the simulation showed fisheries were almost never closed when managed under fixed harvest rate constraints (Figure 4.12a). Conservation outcomes (percent of returns <10% Smsy) were good with low harvest rate constraints (for more aggregated simulations) and worsened as the harvest rate constraint increases beyond the Umax of the less productive stocks (Figure 4.12c).   Tradeoff curves generated for each level of aggregation showed that conservation outcomes can be maximized at any level of aggregation, but there is a benefit in terms of yield of managing at a more aggregated level, i.e. of ignoring conservation-escapement goals for minor stocks (Figure 4.13).   4.4 Discussion Fisheries are usually modeled to determine how to manage harvest at scales ranging from estimating Smsy or Umsy for a single stock using spawner recruitment analysis (e.g. Ricker 1954, Daklberg 1973) to a Management Strategy Evaluation computing performance metrics to identify which management procedures make the most preferred trade-offs between multiple objectives (including socio-economic and biological impacts) (e.g. Punt et al. 2016).  An LP model can be used to examine how different management strategies impact a mixed stock fishery; this allows an intermediate level of complexity to be evaluated easily.  Here the LP is 83  used to model the impacts of river mouth commercial fisheries on multiple stocks co-migrating through the fishing grounds; with extension the same LP framework can be used to model more complex spatial and temporal fisheries to explore the impacts of multiple fisheries on different stocks.  This LP model allows us to explicitly model the temporal pattern of fisheries through the fishing season and demonstrate how a mismatch in timing of fisheries to abundance can lead to lost harvest (Adkison and Cunningham 2015).  It also integrates bycatch constraints into management strategy modeling.  The optimum harvest strategy for a fishery might be different if the biological constraints of mixed stock fisheries are actively modeled, instead of being applied as a constraint after the strategy for the most abundant stock has been chosen (e.g. for Sakinaw sockeye and Interior Fraser River coho window closures are applied independently of the escapement or harvest plan for Fraser sockeye (DFO 2017)).    There is a trend in salmon management to move from management characterized by aggregation of stocks and management of fisheries by target species to management by stock.  Some authors (Guillen et al. 2013, Benson et al. 2016) have shown that mixed stock fisheries lose a great deal of value when all constituent stocks are managed to MSY escapement targets.  However, there remains a need to manage fisheries to safeguard salmon genetic diversity.  Unfortunately, the current WSP is sometimes interpreted as requiring all stocks to be managed to an escapement target.  This is not a practical solution for Pacific salmon stocks as there is a wide diversity in both life history, and monitoring of stocks (Holt et al. 2009).   Given the significant data gaps in stock-recruitment time series, an LP can be used to generate fishing plans that meet the intent of the WSP without requiring expensive stock based management and monitoring, and without incurring the socio-economic costs of foregone harvest and unpredictable fishing opportunity.  84  This analysis shows that harvest rate constraints can be used to safeguard weak stocks co-migrating through a mixed stock fishery. In the absence of stock specific benchmarks and complex evaluation of management strategies to meet those benchmarks, the LP model with harvest rate based constraints seems to enable fisheries while remaining true to the spirit of the WSP; that is, restricting overharvest of the salmon populations in the mixed stock fishery, while maximizing the socio-economic benefits of harvest.  Further, the analysis presented here shows that finer-scale stock aggregation is not required when managing a mixed stock fishery using harvest rate constraints; outcomes in terms of harvest and escapement are consistent across all levels of aggregation.    Linear programming models can be used to create in-season fishing plans that can increase fishery yields and improve conservation outcomes. However, it is important to note that findings here are generated assuming both no implementation error (Holt and Peterman 2006) and accurate knowledge of stock size. Creating an in-season fishing plan based on optimized linear programming results (or any method) runs the risk of overharvesting in specific situations where 1) a small return comes in early, mistakenly giving the impression of a large, normally timed run and 2) abundance-based harvest control rules are misapplied (i.e. errors in estimating the run size result in a harvest target that is too high, and a high harvest is taken following the in-season optimum pattern before the true run size is calculated).  Presumably to avoid such problems, the current management practice is to delay harvest until the run size has been confirmed, then attempting to catch the full TAC before steelhead closures come into effect.  This current practice has twin negative effects.  First, it tends to concentrate the harvest on a small timing component of the return resulting in uneven harvests on the stocks that make up the aggregate 85  run.  The result is that some stocks are subjected to a very low harvest rate while other stocks are subjected to harvest rates that exceed Umsy (Korman and English 2013).  The second consequence is that there is lost harvest when the delay in initiating fisheries and the early closure to protect steelhead restrict the fishing time so that the harvest called for in the harvest control rule cannot be taken.  Additionally, the long-term implication may be selection for earlier run timing, or deterioration of the variability in stock run timing which will be detrimental in the face of warmer, higher discharges already observed with climate change (Rand et al. 2006, Schindler et al. 2010, Reed et al. 2011).   The LP solution calls for fishing early to avoid this “squeeze”, but it is unclear whether the perceived increase in risk of overfishing by doing so will be acceptable to DFO managers.  The linear programming model presented does not consider the likelihood of fisheries choosing not to pursue a very small harvest at all, in years/weeks for which Ueconi is low.  It is likely that the Ueconi used is a conservative overestimate of exploitation rate when returns are low. This overestimate of exploitation rate at low abundance by the linear programming solution could mitigate some of the implementation error (i.e. the fishery called for using the LP solution would not be prosecuted as fully as modeled when returns are low resulting in a less severe overharvest when there is a misapplication of abundance-based rules).  The economics of running a fishing vessel would make it likely that harvests would not be taken at very low levels (Gordon 1954, Tidd et al. 2011).  The economics in this implementation of a linear programming optimization are represented as fixed upper constraints on weekly harvest; however a better understanding of the costs (fixed and variable) could be used to inform the objective function of the optimization 86  producing a more realistic approximation of fishery behavior in which fishers might not approach the economic constraint at all.  One of the strengths of the LP approach is the ability to explore the impact that overlap in run timing and variability in run timing has on the ability to meet harvest targets in a mixed stock fishery when constrained by conservation or allocation concerns for co-migrating stocks.  In Bristol Bay fisheries several studies demonstrate that there is a substantial cost to fisheries of a mismatch between return timing and openings and a danger to stock structure (Adkison and Carney 2014, Adkison and Cunningham 2015).  Stock-recruitment analysis indicates that smaller and less productive stocks of the Skeena system can sustain harvest rates close to the Umsy harvest rate of the large productive sockeye stocks (Walters et al. 2008).  However, in the case of steelhead, an allocation decision to restrict impacts on this species limits the ability to maximize yield.  By allowing higher impacts on steelhead, the magnitude of forgone harvest can be reduced and harvest be more balanced across the sockeye stocks being targeted.  In large systems like the Skeena River, it is possible to implement harvest management tactics that involve spatial as well as temporal structuring of exploitation rates, and such options can in principle be represented in the LP framework.  For example, the most productive Skeena sockeye stocks are the enhanced Fulton River and Pinkut Creek spawning channel stocks, which can sustain higher exploitation rates than any of the wild stocks.  At present, restricted harvesting in the river-mouth fisheries leads to substantial harvestable surpluses (“over escapement”) of these stocks to their stream mouths in Babine Lake, and there is a program to harvest these surplus fish (so-called ESSR, Escapement Surplus to Spawning Requirements fisheries), which provide 87  terminal fishery harvest opportunities, but the quality of flesh is lower.  Walters et al. (2008) compared long term expected yields under mixed stock harvesting to the maximum achievable if each stock were fished to its optimum level, and concluded that there would not be a substantial (<10%) gain by moving entirely to in-river terminal fisheries.  Future analyses of Skeena harvest policies should likely include at least some exploration of ESSR options as a way to maximize value of the fisheries when constrained by conservation or allocation needs for other fisheries (e.g. as a potential way to avoid steelhead by-catch or to enable stock specific FSC fisheries).  88  Table 4.1.  Summary of values used to parameterize the simulated populations and optimization.     Parameter Description ValueVulnerability of Sockeye to Fishery 1Vulnerability of Pink to Fishery 1Vulnerability of Coho to Fishery 1Vulnerability of Chum to Fishery 1Vulnerability of Chinook to Fishery 1Vulnerability of Steelhead to Fishery 1Value of Sockeye to Fishery 30Value of Pink to Fishery 5Value of Coho to Fishery 1Value of Chum to Fishery 1Value of Chinook to Fishery 30Value of Steelhead to Fishery 0Mean recruitment anomalies 0Standard deviation of recruitment anamolies 0.6Autocorrelation in recruitment anomalies 0.589   Figure 4.1.  Distribution of historic peak of return of all species of salmon to the Tyee test fishery (1956-2007).   90   Figure 4.2.  Weekly maximum observed harvest rates (1982-2007).  Boxplots show the distribution of observed weekly harvest rates, the red points are the maximum observed values used as an economic constraint Ueconi.  91     Figure 4.3.  Species-specific annual recruitment deviates used in retrospective analysis.  92                 Figure 4.4.  Boxplots of stock specific Ricker a parameters (upper) and histograms of associated Umsy values (lower) used in the simulations presented by species. 93   Figure 4.5.  Patterns of observed and predicted optimal weekly harvest rates for the Skeena River mixed species Pacific salmon fishery. Panel (a) shows observed distribution of weekly harvest rates from 1982-2007. Panels (b-c) show the distributions of optimal weekly harvest rates suggested by retrospective analysis, using Umax for coho, chum, chinook, and pink salmon species as well as Uecon from the weekly maximum observed harvest rates (1982-2007) assuming: (b) maximum allowable steelhead harvest rate (HR) of 3%; and (c) no steelhead allocation constraint.  Panel (d) summarizes the difference in outcome between historical and retrospective fishing patterns under the different scenarios (1 no steelhead allocation constraint, and 2 steelhead constrained to no more than 3% HR). Dark lines represent median values, boxes represent the interquartile range and whiskers represent the full range.(a) (b) (c) (d) difference in sockeye catch week of fishing season harvest rate harvest rate harvest rate scenario 94     Figure 4.6.  Scenario: no steelhead constraint showing the pattern of optimum weekly harvest rate from retrospective analysis (a), using Umax as a conservation constraint and Uecon from the weekly maximum observed harvest rates (1982-2007), without an allocation constraint for steelhead.  Panel (b) shows the annual sockeye harvest by brood year with the red line representing the historical harvest and the black the optimized retrospective harvest.  Panel (c) shows the annual difference between retrospective and optimized harvest, while panel (d) summarizes the overall increase in sockeye harvested.   Year Year catch (number of sockeye) difference (number of sockeye) difference (number of sockeye) Week harvest rate 95   Figure 4.7.  Scenario: 3% steelhead constraint showing the pattern of optimum weekly harvest rate from retrospective analysis (a), using Umax as a conservation constraint and Uecon from the weekly maximum observed harvest rates (1982-2007), with an allocation constraint of no more than 3% harvest rate for steelhead.  Panel (b) shows the annual sockeye harvest by brood year with the red line representing the historical harvest and the black the optimized retrospective harvest.  Panel (c) shows the annual difference between retrospective and optimized, while panel (d) summarizes the overall decrease in sockeye harvested.   difference (number of sockeye) difference (number of sockeye) catch (number of sockeye) Year Year Week harvest rate  96   Figure 4.8.  Impact of different conservation constraints applied to simulated fisheries using retrospective recruitment deviates, and run timing patters (1956-2007).  In both cases Ueconi constraints were applied based upon historic observed maximum weekly HRs. Panel (a) shows the impact of different levels of conservation constraint applied to bycatch species on average sockeye catch where the conservation constraint is expressed as a harvest rate cap of between 0 and 100% allowed on the by-catch species. Panel (b) shows the impact of different levels of conservation constraint on yield where each bycatch stock is constrained to have an escapement greater than or equal to its conservation goal.  In this figure the escapement goal is calculated as a percent of each stock’s Smsy.  (in panel (b) the red line represents the % of years that would have been closed if this constraint had been applied).97     Figure 4.9.  Average yield in the mixed stock fishery assuming Uecon constraints on weekly harvest, Umsy as conservation constraints on all stocks, and varying the allocation constraint for steelhead between of 0 and 100% allowable harvest rate.   98   Figure 4.10.  Effect of using different escapement targets as conservation constraints on the non-target stocks on yield at different levels of aggregation.  Each dot represents the average outcome of multiple simulations of many stocks with management controls being applied at different levels of aggregation. (Black dots are aggregated to species level, blue to management unit or conservation unit level, and red to stock level).  The top pane (a) shows the effect on average yield in the fishery of applying conservation constraints based upon escapement targets.  The center pane (b) shows the effect of different escapement targets as conservation constraint on fishing opportunity measured as proportion of seasons closed to fishing, and the bottom pane (c) shows the impact of escapement based conservation constraints on the achieved escapements (here low escapement is considered <10% Smsy). average yield (number of salmon) closed seasons (percent) stocks low (percent) escapement constraint (%Smsy) 99   Figure 4.11.  Trade-off between conservation outcomes and yield for mixed stock fisheries simulated at different levels of aggregation with an escapement based conservation constraint. Each dot represents that average outcome of multiple simulations of many stocks with management controls being applied at different levels of aggregation. (Black dots are aggregated to species level, blue to management unit or conservation unit level, and red to stock level).   stocks low (percent) average yield (number of salmon) 100   Figure 4.12.  Effect of using different harvest rates as conservation constraints on non-target stocks on yield at different levels of aggregation. Each dot represents the average outcome of multiple simulations of many stocks with management controls being applied at different levels of aggregation. (Black dots are aggregated to species level, blue to management unit or conservation unit level, and red to stock level).  The first pane shows the effect of different harvest rates as conservation constraint on fishing opportunity.  The second panel shows the effect on average yield in the fishery of applying conservation constraints based upon harvest rates, and the final panel shows the impact of harvest rate conservation constraints on the achieved escapements (here low escapement is considered <10% Smsy).   average yield (number of salmon) harvest rate constraint  stocks low (percent) closed seasons (percent) 101   Figure 4.13.  Trade-off between conservation outcomes and yield for mixed stock fisheries simulated at different levels of aggregation with harvest rates applied as conservation constraints. Each dot represents the average outcome of multiple simulations of many stocks with management controls (i.e. constraints) being applied at different levels of aggregation. (Black dots are aggregated to species level, blue to management unit or conservation unit level, and red to stock level).  stocks low (percent) average yield (number of salmon) 102  Chapter 5: Improved estimates of run timing and size for Skeena River sockeye using a Bayesian state-space model In-season harvest management of Pacific salmon (Oncorhynchus spp.) stocks is extremely time-sensitive; fishing seasons are short and decisions about harvest levels have to be made while information about the run size and timing is still being collected.  Harvest control rules that use stock size to determine allowable harvest rates, or allowable catches, require accurate abundance estimates.  To improve in-season estimates of abundance, a Bayesian state-space model that quantitatively incorporates prior knowledge about the run timing and stock size from several sources, including historical run timing, stock-recruitment data, and previous year classes was developed and tested with simulated and Skeena River data.  With simulated data, the Bayesian state-space method made somewhat conservative abundance estimates early in the season, but slightly over-predicted abundance late in the season. However, overall run size estimates were more accurate and precise than other methods.  With Skeena River data, the Bayesian state-space methods performed better at estimating abundance than the current in-season area-under-the-curve (AUC) model. 5.1 Introduction Accurate estimates of abundance are necessary for harvest-based management. Fisheries targeting migrating Pacific salmon (Oncorhynchus spp.) stocks are typically managed using a harvest control rule where a fixed number of fish can be harvested after an escapement goal is met.  This type of management requires estimating in-season abundance, which can be difficult and often leads to suboptimal fishing efforts and catches (Adkison and Cunningham 2015, Link and Peterman 1998).  Harvest rates based on inaccurate in-season abundance estimates may fail 103  to maximize benefit from the resource, or create a risk of overharvesting.  In addition, timely run size estimates are essential for abundance-based harvest control rules because the majority of the harvest takes place when salmon are quickly migrating through marine and freshwater fishing areas.  Although early underestimates of allowable harvest can be somewhat corrected by later additional in-river harvest, the commercial and First Nations fisheries often resist this method due to the reduced value of in-river fish (Su and Adkison 2002). Fish captured in-river have begun the physiological changes associated with freshwater spawning (Groot and Margolis 1991), which rapidly degrades the condition of the fish, reducing their food and commercial value.  New modelling tools that more accurately and precisely estimate run size and timing can are needed to minimize risk of overfishing and optimize the timing of fishing effort and the size of catches In-season run size and timing estimates for Pacific salmon have been calculated in a variety of ways.  One of the oldest methods, referred to as the area under the curve (AUC) method, is to expand in-season catches by the proportion of the run expected to be in the fishery (commercial or test) at any particular time.  However, run timing, as well as run size, varies between years (Figure 5.1), so methods that rely upon an assumed run timing are inaccurate and imprecise until it is possible to correct the estimate of run timing in-season. Typically, this correction is not possible until half of the run has arrived (i.e. when catches begin to decline), which often leads to poor estimates of total run size at the beginning of the fishing season.  This becomes dangerous in the scenario of a “small run coming early”, where an earlier than normal run timing is incorrectly interpreted as a large run size, causing large overestimates of the run size at the beginning of the fishing season.  The consequence may be overzealous harvest with associated 104  conservation implications (Adkison and Cunningham 2015, Catalano and Jones 2014). Alternately, if risk averse managers become disillusioned with the repeated poor performance of the method, they may consistently set low catch limits, leading to lost harvest opportunities and associated socio-economic costs.  The imprecision of early in-season abundance estimates along with the importance of accurate run size for abundance-based harvest control rules has led to several suggestions for better ways to estimate run size.  A common approach is to combine pre-season forecasts of run size with in-season data to improve run size estimates.  Walters and Buckingham (1975) used a weighted average method to combine Ricker stock-recruitment estimates of run size with in-season run size estimates for sockeye salmon (O. nerka) on the Skeena River, British Columbia (BC).  Run size for Bristol Bay, Alaska (AK) sockeye fisheries has also been estimated using the weighted average and Bayesian methods to combine preseason forecasts of run size with in-season data, including cumulative commercial and test fishery catch per unit effort (CPUE), total commercial catch, and observed escapements (Catalano and Jones 2014, Fried and Hilborn 1988). Hyun (2002) and Hyun et al. (2005) expanded upon these analyses, by including test fishery catches, age-specific proportions from the test fishery, commercial and subsistence fishery catches, observed escapements, and age-specific proportions from the stock-specific run size, in the joint estimation of the run size and timing of five sockeye salmon stocks in the Bristol Bay run.  