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Simulation models for estimating productivity and trade-offs in the data-limited fisheries of New South.. Forrest, Robyn Elizabeth 2008-12-31

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SIMULATION MODELS FOR ESTIMATING PRODUCTIVITY AND TRADE-OFFS IN THE DATA-LIMITED FISHERIES OF NEW SOUTH WALES, AUSTRALIA by ROBYN ELIZABETH FORREST B.A., Curtin University, 1988 B.Sc. (Hons 1, University Medal), University of Sydney, 2000  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Resource Management and Environmental Studies)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) December 2008 © Robyn Elizabeth Forrest, 2008  Abstract Recent shifts towards ecosystem based fisheries management (EBFM) around the world have necessitated consideration of effects of fishing on a larger range of species than previously. Nonselective multispecies fisheries are particularly problematic for EBFM, as they can contribute to erosion of ecosystem structure. The trade-off between catch of productive commercial species and abundance of low-productivity species is unavoidable in most multispecies fisheries. A first step in evaluation of this trade-off is estimation of productivity of different species but this is often hampered by poor data. This thesis develops techniques for estimating productivity for data-limited species and aims to help clarify EBFM policy objectives for the fisheries of New South Wales (NSW), Australia. It begins with development of an age-structured model parameterised in terms of optimal harvest rate, UMSY. UMSY is a measure of productivity, comparable among species and easily communicated to managers. It also represents a valid threshold for prevention of overfishing. The model is used to derive UMSY for 54 Atlantic fish stocks for which recruitment parameters had previously been estimated. In most cases, UMSY was strongly limited by the age at which fish were first caught. However, for some species, UMSY was more strongly constrained by life history attributes. The model was then applied to twelve species of Australian deepwater dogshark (Order Squaliformes), known to have been severely depleted by fishing. Results showed that the range of possible values of UMSY for these species is very low indeed. These findings enabled a preliminary stock assessment for three dogsharks (Centrophorus spp.) currently being considered for threatened species listing. Preliminary results suggest they have been overfished and that overfishing continues. Finally, an Ecopath with Ecosim ecosystem model, representing the 1976 NSW continental slope, is used to illustrate trade-offs in implementation of fishing policies under alternative policy objectives. Results are compared with those of a biogeochemical ecosystem model (Atlantis) of the same system, built by scientists from CSIRO. While there were large differences in model predictions for individual species, they gave similar results when ranking alternative fishing policies, suggesting that ecosystem models may be useful for exploring broad-scale strategic management options.  ii  Table of contents Abstract........................................................................................................................................................................ii Table of contents ........................................................................................................................................................iii List of tables................................................................................................................................................................vi List of figures............................................................................................................................................................viii Acknowledgements.....................................................................................................................................................xi Dedication .................................................................................................................................................................xiii Chapter 1. General introduction................................................................................................................................1 Context .....................................................................................................................................................................1 Background ..............................................................................................................................................................1 Fisheries off the coast of New South Wales...........................................................................................................16 Aims of the project .................................................................................................................................................20 Figures....................................................................................................................................................................23 Chapter 2. An age-structured model with leading management parameters, incorporating age-specific selectivity and maturity ............................................................................................................................................26 Introduction ............................................................................................................................................................26 Population model with MSY and UMSY as leading parameters ..............................................................................29 Equilibrium properties: relationships between life history, density dependence and UMSY....................................33 Bayesian estimation of MSY and UMSY..................................................................................................................34 Results ....................................................................................................................................................................36 Discussion ..............................................................................................................................................................37 Acknowledgements ................................................................................................................................................41 Tables .....................................................................................................................................................................42 Figures....................................................................................................................................................................43 Chapter 3. Extension of a meta-analysis of 54 fish stocks for evaluating effects of life history, selectivity and density dependence on optimal harvest rate UMSY .................................................................................................47 Introduction ............................................................................................................................................................47 Methods..................................................................................................................................................................50 Deriving UMSY for 54 Atlantic stocks .................................................................................................................50 Uncertainty in parameter values .......................................................................................................................53 Effect of selectivity on UMSY ...............................................................................................................................53 Results ....................................................................................................................................................................54 Derived estimates of UMSY..................................................................................................................................54 Relationship between density dependence, SPR0 and UMSY................................................................................55 Relative effects of selectivity ..............................................................................................................................57 Discussion ..............................................................................................................................................................60 Acknowledgements ................................................................................................................................................65 Tables .....................................................................................................................................................................67 Figures....................................................................................................................................................................73  iii  Chapter 4. Optimal harvest rate for long-lived, low-fecundity species: deepwater dogsharks of the continental slope of southeastern Australia ................................................................................................................................84 Introduction ............................................................................................................................................................84 Methods..................................................................................................................................................................87 Calculating the upper limit of UMSY ...................................................................................................................87 Systematic exploration of the effects of life history and selectivity parameters on UMSYLim ...............................90 Application to deepwater dogsharks..................................................................................................................90 Demographic analysis .......................................................................................................................................92 Results ....................................................................................................................................................................94 Systematic calculation of maximum possible UMSY ............................................................................................94 Dogshark results................................................................................................................................................95 Demographic analysis .......................................................................................................................................96 Discussion ..............................................................................................................................................................97 Acknowledgements ..............................................................................................................................................103 Tables ...................................................................................................................................................................104 Figures..................................................................................................................................................................109 Chapter 5. Preliminary reconstruction of catch and harvest rate history of an extremely data-poor genus of dogshark (Centrophorus) on the upper continental slope of New South Wales, Australia ...............................120 Introduction ..........................................................................................................................................................120 Methods................................................................................................................................................................123 Reconstruction of time series of catch and effort.............................................................................................123 Preliminary effort-driven model to estimate historical harvest rates ..............................................................129 Results ..................................................................................................................................................................134 Discussion ............................................................................................................................................................136 Acknowledgements ..............................................................................................................................................141 Tables ...................................................................................................................................................................142 Figures..................................................................................................................................................................153 Chapter 6. Evaluation of historical fisheries management options for New South Wales trawl fisheries: comparison of two ecosystem models ....................................................................................................................165 Introduction ..........................................................................................................................................................165 Methods................................................................................................................................................................172 Modelling frameworks .....................................................................................................................................172 Study area and period......................................................................................................................................173 The models.......................................................................................................................................................174 Optimal policy search......................................................................................................................................176 Comparison of Ecosim and Atlantis ................................................................................................................178 Results ..................................................................................................................................................................180 Optimal policy search......................................................................................................................................181 Comparison of individual groups ....................................................................................................................182 Performance of optimal policies......................................................................................................................184 Ranking of policies ..........................................................................................................................................186 Trade-offs ........................................................................................................................................................187 Discussion ............................................................................................................................................................188 Conclusions ..........................................................................................................................................................195 Acknowledgements ..............................................................................................................................................197 Tables ...................................................................................................................................................................198 Figures..................................................................................................................................................................210 Chapter 7. General discussion: towards ecosystem based fisheries management in New South Wales ..........225 Summary ..............................................................................................................................................................225 Further comments: progressing towards EBFM in NSW.....................................................................................231 References ................................................................................................................................................................237  iv  Appendix A to Chapter 2. Derivation of α from UMSY .........................................................................................273 Appendix B to Chapter 2. Growth, maturity and gear selectivity functions......................................................276 Appendix to Chapter 3. UMSY-CR curves for 54 Atlantic fish stocks..................................................................278 Appendix to Chapter 4. Distributions of input parameters in dogshark model ................................................288 Appendix 1. Ecopath with Ecosim model of the continental shelf and slope of New South Wales ..................294 Introduction ..........................................................................................................................................................294 Time series data and calibration ...........................................................................................................................314 Appendix 2. List of species and taxonomic groups in the marine ecosystem of NSW.......................................336 Co-authorship statement ........................................................................................................................................356  v  List of tables Table 2.1. Life-history and selectivity parameters used in the model. .......................................................................42 Table 3.2. Pearson’s correlation coefficient, r, for relationship between logged life history/selectivity parameters and mean UMSY ............................................................................................................................................................69 Table 3.3. Parameters used to make Figures 3.7 ........................................................................................................70 Table 3.4a. Mean values of UMSY obtained for the 54 stocks under a range of values of ah assuming Ricker recruitment. .................................................................................................................................................................71 Table 3.4b. Mean values of UMSY obtained for the 54 stocks under a range of values of ah assuming Beverton-Holt recruitment ..................................................................................................................................................................72 Table 4.1. Life history parameters that were systematically varied in the generic dogshark model. Every parametercombination was tested. ah = age at 50% first harvest; amax = maximum age; amat = age at 50% maturity; κ = von Bertalanffy growth rate; LS = litter size; L∞ = maximum length; a0 = theoretical age when fish has zero length; lwa and lwb = scalar and exponent of length-weight relationship; σs = standard deviation of logistic selectivity curve; σm = standard deviation of logistic maturity curve.........................................................................................................104 Table 4.3. Mean and modal values of 100 Monte Carlo estimates of UMSYLim for 12 species of dogshark (see Figure 4.3 for boxplots). .......................................................................................................................................................106 Table 4.4. Mean and modal values of 1000 Monte Carlo estimates of the intrinsic rate of growth r obtained using the demographic approach (see Figure 4.5 for density plots)....................................................................................107 Table 4.5. Correlation coefficients, slopes and intercepts of the relationship between the mean values of r (Table 4.4) and UMSYLim (Table 4.3) across all 12 species of dogshark, for the eight tested values of ah (age-at-50%-firstharvest). See Figure 4.6.............................................................................................................................................108 Table 5.1. Summary of locations and grounds surveyed during the upper slope trawls..........................................142 Table 5.2. Mean (and s.e.) catch rates (kg h-1) for Centrophorus spp. caught in tows on the upper slope between 300 and 525 m during the 1976-7 (n = 130 tows), 1979-81 (n = 150 tows) and 1996-7 (n = 81 tows) surveys by the FRV Kapala. ......................................................................................................................................................................143 Table 5.3. Number of vessels actively fishing on the continental slope of NSW; reported effort (hours) of vessels that caught dogsharks in depths 300-600 m; and effort predicted from the exponential relationship shown............144 Table 5.4. Nominal landings of undifferentiated Squalidae and undifferentiated Centrophorus in the State and Commonwealth catch databases................................................................................................................................145 Table 5.5. Centrophorus as proportion of undifferentiated Squalidae in landings in the NSW State and ISMP databases. ..................................................................................................................................................................146 Table 5.6. Proportions of the three species of Centrophorus in NSW represented as proportion of total Centrophorus catch from the ISMP observer database. ............................................................................................147 Table 5.7. Mean proportions of the three species of Centrophorus in NSW as proportions of total Centrophorus catch and total Squalidae catch from the Kapala database........................................................................................148 Table 5.8. Minimum and maximum estimates of carcass landings and whole weight catch of Centrophorus in NSW to be used for priors in stock assessment model........................................................................................................149 Table 5.9. Minimum and maximum estimates of annual catch (t) for the three species of Centrophorus in NSW, based on the mean observation in the 1996 Kapala surveys. ....................................................................................150 Table 5.10. Derivation of recruitment parameters for the age-structured model......................................................151 Table 5.11. (a) Mean estimates of B0 and qc for all values of ah for the minimum catch scenarios; and (b) for the maximum catch scenarios .........................................................................................................................................152 Table 6.1. Groups for model comparison. ................................................................................................................198 Table 6.1 cont...........................................................................................................................................................199 * Species under quota since 1992Table 6.2. Indices of relative abundance used to tune the models (only years between 1976 and 1996 were used). .........................................................................................................................199 Table 6.2. Indices of relative abundance used to tune the models (only years between 1976 and 1996 were used).200 Table 6.3. Objective function and resulting optimal trawling effort (relative to the 1976 trawling effort) found by Ecosim’s fisheries optimisation routine (see text). Results are the mean of five searches starting with random fishing efforts. .......................................................................................................................................................................201 Table 6.4a. List of biological indicators to measure performance of alternative policies in the models. Functional groups included in the calculation of each indicator are also shown (see Table 6.1 for description of functional groups). Indicators superscripted by P are primary indicators that directly address the policy objectives set out in Table 6.3....................................................................................................................................................................202  vi  Table 6.4b. List of fishery indicators to measure performance of alternative policies in the models. Functional groups included in the calculation of each indicator are also shown (see Table 6.1 for description of functional groups). Indicators superscripted by P are primary indicators that directly address the policy objectives set out in Table 6.3....................................................................................................................................................................203 Table A1.1. Functional groups of the Ecopath model. See Appendix 2 for more complete lists of representative species / taxonomic groups. ......................................................................................................................................326 Table A1.2. Diet matrix used in the model. Based on SPCC (1981); Bulman et al. (2001; 2006); Kailola et al. (1993) and other sources referred to in the text.........................................................................................................328 Table A1.3. Parameters of the model after balancing. Parameters shown in bold were estimated by Ecopath........332  vii  List of figures Figure 1.1. Equilibrium (a) yield and (b) biomass for five hypothetical species in a multispecies fishery, where the x-axis represents long-term fixed harvest rate and the y-axis represents relative equilibrium yield or biomass that would be obtained after long-term harvesting at the fixed harvest rate. On each graph, the solid line represents the least productive species and broken lines from left to right represent progressively more productive species...........23 Figure 1.2. Stock recruitment relationship for a hypothetical fish population. ..........................................................24 Figure 1.3. Map of the study area. Depth contours are measured in fathoms (1 fathom = 1.83 metres). Note that most fishing occurs in waters shallower than 1000 metres (Larcombe et al. 2001). Source: Jim Craig (NSW DPI). 25 Figure 2.1. Effect of different parameters on the relationship between leading productivity parameter UMSY and the derived compensation ratio, CR for a hypothetical species.........................................................................................43 Figure 2.2. (a) Catch (thousands of tons) and (b) CPUE (tons per standardised trawler hour) for Namibian hake, used to fit the models. .................................................................................................................................................44 Figure 2.3. Density plots showing relative posterior probability density distributions ..............................................45 Figure 2.4. Trace plots of iterations vs sampled values for each estimated parameter indicating convergence of the estimates......................................................................................................................................................................46 Figure 3.1. Relationship between UMSY and CR for a hypothetical stock, with dashed lines showing a unique pair of UMSY and CR values. ...................................................................................................................................................73 Figure 3.2. Mean (+ s.e.) estimates of UMSY for the 54 stocks of Goodwin et al. (2006) under Ricker (grey bars) and Beverton-Holt (black bars) assumptions about the stock-recruitment relationship. UMSY values are the means of 100 Monte Carlo runs (see text). See Table 3.1 for description of stocks..........................................................................74 Figure 3.3. Relationships between CR and UMSY under (a) Ricker and (b) Beverton-Holt recruitment. See text for correlation coefficients. Note logarithmic scale and differences in scale of y-axis.....................................................76 Figure 3.4. Correlations between log life history parameters and UMSY for the Ricker model. Graphs show (a) M, (b) amat, (c) κ, (d) W∞, (e) amax and (f) SPR0. Correlation coefficients are given in Table 3.2. Note logarithmic scale. .....................................................................................................................................................................................77 Figure 3.5. Correlations between log life history parameters and UMSY for the Beverton Holt model. Graphs show (a) M, (b) amat, (c) κ, (d) W∞, (e) amax and (f) SPR0 for the Beverton-Holt model. Correlation coefficients are given in Table 3.2. Note logarithmic scale................................................................................................................................78 Figure 3.6. Correlations between (a) SPR0 estimated by Goodwin et al. (2006) and SPR0 obtained in the present study; and (b) lnSPR0 (present study) and lnCR published by Goodwin et al. (2006)................................................79 Figure 3.7. Relationship of SPR0 to (a) W∞; (b) κ ; (c) amat; and (d) M, for a hypothetical fish stock........................80 Figure 3.8. Relationship between UMSY and CR for five hypothetical stocks with SPR0 = 9.....................................81 Figure 3.9. Predicted UMSY for four example stocks over a range of ages at first harvest under Ricker (left panel) and Beverton-Holt (right panel) assumptions for the stock-recruitment relationship. ................................................82 Figure 3.10. Predicted UMSY-CR curves for the four example stocks in Figure 9, over a range of ages at first harvest under Ricker (left panel) and Beverton-Holt (right panel) assumptions for the stock-recruitment relationship. Published estimates of CR for each stock (Goodwin et al. 2006) are shown as horizontal dotted lines. ....................83 Figure 4.1. Relationship between UMSY and α and under Beverton-Holt recruitment for a hypothetical species. The asymptotic upper limit of UMSY is represented as a dashed vertical line (see text). The shaded area represents undefined hypotheses for UMSY that give α < 0 (see text). ........................................................................................109 Figure 4.2. Contour plots showing maximum possible UMSY (i.e., UMSYLim) over a range of tested values of ah and κ. Left to right shows the effect of increasing litter size, LS, on UMSYLim. Top to bottom shows effect of increasing amat. ...................................................................................................................................................................................110 Figure 4.3. Box and whisker plots showing median (black bar), interquartile range (box) and 1.5IQR (whiskers) of estimated UMSYLim from 100 Monte Carlo simulations for 12 species of Australian dogshark over a range of age-at50%-first-harvest, ah (continued overleaf). ...............................................................................................................112 Figure 4.4. Relative densities of maximum possible compensation ratio CR (right) for 12 species of dogshark implied by the unfished juvenile survival rate (left); see text and Figure 1.2. Density plots show results from 100 Monte Carlo simulations. ..........................................................................................................................................114 Figure 4.5. Estimates of r (i.e., UMax) obtained from the demographic method (results of 1000 Monte Carlo simulations)...............................................................................................................................................................117 Figure 4.6. Relationship between the mean values of r (Table 4.4) and UMSYLim (Table 4.3) across all 12 species of dogshark, for four of the eight tested values of ah (age-at-50%-first-harvest). See Table 4.5 for correlation coefficients, and values of slopes and intercepts.......................................................................................................119  viii  Figure 5.1. (a) Relationship between number of vessels actively fishing on the continental slope (300-600 m) and nominal effort (hours) for boats reporting dogshark landings for the years 1986-2005; and (b) estimated (1968-1985) and nominal (1986-2005) effort (hours) for boats catching dogsharks on the continental slope. .............................153 Figure 5.2. Reported landings (t) of dogsharks in (a) the NSW State database (excluding landings known to have been reported in the SETF); (b) the SETF Annual database for years after dogshark catches were disaggregated; and (c) the SETF Slope database for years after dogshark catches were disaggregated. The latter is shown to illustrate the rise in landings of Centroscymnus and Deania spp.on the continental slope after 2002, although these data were not used in the present analysis. ......................................................................................................................................154 Figure 5.3. Reported landings of all dogsharks combined in the NSW State and SETF databases..........................155 Figure 5.4. (a) Proportions of the four reporting categories of dogsharks (as proportion of total dogshark landings) in the NSW State fisheries (excluding the ‘Other’ category); and (b) dogshark proportions in the NSW State database’s “Other” fishery (i.e., SETF) for the years data are available. ..................................................................156 Figure 5.5. Mean (+ s.e.) reported proportions of Centrophorus spp. across years (1993-2003) in the ISMP observer database, expressed as proportion of whole (i.e., discarded + retained) Centrophorus catch (see Table 4 for annual proportions)...............................................................................................................................................................157 Figure 5.6. Proportion