Additionally, combining in-season catches with in-season factors, such as sex ratios in pink salmon (O. gorbuscha), has been used to improve predictions of run size and timing in southeast Alaska (Zheng and Mathisen 1998).  As an alternative to the weighted average method, catch in any particular day can be used to predict the final run size, as a linear relationship between these 105  variables has been demonstrated for Bristol Bay (Mundy 1979) and Skeena River (Cox-Rogers 1997) sockeye runs. However, this method is not currently used.     The Skeena River is home to commercial fisheries for sockeye, pink, and chinook (O. tshawytscha) salmon, all of which are managed in-season. The commercial fishery primarily takes place near the river mouth or slightly in-river.  A gillnet fleet targeting sockeye salmon takes the majority of the commercial catch, while catches of the other species depend on their timing and abundance.  The pink and sockeye fisheries in this area are managed with an abundance-based harvest control rule, but  delays in estimating abundance and uncertainty about the accuracy of these estimates has led to delayed openings for the commercial fisheries.  When fishery openings are delayed it can result in two problems: the inability to harvest the target amount results in opportunity cost to the fisheries; and the concentration of harvest on a small proportion on the run, which unevenly impacts the stocks in the run (Adkison and Cunningham 2015). In this paper, we compared the current method of estimating run size for various salmon species on the Skeena River to both a new Bayesian state-space method and an earlier weighted average method (Walters and Buckingham 1975).  Using both simulated and historical data, we demonstrate that improved run size estimation can be achieved with analyses that explicitly incorporate multiple sources of in-season data and prior knowledge about run size and timing. 5.2 Methods To examine the performance of the new Bayesian state-space method, estimates of run size and timing were compared between the new model, the existing AUC method, and the weighted average model proposed by Walters and Buckingham (1975).  The three models were first 106  applied to historical data from the Skeena River to examine their retrospective performance in estimating run size and timing of the salmon stocks during the fishing season.  Simulation tests were then conducted to evaluate performance of the three models in distinguishing the scenario of a “small run coming early”, which can cause large overestimates of the run size early in the season and overly large harvests in response.  5.2.1 Modeling Details 5.2.1.1 Area under the curve method (AUC) The AUC method is the current method used in-season to estimate Skeena River salmon run size (?̂?𝑡).  With the AUC method, the cumulative sum of the catch (Ci) and escapement (Ei) up to day i is inflated by the cumulative proportion of the run that has passed the main fishing grounds by day i (∑ 𝑝𝑑𝑖𝑖0 ).   ?̂?𝑡 =∑ 𝐶𝑖𝑖0 +∑ 𝐸𝑖𝑖0∑ 𝑝𝑑𝑖𝑖0     (1) ∑ 𝑝𝑑𝑖𝑖0  can be calculated using the logistic approximation of the cumulative normal distribution, with a mean corresponding to the day that the peak of the run will arrive at the test fishery (runmean) and a standard deviation (runsd) that reflects the spread of the run timing around that peak. Both runmean and runsd  are based on returns in previous years.   𝑝𝑑𝑖 =1(1+𝑒𝑥𝑝(−1.7∗(𝑖−𝑟𝑢𝑛𝑚𝑒𝑎𝑛)𝑟𝑢𝑛𝑠𝑑)) (2) The key assumption in calculating pdi  is that the run timing is the same between years (i.e. runmean and runsd are stationary), yet this  is rarely true, as demonstrated in chapter 3 (Figure 5.1), and violation of this assumption leads to poor predictive ability for the AUC method.  The AUC 107  method improves once the peak of the run has passed, as runmean and runsd can be calculated for the current year.  This improvement requires in-season correction of the model, and variability in the test fisheries catches can make it difficult to determine when the peak of the run has arrived when using visual inspection of the data or fitting eq. (2) to those data. 5.2.1.2 Weighted average method To improve in-season estimation of sockeye and pink run size, Walters and Buckingham (1975) use a weighted average of the in-season AUC estimate and a pre-season forecast.  The pre-season estimate  is the Ricker stock-recruit prediction of the run size inyear t (Rt), which depends on the escapement r years earlier (St-r), where r is the average generation time: 𝑅𝑡 = 𝑆𝑡−𝑟 ∗ 𝑒(𝑎−𝑏∗𝑆𝑡−𝑟)   (3) The in-season estimate comes from the AUC method.  These two run size estimates are combined into a weighted average as: ?̂?(𝑊) = 𝑤𝑖 ∗ (𝑅𝑡) + (1 − 𝑤𝑖) ∗ (𝑅?̂?) (4) The weighting factor (wi) varies over the fishing season as: 𝑤𝑖 =𝜎?̂?𝑖2𝜎𝑅𝑡2 +𝜎?̂?𝑖2     (5) Walters and Buckingham (1975) derive the approximate variance of the in-season estimate (𝜎?̂?𝑖2 ), showing how the variance decreases as both the catch and the portion of the run that has passed the fishing area increase.  The variance of the pre-season estimate (𝜎𝑅𝑡2 ) is fixed, so as the fishing season progresses the pre-season estimate of run size is given less weight.   108  5.2.1.3 Bayesian state-space method Bayesian methods have become a useful tool for fisheries management and modeling, and have grown in popularity since their introduction to fisheries applications in the 1990s (e.g. Hilborn et al., 1994; McAllister et al., 1994; Schnute, 1994; Walters and Ludwig, 1994; Reed and Simons, 1996;Kinas, 1996; Punt and Hilborn, 1997).  Bayesian methods apply Bayes’ theorem to determine the posterior probability distribution of some factor of interest.   Bayes theorem states that:  𝑃(𝐴|𝐵) =𝑃(𝐵|𝐴)𝑃(𝐴)𝑃(𝐵)    (6) where P(A|B), the posterior, is the degree of belief in the factor of interest, A, taking into account some data, B.  P(A) is the initial prior assumption about hypothesis A, and P(B|A)/P(B) represents the support that data B provides for hypothesis A.  Punt and Hilborn (1997) introduce the use of Bayesian methods for fisheries, while Kinas and Andrade (2007) review more recent applications of Bayesian methods to fisheries, and Gelman et al. (2014) details the theory for developing Bayesian models.  Modern computers and statistical programing languages allow estimation of the posterior probability distributions, which can be linked to important parameters for management. State-space models operate from the principle that a population has a true state, which is subject to natural variability. Observation of this population is a process that introduces additional sources of variability.  When estimating run size and timing of salmon returns, the two types of uncertainty in any estimate within a season are the “process errors” in size and timing of the return of salmon stocks, and the “observation errors” in measurement and sampling.  Building a 109  state-space model requires accounting for randomness in the state of the population and in the observations of that population (Meyer and Millar 1999, Millar and Meyer 2000, Walters and Martell 2004).  The new model in this chapter combines the Bayesian and state-space techniques in order to evaluate the run size and timing of a salmon stock described by nonlinear equations with several sources of error.   The Bayesian state-space model developed for estimating salmon run size and timing uses a process model of the true state of the salmon run in a time period, and an observation model for the observation process that occurs within a season.  The model assumes that the salmon run within a season is described by a normal distribution, whose mean describes the date that 50% of the run arrives at the test fishery, and whose standard deviation describes the spread of the run around that date.   The expected number of fish Ni arriving on any day i is again estimated using the logistic approximation of the cumulative normal distribution: 𝑁𝑖 = ?̂?𝑡 ∗ (𝑝𝑑𝑖 − 𝑝𝑑𝑖−1).  (7) The ?̂?𝑡 parameter is again an estimate of the total run size in year t and acts as a multiplier by which the normal distribution of run timing is inflated.  This process model explicitly predicts the number of fish at the test fishery in any day of the fishing season. The logistic approximation does not allow for random process deviations from the normal arrival curve shape. Although such deviations, including multi-modal arrival patterns, are commonly observed in more southerly sockeye stocks (e.g. Fraser River), retrospective analysis of run timing patterns (chapter 3) does not indicate such deviations to be common or strong in the Skeena River. 110  The observation model is shaped by how the fish are observed.  Although any observation models are possible, we chose a catch model for the test fishery.  In this model the salmon run is caught in a fishery whose CPUE and catch can be used to infer the run size and timing of the process model.  The test fishery observation model fits the observed catch to a predicted catch in the test fishery in any day (C(T)i).   𝐶(𝑇)𝑖 = 𝑞𝑡𝑒𝑠𝑡 ∗ 𝑁𝑖     (8) Where qtest is the estimated annual catchability of the test fishery and Ni are the expected fish vulnerable to the test fishery in any day.  The observed daily test fishery catches are assumed to be measured with normally distributed error.  The magnitude of the error is estimated in-season.  The test fishery on the Skeena River is physically located upriver from the main fishing ground so the number of fish vulnerable to the test fishing gear must have the catch from the commercial fishery (Ci-1) seaward of the test fishery considered before estimating the test fishing catch.  Three strategies were explored to account for the potential impacts of the seaward fisheries upon the test fishery catches.  The first method assumes catch from previous days is removed from the current days abundance of fish vulnerable to the test fishery based a fixed migration assumption from each fishery.      𝑁𝑖 = 𝑁𝑖 − 𝐶𝑔𝑖𝑙𝑙𝑖−1 − 𝐶𝑠𝑒𝑖𝑛𝑒𝑖−2                   (9) with a second observation model for the commercial catch and effort fit to the previous days catch. 𝐶𝑠𝑒𝑖𝑛𝑒𝑖 = 𝑞𝑠𝑒𝑖𝑛𝑒 ∗ 𝐸𝑠𝑒𝑖𝑛𝑒𝑖 ∗ (𝑁𝑖 )   (10) 111  𝐶𝑔𝑖𝑙𝑙𝑖 = 𝑞𝑔𝑖𝑙𝑙 ∗ 𝐸𝑔𝑖𝑙𝑙𝑖 ∗ (𝑁𝑖 − 𝐶𝑠𝑒𝑖𝑛𝑒𝑖−1  ) (11) The second method explored also assumed catch from previous days was removed from the fish vulnerable to the test fishery.  Only a gillnet commercial observation model is fit, and the gillnet catch and effort data are fit to an average Ni from the three previous days. 𝐶𝑔𝑖𝑙𝑙𝑖 = 𝑞𝑔𝑖𝑙𝑙 ∗ 𝐸𝑔𝑖𝑙𝑙𝑖 ∗ ∑ (𝑁𝑖−2 − 𝐶𝑖−3)31   (12) The final method explored was to only fit to days were there was no large fisheries for the two previous days.  (i.e. do not fit the test fishery observation model when the commercial opening could be cutting a large hole in the run).  All of the methods of dealing with the commercial catch have similar performance, however the final method was chosen because of the timing of data availability in-season.  Commercial catch is reported by hail and verified by landing, often by the time a catch monitoring program has verified the effort and catch data the fishery is finished, so while very useful to reconstruct the abundance, but it is not received in a timely enough way to inform the estimates.  Given that the fishing areas covered by the commercial fleet can cover more than one of migration it is challenging to reconstruct the impact of the fisheries on the number of fish vulnerable to the test fishery in time to inform the in-season estimate of abundance.  In the absence of highly detailed spatial and temporal catch and effort data (e.g. via electronic logbooks or smaller fishery areas) the observation model is applied only on days in which there have been no seaward fishing for two days before.  5.2.2 Data Data available for estimating the sockeye run size includes a mix of pre-season information and information collected within the season.  Data available pre-season includes; sibling estimates 112  (i.e. estimates of age 4 sockeye returning in a given year are related to return of age 3 sockeye returns from the previous year), and spawning numbers the previous generation used to make pre-season abundance estimates.  In-season data includes commercial fishery opening dates, estimates of escapement to the spawning grounds (later in the season), and test fishery catches.  This data can be used to generate in-season estimates of abundance, run timing and whole river escapement.   LGL Ltd. and the Canadian Department of Fisheries and Oceans (DFO) provide estimates of total returns from post-season reconstructions that can be used to judge the performance of the different models in estimating the run size.  Test fishery data are available for the years 1956-2006, while catch, effort and reconstructed returns are available from 1982-2006.  (Cox-Rogers DFO stock assessment personal communication) 5.2.3 Prior Information The long historical time series and extensive post season reconstructions of abundance in the test fishing areas at specific times allowed us to estimate the catchability of the test fishery for every year of operation y.  𝑞𝑡𝑒𝑠𝑡𝑦 =∑ 𝐶(𝑇)𝑖∑ 𝑁𝑟𝑒𝑐𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑒𝑑𝑖,𝑡   (13) The mean and standard deviation of the observed annual catchabilities were used as the prior estimate of catchability in the Bayesian state-space model.  The Ricker stock-recruitment relationship for sockeye of the Skeena River provides a prior estimate for the run size, as well as an estimate of the variance of that estimate in log space. 𝑅𝑡 = 𝑆𝑡−4 ∗ 𝑒(𝑎−𝑏∗𝑆𝑡−4+𝜔𝑡)    (14) 113  Here 𝜔𝑡 were the recruitment anomalies describing the deviations of true recruitment from the expected recruitment.  The parameters of the stock-recruit function including a time series of 𝜔𝑡 values were presented in Walters et al. (2008).  Figure 5.2 summarizes the stock-recruitment data, and the variability around it.  The same stock-recruitment data that provides priors for the variance of the pre-season estimates of abundance using the Ricker model also includes time series of sibling ratios.  Sibling ratios can be used to calculate a second pre-season forecast of abundance (as in Peterman 1982, Figure 5.3): 𝑙𝑛(𝑅𝑡) = 𝑎 + 𝑏 ∗ log (𝑅𝑡ℎ𝑟𝑒𝑒 𝑦𝑒𝑎𝑟 𝑜𝑙𝑑𝑠𝑡−1) + 𝜀𝑡  (15) Peterman uses a linear regression in log space where a is the intercept and b is the slope of the line and Ɛt are the normally distributed differences between the observed and predicted returns to predict the return of older age cohorts of salmon from younger siblings.  This pre-season estimate and the observed return can be used to estimate the variance associated with this pre-season estimate, and incorporated into the Bayesian state-space model as a prior estimate.  The test fishery and reconstruction work are summarized in Walters et al. (2008) and available through the DFO (Tyee website http://www-ops2.pac.dfo-mpo.gc.ca/fos2_Internet/Testfish/rptDTFDTyeeParm.cfm?fsub_id=585), which provides annual distributions of the sockeye run that can be used to generate prior distributions for the mean and the standard deviation of the normal curve that approximates the run (Figure 5.4).  The Bayesian state-space model defined by eq. (7) and (8) was implemented in the Stan (Carpenter et al. 2017, Stan Development Team 2018) programing language. A posterior probability function for the model and posterior probability distributions for the parameters of interest (in this case, run size, mean run timing, and the standard deviation of the run) 114  were estimated using MCMC sampling (Stan Development Team 2014) the posterior sample size was 12,500 steps, with a burn in of 12,500 steps, the convergence of the model was checked using the potential scale reduction factor and visual inspection of trace plots).  5.2.4 Retrospective analysis Historical data from the Skeena River fisheries was used to evaluate the three different methods (AUC, weighted average, and Bayesian state-space) under conditions with real world variability in fishery operation, run size, and run timing.  This was done to quantify accuracy and precision in run size estimates across the three models and to compare how soon in the season those results were obtained. Models that produce credible run size estimates with fewer days of in-season data are more useful to managers in providing information used to set harvest limits.  5.2.5 Simulation To evaluate the ability of the models to distinguish a small sized run coming early, the three models were used to predict run size when subjected to a number of different run size and timing scenarios; by using a mean of the historical fishing efforts reported by the DFO where available (Cox-Rogers pers. com) and from Walters et al. (2008) and catch predicted from the weekly efforts and estimated catchabilities (qi) for the fisheries.  Estimates were generated for 10 weekly time steps through 50 simulated fishing seasons.  The data was simulated with a small return of 600,000 sockeye arriving 20 days before the normal peak of the run.  5.3 Results Retrospective analysis shows that the Bayesian state-space method and the weighted average method both show improved predictive ability of total run size over the AUC method at the 115  beginning of the fishing season (Figure 5.5). The weighted average and Bayesian state-space methods both tend to underestimate run size at the beginning of the fishing season while the area under the curve method over predicts run size (Figure 5.5).  The Bayesian state-space method continues to provide underestimates through the fishing season, while the weighted average and the AUC method tend to overestimate the final run size.  In general the Bayesian state-space method provides a slightly more accurate and precise estimate of the true run size. When examining performance of the three different models using 26 years of retrospective data, all models had poor predictive ability in the early part of the season due to uncertainty in run timing.  Variability in test fishery catches and low numbers of fish available to the test fishery early in the season resulted in little information to update run size estimates for the weighted average and Bayesian state-space methods.  As a result, the weight of information for these methods is entirely on the pre-season forecasts during the early stages of the fishing season. Preseason estimates are mostly based upon stock-recruit analysis and sibling estimates that both allow for the possibility of large returns but treat them as very unlikely (Figure 5.2 and Figure 5.3) and as a result, the in-season Bayesian state-space and weighted average estimation models tend to underestimate large runs early in the fishing season (Figure 5.5). As the season progresses, the test and commercial fisheries have increased catches, so the catches in the commercial and test fisheries become the main determinant of the run size estimate.  In contrast, the AUC method does not formally use pre-season data, so consistently overestimates abundance early in the season.  Estimating run size of a simulated “small run coming early” suggests that the Bayesian state-space method is consistently better at detecting this special case than the AUC method or the 116  weighted average methods (Figure 5.7).  The models informed by stock-recruitment or other pre-season indices begin by overestimating the run.  The estimate of run size improves for the Bayesian state-space model as test fishery information is incorporated. Test fishery information indicated the run is peaking, resulting in the Bayesian state-space model estimates quickly improving, but continuing to have a +40% bias. The weighted average method improves more slowly as test fishery information accumulates, but mean estimates still show +80% biases.  The AUC method is extremely positively biased early in the season but bias quickly declines as more information accumulates. As the peak of the run passes, AUC shows a relatively high negative bias in run size for the remainder of the season. 5.4 Discussion Salmon stock management is often closely monitored and controlled in-season (Woodey 2000, Dankel at al. 2008).  Therefore, any harvest control rule that depends on stock sizes to determine allowable harvest rates, or allowable catches, requires reliable in-season estimates of abundance.  Without reliable in-season estimates of stock size an unreasonably high implementation error will be introduced (Peterman 2004).  A key problem with managing mixed stock fisheries is bycatch of co-migrating species and stocks (DFO 2005). Early determination of run size and timing of different species or stocks allows managers to trade-off harvests of different stocks or species within a useful time-frame.  The Bayesian state-space method developed here is a significant improvement on the current approach, which is based upon a fixed estimate of run timing (the AUC method).  In addition, the Bayesian state-space method provided two improvements to the run size and timing estimates, which will benefit managers.  First, it provides an explicit measure of the uncertainty in the forecasts, which allows managers to 117  quantitatively judge the risk of overfishing.  Second, the Bayesian state-space method can more quickly detect the dangerous failure case for salmon management where a small run comes early and appears to be a large or normally sized run, thus providing a more reliable and timely estimate of run size.   The Bayesian state-space method developed here improved timeliness and accuracy of run size estimates for migrating salmon. This method was better at estimating run size earlier in the return and at detecting a “small run coming early”.  There are multiple benefits associated with earlier and more accurate estimates of return size, including benefits for both conservation and commercial fishing (Walters and Pearse 1996, Link and Peterman 2011, Adkison and Cunningham 2015).  More accurate estimates of run size early in the return increase the possibility of avoiding the potentially catastrophic overharvesting associated with misreading a “small run coming early”. Additionally, earlier determination that a small run is coming allows managers to restrict or close fisheries sooner, thereby reducing the chance for accidental overharvest and accruing conservation benefits.  Earlier estimates of smaller runs have economic value as well because earlier estimates allow harvesters to make a decision about exiting the fishery to pursue other activities without the fear of missing a large harvest opportunity.  Economic benefits for the commercial fishery are also generated when a large run is  detected early.  Earlier estimates of large runs gives fishers more time to harvest larger than usual returns before the fishing season ends due to closures designed to meet allocation or conservation goals for co-migrating stocks. One drawback of the Bayesian state-space method is that it tended to overestimate run size at the end of the fishing season. This could lead to higher than desired harvests, if abundance-based TAC accumulates because fishery openings are delayed.   118  Enabling earlier fisheries by generating an earlier estimate of run size can avoid “tail end loading”, or overharvesting a portion of the run because harvests are compressed into a shorter time period by delays in estimating run size.  