of Squalids that were discarded as proportion of (a) retained catch and (b) total catch, as reported by ISMP observers. Only Centrophorus spp. and two other significant slope species are shown. Note that discarding of deeper water species (Dalatias licha and Etmopterus spp.) was also significant................................158 Figure 5.7. Fits to survey index for the three best-fitting values of ah (see text). Top: All Centrophorus; Bottom: C. harrissoni. Dark lines show fits using minimum catch scenarios, lighter lines show fits using maximum catch scenarios....................................................................................................................................................................159 Figure 5.8. Fits to estimated catch for the three best-fitting values of ah (see text). Top: All Centrophorus; Bottom: C. harrissoni. Dark lines show fits using minimum catch scenarios (open circles), lighter lines show fits using maximum catch scenarios (solid circles)...................................................................................................................160 Figure 5.9. Estimated historical catches for the three best-fitting values of ah. Top: All Centrophorus; Bottom: C. harrissoni. Dark lines show fits using minimum catch scenarios, lighter lines show fits using maximum catch scenarios....................................................................................................................................................................161 Figure 5.10. Estimated historical harvest rate for the three best-fitting values of ah. Top: All Centrophorus; Bottom: C. harrissoni. Dark lines show fits using minimum catch scenarios, lighter lines show fits using maximum catch scenarios....................................................................................................................................................................162 Figure 5.11. Sensitivity of estimated historical Ct and Ut to value of κ (top) and amat (bottom) for ah = 5 for C. harrissoni. Simulations were done using the minimum catch scenario. ...................................................................163 Figure 5.12. Sensitivity of estimated historical Ut to value of CR for ah = 5 with (a) amat = 15; (b) amat = 20; and (c) amat = 30 (see text for meaning of Max and Min CR) for C. harrissoni. Simulations were done using the minimum catch scenario. ...........................................................................................................................................................164 Figure 6.1. Map of the study area showing compartments used in the Atlantis model. ..........................................210 Figure 6.2a. Relative biomasses predicted by Ecosim (solid line) and Atlantis (dashed line) for 16 species, with the models driven with historical catches or fishing mortality (see text). .......................................................................211 Figure 6.2b. Relative biomasses of shark groups predicted by Ecosim (solid line), with the model driven by estimated historical catch rates (Chapter 5, see Appendix 1), compared with relative catch rates (solid circles) observed in the surveys (Graham et al. 2001)...........................................................................................................212 Figure 6.3. Ecosim predicted biomass (t.km-2) under the eight optimal fishing policies for five coarse functional groups. Omn = omnivorous, pisc = piscivorous........................................................................................................213 Figure 6.4. Relative (to 1976) biomasses of groups, as predicted by Atlantis (grey bars) and Ecosim (white bars), for which qualitative agreement was good under some or all policies (see Table 6.5). ............................................214 Figure 6.5. Relative (to 1976) biomasses of groups, as predicted by Atlantis (grey bars) and Ecosim (white bars), for which qualitative agreement was very poor (see Table 6.5)................................................................................215 Figure 6.6. Relative (to 1976) biomasses of groups, as predicted by Atlantis (grey bars) and Ecosim (white bars), which were insensitive to changes in fishing effort and for which qualitative agreement was poor (see Table 6.5 and text). ..........................................................................................................................................................................216 Figure 6.7. Relative (to 1976) biomasses of groups, as predicted by Atlantis (grey bars) and Ecosim (white bars), which were insensitive to changes in fishing effort and for which qualitative agreement was poor (see Table 6.5 and text). ..........................................................................................................................................................................217 Figure 6.8. Predicted catch of key species under five of the eight policies. Policies Aii, Aiii and D are omitted for clarity (results for Policy D were very similar to policy B; results for policies Aii and Aiii were intermediate between results of Ai and Aiv). Note, policy E refers to the Status quo policy. .......................................................218  ix  Figure 6.9. Indicators based on biomass of key groups of species (see text and Table 6.4a) , as predicted by Atlantis (grey bars) and Ecosim (white bars). Values represent 1996 value of each indicator, relative to its 1976 value......219 Figure 6.9 continued. Indicators based on biomass of key groups of species (see text and Table 6.4a) , as predicted by Atlantis (grey bars) and Ecosim (white bars). Values represent 1996 value of each indicator, relative to its 1976 value..........................................................................................................................................................................220 Figure 6.10. Indicators measuring biodiversity (Kempton’s index; Kempton and Taylor 1976); and the ratios of pelagic to demersal teleosts and piscivorous to planktivorous teleosts, as predicted by Atlantis (grey bars) and Ecosim (white bars)...................................................................................................................................................221 Figure 6.11. Indicators based on total catch and value and catch and value of quota species, as predicted by Atlantis (grey bars) and Ecosim (white bars). Absolute predicted 1996 values are shown (see text and Table 6.4b)............222 Figure 6.12. Performance of the eight different policies (see text and Table 6.3) in terms of eleven of the indicators shown in Table 6.4. All indicators are shown as predicted 1996 value relative to 1976 value. ................................223 Figure 3A.1. UMSY-CR curves for stocks for which recruitment compensation was the most limiting factor determining UMSY, assuming Ricker recruitment. Curves are shown for seven values of age at recruitment to the fishery, 0-6. ...............................................................................................................................................................278 Figure 3A.2. UMSY-CR curves for stocks for which recruitment compensation was the most limiting factor determining UMSY, assuming Beverton-Holt recruitment. Curves are shown for seven values of age at recruitment to the fishery, 0-6. .........................................................................................................................................................279 Figure 3A.3. UMSY-CR curves for stocks for which life history parameters were the most limiting factor determining UMSY, assuming Beverton-Holt recruitment. Curves are shown for seven values of age at recruitment to the fishery, 0-6. ............................................................................................................................................................................280 Figure 3A.4. UMSY-CR curves for stocks for which selectivity was the most limiting factor determining UMSY, assuming Ricker recruitment. Curves are shown for seven values of age at recruitment to the fishery, 0-6. ...........281 Figure 3A.5. UMSY-CR curves for stocks for which selectivity was the most limiting factor determining UMSY, assuming Beverton Holt recruitment. Curves are shown for seven values of age at recruitment to the fishery, 0-6.285 Figure 4A.1. Probability distributions of the four parameters (κ, LS, amat and amax) treated as uncertain in the analysis for 12 species of Australian dogshark. ........................................................................................................288 Figure A1.1a. Trophic level of the model’s 56 living functional groups. See Table A1.1 for description of groups and A1.2 for diet composition. Size of the circle indicates relative biomass. ...........................................................334 Figure A1.2. Comparison of total catch (thousands of tonnes) reported from estuarine and ocean fisheries in the NSW historical catch database (Pease and Grinberg 1995) and the current NSW State catch database...................335  x  Acknowledgements This thesis would not have been completed without the generous assistance of many people, to whom I am indebted. My supervisor, Tony Pitcher provided me with this opportunity and has been an insightful and patient advisor. I thank him for his ideas and wisdom, and the generous hospitality he and Val have given over the years. James Scandol always gave pragmatic, intelligent advice, and has been a valued friend throughout. Steve Martell taught me most of what I know about programming and modelling and is thanked for always having an open office door when I needed an answer to yet another question. My other supervisory committee members, Les Lavkulich and Jackie Alder, are also thanked for all their help. Special thanks must go to Carl Walters, who gave me so much advice, encouraged me to publish the UMSY paper, and inspired many of the ideas that have formed the basis of this thesis. It has been a priviledge and I am richer for having had the opportunity to work with him. From CSIRO, Beth Fulton, Marie Savina, Catherine Bulman and Ross Daley were superb colleagues and I am fortunate to have worked with them. Neil Klaer, Peter Cui, Scott Condie, Fred Pribac, Sally Wayte, Alistair Hobday, Jock Young, Jeffery Dambacher and Geoff Tuck also generously gave advice and data. The scientists of NSW Department of Primary Industries were incredibly generous with their time, ideas, data and insights into the fisheries and ecosystem of NSW. Special thanks go to Steve Kennelly, Ken Graham, Kevin Rowling, Charlie Gray, Bruce Pease, John Stewart, Dennis Reid, David Pollard, Phil Gibbs, Carla Ganassin, Geoff Liggins, Doug Ferrell, Jim Craig, Jeff Murphy, Rob Williams, Steve Montgomery, Aldo Steffe, Tracey McVea and Karen Astles, with sincere apologies to anyone I have forgotten.  xi  Thanks also to the Australian scientists who generously provided data, manuscripts and information that were essential to the project. They are Sonia Talman, Matias Braccini, Charlie Huveneers, Rob Harcourt, Kylie Pitt, Gretta Pecl, David Rissik, Ian Tower, John Garvey, Neil Gribble, Keith Martin-Smith and Bronwyn Gillanders, again with apologies to anyone unmentioned. Funding for this project was provided by the NSW Department of Primary Industries. I was also the recipient of Charles Gilbert Heydon Travelling Fellowship in Biological Sciences, awarded by the University of Sydney. The Cecil and Kathleen Morrow Scholarship, awarded by the UBC Fisheries Centre, funded my travel to Hobart. In addition, Daniel Pauly, Villy Christensen, Amanda Vincent, Murdoch McAllister and Rick Stanley provided contract work when I needed it and I am grateful to them for this. Robert Ahrens gave his time, talked through ideas, gave essential advice, answered endless questions and shared my love of classical music. Much of the work in this thesis would have been impossible without him. Mention must also go to Bob Lessard, who took me under his wing when I arrived, helped me build my first model and, in many ways, provided the network I needed to do this project and enjoy life in British Columbia. As well as friendship, fellow students Nathan Taylor, Mike Melnychuk, Cameron Ainsworth, William Cheung, Kristin Kaschner and Vasiliki Karpouzi provided material help with this work. My Vancouver friends have been integral to my life within and beyond this project. In particular, Adie Deeks, Deng Palomares, Bob Hunt, Sheila Heymans, Erin Rechisky, Meaghan Darcy, Yajie Liu, Charlie Wilson, Hilary Lindh, Jodie McCutcheon, Brad Fedy, Ian McCulloch, David Bryan and Valeria Vergara have explored the Pacific northwest with me and helped make it my home. Thanks also to all my other friends in the Fisheries Centre who have made my time here so special. Special thanks too to Cherie Hart, who has been a supportive and loyal friend since the beginning of my scientific journey. Finally, I thank my partner, Chris O’Grady for everything. I would not have made it without his unfailing love and support.  xii  Dedication  For my mother Gillian Forrest and my grandmother Daisy Forrest  xiii  Chapter 1. General introduction Context The government of the State of New South Wales (NSW), Australia, has undertaken to increase its investment in simulation modelling to aid in development of sustainable fishing strategies. One aspect of this aim is to develop models to aid understanding of “ecosystem-based fisheries management” (EBFM) and its meaning to the State’s fisheries. To this end, in 2002 the NSW Department of Primary Industries (NSW DPI, formerly NSW Fisheries) engaged in a Memorandum of Understanding with the University of British Columbia Fisheries Centre to address this need. Results of this collaboration are presented in this thesis. This introductory chapter provides a background to the study. It begins with a discussion of sustainability, as it is currently applied to natural resource management in Australia and throughout the world, before reviewing issues important for ecosystem-based management of fisheries. Fisheries operating off the coast of NSW are briefly discussed and, finally, the aims and outline of the thesis are provided.  Background Australia ratified the Third United Nations Convention on the Law of the Sea (UNCLOS; United Nations 1983) in 1994. In doing so it gained international recognition of its right to custodianship of one of the largest marine areas in the world, covering an estimated 16 million square kilometres (Commonwealth of Australia 1998). This has conferred upon Australia not only rights to the wealth contained within its seas, but also the responsibility to manage its marine environment and living resources in a sustainable manner. A consequence has been the development of Australia’s Oceans Policy, which was established as an “integrated and comprehensive” approach to address Australia’s management and conservation obligations under UNCLOS (Commonwealth of Australia 1998; Wescott 2000; Alder and Ward 2001). These developments followed previous Australian initiatives for sustainable development, the most significant of which was introduction of the Australian National Strategy for Ecologically Sustainable Development (ESD) (Council of Australian Governments 1992; Fletcher et al. 1  2002). ESD has now been accepted as the basis of management of natural resources, including fisheries, throughout Australia and is a management objective of all State and Commonwealth (i.e., Federal1) natural resource agencies (Scandol et al. 2005). The principles of ESD are codified in the Commonwealth Environment Protection and Biodiversity Conservation Act 1999 (EPBC Act), which includes provisions that have consequences for all Commonwealth fisheries and for State fisheries that export their product (Fletcher 2003; Scandol et al. 2005; Gibbs 2008). Definitions of sustainability Sustainability is one of the most commonly-stated goals of fisheries management. Early definitions of sustainability in fisheries were concerned with single species and were principally aimed at maximising economic returns. The concept of maximum sustainable yield (MSY), which aims to identify the most efficient exploitation rate for maximising long-term yield (Schaefer 1954; Clark 1976; reviewed by Ludwig 2001), was developed in the context of a utilitarian worldview, where natural resources were viewed mainly as commodities (Holling et al. 1998). Recognition of limitations of this approach, in a world with increasing environmental problems and a growing human population, led to an internationally-recognised range of definitions of sustainability that extended beyond the view of ecosystems simply for their consumptive value (IUCN/UNEP/WWF 1980; WCED 1987). Sustainable use of natural resources is now commonly understood to include maintenance of biodiversity and functioning ecosystems, accounting for the interconnectedness of human and ecological systems; and consideration of the needs of future generations, as well as meeting current resource needs (WCED 1987). As definitions of sustainability expand to include more human and ecological dimensions, however, there is a danger of them becoming too imprecise to be of management use or too open to interpretation (Suter 1993; Mace 2001). It has also been argued that sustainability of present conditions is an inappropriate goal for fisheries management, where many ecosystems have been significantly altered by fishing (Pitcher and Pauly 1998). These authors propose that restoration of ecosystems is a more appropriate management goal that would result in significant gains, both in existence and consumptive terms (see also Pitcher 2001; 2005; Pitcher and Ainsworth 2008). Broadly-stated sustainable management initiatives 1  Australia became a federated country in 1901 when the British colonies of New South Wales, Victoria, Queensland, South Australia, Tasmania and Western Australia joined to become the States of the Commonwealth of Australia. The Australian Capital Territory and Northern Territory and seven offshore territories are also administered by the Commonwealth Government.  2  have also been criticised for failure to adequately acknowledge the role of uncertainty in preventing scientific consensus and for being vague in identifying links between scientific understanding and achieving sustainability (Ludwig et al. 1993). There is now recognition that indicators of sustainable management need to be precisely defined in terms of different sustainability objectives and linked to specific management approaches (Lackey 1998; Robinson 2001). This implies a need to recognise that different sustainability objectives may be in conflict and may vary widely among stakeholders (Suter 1993; Lackey 2001; Mace and Reynolds 2001). For example, maintaining large biomasses of some species may be incompatible with maintenance of economically viable fisheries on other species. Successful management of fisheries will therefore include explicit identification of trade-offs, and incorporate approaches for deciding where to operate along trade-offs, while recognising that different stakeholders have a diverse set of values and objectives (Lackey 2001; Walters and Martell 2004). This will also involve setting qualitative and quantitative measures of the expected benefits, costs, and risks associated with alternative management actions (Murawski 2000; Hall and Mainprize 2004). Ecosystem-based fisheries management Following global trends over the past decade, the concept of ecosystem based fisheries management (EBFM) has been introduced into the Australian policy arena at both State and Commonwealth levels (Fletcher 2003; Scandol et al. 2005). EBFM is defined as a set of concepts or principles that encapsulate ideas for managing fisheries in ways that recognise their potential to alter whole ecological and human systems (Larkin 1996; Pitcher 2000; FAO 2003; Ward et al. 2003; Pikitch et al. 2004). For example, one of the stated aims of EBFM in Australia’s Oceans Policy is to: “Maintain ecological processes in all ocean areas, including water and nutrient flows, community structures and food webs, and ecosystem links … [and] … Maintain marine biological diversity, including the capacity for evolutionary change and viable populations of all native marine species in functioning biological communities” (Commonwealth of Australia 1998). The FAO’s Technical Guidelines for Responsible Fisheries (FAO 2003) state that under an ecosystem approach to fisheries, fisheries management should respect the following principles: fisheries should be managed to limit their impact on the ecosystem to the extent possible; ecological relationships between harvested, dependent and associated species should be maintained; the precautionary approach should be applied because the knowledge on ecosystems is incomplete; and governance should ensure both human and ecosystem well-being 3  and equity. The last point is sometimes expanded to more explicitly describe human considerations. For example, the Worldwide Fund for Nature’s EBFM policy document states as one of its principles that “A successful ecosystem-based management system will recognise economic, social and cultural interests as factors that may affect resource management” (Ward et al. 2002). A recent evaluation of the performance of 33 countries in meeting the EBFM criteria outlined in Ward et al. (2002), found that most countries underperformed in terms of both development of policy and implementation of EBFM (Pitcher et al. in press). This reflects the political and institutional challenges associated with adoption of principles of EBFM and the gradual pace of reform at these levels. Fisheries managers throughout Australia are now faced with the difficult question of what they must do differently to meet the requirements of EBFM. At a recent meeting of the Australian Society for Fish Biology, Fletcher (2003) concluded that existing principles of ESD, for which legislation is already in place, were consistent with principles of ecosystem management. Scandol et al. (2005) made a similar finding. However, while guidelines and principles for implementing ESD have components relevant to EBFM, which include attention to impacts on the biological community, water quality and habitat quality (Fletcher et al. 2002), they presently lack detail on appropriate ways to measure these components or assess their performance (Scandol et al. 2005). Identification of appropriate management strategies for EBFM and ESD in Australia will involve articulation of what is meant by sustainability; identification of species impacted by fisheries; development of some understanding of the nature of interactions between marine organisms and fisheries in marine ecosystems; and evaluation of the contributions of marine ecosystems to society. Many of these needs are beyond the current level of management experience, and there are large data-gaps in most of these areas. At the Commonwealth level, there have been a number of initiatives to improve information for EBFM (e.g., Fulton et al. 2005a,b; 2007; Smith et al. 2007). Substantial funding has been provided to survey and map Commonwealth fishing grounds and to conduct research into fields such as trophic ecology, habitat-use and productivity – particularly off the southeast coast (e.g., Bax and Williams 2000). Considerable resources have also been allocated for development of comprehensive management frameworks (Hobday et al. 2006; Smith et al. 2007) and the modelling tools needed to support EBFM (e.g., Fulton et al. 2005a,b; 2007a). At the State level, 4  fisheries tend to be smaller, lower in value and managed with policies based on cost-recovery (e.g., McColl and Stephens 1997; NSW Fisheries 2001). Because of this, fisheries management agencies have not invested heavily in assessment of commercial fish stocks and the status of the majority of commercial species in Australia is unknown or is unpublished (Phillips et al. 2001). Formal stock assessment tends to be the exception rather than the rule, generally being applied only to the most valuable species (such as abalone and rock lobster). As a result, there is currently little ecological information with which to frame EBFM strategies (Hall 2003; Gibbs 2008; Gray 2008). Research into marine ecosystem processes for management of Australia’s smaller fisheries is not likely to receive priority in the near future, and this type of information would not be easily integrated into existing management frameworks (Scandol et al. 2005). Adoption of EBFM at this level may therefore be a gradual process, initially requiring development of simple assessment tools, based on routinely-collected data, and identification of robust measures for tracking progress. Setting of qualitative and quantitative measures of the expected benefits, costs, and risks associated with alternative management actions needs to be part of the process of implementing EBFM (Murawski 2000; Hall and Mainprize 2004; Pikitch et al. 2004). Recently, a set of international guidelines has been developed by the FAO to support translation of high-level EBFM policy goals to an operational level (FAO 2003). Steps to implementation of operational EBFM listed in the guidelines include: 1) identification of operational objectives; 2) development of indicators of system-state and setting of corresponding reference points (as targets or limits); 3) use of indicators and reference points as management performance measures (i.e. the difference between the value of an indicator and its target or limit reference point); 4) application of decision rules based on management performance measures; and 5) monitoring and evaluation of management performance. In this framework, indicators are ecosystem properties that are thought to be modified by the fishery. They should reflect parameters that can be measured or estimated with a degree of certainty and, when compared with agreed target and limit reference points, provide a measure of management performance (FAO 2003). There is now a very large body of literature (e.g., review 5  by Fulton et al. 2005a; Hall and Mainprize 2004; papers in Cury and Christensen 2005) on possible metrics that could be used as indicators of fisheries-induced changes on ecosystems. While indicators and reference points for management of single species have been used in the above framework for some time (Caddy and Mahon 1995; Caddy and McGarvey 1996; Caddy 1999), their adaptation to an ecosystem context is still relatively new. Fisheries in marine ecosystems The term ecosystem was first suggested by Tansley (1935) and the concept was later expanded to include feedback loops that could lead to equilibrium, using theory from systems analysis. Odum (1953) defined an ecosystem as a “… natural unit that includes living and non-living parts interacting to produce a stable system in which the exchange of materials between the living and nonliving parts follows circular paths …”. Concepts of equilibrium, resilience and stability were developed in the 1970s (Holling 1973; May 1973), where predator-prey cycles, competitive interactions and complexity of the system were discussed in terms of the stability they conferred on the system. While the ecosystem concept is probably the most useful framework for discussing the broadscale impacts of human activity on the natural environment, there is debate over whether ecosystems are observable natural entities or whether the ecosystem is a human construct (O’Neill 2001). One of the main arguments against ecosystems being observable natural entities is the issue of boundaries and closure. Suter (1993) suggested that ecosystems do not exist until a policy or problem is specified, at which point ecological boundaries intuitively follow, i.e., if one considers all the processes directly or indirectly acting on organisms, including local and global processes, the boundaries of any ecosystem logically extend to include the whole biosphere. This implies that ecosystems cannot be delimited without a scientific or policy concern (Lackey 1998; 2001). In the context of marine fisheries, ecosystems are usually thought of conveniently as regions of management jurisdiction, which may have natural geographical or oceanographic boundaries and contain all or most of the life-history phases of managed populations. Often, ecosystems are defined by type of habitat with distinctive compositions of species and physical characteristics, e.g., estuarine, arctic or pelagic ecosystems. Questions about the impacts of fisheries on marine ecosystems usually focus on the ability of fisheries to alter the relative abundances of harvested and non-harvested species and possibly directly or indirectly alter ecological processes such as 6  competition and predation. Pitcher (2001) identified five major mechanisms by which fisheries alter the structure of marine ecosystems: 1) selective removal of large, long-lived species with low rates of natural mortality; 2) alteration of habitats by trawl gear; 3) reduction of predation by benthic fish leading to an increased biomass of forage species (“fishing down marine foodwebs”; Pauly et al. 1998); 4) trophic cascades (reviewed by Pinnegar et al. 2000); and 5) increasing instability and unpredictability in the system. Establishing clear explanatory patterns in the relative abundances of interacting species in marine ecosystems is difficult, however, because of: (i) the highly stochastic nature of the natural environment; and (ii) the complexity of interactions among biotic and abiotic processes in marine ecosystems. Trophic interactions Link (2002a) presented an extremely complex marine food web, representing the Northeast US Shelf, which had 80 functional groups each having an estimated average of 19 trophic interactions with other groups. Large numbers of trophic interactions such as this lead to highly connected systems in which the effects of fisheries cannot be easily predicted. Even in systems with relatively few species, complex indirect trophic pathways may lead to unexpected effects of fisheries and other human actions (May et al. 1979; Yodzis 1994; 2000; 2001). For example, there are often proposals to cull top predators (e.g., seals) in order to increase production of their commercially-fished prey (Yodzis 2001; Lessard et al. 2005). However, the presence of intermediary or competing predators that may also benefit from the cull may result in further reductions of the species the cull was intended to benefit (Punt and Butterworth 1995; Yodzis 2000; 2001). Other types of indirect effect occur when trophically-connected species feed on each other at different stages of their life-history, leading to ‘cultivation-depensation’ effects, which occur when juveniles of a predator are eaten by the adults of one of its prey species (Rudstam et al. 1994; Walters and Kitchell 2001). Further examples of complex interactions among fisheries and marine ecosystems can be found in May et al. (1979; krill and marine mammals); Sainsbury (1991) and Sainsbury et al. (1997; alteration of fish habitat); Livingston and Tjelmeland (2000; boreal systems); and Bogstad and Mehl (1997; Barents Sea). Technological interactions Technological interactions occur when multiple species are caught in the same fishing gear. Most fisheries are non-selective to some degree and catch a range of species, including those that 7  are targeted as well as some that are not. In some fisheries (e.g., shrimp trawls), the non-target component of the catch (bycatch) may exceed the targeted component by a large percentage (Alverson et al. 1994). The unwanted portion of the catch is frequently discarded. The issue of bycatch has received much attention in recent years because of its wastefulness (Alverson et al. 1994) and because of impacts on charismatic species such as birds, marine mammals, turtles or pelagic sharks (Tasker et al. 2000; Bache 2003; Cox et al. 2007; Gilman et al. 2008). While there has been a lot of progress in development of technological methods to avoid bycatch, these mainly involve exclusion of large animals from trawl nets, exclusion of fish from shrimp nets or devices that deter birds from longlines (e.g., Kennelly and Broadhurst 2002; Cox et al. 2007). In many cases, when non-target species are of similar morphology and occupy the same habitat as target species, selectivity cannot be adjusted to exclude all unwanted species. Besides this, many fisheries intentionally target multiple species simultaneously or multiple stocks of the same species. The complexity of interactions in marine ecosystems can obscure the identification of appropriate policy objectives. Ecosystem-oriented objectives in fisheries management are usually stated in high-level policies. Consequently, they are often broadly defined and difficult to incorporate directly into management plans where consequences of prospective management actions must be related to management objectives (Sainsbury et al. 2000). Skeptics of operational ecosystem based management point out that concepts such as ‘ecosystem health’ and function are vaguely defined and mask real issues, such as difficult trade-offs associated with managing human activities in ecosystems (Lackey 1998; 2001). Some authors have cautioned that management will fail if management strategies are forced upon fishers without adequate incentives (Hilborn 2004; 2007c; Grafton et al. 2006); or that factors such as inter-agency conflicts, incompatible databases, a lack of research on ecosystem functioning, inconsistent planning cycles and differing agency organizational structures will impair development of a coordinated approach to actively implement EBFM (Szaro et al. 1998). To overcome some of these problems, methods of implementing EBFM are currently being widely discussed in the fisheries science and policy arenas (Murawski 2000; FAO 2003; Fletcher 2003; Hall and Mainprize 2004; papers in Browman et al. 2004).  