Tail end loading  leads to selection for fish with earlier return timing, which may reduce natural run time variability.  This is especially relevant as climate change impacts in-river temperature and discharge patterns throughout the season (Quinn and Adams 1996, Rand et al. 2006, Reed et al. 2011).  For commercial fisheries, timely estimates of run size are required when using an abundance-based harvest control rule in order to enable more of the fisheries to occur in the ocean, rather than in-river.  This is desirable in many situations: first, to allow fisheries to maximize the food and commercial value of landed salmon (Su and Atkinson 2002); and second, to extend the fishing season, allowing access to abundance-based TAC over a longer time period. Extending the fishing season also helps prevent overloading processing plants, which reducing landed value (e.g. Lewis and Shriver (2017) document the capacity limits of Bristol Bay plants).  As the Bayesian state-space method generates probability distributions, clearly presenting the uncertainty in the in-season estimates, this method may lead to renewed discussion of appropriate harvest control rules to manage in the face of uncertainty.  Stimulating exploration of harvest control rules that are robust to uncertainty  could be as valuable to the management of these fisheries as the increase in management performance associated with the improved in-season estimates in the Bayesian state-space method.  The increasing costs associated with monitoring salmon fisheries and escapements that are required to collect the information that feeds the population models that are generally considered when setting harvest control rules (Hilborn and Walters 1992, DFO 2004, Walters and Martel 2004) continue to provide challenges 119  for management agencies (Cohen 2012c).  Explicitly making clear the uncertainty associated with in-season estimates of abundance should help demonstrate uncertainty associated with management actions (i.e. implementation error) and foster an awareness of the need to explore rules that explicitly consider the precision and accuracy of the in-season information available.      This Bayesian method is explicit about the uncertainty associated with run size estimates and can be used to quantify risk of overharvest while making in-season management decisions.  An additional benefit of being able to quantify the uncertainty associated with the in-season management process should improve modeling work to explore new HCR (e.g. Holt and Peterman (2006) apply a fixed annual implementation error).  However, this work demonstrates that the timing on the decisions will change the degree of uncertainty with which they are made. The costs of management of salmon stocks are increasing and management agencies are looking to reduce cost of management.  The Bayesian state-space approach is an improvement to run size estimation that uses existing data sets, and because of the state-space nature of the model additional observation models can be judged in terms of expected improvements to the run size estimates, which would allow the expected benefit of new programs to be considered at the same time as the costs. Both the Bayesian and Walters-Buckingham methods presented here could be improved upon by adding additional pre- or in-season data to improve the timeliness and precision of the estimates.  For example, the uncertainty in estimates of run size, timing, and harvest rate can all be drastically reduced by incorporating tagging studies to produce both direct estimates of harvest rate in particular fisheries (Walters and Martel 2004) and mark recapture estimates of daily and total fish passage (as in Grant et al. 2014) which will improve estimates of catchability in test 120  and commercial fisheries.  More precise estimates of catchability in test fisheries in particular would lead to improvements in run size estimates (English et al. 2011).  Alternately, the sequential nature of many salmon fisheries lends themselves to multiple test fisheries.  These test fisheries could be self-supporting where the test fishery is operated over an extended fishing season and paid for by the catches associated with this extended season. Multiple opportunities exist for improving timeliness and accuracy of in-season estimates and these should be more fully considered in the future.  121   Figure 5.1.  Distribution of run timing of Skeena River sockeye, a time series of 50% dates (solid points) and duration of the sockeye return (bars show the 95% distribution of the sockeye return in any year) 1982-2007.   Year Sockeye return (Julian date) 122   Figure 5.2.  Skeena River sockeye stock-recruitment relationship.  Ricker parameters and spawner and return estimates presented in Walters et al. 2008.    Escapement(t-4) (1000s sockeye) Return(t) (1000 sockeye) 123    Figure 5.3.  Sibling relationship for Skeena River sockeye salmon.  Sibling relationship is calculated as ln(Rt)=a+b*log (Rthree year oldst-1) +εt where a=11.48 and b=0.28.   Age 4 Return(t) (1000  sockeye) Age 3 Return(t-1) (1000 sockeye) 124   Figure 5.4.  Distribution of run timing of Skeena River sockeye.  Panel (a) shows a histogram of dates by which half of the return has passed the test fishery, panel (b) shows standard deviation of a normal curve fit to sockeye catches at the test fishery (n=51).  Density Density Distribution of means Distribution of SDs 125    Figure 5.5.  Retrospective performance of the different in-season run size estimation models.  The boxplots show the proportion difference between the reconstructed abundance and in-season run size estimates generated with the different models.  Estimates are generated at 10 different time steps through the 26 fishing seasons for which the models were run.  Panel (a) shows the performance of the Bayesian model, panel (b) shows the Walters-Cunningham model, and panel (c) shows the area under the curve model.  assessment period assessment period  assessment period  difference (proportion) difference (proportion) difference (proportion) 126    Figure 5.6.  Time series and distribution of Tyee test fishery annual catchability.  Panel (a) shows the time series of Tyee catchability calculated by comparing the total annual catch in the test fishery to the total reconstructed annual return.  Panel (b) shows the histogram of these catchabilities that was used as a prior for the Bayesian model.  catchability  (qt) catchability  (qt) year  frequency  127     Figure 5.7.  Performance of the three models when confronted with a small early run.  The boxplots show the proportion difference between the simulated abundance and run size estimates generated with the different models.  Estimates are generated at 10 different time steps through 50 fishing seasons for which the models were run.  Data was simulated with a return of 600,000 sockeye arriving 20 days early (the peak of the sockeye run arrived between assessment periods 3 and 4).  Panel (a) shows the performance of the Bayesian state-space model, panel (b) shows the Walters-Cunningham model, and panel (c) shows the area under the curve model with the proportion differences shown on the log scale. assessment period assessment period assessment period difference (proportion) difference (proportion) difference (proportion) 128  Chapter 6: Prediction of harvest management performance for a multispecies salmon fishery under alternative harvest control rules and in-season implementation approaches A closed loop simulation model was built to explore the interaction between fisheries management strategies and the dynamics of several species of Pacific salmon (Oncorhynchus spp.). The simulation model was based on the salmon fisheries of the Skeena River and explores the potential impacts of different harvest control rules (HCRs) and in-season management practices on this mixed species fishery.  The populations modeled for this simulation were the five species of Pacific salmon and steelhead (O. mykiss) returning to the Skeena River.  Specifically, use of the simulation model exposed interacting effects of management decisions, HCRs, errors in observations, and management systems on outcomes in a mixed species salmon fishery.  In-season abundance estimation errors have the largest impact on the ability of the management system to maximize yield.  Several of the HCRs evaluated have similar escapement outcomes to the current HCR, but have different yield outcomes. This work shows that implementation error, when modeled using an in-season estimation submodel, does not have as great an impact on fishery system performance as previously believed. Additionally, simulations demonstrate the consequences of precautionary harvest policies on short- and long-term fishery objectives. These simulations have suggested several serious problems with implementation of Wild Salmon Policy with respect to fishery objectives and suggest several changes to implementation, which would improve yield without compromising conservation objectives at the species level within the Skeena River watershed. The simulation model used here increases our understanding of the Skeena River salmon fishery system and, with some modifications, 129  could be used as part of a management strategy evaluation process to explore likely outcomes of different HCRs on the Skeena River in terms of escapement and yield in fisheries.   6.1 Introduction Salmon management in Canada, and most other jurisdictions, is a delicate balancing act, with conflicting objectives in a complex and unpredictable environment.  Canadian salmon management first aims to meet biological escapement goals under the Wild Salmon Policy (WSP) and First Nations Food, Social, and Ceremonial (FSC) fisheries needs, and then seeks to enable commercial and recreational harvest opportunities. Most salmon fisheries operate with a mix of stocks or species that have different but overlapping run timing and productivity. Moreover, salmon migrate through the system quickly, yet flesh quality and market value of fish is highest when harvested in the marine environment (Groot and Margolis 1991, Su and Atkinson 2002). Therefore every in-season fishery decision involves accommodating conservation and harvest outcomes with incomplete information and a time constraint. To rationalize and expedite in-season decisions, management agencies often use a harvest control rule that determines what, if any, harvest rate to apply at an estimated abundance.  Harvest control rules (HCRs) should be developed to manage the harvest of different species of fish in a way that optimizes fishery performance against objectives.  The concept of such rules grew from ideas about optimum fishing (Grahm 1935, Beverton and Holt 1954, Ricker 1958) and over the years different methodologies for exploring the likely impacts of alternative HCRs have evolved, as have the rules (e.g. numerical optimization (Ricker 1958), and the use of Monte Carlo methods (Hilborn and Walters 1992).  The current best practice for evaluating the ecological, social, and economic impacts of harvest control rules is the use of closed loop 130  simulations as part of a management strategy evaluation (Walters and Martell 2004, Punt et al. 2016).    Closed loop simulation refers to the simulation of a complete fishing system, including data collection and decision making processes. The purpose of closed loop simulation is to determine the performance of different harvest control rules against objectives across a variety of time-scales. Salmon management systems often include economic objectives (e.g. maximize harvest, profit), social objectives (e.g. meet First Nations obligations, maximize employment, equity among fleets or vessels), and conservation objectives (maintain viability of the six species modeled).  The closed loop simulation framework requires the use of multiple sub-models to allow the model to capture the potential impact of different contributions to management uncertainty (Walters 1986, Cox and Kronland 2008, Butterworth 2007).  Closed loop simulation is necessary because there are often non-intuitive results when combining multiple sources of errors across multiple systems (Hilborn and Walters 1992, Walters and Martell 2004, Butterworth 2007, Punt et al. 2016).  This type of modeling is critical because understanding the cumulative effect of each source of uncertainty requires an analysis that takes into account both data collection and in-season management, as well as the choice of control rule and the variability in recruitment of component species. Closed loop simulation evaluates each of these factors to integrate the sources of errors so the impacts of different proposed HCRs are better represented. Closed loop simulation is often seen as a necessary component of management strategy evaluation, but is a powerful tool in its own right because it can be used to explore the interactive impacts of various error sources within the management system.  131  Management uncertainty arises from the contributions of different types of errors, including: 1) incorrect in-season abundance estimates (Walters and Buckingham 1975, Link and Peterman 1998, Holt et al. 2009, Adkison and Cunningham 2015); 2) incorrect implementation of HCRs (Holt and Peterman 2008); and 3) stock assessment errors (Holt and Peterman 2008, Grant et al. 2011), which lead to errors in setting biological reference goals. Closed loop simulation models integrate the impacts of these types of errors with the natural variability of populations (Peterman 1981) allowing the potential performance of different management approaches and HCRs to be examined.   On the Skeena River data are collected in-season at the species level, providing managers with estimates of catch by species in the commercial fisheries and at a test fishery.  Implementation of stock specific management would require in-season stock composition data to be collected from test fishery and commercial catches.  The stock composition of the total species runs would then need to be estimated.  It is currently not practical to collect information at this scale in a timely manner.  The management scale used on the Skeena River is the species level, and it is more realistic to model the in-season decision making process at this scale, using the information available to managers each week.  In this paper, a closed loop simulation model was used to examine the impacts of several potential strategies for managing a mixed species salmon (Oncorhynchus spp.) fishery. The closed loop simulation model was applied to the Skeena River fisheries to demonstrate how compromises between escapement of co-migrating weak species and harvest of more abundant target species are dependent on the type of HCR chosen and the magnitude of errors in data 132  collection.  This is a new application of a closed loop simulation to a mixed species fishery that incorporates an explicit management decision making model (an implementation model) that optimizes the in-season decision process at a weekly time scale within the fishing season, reflecting the in-season management process.  Management uncertainty (or implementation error) is evaluated in a more realistic fashion than in previous analyses. Namely, I explicitly modeled the weekly decisions made with imperfect information and error applied to results of each decision, rather than modeling implementation error as a variance applied to either the annual harvest rate or catch amount (Holt and Peterman 2008, Punt et al. 2016).  Interestingly, early closed loop simulations revealed that chum (O. keta) salmon bycatch restrictions on sockeye (O. nerka) exploitation and yield is much more limiting to sockeye fisheries than steelhead (O. mykiss) bycatch, which has previously been found as the primary limitation on sockeye yield.  As a result, the focus shifted to examining chum salmon bycatch and sockeye fisheries and the impact on chum recovery.    In this set of simulations the stock-specific dynamics within each species were not modeled, because data collected from the Skeena River salmon fisheries are at the species-level.  Species were treated as unit stocks with recruitment parameters reflecting the aggregate returns to the river.  The decision to use species level aggregates rather than modeling the multiple stocks contributing to the aggregate returns means that the results presented here cannot be used to examine the likelihood of extirpation of weak stocks within each species aggregate.  However, on the Skeena River, there is high overlap in run timing among stocks (except for a few sockeye stocks) so solutions developed by the in-season management model using species scale information would not be much different than those obtained with stock specific abundances.  133  Previous authors (Walters et al. 2008, Holt and Bradford 2011, Holt and Folkes 2015, Chapter 2) have explored the impacts of different harvest rates on stock complexes with a range of productivities.  However, they have not explicitly modeled the in-season decision making and harvest processes.   The focus of this investigation is the interaction between in-season information and harvest decisions.  The impact of imprecise in-season information on the ability of a management system to implement the desired HCRs can be evaluated by embedding an in-season model in the closed loop control structure.    6.2 Methods The fisheries system for the Skeena River salmon populations and fisheries were modeled as a system at both annual and within-year timescales (Figure 6.1) in a nested model structure (Adkison and Cunningham 2015, Holt and Peterman 2008).  The closed loop optimization included the following sub-models: 1) Ricker stock-recruitment function that simulated the biological processes between spawning and return to the fishery for multiple species; 2) an in-season run size model that simulated errors and biases (Chapter 4) of in-season run size estimates; 3) a linear programming optimizer (Chapter 3) that simulated the in-season management process of using run size estimates and applied constraints and HCRs to generate fishing plans (similar to the in-season management models for Skeena (Cox-Rogers 1994) and pre-season model for Fraser sockeye (Cave and Gazey 1994); and 4) a capture model which generated observed data on catch and escapement, which are fed back into the run size (2) and linear programming (3) models.  The biological process model included six populations: the five major west coast Pacific salmon species (sockeye, pink (O. gorbusha), chum, coho (O. kisutch), and chinook (O. tshawytscha)), 134  and co-migrating steelhead trout.  Simulations of long term population change were parameterized using Ricker stock-recruitment estimates fit to the escapement and catch data prepared by Walters et al. (2008) and aggregated to the species level (species-specific parameter values used for this model are presented in Table 6.1).  A fixed age-at-maturity was assumed for the populations, and recruitment deviates were generated using autocorrelated (𝜌 = 0.6) draws from a normal distribution with mean of 0 and standard deviation of 0.6 (Hawkshaw and Walters 2015, Walters et al. 2008).  In-season abundance was simulated using run timing information from Chapter 3, and the six modeled populations were assumed to return with normally distributed run timing through the fishing area, with substantial differences among species in timing of entry to the fishery (Figure 6.2).  Inter-annual variation in run timing was simulated using deviates in peak arrival date generated using random draws from normal distributions that approximate the observed variability in the run timing of each species (Chapter 3).    Within the closed loop model, long term management system constraints and targets were derived from new estimates of the Ricker parameters of the six populations, obtained by using linear regressions of the natural logarithm of recruits per spawner on spawner abundance (Hilborn and Walters 1992).  The in-season management model included a linear programming algorithm for maximizing the value of the catch with economic and conservation constraints.  The linear programing algorithm was re-run each simulated week with abundances updated based upon weekly estimates of run size and timing from the in-season run size model; the conservation and total allowable harvest rate constraints could vary each week of the simulated fishing season based on updated estimates of relative run timing, abundances, and HCRs.    135  Error in the harvest process can occur in three ways; 1) implementation error; 2) escapement estimation error; and 3) abundance estimation error. Implementation error was modeled as a lognormal variation around the target weekly harvest rate, rather than the total seasonal harvest rate (Peterman 2004, Eggers 1993) with a standard deviation of 0.06 (Cox-Rogers 1994),   𝐻𝑟𝑠,𝑡 ≈ 𝐿𝑜𝑔𝑛𝑜𝑟𝑚𝑎𝑙(𝐻𝑟𝑡𝑎𝑟𝑔𝑒𝑡𝑠,𝑡, 0.06).   (1) Implementation errors also occur by managing to the wrong management goal, which occurs as a result of errors in stock assessment and errors in in-season run size estimation.  Error in assessing spawners feeds into errors in estimating recruitment parameters and derived management targets.  Observed escapement (𝐸𝑜𝑏𝑠𝑡) is usually assumed to be related to true escapement (𝑆𝑡) as (Walters and Martell 2004, Su and Peterman 2012):  𝐸𝑜𝑏𝑠𝑡 = 𝑆𝑡 ∗ 𝑒𝑥𝑝(𝑣𝑡) where 𝑣𝑡 ≈ 𝑁(0, 𝜎2)  (2) Escapement estimation error was simulated as above with 𝜎2  equal to 0.17, 0.3, or 0.5, as suggested by Su and Peterman (2012). Escapement assessment programs conducted by the Canadian Department of Fisheries and Oceans (DFO) vary in their ability to produce estimates of error (Ogden et al. 2015), so a single numeric value for the standard deviations in escapement estimates was not available to be referenced, nor was a time series of standard deviations in annual escapement estimates.  For all simulation tests, the preseason forecast used each year to make the first week’s management decision was equal to the modal (most likely) prediction from the Ricker model with that year’s current parameter estimates.  Other preseason forecasting methods (e.g. using 136  environmental variables and/or returns of younger fish the previous year) were not tested because none of these has historically performed consistently better than the simple stock-recruitment forecast.  The in-season run size model simulated a run size estimate for every week from a normal distribution with a mean value of the true return modified using the precision and bias changes detected in retrospective evaluation of in-season run size models over the course of the fishing season (estimated in Chapter 5).  Generally this led to an improvement in run size estimates (from pre-season forecasts) only after at least half of each run had been seen as catch or escapement.  The model was run with a burn-in phase where the annual loop was conducted for 25 years with the historical harvest rates (Walters et al. 2008).  This burn-in period allowed the management sub-model to be parameterized with estimates of SMSY, UMSY, UMAX, based on observed escapements and catches fed into the Ricker model (Hilborn and Walters 1992).  