8  Trade-offs in fisheries Active consideration of trade-offs will be one of the most important components of EBFM (Pitcher and Cochrane 2002; Christensen and Walters 2004a; Hilborn et al. 2004; Walters and Martell 2004; papers in Mote Symposium 2004). Walters and Martell (2004) list the main tradeoffs affecting fisheries management decisions, which include abundance of fish vs fishing effort; profit vs employment; present vs future harvest; and public expenditure on fisheries vs expenditure on other public services. Two trade-offs specific to EBFM are harvest of valued species vs abundance of other species that depend on these species for food (predator-prey tradeoff); and abundance of unproductive stocks and species vs harvest of more productive stocks when non-selective gear catches them all (biodiversity-productivity trade-off). Predator-prey trade-off Effects of trophic interactions on calculation of sustainable yields were first shown by May et al. (1979) and have since been demonstrated by Yodzis (1994), Christensen and Walters (2004a) and Ainsworth and Pitcher (2008). One of the few attempts to explicitly take trophic interdependencies into account in fishery management is that of the Convention on Conservation of Antarctic Marine Living Resources (CCAMLR), where krill harvests are set with consideration for the needs of species that depend on krill for food (Constable 2000; Constable et al. 2001). Such management systems require the setting of clear goals – in this case maintenance of abundance of high trophic level species such as seals and whales. Detection of fishery-induced impacts on tropic interactions may be more straightforward in less diverse ecosystems where trophic interactions are strong (e.g., ecosystems at high latitudes Rudstam et al. 1994; Bogstad and Mehl 1997; Constable 2000). In more complex systems, where trophic interactions may be weaker and more diffuse (Link 2002a; Yodzis 2000), direct evaluation of this trade-off will not be possible for most species. Indicators of overall trophic trends may, therefore, provide useful proxies for measuring the effects of fisheries on trophic dynamics. There is now a growing literature on possible metrics that could be used as indicators of fisheries-induced changes on trophic interactions in ecosystems (e.g., papers in Cury and Christensen 2005; reviewed by Fulton et al. 2005a). For example, indicators tracking trends in trophic composition of catches have been used to demonstrate serial depletion in several systems (Pauly et al. 1998). Other indicators based on 9  trophic structure of ecosystems that can be evaluated using ecosystem models have been reviewed by Christensen (2000). One problem with composite trophic indicators based on landings is that similar results can arise from different causal mechanisms and results may not, therefore, reflect the underlying state of the ecosystem but may instead be due to external effects, such as changes in market patterns or spatial structure of fishing fleets (Essington et al. 2006). While analysis of suites of indicators to infer impacts of fishing on ecosystems has great potential for focusing discussion with managers and stakeholders, there has been little progress in determining how they might practically be used in making management decisions or negotiation of trade-offs – mainly due to uncertainty about ecosystem processes and lack of credible, local models to predict how systems would respond to proposed management actions (Hall and Mainprize 2004). Productivity-biodiversity trade-off The productivity-biodiversity trade-off (Walters and Martell 2004) arises from technological interactions. The issue of non-selectivity in fisheries means that even well-intentioned management plans can lead to overfishing of some species, as some species or stocks will naturally have greater resilience to fishing than others (Ricker 1958; Paulik et al. 1967; Hilborn 1976; Hilborn 1985a). Paulik et al. (1967) noted that yields from mixed stock fisheries would always be lower than if the stocks were optimally harvested separately. This effect also is wellknown in single species multi-stock fisheries, such as those for Pacific salmon. Hilborn (1985a) showed that the presence of stocks of differing productivity in a mixed stock Pacific salmon fishery would lead to over-optimistic management targets if stocks were assessed as a single unit, and this would therefore lead to overfishing of less productive stocks. One way to think about implications of the productivity-biodiversity trade-off is to consider its extremes (Mace and Reynolds 2001). At one extreme, managing to maximise fishery productivity inevitably leads to overfishing of some species while sustainable yields are achieved for others. At the other extreme, managing so that no species are overfished (‘weak stock’ management) can result in significant reductions in total yield (Hilborn et al. 2004). This difficult and inevitable trade-off is seldom explicitly acknowledged in fishery management and usually happens ‘by default’ (Walters and Martell 2004). A common characteristic of fishery development arising from this trade-off is rapid depletion of less productive species as more 10  productive species continue to attract fishing effort (Pauly 1995; Pitcher and Pauly 1998; Pitcher 2001). Fishery-independent surveys in Australia have shown evidence of such effects in the Gulf of Carpentaria (Harris and Poiner 1991); the North West Shelf (Sainsbury 1991; Sainsbury et al. 1997); and the continental slope of NSW (Andrew et al. 1997; Graham et al. 2001). Related to this trade-off is one of the most familiar trade-offs in fisheries: that between current and future harvests. This is the trade-off between short-term and long-term yields or profits. Clark (1973; 1976; reviewed by Ludwig 2001) showed that living resources will frequently be treated as non-renewable resources by fishers, especially as discount rates approach or exceed natural population growth rate. This is because reliance on future catches is more risk prone than taking catches now and investing profits elsewhere. In these cases, it may become economically rational to exploit low productivity species to extinction. The effect is magnified if low productivity species are caught as bycatch or are low in value and management priority (Bonfil 2004). Figure 1.1a illustrates the biodiversity-productivity trade-off in terms of long-term yield for five hypothetical species of differing productivity. For any one of the hypothetical species, there is some optimal harvest rate that would maximise yield, indicated by the peak of the curve. Figure 1.1b shows corresponding equilibrium biomasses at the same harvest rates. Figure 1.1 illustrates that, where there are technological interactions among species, optimally harvesting some species may be enough to drive less-productive species to commercial or even biological extinction. The productivity-biodiversity trade-off therefore has significant implications for lowproductivity species in multispecies fisheries, where there may be very strong conflict between economic interests and conservation concerns (Reynolds et al. 2001; Hilborn et al. 2004). Sharks, skates and rays, which typically have lower productivity than most teleosts (Smith et al. 1998; Walker 1998; Cortés 2002), may be particularly at risk to these effects (Walker 1998; Musick et al. 2000; Dulvy et al. 2000; Graham et al. 2001; Dulvy and Reynolds 2002). It is important to recognise that solutions to trade-offs are subjective and science has no power to determine ‘right’ or ‘wrong’ solutions (Lackey 2001). Walters (2003) argued that the only way for managers to approach difficult trade-offs such as the differential productivity problem is to honestly appraise the trade-off and have managers, fishers and other stakeholders negotiate where along the trade-off they would like to be. Formal methods exist for evaluating utility of alternative outcomes to different stakeholders (Keeney and Raiffa 1976), although informal 11  methods involving negotiations among stakeholders (Smith et al. 1999) are also effective. The legal system may also be used in conflict resolution relating to fisheries. For example, in 2000 the New South Wales Land and Environment Court found that commercial fishing licences had to meet the requirements of the Environmental Planning and Assessment Act 1979 (EP&A Act) and, therefore, that environmental impacts of all commercial fisheries had to be assessed (Gibbs 2008). This necessitated a major change in the way that fisheries are assessed and managed in NSW. Similarly, the Commonwealth EPBC Act is a powerful instrument that has the potential to affect many aspects of fishery operations. The 2006 listing of orange roughy (Hoplostethus atlanticus) as a Threatened Species under the EPBC Act has resulted in development of a comprehensive conservation programme for the species (which is Australia’s first commerciallyharvested fish to be listed), which includes spatial fishery closures (AFMA 2006). In all of these approaches, the role of fisheries scientists is to present scientific evidence to inform decisions and to honestly communicate the uncertainty surrounding the information presented (Ludwig et al. 1993; Walters and Martell 2004). Productivity of fished populations A first step in evaluation of the productivity-biodiversity trade-off and risks to low productivity species is estimation of the relative productivity of harvested species. The ecological basis for sustainable fishing is that most, if not all, fish populations show some degree of improvement in productivity as the adult population is reduced below carrying capacity (Ricker 1954; Beverton and Holt 1957). Productivity is an intrinsic property of fish populations determined by rates of growth, mortality and recruitment. Recruitment productivity is usually understood to be a function of density dependent processes leading to improvement in the rate of juvenile survival as adult stock size is reduced from its unfished state (reviewed by Rose et al. 2001; Myers 2002). Density dependent mechanisms of population regulation (i.e., negative feedback mechanisms) appear to be ubiquitous in natural populations (Brook and Bradshaw 2006). In coastal fish species, density dependent effects probably occur mainly in juvenile demersal life stages (Myers 2002). It is usually assumed in fisheries science that density dependent processes occur before fish recruit to the fishery (Myers and Mertz 1998), although this may not always be a valid assumption (Gazey et al. in press). Mechanisms for improvements in juvenile survival rate at lower densities include: decreased territorial behaviour; reduced competition for food and space; and decreased vulnerability to predation (Walters and Juanes 1993; Walters and Korman 1999; 12  Rose et al. 2001; Myers 2002). The magnitude of density dependent effects is variable among stocks and species and is understood to be one of the main determinants of the sustainable exploitation rate of a population (Myers 2001). Estimation of recruitment productivity parameters is therefore a core component of fisheries stock assessment (Hilborn and Walters 1992; Punt and Hilborn 1997). There are a number of alternative parameters can be used to represent productivity in fisheries population models, the simplest being the intrinsic rate of population growth, r, from the logistic population growth model (e.g., Schaefer 1954). The slope of the stock recruitment function near the origin, α, i.e., maximum juvenile survival rate (Ricker 1954; Beverton and Holt 1957; see Figure 1.2) is also commonly used. Goodyear (1977) standardized this parameter and expressed it as the recruitment compensation ratio, which is the relative improvement in juvenile survival from the unfished state as spawning stock approaches zero (see also Myers et al. 1999; see Figure 1.2). The steepness parameter of Mace and Doonan (1988) is another standardization widely used in Europe and North America. FMSY is the fishing mortality rate that would produce maximum sustainable yield, MSY. FMSY and its discrete equivalent, annual exploitation rate, UMSY, can be shown to be analytically related to recruitment productivity parameters under some assumptions (semelparous species: Hilborn and Walters 1992; Schnute and Kronlund 1996; iteroparous species: Schnute and Richards 1998; Forrest et al. 2008, Chapter 2; Martell et al. 2008). This implies that a fish population’s sustainable exploitation rate is also a productivity parameter, which, under a given selectivity schedule, is as intrinsic to the population as its biological productivity parameters (Schnute and Kronlund 1996). There are well-known problems with the use of MSY as a management target (Larkin 1977). Notwithstanding ecosystem considerations discussed above, there have been major problems with both estimation and implementation of MSY strategies (Punt and Smith 2001). These problems have been mainly due to incorrect assumptions in estimation of MSY, either in the model or in the data used, and the fact that MSY is a long-term target, while fishers and managers have much shorter time horizons (Holling et al. 1998). Despite these problems, MSY and FMSY are, by definition, indicators of sustainability (at least in a single-species sense) and are based on sound biological theory. In recent years there has been renewed interest in using FMSY as a limit reference point (rather than a target) in both single species and ecosystem-based 13  management contexts (Mace 2001; Punt and Smith 2001). Meta-analytical studies have also suggested that FMSY represents a precautionary limit to fishing mortality for preventing recruitment overfishing (Cook et al. 1997; Punt 2000; NAFO 2003; Mace 1994). As well as being a biologically-valid limit reference point, FMSY can also be useful in communication of trade-offs to fishery managers and stakeholders. FMSY is directly comparable among populations and, unlike some recruitment parameters, is easily interpreted by nonscientists (Schnute and Kronlund 1996). It is also of direct management interest, i.e., it is possible to compare species directly in terms of the amount of fishing that can sustainably be applied. While density dependence in recruitment is a determinant of sustainable exploitation rate, it is not the sole determinant, and it does not follow that a stock with strong density dependence can sustain higher harvest rates per se. In fact, in a recent meta-analysis of 54 Atlantic fish stocks, Goodwin et al. (2006) found that recruitment compensation tended to be stronger in larger, longer-lived, slower-growing stocks – characteristics that tend to be associated with lower resilience to fishing. The idea that fish species have an intrinsic resilience to fishing, which can be presented in terms of a parameter of direct management interest and compared among multiple species (e.g., Fig.1.1), facilitates communication of trade-offs in multispecies or multi-stock fisheries in simple terms, without the implication of setting MSY as a management target. Fishery assessment methods have progressed over the past two decades: equilibrium fitting methods are no longer used for parameter estimation; there is greater awareness of problems with using catch-per-effort data; and advice is now usually given in probabilistic terms (Punt and Smith 2001). In addition, fixed harvest-rate management strategies have been found to be more robust to uncertainty than fixed quota approaches (Walters and Parma 1996; Martell and Walters 2002) and most appropriate to use for low-productivity species (Punt and Smith 1999a). It is in this new context that FMSY may once again be a useful parameter in the EBFM arena. Models as support tools Simulation models are important tools for providing scientific advice for fisheries management. Probably the most common application of models is for estimation of parameters by fitting model predictions to observed data using Bayesian or likelihood methods (Hilborn and Walters 1992; McAllister and Ianelli 1997; Hilborn and Mangel 1997; Punt and Hilborn 1997; Chen et 14  al. 2003). Even in data-limited situations, however, simulation models can be useful heuristic tools (e.g., papers in Kruse et al. 2005; Cortés 1998; Smith et al. 1998; Heppell et al. 1999; McAllister et al. 2001). The complexity, variability and lack of knowledge about marine systems does not preclude making good policy decisions and scientists and managers do not necessarily need detailed knowledge of all system processes to be able to predict that one policy is preferable to another over a wide range of possible states of nature (Walters and Martell 2004). Policies that consistently outperform others under a range of uncertainty in a simulation framework can be considered relatively robust and worthy of further exploration. Models can also help to identify processes most likely to be important to predicting the effects of policy and help to focus research programmes (Walters 1992; Walters and Holling 1990). Since the 1950s, different classes of stock assessment models have been used by fisheries scientists to predict the impacts of fishing on fish stocks. These include surplus production models (e.g., Schaefer 1954); dynamic pool models (Beverton and Holt 1957); and fully agestructured biomass dynamic models (Megrey 1989). Most of these types of models have been applied to single species, although some have been extended to a multispecies context (Murawski 1984; Pope 1991; reviews by Bax 1998; Whipple et al. 2000). In recent years, whole ecosystem models have been developed to help scientists and managers focus on ecosystemscale policy questions (Christensen and Walters 2004b; Fulton 2005b; reviews by Bax 1998; Whipple et al. 2000; and Plagányi 2007). Probably the most widely used of these is the Ecopath with Ecosim (EwE) family of mass balance ecosystem models (Polovina 1984; Christensen and Pauly 1992; Walters et al. 1997). Examples of some applications of ecosystem models built using the EwE can be found in a recent special volume of Ecological Modelling (2004; Volume 172 (2-4)). See Christensen and Walters (2004b) and Plagányi (2007) for discussion of the capabilities and limitations of different ecosystem models. See Fulton (2001) and Fulton and Smith (2004) for comparison of the performance of different ecosystem models. While ecosystem models are unlikely to reach the stage where they can quantitatively and accurately predict all ecosystem dynamics, they may be useful for identifying robust management strategies, exposing trade-offs and clarifying policy objectives. For example, a biogeochemical ecosystem model (Atlantis) has been used for extensive testing of the performance of ecosystem-scale indicators (Fulton et al. 2005b) and for evaluation of trade-offs 15  (Fulton et al. 2007a). EwE has also been used extensively for evaluation of trade-offs and has an in-built optimal policy search routine that maximises an objective function weighted according to the value placed on different policy objectives (papers in Pitcher and Cochrane 2002; Christensen and Walters 2004b; Ainsworth and Pitcher 2005; Cheung and Sumaila 2007; Fulton et al. 2007b). Use of ecosystem models for this purpose allows trophic effects to be accounted for in predicting performance of alternative management options. EwE has also been used to estimate the effects of trophic interactions on achievable MSY (Walters et al. 2005). Results have shown that deterioration in ecosystem structure can occur if harvests of smaller forage species, which form the main prey of larger piscivores, are not constrained. Ecosystem models have also been used for exploration of policy goals for restoration (Pitcher 2001; 2005; Pitcher and Ainsworth 2008). The approach of these authors involves using a variety of scientific, historical and anecdotal sources of information to reconstruct historical ecosystems to demonstrate the potential economic, social and economic gains that could potentially be made with appropriate restoration targets (e.g., Heymans (ed.) 2003; Ainsworth and Pitcher 2005; 2008; Ainsworth et al. 2008). Results have suggested that both consumptive and existence values could be greatly improved, compared to present-day ecosystems. Ecosystem models have also been used to address a large number of ecological questions and to explore hypotheses for observed ecosystem-level changes (e.g., decline of Steller sea lions in the north eastern Pacific: Guénette et al. 2006; collapse of the northern cod fishery: Bundy 2004; shifts in ecosystem structure in Thailand: Christensen 1998). This study aims to use single-species and ecosystem-scale models, incorporating some of the ideas above, to aid understanding of issues important for EBFM in the fisheries off the coast of NSW.  