The estimated management and biological reference points are used to set the HCR being evaluated.  Once the model was initialized an evaluation phase was run where the estimated management parameters and the chosen HCRs were used to drive management decisions for an additional 25 years.  The management parameters were updated in every year of the evaluation phase as an additional year of escapement and catch data became available. This model was repeatedly run with different combinations of HCRs and rules about timing of fisheries.  Each combination was repeated 500 times, each time generating a unique time series of catch and escapement to explore the interacting effect of the different types of error being simulated.   137   Alternative HCRs were simulated under two broad in-season management approaches: 1) allowing fisheries based on pre-season forecasts and in-season information (e.g. fisheries controlled by the Fraser Panel of the Pacific Salmon Commission (Woodey 2000), or 2) using what is considered a more precautionary approach wherein major fisheries are not opened until there is confidence in the estimate of the return size (e.g. DFO-managed sockeye and chum salmon fisheries of the Fraser River (DFO 2017)). The practice of delaying openings for sockeye was of particular concern (Walters et al. 2008) because it has led to “tail end loading” (higher mortality rates on later-arriving fish) and failure to achieve harvest goals because of constraints imposed by conservation requirements for later-arriving species (chum, steelhead, and in the Fraser case interior coho salmon). The simulation tests evaluated a total of 18 combinations of HCR and management approaches commonly used in salmon fisheries (Table 6.2). The performance of all HCRs was explored under best estimates of current in-season and inter-annual errors in escapement assessment and implementation consistent with current operating conditions for the Skeena River salmon fisheries.  For the preliminary analysis, the performance measures were limited to an easily understood set of measures that would address broad economic and conservation concerns.  In a true management strategy evaluation, the setting of objectives would typically be part of the process and might go through several iterative steps with stakeholders.  The performance of the suite of HCR and management approach combinations was evaluated in terms of yield of the sockeye-directed fisheries, and escapement of all species.  The yield objectives evaluated were: average annual catch of sockeye; standard deviation in that catch; the expected utility of the yield 138  ((𝛴(log(Ct+1)) as recommended in Hawkshaw and Walters (2015) and Hilborn and Walters (1992); and the number of simulated years without a fishery.  Escapement objectives were evaluated using the percentage of escapements that fell into that of the Wild Salmon Policy abundance benchmark ranges (SMSY, the escapement which maximized yield, SGEN, the escapement needed to reach SMSY in one generation without fishing, and SEQ, the spawner abundance at equilibrium without fishing) explored in Holt et al. (2009).   Sensitivity and trade-off analyses were conducted by comparing a subset of four management strategies against the current HCR for Skeena sockeye.  The current DFO HCR for Skeena sockeye initiates harvest when a certain escapement target for sockeye is anticipated, then applies a slowly rising harvest rate proportional to run size, with a cap at 40% (DFO 2014).  This HCR was compared to the harvest rate varying with abundance rule recommended by Hawkshaw and Walters (2015) with fisheries openings constrained until the peak of the sockeye run had been detected (SKHWConstrainttiming), fisheries openings that can happen at any time during the sockeye return (SKHW), and an unconstrained UMSY (ALLUMSY), and SMSY approach (ALLSMSY) for all species.  These five HCRs were compared in four ways. First, yield, utility for the sockeye fishery, and mean escapement for all species were compared under each HCR. Second, chum population trajectories were compared among HCRs to determine how each impacts rebuilding of Skeena chum populations. Third, a sensitivity analysis for each of the combinations was performed where each of the error terms was set to high, medium or low values. Sensitivity was evaluated by examining resultant sockeye yield and escapement summaries (% years below SGEN) for chum and sockeye. The fourth comparison was to examine the Ricker stock-recruitment parameters estimated by the model after each simulated fishing season.  The Ricker 139  parameters were estimated for each species and compared for each HCRs explored, to determine how the escapement data generated with different levels of observation error under alternative HCRs might affect uncertainty and bias in management parameters.  6.3 Results Initial modeling evaluated a wide variety of HCRs under two different management approaches (openings constrained to after peak run or unconstrained), using best estimates of variability.  These combinations showed a range of outcomes in terms of both conservation and yield (Table 6.3).  In general all HCRs resulted in higher yield when the management approach applied allowed the opening of fisheries before the peak of the sockeye run was reached, rather than constraining openings until after the peak of the run (Figure 6.3). However HCRs where fishery openings were unconstrained had higher variability in yield among years (Table 6.3; Figure 6.3).  There was little difference in utility (𝛴(log(Ct+1)) between HCRs and opening times, but the SMSY based strategies had lower utility than other HCRs (reflecting roughly 25% of years closed to fishing: Table 6.3; Figure 6.5).   The relative performance of each HCR was dependent on whether the fishery was constrained to open after peak escapement. When opening times were unconstrained, the abundance-based HCR developed in Hawkshaw and Walters (2015; SKHW) was the best performing HCR, based on average total yield over the simulation period, average annual yield, and utility (Table 6.3; Figure 6.3, and Figure 6.5), but also resulted in the second-highest inter-annual variability in yield.  However, when the fishery was constrained to only open after the peak of the sockeye return had been detected, ALLUMSYConstrainttiming, which limits sockeye harvest to respect the 140  estimated UMSY of all species produced the highest average total yield and had the highest utility (Figure 6.3 and Figure 6.5), but had the highest variability.   All HCRs were able to maintain escapements with all species having escapements between the Wild Salmon Policy indicator levels SGEN and SMSY, by the end of the simulation period.  HCRs that explicitly manage all species to specific targets (so-called weakest stock management) showed higher escapements for chum than those that focused on managing sockeye (Figure 6.6 and Figure 6.7). However, all other strategies explored meet conservation objectives for other species, by maintaining escapement of those species between SMSY, and 30% of SMSY (a proxy for SGEN similar to those in Holt and Bradford 2011). In all HCRs for all species, with the exception of chum salmon, escapement was held above the SGEN proxy in more than 90% of the simulated years (Table 6.3).  Starting conditions for most species were slightly depressed, reflecting burn-in of the simulation using reconstructed historic harvest rates by species.  All species showed recovery from the depressed starting conditions.  However, chum recovered most slowly, reflecting the lower productivity of this species (Figure 6.6 and Figure 6.7).  In all strategies chum were rebuilding, but at different rates depending on the amount of harvest of other species had forgone.  Chum recovery was fastest when using a management approach where fisheries are constrained until after the peak of the sockeye return.  No scenarios in the simulation caused chum to become extirpated.  However, this indicates nothing about potential outcomes for individual conservation units (CUs) whereby it could still be possible that one or more of the weaker chum salmon CUs could still be extirpated under the HCRs evaluated.  There were differences in species-level escapement outcomes associated with the timing of the fisheries mandated by the approach chosen for initiating sockeye fisheries; however the impact was most 141  dependent on both the relative run timing of the species (Figure 6.2) and the magnitude of the fisheries impacts.  Constrained timing of fisheries generally led to higher escapements for all species due to lower overall harvests.  Moreover, earlier migrating species had higher escapements when the openings were constrained until after the peak of the sockeye return (e.g. chinook).   The unconstrained Hawkshaw and Walters (2015) HCR outperformed the other HCRs in terms of yield of sockeye (Figure 6.8 and Figure 6.9), while the escapement outcomes for all species except for chum were maximized by the ALLSMSY HCR (Figure 6.10).  In fact, among the five HCRs examined, escapement and fishery outcomes were nearly inverse; those with high fishery outcomes had lower species-level escapement outcomes and vice versa.  Another way to examine the performance of two HCRs is to plot the outcomes of the different harvest control rules against each other; by doing this, we see the dramatic differences in yield from sockeye directed fisheries between the current (SKCURR) and other HCRs.  Higher yields were observed for most years for the SKHW, ALLUMSY and SKHW,Constrainttiming HCRs, whereas lower yield was observed in most years for the ALLSMSY HCR (Figure 6.11).  Low yields associated with the ALLSMSY HCR result from many years of fisheries restrictions when one of the species was below its SMSY target preventing fisheries on co-migrating species.  Escapement outcomes for chum were similar when comparing the current HCR to the other evaluated HCRs.  All HCRs showed differences in mean escapement of chum but the distribution of escapement outcomes overlapped (Figure 6.12).  Though there were slightly lower mean escapements of chum for all four of the contrasting HCRs only the SKHW HCR showed dramatically lower escapement outcomes for chum than the current HCR (Figure 6.12 and Figure 6.13).  Plotting the sockeye 142  yield and chum escapement outcomes directly for each HCR shows the within-HCR trade-off between harvest and escapement (Figure 6.13), demonstrating the gains in yield that can be made with lower chum escapement.  Even while acknowledging this escapement-yield trade-off, it is important to notice that all HCRs showed chum rebuilding; however the speed of rebuilding depended on the HCR employed (the SKHW HCR showed particularly slow rebuilding; Figure 6.15).  For all species except chum, all HCRs had similar escapement outcomes (Figure 6.10) with all species being around SMSY. Strategies that would result in maximized rebuilding of chum were predicted to have significantly reduced harvest of sockeye (Figure 6.14).  Yield of sockeye fisheries depended on the different HCRs, and showed variation between strategies and combinations of errors (Table 6.4). Increasing in-season abundance estimation error with other types of error held constant generally led to declines in yield. The four HCRs with management parameters (escapement targets or harvest rates) derived from stock-recruitment parameters were sensitive to observation error in escapement: as escapement observation error increased, so too did yield.  Observation error in escapement did not impact yield under the current HCR. The interaction of abundance estimation errors, implementation errors, and escapement errors in all three HCRs was directional.  The errors in abundance estimation had a strong negative effect on yield, while errors in implementation and escapement estimation tended to have less strong positive effects on yield.  Errors in abundance estimation overrode the impact of errors in implementation or escapement estimation error.      The standard deviation of the yield of sockeye fisheries depended on the different HCRs, and showed variation between strategies and combinations of errors (Table 6.5). Increasing in-season 143  abundance estimation error generally led to decreases in variation of yield. Observation error of escapement did not impact the variance of the yield under the current HCR.  The SKHW,Constrainttiming HCR was also relatively insensitive to errors in observation of escapement, and had a higher variability in yield when the implementation error was higher, but a lower variability when the abundance estimation errors were higher.  The remaining HCRs with management parameters (escapement targets or harvest rates) derived from stock-recruitment parameters were sensitive to observation error in escapement: as escapement observation error increases, so too does variability in yield.  The interaction of abundance estimation errors, implementation errors, and escapement errors in all three HCRs was directional.  Errors in abundance estimation had an inverse effect on variability in yield, while errors in implementation and escapement estimation tended to have less strong positive impacts on variation on yield.  Errors in abundance estimation overrode the impact of errors in implementation or escapement estimation error.  Escapement outcomes were also sensitive to the magnitude of each type of error. Table 6.6 and Table 6.7 show escapement of chum and steelhead relative to SGEN under the five simulated HCRs when errors were applied to in-season abundance estimation, implementation and escapement observation. Increased variability in in-season estimates of abundance generally led to higher chum and steelhead escapements. Escapement estimation errors led to a proportional reduction in species-level escapement outcomes using each of the four new candidate HCRs. Larger errors in estimating escapement generally artificially reduced escapement relative to targets, or increased harvest rate leading to more instances of lower escapement. The current HCR is insensitive to errors in estimating escapement.  These types of errors did not impact the 144  species-level escapement outcomes because the current HCR is set independent of stock-recruitment parameters.  Errors in implementation often resulted in lower escapements and higher harvests, but these changes were marginal (between 0.021-2.148% more sockeye harvested on average between high and low implementation error depending on other errors and HCR) because the in-season weekly harvest decisions allowed for in-season correction (adaptation).   Errors in escapement estimates can lead to large biases in estimating Ricker recruitment model parameters (Figure 6.17 – Figure 6.18). The HCRs examined did not provide improvements to stock-recruitment parameter estimates (i.e. did not result in better estimates of Ricker a and b parameters). Current and proposed strategies are not probing strategies designed to explore the capacity and productivity of the species.  Examining the net impact of the errors shows that estimates of Ricker b and SMSY were close to the simulated values for some species.  However, estimates of Ricker a and UMSY values were biased high (Figure 6.16) leading to overestimates of productivity and underestimates of escapement management targets (i.e. UMSY and SMSY). When comparing estimates of Ricker a across different error regimes it is apparent that there was a breakdown in the ability to reliably estimate Ricker stock-recruitment parameters when observation errors became too high (Figure 6.17 and Figure 6.18).  Estimates were variable but not biased at lower levels of escapement error; at higher levels there was an obvious bias towards overestimating both Ricker a and b values. 6.4 Discussion Harvest control rules (HCRs) should be tested in a closed loop simulation in order to explore the trade-offs that arise in a mixed species fishery.  The best performing HCRs identified here were 145  subject to a sensitivity analysis that show management uncertainty arise from contributions of different types of errors.  The closed loop simulation developed here can be used not only to inform decisions about what HCR is preferred, but also to evaluate the possible impacts of changes to management systems and monitoring programs.    Evaluating the outcomes of HCRs on a mixed species system driven by the desire to harvest a subset of the more abundant species requires an evaluation of the impacts of fisheries on all affected species.  Many closed loop evaluations have been focused only on the impacts of a fishery on the target species (Punt 1992, Butterworth and Bergh 1993, Butterworth et al. 1997, de la Mare 1996, Smith et al. 1999, Punt and Smith 1999).  This results in an evaluation that fails to incorporate important drivers of management decisions that are not explicitly tied to the stock or species being managed, and produces advice that has not been evaluated against an appropriate suite of performance measures for the system.  Results from the interaction of multiple populations and systems are not intuitive and modeling is required to judge the likely outcomes of any planned management system (Hilborn and Walters 1992, Walters and Martell 2004, Holt and Peterman 2008, Punt et al. 2016).    A wide selection of HCRs operating on several species were evaluated in this modeling effort.  It was found that HCRs that performed well in terms of yield (or utility) were ones that avoided species-specific escapement targets, yet still had abundance-based changes in target exploitation rate.  Multi-stock modeling of the Fraser River salmon populations show this same pattern, with the optimum HCR balancing abundance based harvest rates across the stocks (Pestal et al. 2008).  Pestal et al. (2008 and 2011) and Cass et al. (2004) also show that for the sockeye fisheries of the 146  Fraser River, when modeling multiple stocks, HCRs which tried to achieve maximum production for each species (e.g. using fixed escapement constraints by species, or managing to maximize production from all species) often gave up potential harvest of the aggregate by trying to maximize the individual species outcomes.  Several authors (Hilborn 1985, Kope 1992, Cass et al. 2004 Hilborn et al. 2012) demonstrate that even in a simulated two stock fishery, if the mixed stock fishery is managed to a single harvest rate, there is a trade-off between the sustainable yield of the aggregate and the degree of over or under exploitation of the component stocks.  The simulations presented here show that fixed escapement constraints are even more limiting in mixed species fisheries because of the well explored trade-off between fixed escapement yield and number of years without fishing (Hilborn and Walters 1992), which can be acceptable if the escapement results in higher yield over the long-term.  In a mixed species situation, the trade-off does not apply: any low return will close the fishery and as the number of escapement constraints increases, more constraints result in more years of closed fisheries (Chapter 3).    Modeling at the species aggregate level in both the model used to simulate the population dynamics (i.e., the “operating model”) and the HCRs has some practical conveniences for this situation, but comes with a possible concern as well.  Modeling harvest control rules at the stock (or conservation unit (CU)) scale for all the salmon stocks of the Skeena River would result in the use of models that does not accurately reflect the in-season and inter-annual management processes.  The problem of balancing extirpation risk and harvest rates has been explored on the Skeena (Walters et al. 2008, Chapter 2) and in other contexts (e.g. for Fraser River sockeye Pestel et al. 2008 and 2011) and it has been shown that there is not substantial risk of extirpation of weaker stocks when managing to an aggregate harvest target, particularly when managing 147  with exploitation rate-dependent HCRs.   Developing a simulation model at the species level rather than at the CU level that could still give indications of species-level yield and escapement outcomes that would not be entirely inaccurate.   More importantly, data are collected decisions are currently made at the species level in-season.    Keeping the candidate HCRs evaluated in this chapter at the species level means that expensive changes to the management system would not be required. However, even though it is a great convenience to apply a simulation model at the species level, there is  a danger that significant differences in run timing within the aggregates could lead to disproportionately high harvests on sub-stocks within the aggregate (Quinn et al. 2007, Carney and Adkison 2014).  The potential impact is that when evaluating the performance of HCRs, the risk of overharvest and extirpation is underestimated because the operating model lumps conservation units for each of the salmonid species.  If annual stock specific run timing information begins to be collected, it could be used within this modeling framework to further explore the sensitivity of these results to mismatches in run timing.  Incorporation of stock structure, as well as exploration of future productivity scenarios, should be incorporated as components of a future management strategy evaluation.  Correct description of errors in the management and biological process in a closed loop model is an important part of evaluating the possible outcomes of different HCRs.  By explicitly describing and varying several different types of error, the present simulation evaluation shows how implementation error, run size estimation error, and errors in the measurement of stock-recruitment data feed into the success or failure of a management approach.  Holt and Peterman (2008) model the impacts of implementation error and find it to have a low impact on yield when managing with a HCR based on a harvest rate; they find a larger impact when considering fixed 148  escapement HCR.  This is in contrast with the modeling work shown here that finds very low impacts of implementation error on yield.  This is likely a result of the difference in model structure.  Holt and Peterman apply the HCR on an annual time step based upon a pre-season forecast, while in this model the run size estimate is updated in-season and multiple fisheries decisions are made taking into account the information on run size and catch to date available within each fishing season.  In the case of errors in implementation of management decisions, the weekly time step of the fishery means that an over or under harvest in one week has the potential to be corrected in subsequent weeks.  Also in practice the effort response to abundance will tend to minimize the likelihood of an overharvest when abundance is very low (Walters and Martell 2002).    In this study, errors in abundance estimates in-season tend to have less impact on ability to meet escapement targets than other studies (Adkison and Cunningham 2015), as on the Skeena River the in-season abundance estimates are 1) biased low, and 2) are evaluated several times within the fishing season as more in-season information develops.  This means that there are several opportunities to correct mistakes in estimation of run size, and the bias towards underestimating the return when combined with the economic constraint on early timed harvests corrects the issue observed by Adkison and Cunningham (2015) of overharvest of small early timed returns.    Holt and Peterman (2008) and other authors (Walters 1986, de la Mare 1996, Cooke 1999) also recommend incorporating learning into modeling of the management system.  The model presented here takes the step of allowing updates to the management parameters (where HCRs with biologically derived management parameters are updated as more years of escapement and 149  recruitment are observed), and demonstrates that the impact of errors in escapement estimation (the well-known error-in-variables problem) resulted in increasing variability in yield over time as the errors in escapement estimates increased.  Errors in escapement estimates have been demonstrated to bias estimates of recruitment parameters, which means any harvest control rule based on stock-recruitment parameter estimates (e.g. estimates of SMSY) will be aiming for the wrong targets.  There is a directional bias of unknown strength predicted for Ricker parameter estimates (Hilborn and Walters 1992), which is quantified in this simulation.  The range of possible biases is shown to increase with increasing levels of observation errors in escapement estimation.    The cost of management is a perennial concern for management agencies around the world (Wallace and Flaaten 2000, Arnason 2001, Cox 2001).  Understanding the impact of errors in data collection and in-season processes on performance of the management system should inform decisions when budget restrictions require reductions in monitoring, escapement assessment, or in-season management costs.  For the Skeena River, an in-season run size abundance estimate does not exist for non-sockeye species (Ivan Winther, DFO stock assessment, personal communication), so choosing a HCR that relies on in-season abundance estimates for these species (such as a strategy that manages all species to SMSY) would require potentially costly changes to the management system.  If greater harvest opportunity or better in-season understanding of conservation risks are desired, a more complicated in-season management system should yield more harvest when abundances are higher than expected and reduce risk of missing escapement targets when abundances are lower than expected.  If the costs of the current in-season management system are too high, a move towards a simple system (such 150  as a fixed harvest rate or fixed fishing schedule) could yield moderate harvests at low risk to co-migrating species.  Gazey and Palermo (2000) report that changes to the in-season assessment for Fraser River chum salmon was leading to a mismatch with the management system.  This mismatch was used to justify moving towards a simpler and less costly management system where multiple test fisheries and in-season abundance estimates are replaced with a low fixed harvest rate target for the mixed stock fishery, with terminal fisheries targeting stock specific abundances (Van Will et al. 2009).  Because escapement assessment error and implementation error have a predictable directional effect on yield and escapements outcomes, and study design for catch monitoring and escapement programs can readily be used to estimate the variability in estimates these programs produce, it is easy to tie the investment in monitoring programs to yield and escapement outcomes.    The timing of the start of fisheries relative to return has a dramatic impact on the ability of a fishery to harvest the abundant species in a mixed species fishery.  Delaying fisheries is shown to have a significant cost to fisheries in terms of foregone harvest, without increasing the risk of extirpation.  This has been demonstrated by other authors, as either weak stock constraints imposed on the more productive stocks (Kope 1992, Pestal et al. 2011), or through a mismatch between openings and return timing (Adkison and Cunningham 2015).  Pestal et al. (2011) use the average difference in run timing between co-migrating stocks of Fraser River sockeye to estimate the amount of harvest that might be forgone in mixed stock fisheries.  In this study, modeling the in-season information collection and management decision making process allows direct estimation of the degree of forgone harvest arising because of overlap constraints and mistiming of the fisheries.  Adkison and Cunningham (2015) show that errors in characterizing 151  the timing of the return can lead to over-harvest when the return is earlier than expected, and under-harvest when the return is later (or larger than expected).  In this study HCRs which wait until the run size is known before beginning to harvest produce less yield than the same types of HCR that are not constrained in opening time.  A possible alternative to the complicated HCRs recommended in this study would be to simply manage with fixed fishery opening schedules, determined before each fishing season.  At least some historical salmon management appears to have taken that approach, e.g. over many years there were few changes in weekly fishery openings on the Skeena (Walters et al. 2008). Carney and Adkison (2014) suggest a number of benefits from the approach, including more predictable catches and more even spreading of harvest rates over the run timing patterns, leading to reduced risk of selection for changes in run timing and less distortion of the escapement sex ratio.    A stock specific modification of this closed loop analysis could be applied in a situation with large separation in return timing between stocks.  Fraser River sockeye fisheries would be excellent candidates for a stock specific version of this model.  Fraser River sockeye have significant separation in return timing and have an in-season management system that collects stock specific abundances and run timings.  This would allow a stock specific version of the model to be run and would be an improvement on the current treatment of stock overlap in the existing models (Cass et al. 2004, Pestal et al. 2008 and 2011).    Future work to evaluate the differences in run timing of the stocks that make up each species aggregate on the Skeena (via genetic analysis of fish captured in the test fishery) could enable a parametrization of this model at a stock specific level to explore the sensitivity of HCRs to the 152  overlap in run timing of the Skeena River stocks; however the multi-stock simulations in Chapter 2, and the equilibrium analysis in Walters et al. (2008) both predict low risk of expiration of any stock on the Skeena River (though a high proportion are predicted to be overfished).  More work focusing on incorporating structural uncertainty in the biological model, including exploring different stock timing scenarios and different productivity scenarios, could be part of incorporating the closed loop model presented here into a Management Strategy Evaluation.  Perhaps the most important practical finding from my simulations is that DFO (and PSC in the Fraser sockeye case) should consider abandoning the “precautionary” approach of delaying fishery openings until better run size information becomes available.  As noted above, such delays can result in tail end loading of exploitation rate on later components of species run timing patterns, along with failure to achieve harvest goals before constraints due to conservation needs for later timed species become important.  While average escapements were reduced when delays were not used, none of these reductions led to substantially lower probability of achieving Wild Salmon Policy benchmarks or to substantial loss of yield due to sometimes getting lower spawning abundance than would produce maximum long term yield. This suggests that the current implementation of the Wild Salmon Policy may not appropriately consider all DFO fishery sub-objectives (short- and long-term conservation and utility objectives) and should be re-considered in light of these and other findings (Adkison and Cunningham 2015).     153  Table 6.1.  Population parameters assumed for simulation models.   Species Ricker a Ricker b Age of MaturitySockeye 1.6 5.71E-07 4Pink 1.1 2.44E-07 2Coho 1.3 2.85E-06 4Chum 0.9 1.88E-05 4Chinook 1.4 1.25E-05 5Steelhead 1.33 1.66E-05 5154   Table 6.2.  Abbreviations used to distinguish between simulated HCRs. The format for abbreviation of HCR names is TARGET SPP[HCR TYPE], Constraint[Constraint type]. This allows the reader to see the main objective and constraints of a HCR.  Abbreviation StrategySKUMSY,ConstraintUMAX UMSY harvest rate (Sockeye) - Constrained such that each other species harvest rate is less than its UMAXSKUMSY UMSY harvest rate (Sockeye)SKSMSY,ConstraintUMAX Fixed SMSY Escapement (Sockeye) - Constrained such that each other species harvest rate is less than its UMAXSKSMSY Fixed SMSY Escapement (Sockeye) SKHW,ConstraintUMAX Utility Rule (Sockeye, Hawkshaw and Walters 2015) - Constrained such that each other species harvest rate is less than its UMAXSKHW Utility Rule (Sockeye, Hawkshaw and Walters 2015) ALLU40 Fixed harvest rate all stocks (40%) ALLSMSY Species specific escapement targets (SMSY)ALLUMSY Use species specific UMSY harvest rate targets SKUMSY,Constrainttiming,UMAX UMSY harvest rate (Sockeye) - Constrained opening time, each other species harvest rate is less than its UMAXSKUMSY,Constraint timing UMSY harvest rate (Sockeye) - Constrained opening timeSKSMSY,Constrainttiming,UMAX Fixed SMSY Escapement (Sockeye) - Constrained opening time, each other species harvest rate is less than its UMAXSKSMSY,Constrainttiming Fixed SMSY Escapement (Sockeye)  - Constrained opening timeSKHW,Constrainttiming,UMAX Utility Rule (Sockeye, Hawkshaw and Walters 2015) - Constrained opening time, each other species harvest rate is less than its UMAXSKHW,Constrainttiming Utility Rule (Sockeye, Hawkshaw and Walters 2015) - Constrained opening timeALLU40,Constrainttiming Fixed harvest rate all stocks (40%) - Constrained opening timeALLSMSY,Constrainttiming Species specific escapement targets (SMSY) - Constrained opening timeALLUMSY,Constrainttiming Use species specific UMSY harvest rate targets - Constrained opening time155  Table 6.3a.  Performance measures and outcomes for a suite of Harvest Control Rules (without timing constraint).  Bold values highlight the “best performing” strategy by performance measure.     SKUMSY,ConstraintUMAXSKUMSYSKSMSY,ConstraintUMAXSKSMSYSKHW,ConstraintUMAXSKHWALLU40ALLSMSYALLUMSYPerformance Measure SpeciesEscapement<Smax Sockeye 86.3% 89.4% 88.2% 92.7% 89.6% 93.7% 77.2% 61.5% 72.2%Pink 91.8% 94.0% 91.3% 93.1% 93.0% 95.8% 84.0% 72.5% 85.8%Coho 89.7% 92.0% 89.1% 92.3% 91.5% 94.2% 81.7% 71.7% 85.0%Chum 99.8% 99.9% 99.6% 99.7% 99.9% 100.0% 97.2% 81.8% 85.3%Chinook 91.2% 94.0% 90.2% 92.0% 93.8% 96.0% 82.0% 62.3% 68.1%Steelhead 88.4% 90.4% 87.5% 90.7% 89.8% 92.5% 80.2% 73.4% 87.8%Escapement<Smsy Sockeye 9.2% 10.4% 6.5% 9.1% 11.9% 15.4% 5.6% 3.4% 4.6%Pink 37.5% 43.4% 38.0% 46.9% 42.0% 51.3% 22.8% 14.8% 26.6%Coho 28.6% 32.5% 28.4% 34.7% 31.0% 38.9% 17.5% 11.7% 20.3%Chum 93.0% 96.1% 90.1% 93.5% 95.0% 97.5% 76.0% 44.8% 48.8%Chinook 27.9% 33.9% 27.4% 35.3% 34.6% 43.3% 14.5% 6.4% 8.2%Steelhead 22.7% 27.0% 23.1% 29.2% 23.8% 32.4% 14.5% 11.5% 20.8%Escapement>0.3*Smsy Sockeye 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%(Sgen1 Proxy) Pink 93.7% 92.2% 93.3% 90.9% 92.3% 88.6% 96.0% 97.0% 94.8%Coho 97.7% 97.2% 97.7% 97.0% 97.2% 96.6% 98.6% 99.0% 98.2%Chum 37.5% 32.0% 45.8% 36.4% 32.6% 24.3% 62.4% 82.4% 80.4%Chinook 98.0% 97.9% 98.5% 97.8% 97.9% 97.0% 99.0% 99.7% 99.5%Steelhead 98.2% 97.8% 98.1% 97.7% 98.0% 97.5% 98.8% 99.1% 98.5%Average Total Yield (all years) Sockeye 27,442,784     30,293,545     28,020,980     32,201,180     30,716,284     34,677,368     18,865,105     4,596,933      14,472,418     Average Annual Yield Sockeye 1,055,492      1,165,136      1,077,730      1,238,507      1,181,396      1,333,745      725,581         176,805         556,631         SD of Annual Yield Sockeye 491,100         530,568         618,654         726,512         598,503         660,275         364,674         254,309         276,974         %Year No Fishing Sockeye 0.00% 0.00% 0.69% 0.85% 0.08% 0.04% 0.00% 25.73% 0.00%Log Utility Sockeye 35770 36050 35349 35660 35990 36343 34744 21491 34077156   Table 6.3.  Performance measures and outcomes for a suite of Harvest Control Rules (with timing constraint). Bold values highlight the “best performing” strategy by performance measure.     SKUMSY,Constrainttiming,UMAXSKUMSY,Constraint timingSKSMSY,Constrainttiming,UMAXSKSMSY,ConstrainttimingSKHW,Constrainttiming,UmaxSKHW,ConstrainttimingALLU40,ConstrainttimingALLSMSY,ConstrainttimingALLUMSY,ConstrainttimingPerformance Measure SpeciesEscapement<Smax Sockeye 76.5% 77.0% 73.9% 75.0% 76.4% 76.9% 71.6% 65.7% 72.2%Pink 92.2% 93.5% 88.8% 89.8% 92.2% 93.3% 85.2% 73.0% 85.8%Coho 90.5% 91.7% 86.9% 87.7% 90.8% 91.6% 84.0% 73.5% 85.0%Chum 86.4% 86.7% 85.5% 85.8% 86.4% 86.6% 85.1% 87.3% 85.3%Chinook 71.1% 71.5% 69.0% 69.2% 70.5% 71.2% 68.2% 68.2% 68.1%Steelhead 95.3% 96.6% 91.6% 93.2% 95.2% 96.7% 87.3% 72.9% 87.8%Escapement<Smsy Sockeye 5.5% 5.5% 3.2% 3.0% 5.3% 5.5% 4.5% 3.6% 4.6%Pink 40.5% 45.8% 32.8% 37.2% 40.3% 46.0% 25.7% 15.8% 26.6%Coho 30.9% 34.4% 25.6% 28.1% 30.5% 34.6% 19.3% 12.1% 20.3%Chum 50.9% 51.3% 49.2% 49.7% 50.7% 51.0% 48.7% 52.9% 48.8%Chinook 9.2% 9.8% 8.6% 8.6% 9.3% 9.8% 8.0% 7.7% 8.2%Steelhead 37.0% 43.9% 30.0% 34.8% 37.1% 45.5% 19.0% 11.1% 20.8%Escapement>0.3*Smsy Sockeye 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%(Sgen1 Proxy) Pink 93.2% 91.5% 94.2% 93.8% 93.1% 91.6% 95.2% 96.8% 94.8%Coho 97.7% 97.3% 98.2% 98.1% 97.7% 97.3% 98.4% 98.8% 98.2%Chum 79.8% 79.7% 80.7% 80.3% 80.0% 79.6% 80.5% 78.0% 80.4%Chinook 99.4% 99.4% 99.5% 99.5% 99.4% 99.4% 99.5% 99.6% 99.5%Steelhead 96.8% 95.8% 97.4% 96.9% 96.7% 95.6% 98.6% 99.2% 98.5%Average Total Yield (all years) Sockeye 17,807,606       18,530,867       15,607,758       16,256,772       17,767,212       18,609,421       14,016,205       7,937,458         14,472,418         Average Annual Yield Sockeye 684,908            712,726            600,298            625,260            683,354            715,747            539,085            305,287            556,631              SD of Annual Yield Sockeye 324,607            333,578            369,707            391,852            329,569            348,631            267,370            400,754            276,974              %Year No Fishing Sockeye 0.00% 0.00% 1.54% 1.50% 0.00% 0.04% 0.00% 22.73% 0.00%Log Utility Sockeye 34634 34743 33351 33392 34617 34711 33992 23832 34077157  Table 6.4.  Mean Sockeye Yield outcomes under different error regimes.    HCRIn-season Abundance Estimate ErrorImplementation Error low medium high low medium high low medium highlow low 504,692 504,692 504,692 473,927 531,707 721,901 802,502 846,244 937,309med 504,587 504,587 504,587 477,593 542,845 721,846 804,443 848,327 931,920high 504,664 504,664 504,664 480,104 537,409 713,011 803,175 843,125 930,945med low 396,505 396,505 396,505 195,767 222,709 297,250 693,332 722,863 804,712med 397,558 397,558 397,558 193,523 222,967 298,738 699,840 730,141 807,908high 396,922 396,922 396,922 194,374 226,626 301,443 708,550 719,889 802,671high low 326,210 326,210 326,210 103,984 114,093 158,066 583,979 601,467 651,546med 328,545 328,545 328,545 104,340 114,588 157,269 578,655 603,439 654,045high 332,118 332,118 332,118 104,475 114,530 157,400 584,010 599,023 655,614HCRIn-season Abundance Estimate ErrorImplementation Error low medium high low medium highlow low 603,546           604,002           604,204           1,504,759 1,526,584 1,624,023med 604,219           604,600           604,911           1,509,089 1,526,572 1,621,028high 605,364           605,745           606,209           1,507,310 1,538,899 1,623,178med low 529,094           530,974           534,309           1,150,141 1,160,028 1,199,875med 531,363           531,741           535,766           1,148,444 1,158,257 1,195,635high 533,180           532,984           538,225           1,145,737 1,151,034 1,199,643high low 412,287           412,696           413,934           891,049 894,926 919,434med 413,332           413,502           414,658           887,862 892,292 919,199high 413,115           413,953           415,057           884,084 893,201 916,191SKCURR ALLSMSY ALLUMSYSKHW,Constrainttiming SKHWEscapement Observation ErrorEscapement Observation Error Escapement Observation Error Escapement Observation ErrorEscapement Observation Error158  Table 6.5.  Standard Deviation of Sockeye Yield outcomes under different error regimes.    HCRIn-season Abundance Estimate ErrorImplementation Error low medium high low medium high low medium highlow low 294,872 294,872 294,872 545,141 565,974 628,061 336,601 349,935 400,575med 295,403 295,403 295,403 547,526 571,390 640,022 336,751 356,935 405,725high 296,095 296,095 296,095 549,406 562,340 635,308 341,807 361,986 395,689med low 266,614 266,614 266,614 280,642 294,207 333,270 335,453 363,296 397,288med 269,473 269,473 269,473 277,555 295,231 337,093 344,163 367,689 397,888high 273,267 273,267 273,267 279,162 299,342 342,068 351,154 357,592 402,977high low 240,025 240,025 240,025 189,518 194,405 236,846 330,579 338,330 369,325med 242,785 242,785 242,785 190,223 195,588 237,364 328,037 344,596 366,167high 243,554 243,554 243,554 190,866 196,298 239,387 329,811 339,476 366,257HCRIn-season Abundance Estimate ErrorImplementation Error low medium high low medium highlow low 265,724 265,133 265,115 683,624 686,943 707,645med 266,767 266,229 266,243 687,560 688,383 709,078high 268,473 267,910 268,143 689,322 697,012 707,300med low 255,416 256,790 256,756 559,749 565,121 576,548med 257,523 258,137 257,346 560,110 563,037 574,236high 260,210 261,059 262,393 558,142 561,713 575,403high low 231,501 231,417 232,944 483,161 488,327 478,798med 232,299 233,274 234,390 483,046 487,966 482,520high 231,997 233,837 235,878 484,353 488,654 485,091SKCURR ALLSMSY ALLUMSYEscapement Observation Error Escapement Observation Error Escapement Observation ErrorSKHW,Constrainttiming SKHWEscapement Observation Error Escapement Observation Error159  Table 6.6.  Chum Escapement outcomes under different error regimes  (% years below SGEN).    HCRIn-season Abundance Estimate ErrorImplementation Error low medium high low medium high low medium highlow low 5.46% 5.46% 5.46% 4.58% 4.88% 7.08% 13.12% 14.35% 19.77%med 5.46% 5.46% 5.46% 4.58% 4.96% 7.04% 13.15% 14.54% 20.00%high 5.46% 5.46% 5.46% 4.58% 4.96% 6.88% 13.62% 15.04% 19.69%med low 5.42% 5.42% 5.42% 4.58% 4.85% 5.46% 10.46% 11.62% 14.08%med 5.38% 5.38% 5.38% 4.58% 4.85% 5.46% 10.58% 11.96% 13.81%high 5.38% 5.38% 5.38% 4.58% 4.88% 5.46% 10.65% 11.96% 13.92%high low 5.08% 5.08% 5.08% 4.58% 4.77% 5.15% 9.00% 9.81% 11.15%med 5.08% 5.08% 5.08% 4.58% 4.77% 5.19% 9.31% 9.69% 11.42%high 5.08% 5.08% 5.08% 4.58% 4.77% 5.15% 9.12% 9.77% 11.27%HCRIn-season Abundance Estimate ErrorImplementation Error low medium high low medium highlow low 5.96% 5.96% 6.04% 64.58% 68.04% 76.00%med 6.00% 6.04% 6.08% 65.27% 68.69% 75.46%high 6.08% 6.08% 6.12% 66.00% 68.85% 75.46%med low 5.77% 5.73% 5.69% 31.31% 32.19% 34.88%med 5.73% 5.77% 5.69% 31.81% 32.54% 35.85%high 5.69% 5.73% 5.69% 30.96% 32.50% 35.46%high low 5.35% 5.38% 5.35% 17.46% 18.73% 20.08%med 5.38% 5.42% 5.38% 17.85% 18.73% 20.00%high 5.38% 5.46% 5.42% 18.31% 19.00% 20.12%Escapement Observation Error Escapement Observation ErrorSKHW,Constrainttiming SKHWSKCURR ALLSMSY ALLUMSYEscapement Observation Error Escapement Observation Error Escapement Observation Error160  Table 6.7.  Steelhead Escapement outcomes under different error regimes (% years below SGEN).    HCRIn-season Abundance Estimate ErrorImplementation Error low medium high low medium high low medium highlow low 0.58% 0.58% 0.58% 0.00% 0.04% 0.12% 0.15% 0.15% 0.19%med 0.62% 0.62% 0.62% 0.00% 0.08% 0.12% 0.19% 0.23% 0.23%high 0.58% 0.58% 0.58% 0.00% 0.04% 0.08% 0.15% 0.19% 0.27%med low 0.35% 0.35% 0.35% 0.00% 0.00% 0.04% 0.08% 0.08% 0.12%med 0.35% 0.35% 0.35% 0.00% 0.00% 0.04% 0.08% 0.08% 0.12%high 0.42% 0.42% 0.42% 0.00% 0.00% 0.04% 0.08% 0.08% 0.12%high low 0.19% 0.19% 0.19% 0.00% 0.04% 0.00% 0.08% 0.08% 0.12%med 0.19% 0.19% 0.19% 0.00% 0.04% 0.00% 0.12% 0.08% 0.12%high 0.15% 0.15% 0.15% 0.00% 0.04% 0.00% 0.12% 0.08% 0.12%HCRIn-season Abundance Estimate ErrorImplementation Error low medium high low medium highlow low 2.73% 2.85% 3.12% 0.62% 1.08% 1.50%med 2.81% 2.96% 3.27% 0.62% 0.65% 1.08%high 3.19% 3.23% 3.42% 0.54% 0.69% 1.50%med low 0.65% 0.77% 0.73% 0.23% 0.23% 0.27%med 0.65% 0.73% 0.85% 0.35% 0.31% 0.35%high 0.65% 0.69% 1.00% 0.31% 0.27% 0.31%high low 0.23% 0.27% 0.31% 0.23% 0.23% 0.23%med 0.23% 0.23% 0.31% 0.23% 0.23% 0.23%high 0.31% 0.31% 0.35% 0.27% 0.23% 0.27%SKHW,Constrainttiming SKHWEscapement Observation Error Escapement Observation ErrorSKCURR ALLSMSY ALLUMSYEscapement Observation Error Escapement Observation ErrorEscapement Observation Error161   Figure 6.1.  Model structure for evaluating harvest control rules incorporating multiple types of uncertainty. Escapement, in-season abundance, and application of weekly fishery were all modeled with errors.     In-Season Model   Estimate Abundances Apply in season linear programming decision model  Advance return Apply weekly fishery    Escapement  Catch   Use Ricker Model to generate returns  Annual Model 162   Figure 6.2.  Distributions of observed peak day of migration past Tyee test fishery by species showing migration timing overlap. The box and whisker plots show the distribution of escapement outcomes in every year of the forward simulation, the bar near the center of the box shows the median value, the box shows the interquartile range and the whiskers show the most extreme data point which is no more than 1.5 times the length of the box away from the box. (R Core Team 2013).   163   Figure 6.3.  Average sockeye yield for all surveyed HCRs. Green bars correspond to management scenarios where sockeye harvest was not constrained until after the observed peak of the return, blue bars correspond to management scenarios when sockeye harvest was constrained until after the peak of the run has been observed. Table 6.2 has a listing of the HCRs tested corresponding to the codes on the x-axis.   164   Figure 6.4.  Standard deviation of sockeye yield for all surveyed HCRs. Green bars correspond to management scenarios where sockeye harvest was not constrained until after the observed peak of the return, blue bars correspond to management scenarios when sockeye harvest was constrained until after the peak of the run has been observed. Table 6.2 has a listing of the HCRs surveyed corresponding to the codes on the x-axis.   165   Figure 6.5.  Average utility of sockeye yield for all surveyed HCRs. Green bars correspond to management scenarios where sockeye harvest was not constrained until after the observed peak of the return, blue bars correspond to management scenarios when sockeye harvest was constrained until after the peak of the run has been observed. Table 6.2 has a listing of the HCRs surveyed corresponding to the codes on the x-axis. 166   Figure 6.6.  