Fisheries off the coast of New South Wales New South Wales is located on the south east coast of Australia and is the country’s most populous state (Figure 1.3). Important coastal marine habitats off the coast of New South Wales include estuaries, rocky reefs, mangroves and seagrass beds, as well as diverse continental shelf and slope habitat. Waters tend to be oligotrophic, due to lack of upwelling and tropical water transported south by the East Australia Current and, as a result are less productive than might be 16  expected. The continental shelf is relatively narrow (generally extending to around 20-40 km offshore), and supports invertebrate and finfish fisheries. The history of management of the shelf and slope fisheries of NSW is complex and there have been a number of changes in jurisdictional control since fishing began. Jurisdiction of the coastal waters off NSW is now divided between the State and Commonwealth governments. All waters within 3 nautical miles of the coast are under State jurisdiction. Under the 1979 Offshore Constitutional Settlement (see Rothwell 1994; Rothwell and Haward 1996), jurisdiction over waters off NSW beyond 3 nautical miles is shared between the Commonwealth and State governments. South of Barranjoey Point, (at the northern edge of Sydney, 33° 35’ S), Australian waters beyond 3 nautical miles offshore are wholly under Commonwealth jurisdiction and are managed by the Australian Fisheries Management Authority (McColl and Stevens 1997). North of Barranjoey Point, all waters are under State jurisdiction to 80 nautical miles offshore, beyond which the Commonwealth has jurisdiction to the edge of the Australian Fishing Zone2, 200 nautical miles offshore. Both Commonwealth and State fisheries have undergone significant restructuring over the past three decades (Grieve and Richardson 2001; Tilzey and Rowling 2001). Complex jurisdictional issues pose a number of problems for efficient management of fish stocks in NSW. For example, most trawlers are endorsed to fish in both State and Commonwealth fisheries and there is a period between 1985 and 1997 when there is uncertainty as to whether landings reported to the Commonwealth Government were also reported to the State government. Management problems may also arise as a result of species being distributed cross jurisdictional boundaries, although there has been little documentation of such problems if they occur. Commercial fishing began on the continental shelf of NSW in 1915, with three steam trawlers owned by the NSW government. The continental slope has supported fisheries since the late 1960s (Graham et al. 2001). Until the early 1970s, the fishery operated primarily in continental shelf waters between depths of 50 and 200 metres, targeting mainly tiger flathead (Neoplatycephalus richardsoni) then, following declines in this species, jackass morwong 2  The Australian Fishing Zone (AFZ) was declared in 1979, some fifteen years earlier than the 1994 declaration of Australia’s Exclusive Economic Zone (EEZ). The EEZ did not replace the AFZ – rather there is provision for the two zones to be defined consistently with each other (Rothwell and Haward 1996). The EEZ generally refers to Australia’s jurisdiction over the seabed and its resources (such as oil and gas), whereas the AFZ generally refers to jurisdiction over the water column and living marine resources.  17  (Nemadactylus macropterus), redfish (Centroberyx affinis) and smaller quantities of other demersal fish species (Klaer 2001). In 1968, two Wollongong trawlers began targeting redfish on the NSW upper slope, leading to an expansion of the trawl fishery into upper slope waters to ~600 m depth (Andrew et al. 1997). The expansion onto the slope was further driven by the discovery of large spawning runs of gemfish (Rexea solandri) (Klaer 2001). Currently, the Commonwealth Trawl Sector (CTS; formerly the South East Trawl Fishery) is the largest Commonwealth-managed fishery operating off the coast of NSW. Most of the catch now occurs on the continental shelf and slope from approximately 200 to 600 metres in depth (Tilzey and Rowling 2001). In 1992, Individual Transferable Quotas were introduced into the Commonwealth fishery (Grieve and Richardson 2001). There are now currently 20 species or taxonomic groups under quota in the fishery (Tuck and Smith 2006), although more than 80 species are harvested commercially (see Kailola et al. 1993; Williams and Bax 2001). Stock assessments are available for a limited number of species caught in Commonwealth fisheries (reviewed by Bruce et al. 2002; see Tuck and Smith 2004; 2006 for recent assessments). During the 1970s, Australia’s fisheries were considered ‘underexploited’ and, with the impending 1979 declaration of the 200 nautical mile Australian Fishing Zone, the Australian government provided considerable funding for exploratory surveys of the waters of the southeast Australian slope (Tilzey and Rowling 2001). This led to a set of surveys of the upper continental slope in the 1970s (Gorman and Graham 1976; 1977). The objective of the early surveys was to locate productive trawl grounds and evaluate the viability of demersal slope fisheries. The initial, exploratory upper slope surveys were done in 1976-1977 and were fully replicated twenty years later in 1996-1997, allowing for some striking comparisons of the abundance of many species (Andrew et al. 1997; Graham et al. 1997; Graham et al. 2001). Analysis of the survey data revealed that there had been significant declines in the abundance of many demersal sharks, skates and several species of bony fish on the continental slope. Notable declines were reported for deepwater dogsharks (Centrophorus spp., Squalus spp. and Deania spp.), as well as sawsharks (Pristiophoridae), angel sharks (Squatinidae), school sharks (Galeorhinus galeus) and skates (Rajidae). One of the most significant declines in abundance of bony fishes has been that of gemfish (Rexea solandri), which was shown to suffer severe recruitment failure in the early 1980s (Rowling 1990; 1997a). The research vessel was decommissioned in 1997 and there have been no fishery-independent surveys on the NSW continental shelf or slope since that time. 18  Currently, there are seven commercial marine fisheries operated wholly by the State of NSW: Estuary General, Estuary Prawn Trawl, Ocean Trawl, Ocean Haul, Ocean Trap and Line, Rock Lobster and Abalone. All recreational fisheries operating out of NSW ports, regardless of distance offshore, are also State-managed. Except for the valuable abalone and rock lobster fisheries, which are managed by quotas, all fisheries are managed by input (i.e., effort) controls. Management measures include a complex set of gear and mesh size restrictions, seasonal temporal and areal closures and minimum legal lengths of fish (see NSW Fisheries 2001; Gray 2008). Each fishery has a Management Advisory Committee (MAC) that meets regularly and contributes to management decisions. MAC members include commercial fishers and scientists, representatives of environmental groups, indigenous representatives and scientists from other related disciplines. A Fisheries Management Strategy (FMS) and Environmental Impact Statements (EIS) have recently been developed for all fisheries in accordance with requirements of the EPBC Act, the Environmental Planning and Assessment Act 1979 and the Fisheries Management Act 1994 (Gibbs 2008). The objectives of the EISs are to provide detail needed to augment the FMS; to provide assessment of the current activity of each fishery; and to identify links with other parts of the human and ecological environment (Gibbs 2008). While the Environmental Impact Statements make use of information existing about the fisheries of New South Wales and highlight likely interactions among components of the ecosystem, no new ecological research was done to produce them and all so far point out large gaps in understanding of ecosystem processes and the nature of fisheries impacts on these processes, e.g. “The draft FMS has revealed substantial knowledge gaps that affect the management of the Estuary General Fishery. The knowledge gaps cover four main areas – stock assessments of all retained species, bycatch, accuracy and precision of effort data and ecological interactions among retained species. […] There is little understanding of how fishing pressure affects fish stocks in the Estuary General Fishery. […] Whilst there is some basic knowledge about the general biology of species in the Estuary General Fishery there is little knowledge about how the species interact” (NSW Fisheries 2001, pp E-250-251).  19  Recreational fisheries in New South Wales are significant. The recent national survey of recreational fishing estimated that in the financial year 2000-2001, there were approximately 7.7 million recreational fishing ‘events’ in New South Wales (Henry and Lyle 2003). Catches of several important commercial species were found to exceed commercial catches, a finding consistent with previous surveys of recreational fishing in Australia (Pollock 1980; West and Gordon 1994; Young et al. 1999). Prior to the National Survey of Recreational and Indigenous Fishing (Henry and Lyle 2003), recreational fishing surveys were done on a local basis using various methodologies (e.g., State Pollution Control Commission 1981; West 1993; West and Gordon 1994; Steffe and Macbeth 2002a,b). The National Survey of Recreational and Indigenous Fishing represents the first comprehensive survey enabling comparison of recreational activity across the whole country. It has not, however, been repeated and recreational fishing remains a major source of uncertainty in estimates of total catch of many species (Scandol et al. 2008). There are a number of barriers that have prevented reliable stock assessment for the inshore fisheries of NSW. Estuarine and beach fisheries, are small-scale and extremely complex in terms of the number of species landed, targeting practices and gears used. Also, unreliable effort data for a number of gears has meant that catch per unit effort (CPUE) cannot be calculated in many cases (Scandol and Forrest 2001), although considerable progress has recently been made in identifying reliable CPUE series (Scandol et al. 2008). Life history data and age- and lengthcomposition of catches are routinely collected for many species and are being incorporated into consistent and easily accessible databases (Scandol 2004). Alternative approaches using these kinds of data will therefore be needed as NSW moves towards more ecosystem-based approaches to managing its fisheries (Scandol et al. 2008).  Aims of the project The aim of this collaborative project between NSW Department of Primary Industries and the University of British Columbia’s Fisheries Centre is to provide simulation models to help identify needs for EBFM in NSW. Fisheries in NSW are extremely data-limited and management has not traditionally relied on model outputs for decision-making. The costs associated with collecting data to address the many knowledge-gaps are likely to exceed the 20  funds available for research in the near future and, therefore, simply doing more research, or collecting more data, is not the way forward. Innovative approaches, such as the development of assessment approaches that rely on more-easily and routinely collected data (such as age, growth and reproductive data) that can be used to estimate suitable reference points should play an important role in determining which species are most at risk from fisheries. This thesis aims to provide simulation tools that can contribute to understanding of EBFM; to highlight need for consideration of trade-offs; and to help clarify possible EBFM policy objectives. The thesis begins with presentation of a newly-parameterised age-structured model with productivity parameter, optimal harvest rate, UMSY (Chapter 2). The model has useful equilibrium properties in that it enables examination of the relationship between life history, selectivity, density dependence in recruitment and UMSY. Chapter 3 explores these relationships for 54 Atlantic stocks for which recruitment parameters have been previously published by other authors (Goodwin et al. 2006). Results showed that, for some long-lived, slow-growing species, life history parameters may be the most important determinant of UMSY. Chapter 4 explores this concept further and applies the model to estimate the maximum possible hypothesis for UMSY for dogsharks that have been heavily depleted on the continental slope (Graham et al. 2001). Results suggest that the optimal harvest rate for these species is extremely low under a broad range of hypotheses about the age at first harvest. Chapter 5 evaluates available data for stock assessment of one species of dogshark that has been listed as Critically Endangered by the IUCN (IUCN 2008). The study reveals severe problems in the quality of available data for sharks in southeastern Australia, typical for sharks around the world. Catch and historical effort data are reconstructed and used in a simple preliminary stock assessment. Finally, in Chapter 6, an ecosystem model of the 1976 NSW continental slope. built using Ecopath with Ecosim, is used to illustrate important trade-offs in implementation of alternative fishing strategies with differing management objectives. To evaluate the effects of model structure on results, results are compared with the predictions an Atlantis model of the same system, built by scientists at CSIRO (Savina et al. 2008). It is hoped that these analyses will provide some tools and insights that can be of use towards implementation of EBFM in NSW, despite severe data-limitations. It is also hoped that important trade-offs have been highlighted and may help managers more clearly think about their 21  role in identifying and implementing EBFM policies. In addition to the analyses contained in this thesis, the project has facilitated collaboration between State, Commonwealth and international institutions and compiled a large amount of data and literature relevant to the marine ecosystem of NSW. A workshop held in 2003 brought together more than eighty scientists, managers and interested parties who shared their knowledge of the fisheries and ecosystems of the region. Papers from this workshop have been published (Forrest et al. (eds) 2008) and will also provide a valuable resource for scientists and managers. Preliminary results presented in this thesis were also discussed at an EBFM workshop at the NSW DPI laboratories in Cronulla in July 2007.  22  Figures Biodiversity - Productivity  3 0  1  2  Yield  4  5  (a)  0.2  0.4  0.6  0.8  1.0  0.2  0.4  0.6  0.8  1.0  (b)  60 0  20  40  Biomass  80  100  120  0.0  0.0  Long-term harvest rate Figure 1.1. Equilibrium (a) yield and (b) biomass for five hypothetical species in a multispecies fishery, where the x-axis represents long-term fixed harvest rate and the y-axis represents relative equilibrium yield or biomass that would be obtained after long-term harvesting at the fixed harvest rate. On each graph, the solid line represents the least productive species and broken lines from left to right represent progressively more productive species. 23  (i) Slope = α = RFτ /E Fτ = Juvenile survival rate at low stock size  0.03  0.025 Number of recruits  R0  0.02  (ii) Slope = R0 /E0 = Unfished juvenile survival rate  0.015  0.01  0.005  0  00  2  4  6 8 10 12 14 Spawning Stock Biomass or Eggs  16E0  18  20  Figure 1.2. Stock recruitment relationship for a hypothetical fish population. Points represent observed number of recruits plotted against spawning stock biomass or number of eggs. The solid line shows a fitted Beverton-Holt (1957) stock recruitment curve. Note that the function can be parameterised in terms of spawning stock biomass or in terms of numbers of eggs, E. Note also that number of eggs is often assumed directly proportional to spawning stock biomass (see Chapter 4 for cases where this is an inappropriate assumption). Dashed lines represent juvenile survival rate: (i) close to the origin of the plot; and (ii) at unfished (maximum) production of eggs (i.e., E0 where the 0 subscript indicates fishing mortality F = 0). The maximum juvenile survival rate, i.e., slope of dashed line (i) is called α and occurs at the fishing mortality rate Fτ (Shepherd 1982), which, if applied consistently, would cause extinction of the stock. The ratio of slopes (i) and (ii) is called the recruitment Compensation Ratio, CR (Goodyear 1977; also called αˆ ; Myers et al. 1999) and represents the maximum possible improvement in juvenile survival as stock size is reduced, i.e., CR =  α  R0 / E0  .  