Escapement trajectories for chum salmon for HCRs that initiated harvests before the peak of the sockeye return. The box and whisker plots show the distribution of escapement outcomes in every year of the forward simulation, the bar near the center of the box shows the median value, the box shows the interquartile range and the whiskers show the most extreme data point which is no more than 1.5 times the length of the box away from the box. (R Core Team 2013). The green horizontal line corresponds the SMSY value for chum, while the red horizontal line corresponds to a proxy for SGEN.   Escapement (number of chum salmon) Year of simulation 167   Figure 6.7.  Escapement trajectories for chum salmon for HCRs constrained to initiate harvests after the peak of the sockeye return. The box and whisker plots show the distribution of escapement outcomes in every year of the forward simulation, the bar near the center of the box shows the median value, the box shows the interquartile range and the whiskers show the most extreme data point which is no more than 1.5 times the length of the box away from the box. (R Core Team 2013). The green horizontal line corresponds the SMSY value for chum, while the red horizontal line corresponds to a proxy for SGEN. Escapement (number of chum salmon) Year of simulation 168    Figure 6.8.  The average yield over the simulation period for the five (5) best performing HCRs.   Mean annual yield (number of sockeye)  169   Figure 6.9.  Median utility of the five (5) best performing HCRs.   Mean annual utility (log(Ct+1))  170   Figure 6.10.  Mean escapement by species for the five (5) best performing HCRs. The green horizontal line corresponds the SMSY value for the species, while the red horizontal line corresponds to a proxy for SGEN. Mean annual escapement (number of fish)  171     Figure 6.11.  Sockeye Yield trade-off figures. Scatter plots show the different sockeye harvests obtained in the years of the forward simulations. Grey dotted lines are the 1:1 lines, points above the line indicate that the HCR on the y-axis had higher yield than the current HCR. The blue lines show contours around 20%, 40%, 60%, and 80% of the data points.   Catch (number of sockeye) Catch (number of sockeye) 172   Figure 6.12.  Chum escapement outcomes. Boxplots show chum escapements in the years of the forward simulations. The box and whisker plots show the distribution of escapement outcomes in every year of the forward simulation, the bar near the center of the box shows the median value, the box shows the interquartile range and the whiskers show the most extreme data point which is no more than 1.5 times the length of the box away from the box. (R Core Team 2013). 173     Figure 6.13.  Chum escapement trade-off plots showing the different chum escapements in the years of the forward simulations. Grey dotted lines are the 1:1 lines, points above the line indicate that the HCR on has higher escapement than under the current HCR. The blue lines show contours around 20%, 40%, 60%, and 80% of the data points.   Escapement (number of chum) Escapement (number of chum) 174   Figure 6.14.  Scatter plots showing sockeye yield and chum escapement in the years of the forward simulations. Labels indicate the harvest control rule where the harvest and escapement outcomes are being compared to one another.   Escapement (number of chum) Escapement (number of chum) Escapement (number of chum) Escapement (number of chum) Escapement (number of chum) Catch (number of sockeye)   175    Figure 6.15.  Escapement trajectories for chum salmon for the five (5) best performing HCRs. The box and whisker plots show the distribution of escapement outcomes in terms of % of SEQ in every year of the forward simulation. The grey horizontal line corresponds the SEQ value for Chum.  The text above each plot indicates the HCR being evaluated in each panel.   Escapement (% SEQ) Year of simulation  176   Figure 6.16.  Boxplots showing the distribution of percent errors in recruitment parameter estimates and derived management parameters for each species across all HCRs and error level combinations. Panel (a) shows the Ricker a parameter estimates, panel (b) shows the Ricker b parameter estimates (on a log scale), panel (c) shows the estimates of UMSY, panel (d) shows the estimates of SMSY.   Percent error  Percent error  Percent error  Percent error  177    Figure 6.17.  Ricker a parameter estimate error box and whisker plots separated by escapement observation error regime. The red line corresponds to the true Ricker a value.   Escapement observation error    Escapement observation error  Escapement observation error  Ricker a Ricker a  178     Figure 6.18.  Ricker b parameter estimate error box and whisker plots separated by escapement observation error regime. The red line corresponds to the true Ricker b value.     Ricker b Ricker b Escapement observation error  Escapement observation error  Escapement observation error  179  Chapter 7: Conclusion Salmon management involves balancing different objectives for a diverse spectrum of stakeholders.  Management systems often try, but fail, to properly evaluate the trade-offs between objectives, leading to poor outcomes for fisheries or conservation (Deroba and Bence 2008, Walters et al. 2008, Cohen 2012a, Cohen 2012b, Cohen 2012c).  The work presented in this thesis comprises a suite of analyses that can inform trade-offs in current Pacific salmon fisheries management.  Together, this suite of analyses forms a closed loop simulation, which can be built upon to form the core of a Management Strategy Evaluation (MSE).  The results and models can be directly applied to the Skeena River system or can be generalized for other fisheries.    The work in this thesis focused on addressing several major challenges faced by salmon fisheries management, including: ●  Balancing catch and escapement of multiple stocks in mixed stock fisheries; ● Estimating run timing and size, and the impact of these models on in-season management; and ● Modeling in-season management processes. The results and models developed in this thesis allow the exploration of these challenges and allow managers to evaluate the likely outcomes of different HCRs, improving their ability to make decisions that explicitly trade-off between different objectives. 180  7.1 Research Summary 7.1.1 Chapter 2: Harvest control rules for mixed stock fisheries coping with autocorrelated recruitment variation, conservation of weak stocks, and economic well-being Dynamic programming was used to develop a new HCR for the Skeena River mixed stock  sockeye salmon fishery.  The optimum HCR maximizes the utility of the catch in the mixed stock fishery.  The HCR developed for the mixed stock fishery has a different form than those developed to maximize yield or utility of the catch in the fishery for single stocks. Importantly by considering autocorrelated recruitment variability, instead of assuming independence, there is a dramatic change away from the fixed exploitation rate strategy normally assumed to maximize utility.  The optimum form of the HCR is also different from the rectilinear, or fixed escapement policy rules for management of productive stocks, to rules that involve a smooth increase in target fishing mortality rates with increasing stock size.    A critical finding is that this new HCR offers nearly the same net incomes as a fixed escapement policy, protects escapement when stock sizes are low, and avoids the no-harvesting years that can cause severe economic hardship for fishermen, while being responsive to fluctuations in productivity.  Application of this new HCR on the Skeena River would improve outcomes for fishermen, while still protecting the weaker stocks in the mix from overfishing.  This method can be extended to any mixed stock fishery, allowing for generation of optimum harvest control rules tailored to the mix of stock productivities and the economic objectives of the fishery.   181  7.1.2 Chapter 3: Reconstruction of run timing and harvest rates for Pacific salmon subject to gauntlet fisheries This chapter built and demonstrated an improved run reconstruction method. By allowing for more realistic representation of fish migration through gauntlet fishing areas, this method allows for a more accurate reconstruction of salmon returns to the test fishery.  The improved run reconstruction method is a useful tool that addresses some of the common problems of boxcar models (Gilhousen 1980, Gatto and Rinaldi 1980), and produces better estimates of reconstructed run timings for the Skeena River salmon species and catchability for the fisheries.    When applying this method to the Skeena River gauntlet fisheries, the new method shows that the entry of fish to the fishing areas is normally distributed, consistent with expectation.  This model provides updated estimates of run timing for the major salmon species on the Skeena River, improving representation of the migration of these species in other modeling work.    Two possible additional sources of error should be considered in future studies.  First, for the Skeena River fisheries, the statistical areas in which catch and effort are reported are large, and fishing effort is not always evenly distributed.  Larger fishing areas can lead to concentration of effort in areas, which can generate errors in reconstructing return patterns.  Second, the major information source for the reconstruction is the gillnet test fishery.  Hyperstability in the catch could lead to underestimating the number of fish passing the test fishing gear when abundances are high, because gillnet fishing gear has a well-documented problem of saturation at high abundances (Hansen et al. 1998, Prchalová et al. 2013).  Tagging studies, modifications of fishing areas, or additional test fisheries could be used to explore these issues.  This chapter 182  advances methods for estimating run timing with expected positive impacts on in-season management.  This new run reconstruction model should be applied in situations where there is a combination of catch and effort information from the fisheries targeting migrating salmon, and test fisheries.  It can be easily extended to other salmon fisheries and would likely be an improvement on boxcar models operating at a coarse time-space step (e.g. potential applications include the chinook, sockeye, and chum salmon fisheries of the Fraser and Nass rivers). 7.1.3 Chapter 4: Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming  The linear programming (LP) work developed for this chapter was used to model the impacts of river mouth commercial fisheries on multiple stocks co-migrating through the fishing grounds, and was able to optimize harvest in these fisheries subject to a number of allocation and conservation constraints.  Using an LP model allows us to explicitly model the temporal pattern of fisheries through the fishing season.  Modeling the timing of the fisheries allows several innovations. First, exploration of the optimum patterns of fisheries openings leads to information about how a mismatch in timing of fisheries and returning salmon stocks can lead to lost harvest (similar to that found by Carney and Adkison 2014 and Adkison and Cunningham 2015).  Second, the LP approach allows rapid modeling of the in-season management process enabling more realistic modeling of implementation error, in a closed loop system.  Where a gauntlet fishery exists, an LP should be used to model the in-season fisheries process.  LP can be used in a retrospective manner to generate candidate fishing plans in-season to optimize the fishing 183  within a year, and as a model for the in-season management process in a closed loop simulation model. 7.1.4 Chapter 5: Improved estimates of run timing and size for Skeena River sockeye using a Bayesian state-space model  In this chapter, a Bayesian state-space method for estimating run timing and size was developed and shown to be a significant improvement on the current approach, which is based upon a fixed estimate of run timing (the AUC method). The Bayesian state-space method demonstrates three improvements to the run size and timing estimates produced by other methods (Walters and Buckingham 1975, Cox-Rogers 1997).  The first improvement is providing posterior probability distributions for the estimates of run timing and size.  Explicitly showing both the most likely return size, but also the uncertainty in the forecasts, allows managers to quantitatively balance the risk of overfishing against foregone harvest.  The second improvement is that the Bayesian state-space method estimates the return timing, as well as the run size, so it can more quickly detect the dangerous failure case for salmon management where a small run comes early and appears to be a large or normal sized run (Adkison and Cunningham 2015).  Being able to quantify the performance of the in-season run size forecast (in terms of bias and precision throughout the fishing season) allows improved modeling of in-season processes in a closed loop simulation framework. Most salmon closed loop simulations (e.g.  Pestel et al. 2008, Holt and Peterman, Pestal et al. 2011) apply a fixed annual implementation error, or ignore the impact of implementation error.  The third improvement is that the state-space nature of the model allows the evaluation of additional observation models and provides a framework whereby other types of information can be judged in terms of expected improvements to the run size estimates, which allows the expected benefit of new programs to be considered at the same time as the costs. 184  The run size model presented here can be used immediately to improve the run size estimation procedure in place on the Skeena River and, because of the state-space nature of the model, can easily be adapted to improve estimates of return to other rivers, with the generation of different observation models.  This work also reinforces earlier findings that the timing of fisheries decisions will have dramatic impacts on the outcomes, and further shows how the degree of uncertainty with which in-season decisions are made varies through the fishing season.   7.1.5 Chapter 6: Incorporating uncertainty in assessment and management models using closed loop simulations to evaluate harvest control rules Combining data and models from the previous chapters allowed the development of a closed loop simulation model that was be used to test harvest control rules (HCRs) and explore the trade-offs that arise in a mixed species fishery.  The closed loop simulations can be used to inform decisions about which HCR is preferred, and to evaluate the possible impacts of changes to management systems and monitoring programs.  Perhaps the most important practical finding from the simulations is that there is a significant cost in foregone harvest with the status quo management strategy of delaying fishery openings until better estimates of run size become available.  Timing of fisheries is as important as the HCR in yield to fisheries (similar to Adkison and Cunningham 2015).  Management agencies like DFO (and PSC in the Fraser sockeye case) should consider the costs and risks associated not only with the type of control rule chosen, but the timing of initiation of fisheries.  More realistic characterization of the error in the closed loop model improved the predictions of performance above those that do not explicitly model the in-season processes (Holt and Peterman 2006, Pestel et al. 2008, Pestal et al. 2011).  Closed loop simulation modeling shows 185  the best HCR for Skeena River fisheries (albeit under a limited set of objectives) and could be combined with the existing management planning cycle to develop an MSE for Skeena River fisheries.  When creating MSE or closed loop simulations for other systems, the important lesson here is to carefully model the in-season processes, as timing of fisheries and information to inform fisheries decisions can be as important as the HCR chosen. A simulation model that applies a fixed “implementation error” is likely to miss this important interaction. 7.2 Future Directions The work done in this thesis forms a foundation that can enable future work exploring questions specific to the Skeena River, or to salmon management more broadly.  The issues of instability in objectives, population dynamics, and management tools could all be approached either with the tools developed in this thesis or with extensions to these tools.  As changes in governance take place, including formal adoption of United Nations Declaration on the Rights of Indigenous Peoples (UN General Assembly 2007), evolving interpretation of the precautionary approach (DFO 2005), an updated Canadian Fisheries Act (Fisheries Act 1985, Bill C-68 2018), shifting domestic allocations (DFO 2017), and ongoing renegotiation of the Pacific Salmon Treaty (Pacific Salmon Treaty 1985), management objectives are likely to change.  Toolsets able to explore different objectives for harvest, and different levels of risk associated with escapement or other conservation objectives, will become more important.  The tools presented here can be used to manage with different objectives, and to different constraints, so that management systems can adapt them to meet the decision making needs of an evolving policy landscape.  186  Climate change is expected to lead to increased uncertainty in population dynamics (Harley et al. 2009, Reed et al. 2011).  Salmon populations are expected to be impacted by climate change in a variety of potentially unpredictable ways: as freshwater ecosystems change due to climate warming (Rand et al. 2006, Reed et al. 2011); as estuarine habitats are altered; and as marine ecosystems change due to changes in marine food web composition (Rice 1995, Brown et al. 2010). Management strategies need to be robust to changes in productivity.  The results and tools presented here can be used to explore the impact of productivity, or other dynamic changes, on the ability of the management system to react.  The management systems themselves change over time.  Budgets, biologists, methods for collecting species and stock level life history information, and in-season management tools are all subject to change.  There is a new focus on "Data Limited" assessment methods and policies robust to errors in in-season management (Carruthers et al. 2014, Holt et al. 2017).  The ability to evaluate the likely impact of changes to methods requires comprehensive models that address not only the biology of the stocks, but the interactions of the management tools and how these tools perform.    The models and results presented in this thesis can be extended to meet these challenges.  The dynamic and linear programming model objectives can be updated easily to explore new trade-offs.  Stock structure and life history characteristics are inputs to the modeling tools and can be modified to examine productivity scenarios (Cass et al. 2004, Pestal et al. 2011).  The modeling tools themselves are built with certain assumptions about performance and errors, which can be updated to explore different management scenarios.    187   Expanding the management and monitoring sub-models developed for the closed loop simulations can allow cost, and likely value, of changes to monitoring and management systems to be explored. In addition, the impacts of better or worse in-season management, the cost and value of escapement programs, and the utility of development of run size models for other species or systems can all be explored in the context of the closed loop simulation model. 7.3 Remarks Closed loop simulations like the ones presented in this thesis can form the core of an MSE.  The value of an MSE is in the iterative use of closed loop simulations to evaluate the impact of different strategies within the context of the current management system, and to explore the likely outcomes of changes to the strategies or the components of the management system.  An MSE will continue to inform decision makers as objectives for the fisheries, the management tools, and the biology of the populations being managed change.  Simulation testing of the current HCR shows there is the potential to improve yield in the fisheries either by changing the implementation of the current rule (by fishing earlier) or by changing to a new HCR that should have similar escapement performance.  Incorporation of the modeling tools developed in this thesis to the current management planning process could be done for the Skeena River, as it has for Fraser Sockeye (e.g. Cass et al. 2004, Pestal et al. 2008) and can provide HCRs that are designed to meet the objectives for a range of stakeholders.         188  References Adkison, M.D. and Cunningham, C.J., 2015. The effects of salmon abundance and run timing on the performance of management by emergency order. Canadian Journal of Fisheries and Aquatic Sciences, 72(10), pp.1518-1526. Ahmed, M., 1991. A model to determine benefits obtainable from the management of riverine fisheries of Bangladesh (Vol. 728). WorldFish. Allen, K. 1973.  The influence of random fluctuations in the stock-recruitment relationships on the economic return from salmon fisheries.  In B. Parrish, ed., Fish stocks and recruitment volume 164, pp. 350-359. Rapp. Et Proces Verbaux Reun. Cons. Int. Explor Mer. Arnason, R., 2001. Costs of fisheries management: theoretical and practical implications. Baker, M.R., Schindler, D.E., Essington, T.E. and Hilborn, R., 2014. Accounting for escape mortality in fisheries: implications for stock productivity and optimal management. Ecological Applications, 24(1), pp.55-70. Beacham, T.D., Cox‐Rogers, S., MacConnachie, C., McIntosh, B. and Wallace, C.G., 2014. Population structure and run timing of sockeye salmon in the Skeena River, British Columbia: response to comment. North American Journal of Fisheries Management, 34(6), pp.1171-1176. Benson, A.J., Cooper, A.B. and Carruthers, T.R., 2016. An evaluation of rebuilding policies for US fisheries. PloS one, 11(1), p.e0146278. Berkelaar, M and others (2014). lpSolve: Interface to Lp_solve v. 5.5 to solve linear/integer programs. R package version 5.6.8.  <http://CRAN.R-project.org/package=lpSolve> retrieved on 2018-05-30 Beverton, R.J.H. and Holt, S.J., 1957. On the dynamics of exploited fish populations.  Her Majesty's Stationery Office, London. 533 pages. 189  Branch, T.A. and Hilborn, R., 2010. A general model for reconstructing salmon runs. Canadian Journal of Fisheries and Aquatic Sciences, 67(5), pp.886-904. Brown, C.J., Fulton, E.A., Hobday, A.J., Matear, R.J., Possingham, H.P., Bulman, C., Christensen, V., Forrest, R.E., Gehrke, P.C., Gribble, N.A. and Griffiths, S.P., 2010. Effects of climate‐driven primary production change on marine food webs: implications for fisheries and conservation. Global Change Biology, 16(4), pp.1194-1212. Butterworth, D.S., 2007. Why a management procedure approach? Some positives and negatives. ICES Journal of Marine Science, 64(4), pp.613-617. Butterworth, D.S. and Bergh, M.O., 1993. The development of a management procedure for the South African anchovy resource. In Smith, S.J., Hunt, J.J. and Rivard, D. eds. Risk Evaluation and Biological Reference Points for Fisheries Management. Canadian Special Publication of Fisheries and Aquatic Sciences, pp.83-100. Butterworth, D.S., Cochrane, K.L. and De Oliveira, J.A.A., 1997. Management procedures: a better way to manage fisheries? The South African experience. Global trends: fisheries management, 20, 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(6), pp.985-998. Carney, J.M. and Adkison, M.D., 2014. Using model simulations to compare performance of two commercial salmon management strategies in Bristol Bay, Alaska. Canadian journal of fisheries and aquatic sciences, 71(6), pp.814-823. Carpenter, B., Gelman, A., Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., & Riddell, A., 2017. Stan: a probabilistic programming language. Journal of Statistical Software, 76(1),pp 1 - 32. 190  Carruthers, T., Punt, A., Walters, C., MacCall, A., McAllister, M., Dick, E.J., Cope, J., 2014. Evaluating methods for setting catch limits in data-limited fisheries. Fisheries Research, 153: 48–68. Catalano, M.J. and Jones, M.L., 2014. A simulation‐based evaluation of in‐season management tactics for anadromous fisheries: Accounting for risk in the Yukon River fall chum salmon fishery. North American Journal of Fisheries Management, 34(6), pp.1227-1241. Carney, J.M. and Adkison, M.D., 2014. Evaluating the performance of two salmon management strategies using run reconstruction. North American journal of fisheries management, 34(1), pp.159-174. Cass, A, M. Folkes, G. Pestal. 2004. Methods for assessing harvest rules for Fraser River sockeye salmon. DFO Can. Sci. Advis. Sec. Res. Doc. 2004/025. Cave, J.D. and Gazey, W.J., 1994. A preseason simulation model for fisheries on Fraser River sockeye salmon (Oncorhynchus nerka). Canadian Journal of Fisheries and Aquatic Sciences, 51(7), pp.1535-1549. Cohen, B.I. 2012a. Cohen Commission of inquiry into the decline of sockeye salmon in the Fraser River — final report. The uncertain future of Fraser River sockeye. Vol. 1: The sockeye fishery. Minister of Public Works and Government Services Canada, Ottawa, Ont.  Cohen, B.I. 2012b. Cohen Commission of inquiry into the decline of sockeye salmon in the Fraser River — final report. The uncertain future of Fraser River sockeye. Vol. 2: Causes of the decline. Minister of Public Works and Government Services Canada, Ottawa, Ont.         Cohen, B.I. 2012c. Cohen Commission of inquiry into the decline of sockeye salmon in the Fraser River — final report. The uncertain future of Fraser River sockeye. Vol. 3: 191  Recommendations, summary, process. Minister of Public Works and Government Services Canada, Ottawa, Ont.  Collie, J.S., Peterman, R.M. and Zuehlke, B.M., 2012. A fisheries risk-assessment framework to evaluate trade-offs among management options in the presence of time-varying productivity. Canadian Journal of Fisheries and Aquatic Sciences, 69(2), pp.209-223. Cooke, J.G., 1999. Improvement of fishery-management advice through simulation testing of harvest algorithms. ICES Journal of Marine Science, 56(6), pp.797-810. Cox, A., 2001. Cost recovery in fisheries management: the Australian experience. Cox, S.P. and Kronlund, A.R., 2008. Practical stakeholder-driven harvest policies for groundfish fisheries in British Columbia, Canada. Fisheries Research, 94(3), pp.224-237. Cox-Rogers, S. 1994. Description of a Daily Simulation Model For the Area 4 (Skeena) Commercial Gillnet Fishery. Canadian Manuscript Report of Fisheries and Aquatic Sciences No. 2256, 4(2256). Cox-Rogers, S., 1997. Inseason forecasting of Skeena River sockeye run size using Bayesian probability theory. Fisheries and Oceans Canada, Science Branch. Cox-Rogers, S., Hume, J.M.B., Shortreed, K.S., Spilsted, B. and Department of Fisheries and Oceans, Prince Rupert, BC(Canada). Science Branch, 2010. A risk assessment model for Skeena River sockeye salmon (No. 2920). DFO, Prince Rupert, BC(Canada). Dahlberg, M.L., 1973. Stock-and-recruitment relationships and optimum escapements of sockeye salmon stocks of the Chignik Lakes, Alaska. Cons. int. Explor. Mer, Rapports et Proce-Verbaux, 164, pp.98-105. 192  Dankel, D.J., Skagen, D.W. and Ulltang, Ø., 2008. Fisheries management in practice: review of 13 commercially important fish stocks. Reviews in Fish Biology and Fisheries, 18(2), pp.201-233. Dantzig, G.B., 1951. Maximization of a linear function of variables subject to linear inequalities. New York. De la Mare, W.K., 1996. Some recent developments in the management of marine living resources. Frontiers of population ecology, pp. 599–616. Ed. by R. B. Floyd, A. W. Sheppard, and P. J. D. Barro. CSIRO Publishing, Melbourne. 639 pp Decker. A.S., Hawkshaw, M.A., Patten, B.A, Sawada, J, and A.L. Jantz I. 2014. Assessment of the Interior Fraser Coho Salmon (Oncorhynchus kisutch) Management Unit Relative to the 2006 Conservation Strategy Recovery Objectives. Canadian Science Advisory Secretariat Research Document 2014/086. xi + 64 p. Decker, A.S. and Irvine, J.R., 2013. Pre-COSEWIC assessment of interior Fraser coho salmon (Oncorhynchus kisutch). Fisheries and Oceans Canada, Science. DFO [Department of Fisheries and Oceans]. 2005. Canada's Policy for Conservation of Wild Pacific Salmon. Fisheries and Oceans Canada, Vancouver, BC. 34 p. (Accessed February 20 2015). DFO [Department of Fisheries and Oceans]. 2012. Pacific Region Integrated Fisheries Management Plan, Salmon, Northern B.C., June 1, 2012 to May 31, 2013. Fisheries Management Branch, Fisheries and Oceans Canada. Vancouver, British Columbia. DFO [Department of Fisheries and Oceans]. 2016a, Fishery Operations System, Daily Tyee Test Fishing Data, SALMON GILLNET TEST, Skeena Tyee Gillnet. DFO [Department of Fisheries and Oceans]. 2016b, Spawing Escapement Database. 193  DFO [Department of Fisheries and Oceans]. 2017. Pacific Region Integrated Fisheries Management Plan, Salmon, Northern B.C., June 1, 2017 to May 31, 2018. Fisheries Management Branch, Fisheries and Oceans Canada. Vancouver, British Columbia. Deriso, R., 1985. Risk adverse harvesting strategies. In Resource Management (pp. 65-73). Springer, Berlin, Heidelberg.  Deroba, J.J. and Bence, J.R., 2008. A review of harvest policies: understanding relative performance of control rules. Fisheries Research, 94(3), pp.210-223. Dorfman, R., Samuelson, P.A. and Solow, R.M., 1987. Linear Programming and Economic Analysis. Courier Corporation. Chicago Eggers, D.M., 1993. Robust harvest policies for Pacific salmon fisheries. In Proceedings of the International Symposium on Management Strategies for Exploited Fish Populations. Alaska Sea Grant Report (No. 93-02, pp. 85-106). English, K.K., Edgell, T.C., Bocking, R.C., Link, M.R. and Raborn, S.W., 2011. Fraser River Sockeye fisheries and fisheries management and comparison with Bristol Bay Sockeye fisheries. LGL Ltd. Cohen Commission Tech. Rept, 7, p.190p. Frederick, S.W. and Peterman, R.M., 1995. Choosing fisheries harvest policies: when does uncertainty matter?. Canadian Journal of Fisheries and Aquatic Sciences, 52(2), pp.291-306. Fried, S.M. and Hilborn, R., 1988. Inseason forecasting of Bristol Bay, Alaska, sockeye salmon (Oncorhynchus nerka) abundance using Bayesian probability theory. Canadian Journal of Fisheries and Aquatic Sciences, 45(5), pp.850-855. Fisheries Act, RSC 1985, c F-14, <http://canlii.ca/t/52ql9> retrieved on 2018-05-30 Fogarty, M.J., 1993. Recruitment distributions revisited. Canadian Journal of Fisheries and Aquatic Sciences, 50(12), pp.2723-2728. 194  Gatto, M. and Rinaldi, S., 1980. On the determination of a commercial fishery production model. Ecological Modelling, 8, pp.165-172. Gazey, W.J. and Palermo, R.V., 2000. A Preliminary Review of a New Model Based on Test Fishing Data Analysis to Measure Abundance of Returning Chum Stocks to the Fraser River. Fisheries and Oceans Canada. Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Pewsey, A., Neuhäuser, M., Klein, J.P., Van Houwelingen, H.C. and Ibrahim, J.G., 2014. Bayesian Data Analysis. Graham, M., 1935. Modern theory of exploiting a fishery, and application to North Sea trawling.  Journal du Conseil International pour l’Exploration de la Mer. 10, pp. 264-274 Gilhousen, P., 1980. Energy sources and expenditures in Fraser River sockeye salmon during their spawning migration. New Westminster, British Columbia: International Pacific Salmon Fisheries Commission.  Gordon, H.S., 1954. The economic theory of a common-property resource: the fishery. In Classic Papers in Natural Resource Economics (pp. 178-203). Palgrave Macmillan, London. Grant., S.C.H., Townsend, M., White, B., Lapointe, M., 2014. Fraser River Pink Salmon (Oncorhynchus gorbuscha) Data Review: Inputs for Biological Status and Escapement Goals. Southern Boundary Restoration and Enhancement Fund. Grant, S.C.H., MacDonald, B.L., Cone, T.E., Holt, C.A., Cass, A., Porszt, E.J., Hume, J.M.B. and Pon, L.B., 2011. Evaluation of uncertainty in Fraser sockeye (Oncorhynchus nerka) wild salmon policy status using abundance and trends in abundance metrics. DFO Canadian Science Advisory Secretariat Research Document. Groot, C. and Margolis, L. eds., 1991. Pacific salmon life histories. UBC press. 195  Guillen, J., Macher, C., Merzéréaud, M., Bertignac, M., Fifas, S. and Guyader, O., 2013. Estimating MSY and MEY in multi-species and multi-fleet fisheries, consequences and limits: an application to the Bay of Biscay mixed fishery. Marine Policy, 40, pp.64-74. Hall, D.L., Hilborn, R., Stocker, M. and Walters, C.J., 1988. Alternative harvest strategies for Pacific herring (Clupea harengus pallasi). Canadian Journal of Fisheries and Aquatic Sciences, 45(5), pp.888-897. Hall, S.J. and Mainprize, B., 2004. Towards ecosystem‐based fisheries management. Fish and Fisheries, 5(1), pp.1-20. Hansen, M.J., Schorfhaar, R.G. and Selgeby, J.H., 1998. Gill‐Net Saturation by Lake Trout in Michigan Waters of Lake Superior. North American Journal of Fisheries Management, 18(4), pp.847-853. Harley CD, Randall Hughes A, Hultgren KM, Miner BG, Sorte CJ, Thornber CS, Rodriguez LF, Tomanek L, Williams SL. The impacts of climate change in coastal marine systems. Ecology letters. 2006 Feb;9(2):228-41. Hawkshaw, M. and Walters, C., 2015. Harvest control rules for mixed stock fisheries coping with autocorrelated recruitment variation, conservation of weak stocks, and economic well-being. Canadian Journal of Fisheries and Aquatic Sciences, 72(5), pp.759-766. Hilborn, R., 1985. Apparent stock-recruitment relationships in mixed stock fisheries. Canadian Journal of Fisheries and Aquatic Sciences, 42(4), pp.718-723. Hilborn, R., Pikitch, E.K. and McAllister, M.K., 1994. A Bayesian estimation and decision analysis for an age-structured model using biomass survey data. Fisheries Research, 19(1-2), pp.17-30. 196  Hilborn, R., Quinn, T.P., Schindler, D.E. and Rogers, D.E., 2003. Biocomplexity and fisheries sustainability. Proceedings of the National Academy of Sciences, 100(11), pp.6564-6568. Hilborn, R., Stewart, I. J., Branch, T. A., and Jensen, O.P., 2012. Defining trade-offs among conservation, profitability, and food security in the California Current bottom-trawl fishery.  Conservation Biology 26:257-266. Hilborn, R. and Walters, C.J., 1992. Quantitative fisheries stock assessment: choice, dynamics and uncertainty. Reviews in Fish Biology and Fisheries, 2(2), pp.177-178. Holt, C.A. and Bradford, M.J., 2011. Evaluating benchmarks of population status for Pacific salmon. North American Journal of Fisheries Management, 31(2), pp.363-378. Holt, C.A., Cass, A., Holtby, B., Riddell, B. and Department of Fisheries and Oceans, Ottawa, ON(Canada); Canadian Science Advisory Secretariat, Ottawa, ON(Canada), 2009. Indicators of status and benchmarks for Conservation Units in Canada's Wild Salmon Policy. Canadian Science Advisory Secretariat Holt, C., Davis, B, Dobson, D., Godbout, L., Luedke, W., Tadey, J., Van Will, P., 2017  Evaluating Benchmarks of Biological Status for Data-limited Populations (Conservation Units) of Pacific Salmon, Focusing on Chum Salmon in Southern BC. CSAP Working Paper 2015SAL04 Holt, C.A. and Peterman, R.M., 2006. Missing the target: uncertainties in achieving management goals in fisheries on Fraser River, British Columbia, sockeye salmon (Oncorhynchus nerka). Canadian Journal of Fisheries and Aquatic Sciences, 63(12), pp.2722-2733. Holt, C.A. and Peterman, R.M., 2008. Uncertainties in population dynamics and outcomes of regulations in sockeye salmon (Oncorhynchus nerka) fisheries: implications for management. Canadian Journal of Fisheries and Aquatic Sciences, 65(7), pp.1459-1474. 197  Holtby, L.B., Ciruna, K.A. and Department of Fisheries and Oceans, Ottawa, ON(Canada); Canadian Science Advisory Secretariat, Ottawa, ON(Canada), 2008. Conservation Units for Pacific salmon under the Wild Salmon Policy (No. 2007/070). DFO, Ottawa, ON(Canada). Hyun, S.Y., 2002. Inseason Forecasts of Sockeye Salmon Returns to the Bristol Bay Districts of Alaska (Doctoral dissertation, University of Washington). Hyun, S.Y., Hilborn, R., Anderson, J.J. and Ernst, B., 2005. A statistical model for in-season forecasts of sockeye salmon (Oncorhynchus nerka) returns to the Bristol Bay districts of Alaska. Canadian Journal of Fisheries and Aquatic Sciences, 62(7), pp.1665-1680. Kinas, P.G., 1996. Bayesian fishery stock assessment and decision making using adaptive importance sampling. Canadian Journal of Fisheries and Aquatic Sciences, 53(2), pp.414-423. Kinas, P.G. and Andrade, H.A., 2007. Bayesian statistics for fishery stock assessment and management: a synthesis. Kope, R.G., 1992. Optimal harvest rates for mixed stocks of natural and hatchery fish. Canadian Journal of Fisheries and Aquatic Sciences, 49(5), pp.931-938. Korman, J. and English, K.K., 2013. Benchmark analysis for Pacific salmon conservation units in the Skeena watershed. Prepared for the Pacific Salmon Foundation, Vancouver, BC. Larkin, P.A., 1977. An epitaph for the concept of maximum sustained yield. Transactions of the American fisheries society, 106(1), pp.1-11. Larson, D.M., House, B.W. and Terry, J.M., 1996. Toward efficient bycatch management in multispecies fisheries: a nonparametric approach. Marine Resource Economics, 11(3), pp.181-201. Lewis, B., and J. Shriver. 2017. 2017 Bristol Bay sockeye salmon processing capacity survey summary. Alaska 198  Department of Fish and Game, Special Publication No. 16-08, Anchorage. Link, M.R. and Peterman, R.M., 1998. Estimating the value of in-season estimates of abundance of sockeye salmon (Oncorhynchus nerka). Canadian Journal of Fisheries and Aquatic Sciences, 55(6), pp.1408-1418. Mace, P.M. and Sissenwine, M.P., 2002. Coping with uncertainty: evolution of the relationship between science and management. In American Fisheries Society Symposium (pp. 9-28). American Fisheries Society. Mäntyniemi, S., Kuikka, S., Rahikainen, M., Kell, L.T. and Kaitala, V., 2009. The value of information in fisheries management: North Sea herring as an example. ICES Journal of Marine Science, 66(10), pp.2278-2283. Martell, S.J., Walters, C.J. and Hilborn, R., 2008. Retrospective analysis of harvest management performance for Bristol Bay and Fraser River sockeye salmon (Oncorhynchus nerka). Canadian Journal of Fisheries and Aquatic Sciences, 65(3), pp.409-424. McAllister, M.K., Pikitch, E.K., Punt, A.E. and Hilborn, R., 1994. A Bayesian approach to stock assessment and harvest decisions using the sampling/importance resampling algorithm. Canadian Journal of Fisheries and Aquatic Sciences, 51(12), pp.2673-2687. Mesnil, B., 1996. When discards survive: accounting for survival of discards in fisheries assessments. Aquatic Living Resources, 9(3), pp.209-215. Mertz, G. and Myers, R.A., 1996. Influence of fecundity on recruitment variability of marine fish. Canadian Journal of Fisheries and Aquatic Sciences, 53(7), pp.1618-1625. Meyer, R. and Millar, R.B., 1999. BUGS in Bayesian stock assessments. Canadian Journal of Fisheries and Aquatic Sciences, 56(6), pp.1078-1087. 199  Millar, R.B. and Meyer, R., 2000. Bayesian state-space modeling of age-structured data: fitting a model is just the beginning. Canadian Journal of Fisheries and Aquatic Sciences, 57(1), pp.43-50. Morris, W. F. and Doak, D. F., 2002. Quantitative conservation biology: theory and practice of population viability analysis. p. 135  Mundy, P. R., 1979. A quantitative measure of migratory timing illustrated by application to the management of commercial salmon fisheries, University of Washington, Seattle, Doctoral dissertation. Myers, R.A., 2001. Stock and recruitment: generalizations about maximum reproductive rate, density dependence, and variability using meta-analytic approaches. ICES Journal of Marine Science, 58(5), pp.937-951. Myers, R.A., Barrowman, N.J., Hutchings, J.A. and Rosenberg, A.A., 1995. Population dynamics of exploited fish stocks at low population levels. Science, 269(5227), pp.1106-1108. Myers, R.A., Bowen, K.G. and Barrowman, N.J., 1999. Maximum reproductive rate of fish at low population sizes. Canadian Journal of Fisheries and Aquatic Sciences, 56(12), pp.2404-2419. Myers, R.A., Bradford, M.J., Bridson, J.M. and Mertz, G., 1997. Estimating delayed density-dependent mortality in sockeye salmon (Oncorhynchus nerka): a meta-analytic approach. Canadian Journal of Fisheries and Aquatic Sciences, 54(10), pp.2449-2462. Mundy, P.R., 1979. A quantitative measure of migratory timing illustrated by application to the management of commercial salmon fisheries. Doctoral dissertation, University of Washington, Seattle. 200  Murawski, S.A. and Finn, J.T., 1986. Optimal effort allocation among competing mixed-species fisheries, subject to fishing mortality constraints. Canadian Journal of Fisheries and Aquatic Sciences, 43(1), pp.90-100. Murawski, S.A. and Finn, J.T., 1988. Biological bases for mixed-species fisheries: species co-distribution in relation to environmental and biotic variables. Canadian Journal of Fisheries and Aquatic Sciences, 45(10), pp.1720-1735. Ogden, A.D., Irvine, J.R., English, K.K., Grant, S., Hyatt, K.D., Godbout, L. and Holt, C.A., 2015. Productivity (Recruits-per-Spawner) data for Sockeye, Pink, and Chum Salmon from British Columbia. Canadian Technical Report of Fisheries and Aquatic Sciences 3130. Pacific Salmon Treaty, 1985, United States and Canada, Treaty Doc. No. 99-2 (entered into force, March 18, 1985, renewed 2009) Pestal, G., Ryall, P., Cass, A. and Department of Fisheries and Oceans, Vancouver, BC(Canada). Fisheries and Aquaculture Management Branch, 2008. Collaborative Development of Escapement Strategies for Fraser River Sockeye: Summary Report 2003-2008. Fisheries & Aquaculture Management Branch, Department of Fisheries and Oceans. Pestal, G., Huang, A.M., Cass, A.J. and FRSSI Working Group, 2011. Updated methods for assessing harvest rules for Fraser River sockeye salmon (Oncorhynchus nerka). Canadian Science Advisory Secretariat Research Document, 133. Peterman, R.M., 1978. Testing for density-dependent marine survival in Pacific salmonids. Journal of the Fisheries Board of Canada, 35(11), pp.1434-1450. Peterman, R.M., 1981. Form of random variation in salmon smolt-to-adult relations and its influence on production estimates. Canadian Journal of Fisheries and Aquatic Sciences, 38(9), pp.1113-1119. 201  Peterman, R.M., 1982. Model of salmon age structure and its use in preseason forecasting and studies of marine survival. Canadian Journal of Fisheries and Aquatic Sciences, 39(11), pp.1444-1452. Peterman, R.M., 2004. Possible solutions to some challenges facing fisheries scientists and managers. ICES Journal of Marine Science, 61(8), pp.1331-1343. Peterman, R.M. and Dorner, B., 2012. A widespread decrease in productivity of sockeye salmon (Oncorhynchus nerka) populations in western North America. Canadian Journal of Fisheries and Aquatic Sciences, 69(8), pp.1255-1260. Pike, R.W., 1986. Optimization for engineering systems. Van Nostrand Reinhold Company. Pikitch, E., Santora, C., Babcock, E.A., Bakun, A., Bonfil, R., Conover, D.O., Dayton, P.A.O., Doukakis, P., Fluharty, D., Heneman, B. and Houde, E.D., 2004. Ecosystem-based fishery management. 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), pp.441-464. Punt, A.E., Butterworth, D.S., Moor, C.L., De Oliveira, J.A. and Haddon, M., 2016. Management strategy evaluation: best practices. Fish and Fisheries, 17(2), pp.303-334. Punt, A.E. and Donovan, G.P., 2007. Developing management procedures that are robust to uncertainty: lessons from the International Whaling Commission. ICES Journal of Marine Science, 64(4), pp.603-612. Punt, A.E. and Hilborn, R.A.Y., 1997. Fisheries stock assessment and decision analysis: the Bayesian approach. Reviews in Fish Biology and Fisheries, 7(1), pp.35-63. 202  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(6), pp.860-875. Putman, N.F., Jenkins, E.S., Michielsens, C.G. and Noakes, D.L., 2014. Geomagnetic imprinting predicts spatio-temporal variation in homing migration of pink and sockeye salmon. Journal of The Royal Society Interface, 11(99), p.20140542. Quinn, T.P. and Adams, D.J., 1996. Environmental changes affecting the migratory timing of American shad and sockeye salmon. Ecology, 77(4), pp.1151-1162. Quinn, T.P., Hodgson, S., Flynn, L., Hilborn, R. and Rogers, D.E., 2007. Directional selection by fisheries and the timing of sockeye salmon (Oncorhynchus nerka) migrations. Ecological Applications, 17(3), pp.731-739. R Core Team (2014). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL  http://www.R-project.org/. R. v. Sparrow, [1990] 1 SCR 1075, 1990 CanLII 104 (SCC) Rand, P.S., Hinch, S.G., Morrison, J., Foreman, M.G.G., MacNutt, M.J., Macdonald, J.S., Healey, M.C., Farrell, A.P. and Higgs, D.A., 2006. Effects of river discharge, temperature, and future climates on energetics and mortality of adult migrating Fraser River sockeye salmon. Transactions of the American Fisheries Society, 135(3), pp.655-667. Reed, W.J. and Simons, C.M., 1996. Analyzing catch—effort data by means of the Kalman filter. Canadian Journal of Fisheries and Aquatic Sciences, 53(10), pp.2157-2166. Reed, T.E., Schindler, D.E., Hague, M.J., Patterson, D.A., Meir, E., Waples, R.S. and Hinch, S.G., 2011. Time to evolve? Potential evolutionary responses of Fraser River sockeye salmon to climate change and effects on persistence. PLoS One, 6(6), p.e20380. 203  Ricker, W.E., 1954. Stock and recruitment. Journal of the Fisheries Board of Canada, 11(5), pp.559-623. Ricker, W.E., 1958. Maximum sustained yields from fluctuating environments and mixed stocks. Journal of the Fisheries Board of Canada, 15(5), pp.991-1006. Rice, J., 1995. Food web theory, marine food webs, and what climate change may do to northern marine fish populations. Canadian Special Publication of Fisheries and Aquatic Sciences, pp.561-568. Rothschild, B.J. and Balsiger, J.W., 1971. A linear-programming solution to salmon management. Fishery Bulletin, 69, pp. 117-140. Schindler, D.E., Hilborn, R., Chasco, B., Boatright, C.P., Quinn, T.P., Rogers, L.A. and Webster, M.S., 2010. Population diversity and the portfolio effect in an exploited species. Nature, 465(7298), p.609. Schnute, J.T., 1994. A general framework for developing sequential fisheries models. Canadian Journal of Fisheries and Aquatic Sciences, 51(8), pp.1676-1688. Schnute, J.T., Cass, A. and Richards, L.J., 2000. A Bayesian decision analysis to set escapement goals for Fraser River sockeye salmon (Oncorhynchus nerka). Canadian Journal of Fisheries and Aquatic Sciences, 57(5), pp.962-979. Šmejkal, M., Ricard, D., Prchalová, M., Říha, M., Muška, M., Blabolil, P., Čech, M., Vašek, M., Jůza, T., Herreras, A.M. and Encina, L., 2015. Biomass and abundance biases in European standard gillnet sampling. PloS one, 10(3), p.e0122437. Smith, A.D.M., 1994. Management strategy evaluation: the light on the hill. Population dynamics for fisheries management, pp.249-253. 