Note that R0/E0 is the inverse of unfished eggs per recruit, and, therefore, CR = α E0/R0. Note that in this thesis, E0/R0 is expressed as φE0 (Botsford 1981; see Chapter 2, equation 2.2).  24  Australia NSW  Figure 1.3. Map of the study area. Depth contours are measured in fathoms (1 fathom = 1.83 metres). Note that most fishing occurs in waters shallower than 1000 metres (Larcombe et al. 2001). Source: Jim Craig (NSW DPI).  25  Chapter 2. An age-structured model with leading management parameters, incorporating age-specific selectivity and maturity  Introduction Maximum sustainable yield (MSY) has formed the basis of many fisheries management strategies since at least the 1950s (e.g., Schaefer 1954). Despite well-documented problems with implementation of MSY policies (Larkin 1977; Punt and Smith 2001), the recent shift towards setting the target fishing mortality rate that achieves MSY (FMSY or its dimensionless, discrete equivalent, UMSY) as a limit reference point rather than a target reference point has resulted in renewed interest in MSY as a means of determining precautionary harvest rates in both single species and ecosystem-based management contexts (Mace 2001). Fisheries stock assessment involves estimating key parameters (leading parameters) by fitting a model to fishery dependent or independent data. The leading parameters of a model are those from which other parameters are derived and are of greatest interest in terms of establishing reference points, even though other ‘nuisance’ parameters (e.g., catchability, growth and selectivity parameters) may be required for a fully-specified model (Walters et al. 2006). At the very least, population models require leading parameters that determine the scale and productivity of the population, with the leading parameter describing productivity the main determinant of the behaviour of a fish stock under harvesting and, therefore, its maximum sustainable harvest rate, UMSY. There are a number of ways that productivity can be represented in population models, the simplest being the logistic model’s intrinsic rate of growth, r (e.g., Schaefer 1954). Alternatively, some models use the slope of a stock recruitment function near the origin, α (e.g., Ricker 1954; Beverton and Holt 1957). Goodyear (1977) expressed productivity in terms of the recruitment compensation ratio (CR), which is the relative improvement in juvenile survival as spawning stock abundance is reduced towards zero (see Figure 1.2 for graphic presentation). In common use is a reparameterised version of the Beverton and Holt recruitment function, which uses the steepness parameter, h, defined as the proportion of recruits that are produced when egg production (i.e., spawner abundance) is at 20% of 26  unfished egg production (Mace and Doonan 1988; Hilborn and Walters 1992). Myers et al. (1999) expressed h (called z in their paper) as a function of lifetime spawners per spawner at low abundance, αˆ . Their meta-analysis, based on stock-recruitment data for more than 700 fish stocks, suggested that the magnitude of compensation in recruitment is a relatively conservative property of fish stocks, with the maximum lifetime production of spawners per spawner rarely exceeding 50. Mathematically, αˆ is the equivalent of CR under certain assumptions about fecundity (see section below). Goodwin et al. (2006) reported CR for 54 Atlantic fish stocks, again reporting CR < 50 for the majority of stocks. The finding that CR tends to be confined within certain bounds across multiple species and life histories makes CR a useful productivity parameter for modellers, especially given its analytical relationship to the more familiar h. Biological productivity parameters are usually of secondary interest to managers, who tend to be more concerned with measures such as total allowable catch or maximum sustainable harvest rate. Management parameters must therefore be derived from models, either using analytical or numerical relationships. Simple surplus production models (e.g., Schaefer 1954), which do not explicitly incorporate recruitment, provide a direct analytical relationship between r and UMSY (UMSY = r/2). For semelparous species, UMSY can be expressed as a function of α, using Ricker (1954) or Beverton and Holt (1957) recruitment functions (Hilborn and Walters 1992). Schnute and Kronlund (1996) derived analytical relationships between biological and management parameters using a generalised recruitment function for semelparous species. The resulting stock-recruitment function was parameterised in terms of two leading management parameters, UMSY and MSY, which could be estimated directly using established stock assessment fitting procedures. Schnute and Richards (1998) extended the approach and developed a generalised age-structured model that could be used for iteroparous species, which incorporated a reparameterised stock recruitment function in terms of UMSY and MSY. It assumed knife-edged selectivity and maturity and that natural and fishing mortality occurred separately. Despite these limiting assumptions, their approach enabled direct estimation of UMSY from data for a much broader range of species than had been previously possible. The approach of Schnute and Richards (1998) is extended here by presentation of an alternative formulation of the derivation of α from UMSY, which incorporates age-specific selectivity and maturity. An age-structured population model is used, which utilises Botsford “incidence” 27  functions (Botsford 1981; see Walters and Martell 2004) to calculate equilibrium eggs per recruit and vulnerable biomass per recruit, which simultaneously capture the effects of fishing and natural mortality on fish as they age. The method avoids the assumption of knife-edged selectivity and maturity and is flexible to a wide range of selectivity and maturity schedules. These developments broaden the range of fisheries for which UMSY can be estimated directly. Links between life history and productivity  There is currently much interest in the link between life history traits and productivity, especially for species that are data-limited (Reynolds et al. 2001). While certain life history traits (e.g., late maturity, slow growth, low natural mortality) tend to predispose species towards low values of UMSY, density dependence in recruitment is also an important determinant. Density dependence principally refers to the improvement in juvenile survival rate as spawning stock size is reduced. Density dependent mortality may occur at a number of life history stages but probably occurs principally in juvenile demersal stages for coastal species (Myers 2002). Mechanisms include increased territorial behaviour and greater competition for food as juvenile density increases, which lead to increased time taken to reach sizes less vulnerable to predation (see Hilborn and Walters 1992; Rose et al. 2001; Myers 2002). Foraging arena theory (Walters and Juanes 1993; Walters and Korman 1999; Walters and Martell 2004) has recently been introduced as an overarching explanation for density dependence in juvenile survival rates and predicts that density dependence is an emergent consequence of the trade-off between time spent feeding and risk of predation. Mechanisms leading to density dependence are complex and subject to considerable interannual variability. On average, however, some species show a stronger response to changes in spawning stock size than others. All other things equal, stronger density dependence implies greater resilience to fishing due to the stock’s ability to respond positively to reductions in adult biomass (e.g., Goodyear 1977). Density dependence is difficult to measure in nature due to problems with observing juvenile fish, although the meta-analyses of Myers et al. (1999) and Goodwin et al. (2006) have improved understanding of the likely range of magnitude of these effects. Quantifying interactions among life history parameters, density dependence and sustainable harvest rates could aid in understanding the mechanisms that lead to overfishing and could be useful in design of sustainable fishing strategies. The structure of the model, and its analytical 28  relationship between productivity and UMSY, allows these linkages to be considered simultaneously. Bayesian estimation  Bayesian inference is now in mainstream use in fisheries stock assessment (e.g., Punt and Hilborn 1997; Chen et al. 2003) and has facilitated a general move towards consideration of population and management parameters as probability distributions, rather than point estimates. Once distributions of a model’s leading parameters have been estimated, the past and current state of the fishery, in terms of population size or harvest rates, can also be estimated to determine the probability of exceeding reference points. Combining direct estimation of fishery reference points, such as MSY and UMSY, with a Bayesian approach can improve communication of scientific results considerably (Schnute and Kronlund 1996; Schnute and Richards 1998). Managers are more familiar with the parameters MSY and UMSY than their more abstract biological analogues and, in fully developed fisheries, it is likely that MSY and UMSY lie within management experience. Dialogue between managers and scientists about the range of uncertainty to admit in stock assessments is likely to be more transparent if all parties are discussing parameters with which they are familiar. This paper proceeds as follows. First an age-structured population model that uses MSY and UMSY as leading parameters is presented. Some properties of the model are then briefly described, chiefly in terms of its ability to show relationships between life history, density dependence and UMSY. Finally, a simple Bayesian estimation routine is implemented to illustrate estimation of UMSY directly.  Population model with MSY and UMSY as leading parameters The model is an age-structured population model with leading parameters MSY and UMSY describing scale and productivity of the population respectively. First, the equilibrium structure of the model is described, then time dynamics are incorporated. The key difference between this model and other age-structured models is the analytical linkage between the leading management parameters and recruitment parameters. 29  Equilibrium recruitment (R) under a given constant harvest rate is a function of stock size (expressed in terms of eggs, E) and the leading parameters of the model. Here it is described by the Beverton and Holt (1957) recruitment function, i.e.,  (2.1)  R =  αE 1+ β E  where a recruit is here defined as a fish of age 1. Equilibrium eggs per recruit ( ϕ E ) can be obtained using an “incidence” function (Botsford 1981; Walters and Martell 2004), which captures the effects of natural mortality and fishing mortality over the lifetime of individuals assuming equilibrium conditions, i.e., ∞  (2.2)  ϕ E =∑ l a f a a  where fa is relative fecundity at age (assuming fecundity based on weight and a logistic maturity function, Appendix B to Chapter 2). Survivorship at age, la (the proportion of fish that survive to age a under a given constant equilibrium harvest rate U) is given by 1  if a = 1  A a −1 s a −1 (1 − v a −1U )  if a >1  (2.3) A a =  where sa is natural survival at age. It is assumed here that sa is constant and proportional to the von Bertalanffy growth rate, κ, via the relationship sa = e-M, where M is the instantaneous natural mortality rate, with the simplifying assumption that M = 1.5κ (Beverton and Holt 1959). The term sa (1 − vaU ) represents the survival rate under fishing, sa_fished. Equation 2.3 represents equilibrium survivorship under a particular constant harvesting regime, and enables calculation  30  of useful equilibrium per recruit quantities under different harvesting regimes. Note that unfished survivorship is obtained by setting U = 0. At equilibrium, total egg production is given by E = Rϕ E . Substituting this into equation 2.1 and solving for R gives  (2.4)  R =  ϕE α −1 (Walters and Martell 2004). β ϕE  Using this form of the stock recruitment function, Appendix A to Chapter 2 shows how α can be derived from the leading productivity parameter UMSY. The scaling parameter (β) is more easily obtained from leading parameters UMSY and MSY. First, VBMSY =  MSY , where VBMSY is U MSY  equilibrium vulnerable biomass under UMSY. Recruitment under UMSY is therefore given by RMSY =  (2.5)  VBMSY  ϕVB  , where ϕVBMSY is vulnerable biomass per recruit at UMSY, calculated as  MSY  ∞  ϕVBMSY =∑ la wa va a  with la evaluated at U = UMSY (equation 2.3) and where wa is the mean weight-at-age, (derived from the von Bertalanffy (1938) growth function, see Appendix B to Chapter 2) and va is the mean vulnerability-at-age, defined as the proportion of fish of a given age a vulnerable to the fishing gear. Asymptotic vulnerability can be represented using a simple logistic function (see Appendix B to Chapter 2). Specification of the recruitment function can then be completed by solving equation 2.4 for β (with R and ϕ E evaluated at UMSY), i.e., β =  ϕE  α −1 . RMSY ϕ E MSY  MSY  Once α and β are known, other important biological properties can be derived. Unfished recruitment, R0 is obtained using ϕ E 0 in equation 2.4. Unfished biomass, B0, is then simply a  31  ∞  function of R0 and unfished biomass per recruit, i.e., B0 = R0ϕ B0 , where ϕ B0 = ∑ la wa , with la a  evaluated at U = 0. Another productivity parameter of interest is the recruitment compensation ratio, CR (Goodyear 1977). This represents the maximum possible compensatory improvement in juvenile survival as stock size is decreased by fishing (see Figure 1.2). It is easily derived from α , i.e., unfished juvenile survival rate is  R0 E , but ϕ E 0 = 0 , so unfished survival is simply ϕ E0 -1. Since the E0 R0  maximum juvenile survival rate is α, CR is just the ratio of these two survival rates (Goodyear 1977), i.e., (2.6)  CR = αϕ E0 .  When relative fecundity is described as the product of mean weight-at-age and maturity-at-age (Appendix B to Chapter 2), ϕ E 0 is the same as unfished spawning biomass per recruit (SPR0; Gabriel et al. 1989). Myers et al. (1999) defined maximum lifetime spawners per spawner ( αˆ ) as the product of α and SPR0 and, therefore, the same as CR. When Beverton and Holt recruitment is assumed, the steepness parameter, h, of Mace and Doonan (1988) is related to αˆ (i.e., CR) by h =  αˆ 4 + αˆ  (Myers et al. 1999; see Michielsens and McAllister (2004) for the  Ricker form). The model is made dynamic by simulating changes in numbers, N, at age, a, and years, t, via the equation (2.7)  N a +1,t +1 = N a ,t sa (1 − va ,tU t )  (for a > 1 and t > 1)  Annual harvest rate, Ut, is calculated from annual catch, Ct, i.e.,  32  (2.8)  Ut =  Ct VBt  where VBt is the biomass of fish vulnerable to the fishing gear, (2.9)  VBt = ∑ N a ,t va ,t wa a  Recruits (Rt, i.e., N1,t) are added to the population using equation 2.1 with number of eggs ∞  calculated as Et = ∑ f a N a ,t . The common simplifying assumption was made that the unfished a  stock was at equilibrium and the model was initialised in the first year of fishing with N a ,1 = R0la .  Equilibrium properties: relationships between life history, density dependence and UMSY The equilibrium model can be used to examine the predicted form of the relationship between density dependence (measured by CR) and UMSY. The effect of gear selectivity and life history traits (e.g., growth rate, age at maturity, maximum age and natural mortality) on this relationship can also be modelled. Here, a hypothetical fish species with known life history parameters (Table 2.1) is used to show the effect of increasing: (i) age at first harvest; (ii) von Bertalanffy growth rate; (iii) age at maturity; and (iv) maximum age on the relationship between CR and UMSY. To do this, α was calculated over a range of hypothesised values of UMSY (0 to 1, step size  0.0001), using equation 2.A6, and then converted to CR (equation 2.6). Figure 2.1 shows the form of the relationship between CR and UMSY (note that UMSY is the independent variable). The relationship is not dynamic but rather shows the predicted values of CR under a range of hypothesised values of UMSY (i.e., the degree of improvement in juvenile survival that would be required for each hypothesised value of UMSY to be true). As the hypothesised value of UMSY increases, the strength of recruitment compensation that would be 33  needed for the hypothesis to be true increases rapidly and tends towards a vertical asymptote. Values of UMSY to the right of the asymptote are undefined, representing hypotheses of UMSY for which α was predicted to be negative (therefore impossible). The y-axes in Figure 2.1 at CR = 100 are truncated because, as UMSY approached its maximum possible value, CR tended rapidly towards very large values of CR making comparison of the curves difficult. Since most of the curves become almost vertical by the truncation point, the maximum possible value of UMSY can still be seen. As values of CR >100 seem to be rare (Myers et al. 1999; Goodwin et al. 2006), Figure 2.1 shows the region of management interest. Figure 2.1a shows the relationship between CR and UMSY at different values of age-at-50%-firstharvest, ah. Increasing ah causes the curve to shift to the right, increasing the range of values of UMSY that can be considered possible. Increasing κ (von Bertalanffy growth rate and proxy for  natural mortality) causes the curve to shift to the right, implying a greater range of possible values of UMSY for faster-growing species (Figure 2.1b). Increasing age-at-50%-maturity, amat (Figure 2.1c), or maximum age, amax (Figure 2.1d), however, causes the curve to shift to the left, implying a smaller range and lower possible values of UMSY for later maturing or longer-lived species (although the effect of age at maturity is small). Importantly, Figure 2.1 suggests that, for some species for which Beverton and Holt recruitment can be assumed, there is a maximum possible value of UMSY that can be estimated from life history and selectivity data alone.  