204  Smith, A.D.M., Sainsbury, K.J. and Stevens, R.A., 1999. Implementing effective fisheries-management systems–management strategy evaluation and the Australian partnership approach. ICES Journal of Marine Science, 56(6), pp.967-979. Spencer, P.D., 1997. Optimal harvesting of fish populations with nonlinear rates of predation and autocorrelated environmental variability. Canadian Journal of Fisheries and Aquatic Sciences, 54(1), pp.59-74. Stan Development Team. 2018. The Stan Core Library, Version 2.18.0.   http://mc-stan.org Stefansson, G. and Rosenberg, A.A., 2005. Combining control measures for more effective management of fisheries under uncertainty: quotas, effort limitation and protected areas. Philosophical Transactions of the Royal Society B: Biological Sciences, 360(1453), pp.133-146. Su, Z. and Adkison, M.D., 2002. Optimal in-season management of pink salmon (Oncorhynchus gorbuscha) given uncertain run sizes and seasonal changes in economic value. Canadian Journal of Fisheries and Aquatic Sciences, 59(10), pp.1648-1659. Su, Z. and Peterman, R.M., 2012. Performance of a Bayesian state-space model of semelparous species for stock-recruitment data subject to measurement error. Ecological Modelling, 224(1), pp.76-89. Tidd, A.N., Hutton, T., Kell, L.T. and Padda, G., 2011. Exit and entry of fishing vessels: an evaluation of factors affecting investment decisions in the North Sea English beam trawl fleet. ICES Journal of Marine Science, 68(5), pp.961-971. UN General Assembly, Convention on the Law of the Sea, 10 December 1982, available at: <http://www.refworld.org/docid/3dd8fd1b4.html> [accessed 2 June 2018]. 205  UN General Assembly, United Nations Declaration on the Rights of Indigenous Peoples : resolution / adopted by the General Assembly, 2 October 2007, A/RES/61/295, available at: <http://www.refworld.org/docid/471355a82.html> [accessed 3 June 2018]. Van Will P. R. Brahniuk, L. Hop Wo and G. Pestal . 2009. Certification Unit Profile: Inner South Coast Chum Salmon (Excluding Fraser River). Can. Man. Rep. Fish. Aquat. Sci. 2876: vii + 63p. Vinther, M., Reeves, S.A. and Patterson, K.R., 2004. From single-species advice to mixed-species management: taking the next step. ICES Journal of Marine Science, 61(8), pp.1398-1409. Wallis, P. and Flaaten, O., 2001. Fisheries Management Costs: Concepts and Studies. Walters, C.J., 1975. Optimal harvest strategies for salmon in relation to environmental variability and uncertain production parameters. Journal of the Fisheries Board of Canada, 32(10), pp.1777-1784. Walters, C.J., 1986. Adaptive management of renewable resources. Macmillan Publishers Ltd. Walters, C.J. and Buckingham, S., 1975. A control system for intraseason salmon management. Walters, C.J., Lichatowich, J.A., Peterman, R.M. and Reynolds, J.D., 2008. Report of the Skeena Independent Science Review Panel. Report of the Skeena Independent Science Review Panel to the Canadian Department of Fisheries and Oceans and the British Columbia Ministry of the Environment, Victoria. British Columbia. Walters, C. and Ludwig, D., 1994. Calculation of Bayes posterior probability distributions for key population parameters. Canadian Journal of Fisheries and Aquatic Sciences, 51(3), pp.713-722. 206  Walters, C.J. and Martell, S.J., 2004. Fisheries ecology and management. Princeton University Press. Walters, C. and Parma, A.M., 1996. Fixed exploitation rate strategies for coping with effects of climate change. Canadian Journal of Fisheries and Aquatic Sciences, 53(1), pp.148-158. Walters, C. and Pearse, P.H., 1996. Stock information requirements for quota management systems in commercial fisheries. Reviews in Fish Biology and Fisheries, 6(1), pp.21-42. Ward, B.R., Tautz, A.F., Cox-Rogers, S., Hooton, R.S., 1993. Migration timing and harvest rates of the steelhead trout populations of the Skeena River system.  PSARC Working Paper S93-06. Woodey, J.C., 2000. International management of fraser river sockeye salmon. Sustainable fisheries management: Pacific salmon. Edited by E. Knudson, C. Steward, D. MacDonald, J. Williams, and D. Reiser. CRC Press, Boca Raton, Fla, pp.207-218. Zheng, J. and Mathisen, O.A., 1998. Inseason forecasting of southeastern Alaska pink salmon abundance based on sex ratios and commercial catch and effort data. North American Journal of Fisheries Management, 18(4), pp.872-885. 207  Appendices 208   Appendix A  Supplementary table for Chapter 4: Improved yield and conservation of a multi-stock, multi-species salmon fishery through use of linear programming  Table A.1.  Salmon populations of the Skeen River aggregated to different levels with associated population parameters and data sources. Data sources are: 1) Walters et al. (2008); 2) Korman and English (2013); and 3) Beacham et al. (2014).     Species Data Source Ricker a Ricker b Mean Run Timing (Julian Day)Run Timing Spread (Days)Smsy Seq Umsy UmaxSockeye 1 1.6 5.71E-07 197 15 1738240 2.80E+06 0.46 0.80Pink 1 1.1 2.44E-07 214 9.4 2093850 4.50E+06 0.37 0.67Chum 1 0.9 1.88E-05 225 12.6 18878 48000 0.33 0.59Chinook 1 1.4 1.25E-05 178 16.3 63034 112000 0.43 0.75Coho 1 1.3 2.85E-06 228 14.9 242455 456000 0.41 0.73Steelhead 1 1.33 5.32E-03 219 17 135 250 0.42 0.74209          Sockeye Management Units                                    (with Benchmarks and Run Timing)Data Source Ricker a Ricker b Mean Run Timing (Julian Day)Run Timing Spread (Days)Smsy Seq Umsy UmaxAlastair 1,2,3 1.49 7.96E-05 175 10 7415 18700 0.45 0.78Babine 1,2,3 1.51 6.11E-07 189 10 976747 2480000 0.45 0.78Bear 1,2,3 1.25 5.94E-04 203 10 866 2100 0.40 0.71Johnston 1,2,3 0.37 8.71E-05 175 10 1995 4210 0.16 0.31Kitsumkalum 1,2,3 2.33 1.42E-04 203 10 5523 16400 0.54 0.90Kitwancool 1,2,3 2.93 6.06E-04 203 10 1427 4840 0.58 0.95Lakelse 1,2,3 1.41 7.58E-05 205 10 7464 18600 0.43 0.76Morice 1,2,3 1.79 3.03E-05 182 10 22160 59200 0.49 0.83Motase 1,2,3 1.20 1.07E-03 196 10 466 1120 0.39 0.70Tahlo/Morrison 1,2,3 2.10 1.23E-04 196 10 6028 17100 0.52 0.88Pink 1,2,3 1.10 2.44E-07 214 9.4 2093850 4500000 0.37 0.67Chum 1,2,3 0.90 1.88E-05 225 12.6 18878 48000 0.33 0.59Chinook 1,2,3 1.40 1.25E-05 178 16.3 63034 112000 0.43 0.75Coho 1,2,3 1.30 2.85E-06 228 14.9 242455 456000 0.41 0.73Steelhead 1,2,3 1.33 5.32E-03 219 17 135 250 0.42 0.74210   Creeks/Lakes/Stocks Data Source Ricker a Ricker b Mean Run Timing (Julian Day)Run Timing Spread (Days)Smsy Seq Umsy UmaxBIG USELESS CREEK PK 1 1.1 1.00E-04 214 9.4 4606 10900 0.37 0.66ECSTALL RIVER PK 1 0.6 1.68E-05 214 9.4 16863 36900 0.25 0.46HAYWARD CREEK PK 1 1.1 6.20E-04 214 9.4 745 1760 0.37 0.66HUMPBACK CREEK PK 1 1.1 1.01E-04 214 9.4 4512 10600 0.37 0.66JOHNSTON CREEK PK 1 1.5 6.16E-04 214 9.4 940 2360 0.44 0.77KHYEX RIVER PK 1 0.7 5.24E-06 214 9.4 62254 139000 0.28 0.52KLOIYA RIVER PK 1 1.8 1.07E-03 214 9.4 637 1720 0.49 0.84LA HOU CREEK PK 1 1.1 4.27E-05 214 9.4 11181 26600 0.38 0.68LITTLE USELESS CREEK PK 1 0.4 1.21E-04 214 9.4 1486 3140 0.16 0.32LOCKERBY CREEK PK 1 0.7 2.11E-04 214 9.4 1540 3430 0.28 0.52MCNICHOL CREEK PK 1 1.1 2.78E-04 214 9.4 1665 3930 0.37 0.67MOORE COVE CREEK PK 1 1.4 2.04E-05 214 9.4 27367 67900 0.43 0.75OONA RIVER PK 1 1.4 7.58E-05 214 9.4 7227 17800 0.42 0.74SILVER CREEK PK 1 1.1 2.18E-04 214 9.4 2109 4970 0.37 0.66SPILLER RIVER PK 1 1.1 1.22E-04 214 9.4 3700 8700 0.36 0.65HERMAN CREEK PK 1 0.7 2.50E-04 214 9.4 1329 2970 0.28 0.52LAKELSE RIVER PK 1 1.4 1.54E-06 214 9.4 356696 881000 0.42 0.74DEEP CREEK PK 1 1.0 2.28E-04 214 9.4 1886 4390 0.35 0.63KITSUMKALUM RIVER - LOWER PK 1 0.9 1.53E-05 214 9.4 25759 59000 0.33 0.60ANDESITE CREEK PK 1 1.0 4.72E-04 214 9.4 929 2170 0.36 0.64DOG-TAG CREEK PK 1 1.5 1.34E-03 214 9.4 433 1090 0.44 0.77EXCHAMSIKS RIVER PK 1 1.0 4.36E-04 214 9.4 1010 2360 0.36 0.64EXSTEW RIVER PK 1 1.0 7.99E-04 214 9.4 523 1210 0.34 0.62EXSTEW SLOUGH PK 1 1.7 2.83E-03 214 9.4 234 619 0.48 0.83GITNADOIX RIVER PK 1 1.6 2.84E-04 214 9.4 2159 5540 0.46 0.79KASIKS RIVER PK 1 0.8 5.25E-05 214 9.4 7064 16000 0.31 0.57SCOTIA RIVER PK 1 0.8 2.22E-05 214 9.4 16298 36800 0.30 0.56SHAMES SLOUGH PK 1 1.1 3.64E-04 214 9.4 1276 3010 0.37 0.67SKEENA RIVER - WEST PK 1 1.1 3.54E-06 214 9.4 132959 315000 0.38 0.67ZYMAGOTITZ RIVER PK 1 0.8 1.77E-04 214 9.4 2082 4710 0.31 0.57KISPIOX RIVER PK 1 0.9 2.67E-06 214 9.4 146959 336000 0.32 0.59NANGEESE RIVER PK 1 0.9 2.25E-04 214 9.4 1796 4130 0.33 0.61BULKLEY RIVER - LOWER PK 1 0.9 3.09E-05 214 9.4 12404 28300 0.32 0.58MORICE RIVER PK 1 0.9 3.65E-06 214 9.4 105633 241000 0.32 0.58STATION CREEK PK 1 1.0 4.60E-04 214 9.4 973 2280 0.36 0.65CHICAGO CREEK PK 1 1.7 1.44E-03 214 9.4 455 1200 0.48 0.82FIDDLER CREEK PK 1 0.8 8.51E-04 214 9.4 430 973 0.31 0.56HAZELTON CREEK PK 1 1.6 3.40E-03 214 9.4 181 466 0.46 0.80KITWANGA RIVER PK 1 1.8 8.66E-06 214 9.4 76679 204000 0.49 0.83KLEANZA CREEK PK 1 0.8 1.12E-04 214 9.4 3253 7360 0.31 0.56PRICE CREEK PK 1 0.5 2.22E-04 214 9.4 1006 2160 0.20 0.38BABINE FENCE COUNT* PK 1 1.2 4.83E-06 214 9.4 105084 254000 0.40 0.71BABINE RIVER (SECTION 4) PK 1 1.2 4.83E-06 214 9.4 104911 253000 0.40 0.71BABINE RIVER (SECTION 5) PK 1 1.1 1.41E-05 214 9.4 32271 75900 0.37 0.66FULTON RIVER PK 1 1.0 5.92E-03 214 9.4 73 171 0.35 0.64BEAR RIVER PK 1 1.3 9.35E-05 214 9.4 5631 13700 0.41 0.72211   Creeks/Lakes/Stocks Data Source Ricker a Ricker b Mean Run Timing (Julian Day)Run Timing Spread (Days)Smsy Seq Umsy UmaxBIG FALLS CREEK CN 1 1.8 2.59E-02 178 16.3 26 70 0.49 0.84ECSTALL RIVER CN 1 1.0 4.60E-05 178 16.3 9320 21700 0.35 0.63JOHNSTON CREEK CN 1 0.8 7.05E-05 178 16.3 4979 11200 0.30 0.55KHYEX RIVER CN 1 1.8 9.16E-03 178 16.3 72 192 0.48 0.83KLOIYA RIVER CN 1 1.1 3.57E-04 178 16.3 1262 2960 0.36 0.65COLDWATER CREEK CN 1 1.9 4.33E-02 178 16.3 16 43 0.50 0.85LAKELSE RIVER CN 1 1.9 4.78E-03 178 16.3 144 388 0.50 0.84CEDAR RIVER* CN 1 2.2 2.08E-03 178 16.3 364 1050 0.53 0.89CLEAR CREEK CN 1 1.9 6.38E-03 178 16.3 109 298 0.50 0.85DEEP CREEK CN 1 0.8 1.38E-03 178 16.3 251 562 0.29 0.54KITSUMKALUM RIVER - LOWER CN 1 1.9 1.02E-04 178 16.3 6735 18200 0.50 0.84KITSUMKALUM RIVER - UPPER CN 1 1.8 1.95E-03 178 16.3 347 930 0.49 0.84DOG-TAG CREEK CN 1 2.0 3.96E-02 178 16.3 18 51 0.52 0.87ERLANDSEN CREEK CN 1 1.3 9.34E-03 178 16.3 56 136 0.41 0.72EXCHAMSIKS RIVER CN 1 1.3 3.90E-03 178 16.3 136 333 0.41 0.73EXSTEW RIVER CN 1 1.7 1.24E-02 178 16.3 51 133 0.47 0.81GITNADOIX RIVER CN 1 1.2 4.30E-03 178 16.3 118 283 0.40 0.70KADEEN CREEK CN 1 1.6 3.50E-02 178 16.3 18 47 0.47 0.81KASIKS RIVER CN 1 1.3 3.06E-03 178 16.3 171 417 0.41 0.72MAGAR CREEK CN 1 1.4 5.91E-03 178 16.3 97 242 0.44 0.76SKEENA RIVER - WEST CN 1 1.7 1.17E-03 178 16.3 549 1440 0.47 0.81ZYMAGOTITZ RIVER CN 1 1.4 9.82E-03 178 16.3 58 145 0.43 0.76CULLON CREEK CN 1 1.7 2.50E-02 178 16.3 26 69 0.48 0.82KISPIOX RIVER CN 1 2.3 6.76E-04 178 16.3 1153 3400 0.54 0.90NANGEESE RIVER CN 1 1.6 5.10E-03 178 16.3 123 317 0.47 0.80STEPHENS CREEK CN 1 1.3 4.92E-03 178 16.3 110 271 0.42 0.74SWEETIN RIVER CN 1 1.7 7.63E-03 178 16.3 84 220 0.47 0.81BULKLEY RIVER - LOWER CN 1 1.4 2.33E-03 178 16.3 235 580 0.42 0.74BULKLEY RIVER - UPPER CN 1 1.3 5.37E-04 178 16.3 970 2360 0.41 0.72MORICE RIVER CN 1 1.5 5.82E-05 178 16.3 9981 25100 0.44 0.77NANIKA RIVER CN 1 1.3 2.14E-03 178 16.3 255 627 0.42 0.74SUSKWA RIVER CN 1 1.8 1.54E-02 178 16.3 44 117 0.49 0.84FIDDLER CREEK CN 1 2.0 1.04E-02 178 16.3 69 192 0.51 0.86KITSEGUECLA RIVER CN 1 1.5 7.42E-03 178 16.3 79 199 0.44 0.77KITWANGA RIVER CN 1 1.3 3.80E-04 178 16.3 1403 3430 0.41 0.73KLEANZA CREEK CN 1 1.2 2.49E-02 178 16.3 21 50 0.40 0.71SHEGUNIA RIVER CN 1 1.2 2.61E-03 178 16.3 188 450 0.39 0.69THOMAS CREEK CN 1 1.1 9.71E-04 178 16.3 479 1130 0.37 0.67ZYMOETZ RIVER - LOWER CN 1 1.8 2.11E-03 178 16.3 313 829 0.48 0.83BABINE FENCE COUNT* CN 1 1.2 1.66E-04 178 16.3 2945 7040 0.39 0.69BABINE RIVER (SECTION 4) CN 1 1.2 1.66E-04 178 16.3 2936 7020 0.39 0.69BABINE RIVER (SECTION 5) CN 1 1.2 7.54E-04 178 16.3 680 1650 0.40 0.71FULTON RIVER CN 1 1.2 2.61E-02 178 16.3 19 44 0.38 0.68NICHYESKWA RIVER CN 1 1.7 3.99E-03 178 16.3 163 429 0.48 0.82BEAR RIVER CN 1 1.5 9.87E-05 178 16.3 6145 15700 0.45 0.79SUSTUT LAKE CN 1 4.0 2.48E-02 178 16.3 36 160 0.59 0.98212   Creeks/Lakes/Stocks Data Source Ricker a Ricker b Mean Run Timing (Julian Day)Run Timing Spread (Days)Smsy Seq Umsy UmaxDIANA CREEK CO 1 0.9 1.39E-04 228 14.9 2941 6770 0.34 0.61ECSTALL RIVER CO 1 1.7 3.05E-04 228 14.9 2117 5550 0.48 0.82OONA RIVER CO 1 0.9 1.75E-04 228 14.9 2344 5400 0.34 0.61SHAWATLAN CREEK CO 1 0.9 1.70E-04 228 14.9 2314 5300 0.33 0.59ANDALAS CREEK CO 1 1.0 8.50E-04 228 14.9 485 1120 0.34 0.61CLEARWATER CREEK CO 1 1.4 1.39E-03 228 14.9 402 997 0.43 0.75HERMAN CREEK CO 1 0.9 3.46E-04 228 14.9 1085 2460 0.31 0.57LAKELSE RIVER CO 1 0.9 4.94E-06 228 14.9 78796 180000 0.32 0.59SCHULBUCKHAND CREEK CO 1 1.1 1.14E-03 228 14.9 397 932 0.36 0.65SOCKEYE CREEK CO 1 1.3 1.23E-03 228 14.9 440 1080 0.42 0.74WILLIAMS CREEK CO 1 1.2 7.71E-04 228 14.9 647 1550 0.39 0.70CEDAR RIVER* CO 1 1.0 2.04E-04 228 14.9 2087 4840 0.35 0.63CLEAR CREEK CO 1 0.9 2.84E-04 228 14.9 1423 3270 0.33 0.61DEEP CREEK CO 1 1.0 4.83E-04 228 14.9 854 1970 0.34 0.61DRY CREEK CO 1 0.9 4.42E-04 228 14.9 911 2090 0.33 0.60GOAT CREEK CO 1 0.8 3.32E-04 228 14.9 1120 2540 0.31 0.57KITSUMKALUM RIVER - UPPER CO 1 0.9 3.53E-05 228 14.9 10792 24600 0.32 0.58LEAN-TO CREEK CO 1 1.0 1.10E-03 228 14.9 380 879 0.34 0.62SPRING CREEK CO 1 0.9 8.49E-04 228 14.9 468 1070 0.33 0.60EXCHAMSIKS RIVER CO 1 1.1 3.04E-04 228 14.9 1581 3760 0.38 0.68EXSTEW RIVER & SLOUGH CO 1 1.7 6.77E-04 228 14.9 960 2520 0.48 0.82GITNADOIX RIVER CO 1 1.1 8.41E-05 228 14.9 5593 13300 0.38 0.67KADEEN CREEK CO 1 0.8 7.87E-06 228 14.9 45607 103000 0.30 0.56KASIKS RIVER CO 1 1.1 1.57E-04 228 14.9 2927 6900 0.37 0.66ZYMAGOTITZ RIVER CO 1 1.2 6.46E-04 228 14.9 796 1930 0.40 0.71CLIFFORD CREEK CO 1 0.9 3.07E-04 228 14.9 1266 2890 0.32 0.59CLUB CREEK - LOWER CO 1 0.9 1.39E-04 228 14.9 2828 6470 0.32 0.59CULLON CREEK CO 1 1.1 1.37E-03 228 14.9 332 782 0.37 0.66IRONSIDE CREEK CO 1 0.8 4.49E-05 228 14.9 8189 18500 0.31 0.56KISPIOX RIVER CO 1 1.1 1.40E-04 228 14.9 3267 7690 0.37 0.66MURDER CREEK CO 1 1.0 1.24E-03 228 14.9 347 807 0.35 0.63NANGEESE RIVER CO 1 1.0 2.88E-04 228 14.9 1533 3590 0.36 0.64SKUNSNAT CREEK CO 1 0.9 4.79E-04 228 14.9 808 1850 0.32 0.59STEPHENS CREEK CO 1 0.9 1.88E-04 228 14.9 2063 4710 0.32 0.59BULKLEY RIVER - UPPER CO 1 0.9 1.16E-04 228 14.9 3486 8010 0.33 0.60KATHLYN CREEK CO 1 1.0 9.30E-04 228 14.9 472 1100 0.36 0.64MORICE RIVER CO 1 1.1 1.00E-04 228 14.9 4595 10800 0.37 0.66TOBOGGAN CREEK CO 1 1.4 5.58E-04 228 14.9 1017 2540 0.43 0.76KITWANGA RIVER CO 1 1.1 3.64E-04 228 14.9 1277 3020 0.37 0.67KLEANZA CREEK CO 1 0.8 1.93E-04 228 14.9 1925 4370 0.31 0.57ZYMOETZ RIVER - UPPER CO 1 1.2 4.22E-04 228 14.9 1155 2760 0.39 0.69ACTUAL BABINE FENCE COUNT CO 1 1.0 2.46E-05 228 14.9 17592 41000 0.35 0.64BABINE RIVER (SECTION 4) CO 1 1.2 2.36E-04 228 14.9 2114 5080 0.39 0.70FULTON RIVER CO 1 1.0 3.37E-04 228 14.9 1308 3060 0.36 0.64PINKUT CREEK CO 1 0.8 2.95E-04 228 14.9 1248 2830 0.31 0.57BABINE - UNACCOUNTED CO 1 1.9 3.05E-04 228 14.9 2292 6250 0.50 0.85213   Creeks/Lakes/Stocks Data Source Ricker a Ricker b Mean Run Timing (Julian Day)Run Timing Spread (Days)Smsy Seq Umsy UmaxDENISE CREEK CM 1 0.5 2.26E-03 225 12.6 108 232 0.22 0.41ECSTALL RIVER CM 1 1.6 1.15E-04 225 12.6 5477 14200 0.47 0.80JOHNSTON CREEK CM 1 0.6 1.00E-06 225 12.6 285383 626000 0.25 0.47KHYEX RIVER CM 1 2.5 7.91E-03 225 12.6 103 316 0.56 0.92SILVER CREEK CM 1 0.6 1.34E-03 225 12.6 206 449 0.24 0.45LAKELSE RIVER CM 1 1.9 2.27E-03 225 12.6 306 832 0.50 0.85DEEP CREEK CM 1 1.6 1.40E-02 225 12.6 43 111 0.46 0.79KITSUMKALUM RIVER - LOWER CM 1 1.0 5.49E-04 225 12.6 779 1810 0.35 0.63ANDESITE CREEK CM 1 3.3 1.00E-02 225 12.6 89 330 0.59 0.96DOG-TAG CREEK CM 1 1.1 9.57E-04 225 12.6 503 1200 0.38 0.68ERLANDSEN CREEK CM 1 1.2 1.14E-02 225 12.6 44 107 0.40 0.70EXCHAMSIKS RIVER CM 1 1.5 4.87E-03 225 12.6 121 305 0.44 0.77EXSTEW SLOUGH CM 1 1.1 3.78E-03 225 12.6 120 282 0.36 0.66GITNADOIX RIVER CM 1 0.7 1.16E-04 225 12.6 2758 6130 0.27 0.51KASIKS RIVER CM 1 3.4 9.56E-03 225 12.6 93 351 0.59 0.97SHAMES SLOUGH CM 1 1.6 9.70E-03 225 12.6 65 168 0.47 0.80SKEENA RIVER - WEST CM 1 0.9 9.51E-05 225 12.6 4169 9550 0.33 0.60ZYMAGOTITZ RIVER CM 1 1.5 6.52E-03 225 12.6 92 236 0.45 0.79DATE CREEK CM 1 0.7 6.63E-04 225 12.6 449 990 0.26 0.48KISPIOX RIVER CM 1 0.8 2.50E-04 225 12.6 1484 3370 0.31 0.57MCCULLY CREEK CM 1 1.6 1.84E-02 225 12.6 33 85 0.46 0.79FIDDLER CREEK CM 1 1.7 1.05E-02 225 12.6 63 165 0.48 0.82KITWANGA RIVER CM 1 1.2 9.60E-04 225 12.6 516 1240 0.39 0.70KLEANZA CREEK CM 1 0.9 6.42E-03 225 12.6 60 137 0.32 0.58ZYMOETZ RIVER - LOWER CM 1 0.9 6.58E-04 225 12.6 586 1340 0.32 0.59BABINE RIVER (SECTION 4) CM 1 0.8 2.98E-02 225 12.6 12 27 0.30 0.55Creeks/Lakes/Stocks Data Source Ricker a Ricker b Mean Run Timing (Julian Day)Run Timing Spread (Days)Smsy Seq Umsy UmaxEARLY RUN STLHEAD ST 1 1.0 6.19E-03 214 17 66 159 0.36 0.65LATE RUN STLHEAD ST 1 1.0 6.19E-03 225 18 93 220 0.36 0.65214  Appendix B  Preliminary sensitivity analysis of Linear Programming Method In order to demonstrate the possible impacts of several common types of errors on the results of the retrospective analysis, preliminary sensitivity analyses were conducted. This allows an exploration of some of the potential problems with implementing an optimized weekly Ut strategy.  Three different categories of error were applied to the retrospective analysis.   First, the impact of applying a fixed weekly harvest pattern Ut when the return timing is variable was evaluated by applying the median weekly harvest pattern generated by the retrospective analysis (i.e. the median of all optimized weekly Ut values from Figure 4.5) as a control rule in a new retrospective analysis.  The weekly harvest target chosen was applied regardless of actual return timing which varied considerably from year to year (Figure 4.3).  The harvests specified by the weekly Ut pattern were taken without error and, the new escapements, along with the recruitment deviates, were used to explore the cumulative effect of the change to a fixed weekly Ut harvest control rule on exploitation rates by species (Figure B.1).  Application of a fixed weekly Ut derived from the retrospective analysis leads to less variability in exploitation rate by stock but at a cost in lower than UMSY exploitation rate on sockeye and fewer sockeye per year caught than the optimized solution(Figure B.1c).  The difference in sockeye catch per year between the optimum and fixed weekly had a median (interquartile range) of -91,105 (-177,260 215  to -38,165) sockeye. Figure B.1.  Distribution of exploitation rates by stock for (a) optimized linear programing algorithm, and (b) application of fixed weekly Ut derived from retrospective analysis.  The red dots show UMAX and the green dots show UMSY for each stock.  The difference in total catch by species across all years of the retrospective analysis is shown in panel (c).   Second, the effect of errors in estimation of the Ricker parameters on the optimum linear solution was evaluated by varying the Umax and Umsy values used as optimization targets.  Umax and Umsy values are derived from the Ricker productivity parameter a (following the method of Hilborn 216  1985) as 𝑈𝑚𝑎𝑥 = (1 − 𝑒𝑎) and 𝑈𝑚𝑠𝑦 = (1 − 𝑒(−0.5∗𝑎+0.07∗𝑎2)).  Each simulated year was supplied with a different estimate of the Ricker productivity parameter drawn from a normal distribution with a mean of the estimated population Ricker a value and a CV of 0.1.  The true Ricker parameters (Table 6.1) are used to drive the inter-annual population trajectories, the linear optimization was applied as in the retrospective analysis, but the annual optimizations proceed using the incorrect targets and constraints.  The retrospective analysis was re-run 100 times using the incorrect targets and showed a pattern of misidentifying the optimum weekly pattern (Figure B.2) with a greatly reduced harvest on average in week 8, 9 and 10 leading to fewer salmon per year caught than the optimized solution.  The bulk of the difference was in sockeye catch per year between the optimum and the retrospective analysis with errors in the Ricker parameters.  The difference had a median (interquartile range) of -525,048 (-811,922 to -315,279) sockeye.217    Figure B.2.  Changes to the LP solution for weekly Ut due as a result of changing the constraints of linear programing optimization by assuming a 10% CV in Ricker a parameters (a), bars are the retrospective optimum Ut values derived with misidentified Ricker a parameters, the red dots optimum median weekly Ut values.  The stock specific changes in harvest as a result of the changes to optimum weekly Ut are presented in the second panel (b).  218   Third, the effect of implementation errors due to unpredictable changes in fishing effort and catchability were evaluated by applying the linear programing optimized target weekly harvest rates Ut with implementation error.  The harvests specified by the annual optimized Ut pattern were applied with a normally distributed error with a CV of 0.1 and, the new escapements, along with the recruitment deviates, were used to explore the cumulative effect of the change to harvest.  The retrospective analysis was re-run 100 times applying the implementation error demonstrating a great deal of variability in any particular year between the optimum and the achieved harvest (Figure B.3a) especially at higher expected catches.  The median impact by species was less than the other types of error (Figure B.3b).  The bulk of the difference was in sockeye catch per year between the optimum and the retrospective with implementation error.  The difference in sockeye catch a median (interquartile range) of – 61,969 (-305,280 to – 115,422) salmon.219     Figure B.3.  Effect of implementation errors on annual catches (all species) assuming a 10% implementation error when applying the optimum Ut targets (a).  The stock specific changes in harvest as a result of the error implementing the optimum weekly Ut are presented in the second panel (b) as number of salmon and in the third panel (c) as the % difference in catch. 220    The impacts of several common types of errors on the results of the retrospective analysis are directional, they result in less yield than the optimization performed without error.  The greatest impact on performance relative to optimum appears to be errors in estimation of the Ricker stock-recruitment parameters leading to optimizations seeking the wrong targets.   

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.24.1-0373473/manifest

Comment

Related Items