Bayesian estimation of MSY and UMSY Methods  In this section, the model is used to show how MSY and UMSY and can be estimated using a Bayesian approach. Catch and CPUE data (Figure 2.2) for Namibian Cape Hake (a mixed stock of Merluccius capensis and M. paradoxus), published in Hilborn and Mangel (1997), were used. This dataset was chosen because: i) it will be familiar to many readers; and ii) CPUE is considered to be a reasonable index of abundance because the degree of schooling in hake is relatively low. The fishery began in the mid-1960s and was largely unregulated, resulting in a large decline in CPUE in the first ten years. Following conservation concerns, catches were  34  reduced in the 1970s, which resulted in a slight increase in CPUE (Hilborn and Mangel 1997). Life history and selectivity parameters are provided in Table 2.1. The model with leading management parameters (MSY and UMSY; Model 1) was compared to one with biological leading parameters (R0 and CR; Model 2) to show that very similar results can be obtained using either approach. Model 2 was identical in structure to Model 1, except for the method of calculating the parameters of the recruitment function (i.e., in Model 2 α was obtained from the leading value of CR and equation 2.6; β was then obtained from the leading value of R0 and equation 2.4). In both models, in addition to estimating the leading parameters, the instantaneous natural mortality rate, M, and the standard deviation of the observation error anomalies, σ were also estimated. To obtain the posterior distributions a Metropolis-Hastings algorithm was used, implemented in R, using the function “MCMCmetrop1R” in the MCMC package (Martin and Quinn 2006; R Development Core Team 2006). Markov chain simulation performs a random walk in the parameter space of θ (Model 1: θ = (MSY, UMSY, M, σ) or Model 2: θ = (R0, CR, M, σ)), which converges to a distribution that approximates the joint posterior distribution (Gelman et al. 1995). The algorithm was initialized at the maximum likelihood estimates for θ and proceeded for 110,000 iterations where the first 10,000 were discarded to allow for convergence. Convergence was assessed by visually examining trace plots and plotting running medians of length 50 to ensure the algorithm was sampling from a stable distribution (see Gelman et al. 1995 and Punt and Hilborn 1997 for more details on MCMC methods). For simplicity estimating process error was not attempted. Lognormal observation error was assumed, i.e., CPUEt = qVBtevt, where q is the constant of proportionality (catchability) and vt ~ N(0, σ). The parameters σ and q were treated as uncertain but the maximum likelihood estimate  (MLE) of q in the joint posterior distribution was used, taking the approach of Walters and Ludwig (1994), i.e., assuming a linear relationship between CPUEt and VBt, we estimated zt =  ln(CPUEt ) − ln (VB t ) and  ∞  (2.10) z =  ∑z t  n  t  .  35  The MLE of q was then e z and the observation residuals (dt) used in the log likelihood function were calculated as d t = zt − z . The log likelihood of each observation was thus  (2.11) Lt = ln (σ ) + 0.5 ln(2π ) +  dt  2  2σ v  2  .  Uninformative prior probability distributions were assumed for UMSY and MSY in Model 1 and for R0 in Model 2. A normally distributed prior for M was assumed, i.e., M ~ N(0.21,0.1), with the mean based on the assumption M = 1.5κ (Beverton and Holt 1959). A weak, lognormally distributed informative prior for CR to penalise negative (i.e., impossible) values of CR was also assumed. R0, CR and MSY were log transformed so the relative scales of parameters in the search routine were similar. UMSY was logit transformed to constrain values between 0 and 1. MSY and UMSY had to be estimated numerically in Model 2. For each θ, a Newton-Raphson algorithm was used to search over the derivative of the yield function (equation 2A.1) with respect to U to find the value of U that maximised yield. Note that the most current parameters for these hake species may not have been used and the selectivity schedule is likely incorrect. The choice of priors for CR and M will also influence the results, which should therefore be read as illustrative only.  Results The weak prior placed on CR had the effect of constraining the posterior values of UMSY and MSY to values that were not associated with impossible recruitment parameters (see life history section). The prior placed on M constrained this parameter within plausible biological bounds (i.e., close to 1.5κ; Beverton and Holt 1959) and therefore also prevented UMSY from becoming large. The choice of ah relative to amat also affected the results. For fish populations where most individuals vulnerable to the fishing gear have already had the opportunity to spawn, UMSY must approach unity. Alternatively, harvesting a population at an age before most individuals have spawned results in lower sustainable harvest rates. This is implicit in Figure 2.1a. 36  Figure 2.3 shows density plots of the posterior distributions of the leading parameters in each model. The two models give very similar results for the biological parameters and almost identical results for the management parameters. Note that R0 and CR were obtained analytically in Model 1 and that MSY and UMSY were estimated numerically in Model 2. There was no evidence that the parameter estimates did not converge (Figure 2.4). Figure 2.3 shows that estimation of key management parameters was robust to the choice of leading parameters.  Discussion Schnute and Kronlund (1996) derived α from UMSY for semelparous species. They demonstrated the advantages of their re-parameterised recruitment function in terms of its amenability to Bayesian fitting procedures and, because a parameter with policy relevance could be directly estimated from data, improved communicability of results. The idea was extended to a generalised age-structured model for iteroparous species by Schnute and Richards (1998), who assumed knife-edge maturity and recruitment. The approach presented here extends these previous works by allowing the inclusion of age-specific maturity and recruitment via the Botsford (1981) “incidence” functions, which incorporate age-schedules of fecundity, mortality and vulnerability. The approach was demonstrated using logistic, age-based selectivity and maturity schedules, but the approach is flexible to any formulation of these. For example, domeshaped or log-normal selectivity curves may be more appropriate for species where large or old individuals are able to escape fishing due to behavioural, spatial or market-based effects. Certain simplifying assumptions were made, notably that natural mortality, M = 1.5κ. This relationship, suggested by Beverton and Holt (1959) to be an invariant property of fish populations, is widely applied in fisheries models. However, the model is flexible to this assumption, as well as to the assumption that M is constant with age. The model was used to illustrate some important relationships between density dependence, life history traits and UMSY. It is stressed that the relationship between CR and UMSY shown in Figure 2.1 is not dynamic, but rather represents the degree of improvement in juvenile survival that would be required for each hypothesised value of UMSY to be true. For a species with a given 37  growth, survival, maturity and selectivity schedule, there will be a mean curve describing the relationship between UMSY and CR representing the set of values of CR and UMSY that can be considered possible for the species. This curve can be calculated from life history and selectivity parameters alone, prior to any time series fitting. Figures 1 implies that, for some species, there will be a finite range of possible values of UMSY, with its upper bound at the asymptotic value of UMSY. This is because UMSY maximises yield in terms of weight and is therefore determined by growth, survival and selectivity (Beverton and Holt 1957). The upper bound of UMSY represents the harvest rate beyond which long term yield can no longer be maximised for a given growth and selectivity schedule, no matter how strong recruitment compensation is. If there is no other prior information about the productivity of a species and Beverton and Holt type recruitment can be assumed, there is therefore an upper boundary of UMSY that can be estimated from life history and selectivity data alone. For species with very steep UMSY-CR curves (curves with an upper boundary very far to the left of the UMSY-axis), uncertainty in UMSY can be reduced considerably, even if the actual value of UMSY cannot be estimated due to lack of historical data. If reasonable estimates of CR are available for similar species or from meta-analysis, it may also be possible to construct a reasonable prior for UMSY for data-limited species. The effects of selectivity and life history parameters on the relationship between CR and UMSY are not surprising. Increasing (long-term) age at 50% first harvest, ah, causes the UMSY-CR curve to become less steep and shift to the right (Figure 2.1a). Assuming that the value of CR is a fixed property of a population independent of ah, this implies that a greater maximum sustainable harvest rate could be achieved by more selective fishing gear allowing younger fish to escape. This idea is a well-known result of per-recruit type analyses (Beverton and Holt 1957). The relationship between κ and UMSY was also very strong. In the equilibrium formulation, κ was used in the model twice: 1) as growth rate affecting the rate at which fish reach maximum weight; and 2) as a proxy for natural mortality, M, affecting the survivorship schedule (equation 2.3). Although these two effects were confounded, they had the same qualitative effect on the UMSY-CR curve, i.e., increasing κ caused the curve to become less steep. For a given value of UMSY the amount of recruitment compensation required to support that UMSY was less for fastergrowing species because: 1) asymptotic maximum weight was reached earlier; and 2) the population had faster turnover. Increasing age at maturity, amat, had a weak influence on the relationship between κ and UMSY, although it did cause a slight increase in steepness and a shift 38  to the left. All other things equal, species with later maturity have a smaller lifetime reproductive capacity and a greater chance of being harvested before they have reproduced. Increasing maximum age, amax, similarly caused the curve to shift to the left. Higher CR required to support a given UMSY for longer lived species could be a result of the relatively smaller contribution of older age classes to the total yield due to the decaying survivorship function. It should be noted that life history parameters tend to covary and can rarely be considered in isolation, i.e., longer-lived species tend to mature later, grow slower, have lower natural mortality. The effects of single parameters on the steepness of the UMSY-CR curve were singled out, not because these curves necessarily have applicability in themselves, but because they allow the complexity of the interaction among life history traits, selectivity, density dependence and sustainable harvest rate to be seen. Maximum sustainable harvest rate is not a simple function of selectivity, density dependence or individual life history parameters but a complex result of them all. Simplistic assumptions about the effects of one of these factors on UMSY should not be made without consideration of the other influential factors. Life history information is easier and cheaper to obtain than recruitment and abundance data, and is routinely collected. Growing conservation concerns and current trends towards more ecosystem-based approaches of managing fisheries (e.g., FAO 2003; Pikitch et al. 2004) require consideration of the impacts of fisheries on many more species than previously and there is now a very large body of literature studying the link between life history traits and productivity for data-limited fish. For example, McAllister et al. (2001) demonstrated three approaches that could be used to estimate r for elasmobranchs using only life history information. Beddington and Kirkwood (2005) presented a method for estimating FMSY based on Beverton and Holt (1959) invariants and parameters describing growth, length at first capture and the steepness parameter, h. Goodwin et al. (2006) showed correlations between a composite life history parameter (unfished spawners per recruit, SPR0), α and the compensation ratio, CR, for 54 Atlantic teleosts for which stock-recruitment data were available. They found a strong negative correlation between SPR0 and α, and a positive correlation between SPR0 and CR and discussed evolutionary reasons for these observations. Jennings et al. (1999) and Denney et al. (2002) also searched for correlations between life history and productivity. The general approach of these papers was to analyze stocks for which informative data exists about productivity (e.g., 39  population response to fishing pressure) and draw conclusions that could be used in development of management strategies for data-limited species. It is suggested that the model could contribute to such approaches as it provides a link between life history, density-dependence and UMSY simultaneously. A simple Bayesian estimation routine was used to illustrate the parameter estimation process. A model with leading management parameters (MSY and UMSY) was compared with a model structurally identical except for its leading parameters (R0 and CR). The same posterior probability densities for management parameters were obtained in both cases. However, it is argued that the first model is advantageous for two reasons: 1) it is more efficient (there is no need to numerically estimate MSY and UMSY); and 2) it enables improved communication of scientific results. Determination of appropriate informative priors is one of the most difficult aspects of stock assessment (see Punt and Hilborn 1997) and the preliminary phases of stock assessment often involve intensive modelling and testing sessions to determine plausible ranges of leading biological parameters. These ranges are often based on the plausibility of the model’s predicted MSY (or UMSY). Hoenig et al. (1994) have suggested methods for constructing informative priors on MSY based on historical catch and effort data. Simple analytical relationships have also been suggested for obtaining rough estimates of MSY and UMSY (e.g., Gulland 1971; Patterson 1992), which could be used in construction of priors. Models such as the one presented here and that of Schnute and Richards (1998) enable this information to be used in direct estimation of UMSY, a parameter of primary management interest. It is suggested that dialogue between scientists and managers will be improved if the parameters at the forefront of the analysis are familiar to all parties. It is also suggested this may work in both directions, as managers with a long history of involvement in a fishery will be better able to contribute to the stock assessment process if the focus is on parameters with which they have direct experience. In summary, this chapter has presented a model with several advantages: 1) it enables direct estimation of parameters of principle management interest; 2) it is flexible to a very wide range of assumptions about growth, survival, maturity and selectivity, including the form of these relationships; and 3) it provides a means of analysing the interaction among important selectivity and life history parameters, density dependence and maximum sustainable harvest rate. It is  40  amenable to Monte Carlo-type approaches to account for uncertainty in input parameters as well as to Bayesian or likelihood approaches for estimating leading parameters.  Acknowledgements James Scandol and three anonymous reviewers provided for useful comments on this and an earlier version of the manuscript. Robert Ahrens, Olaf Jensen and William Pine gave helpful advice during development of the paper. This work was funded in part by the Charles Gilbert Heydon Travelling Fellowship in Biological Sciences, awarded to R.F. by the University of Sydney, Australia; by a grant provided to the UBC Fisheries Centre by the NSW Department of Primary Industries, Australia; and through a National Sciences and Engineering Research Council of Canada (NSERC) Scholarship to M.M.; and through an NSERC Discovery Grant to C.W.  41  Tables Table 2.1. Life-history and selectivity parameters used in the model. Parameters are described in the text. Parameter L∞ κ a0 lwa lwb amax amat ah  Hypothetical fish 60 cm 0.12 y-1 -0.5 0.0001 3 15 y 2y 3y  Namibian hake 111 cm a 0.14 y-1 a 0 0.00001 b 3b 25 y b 4yc 3yd  a. Jones 1974 (cited in FishBase, www.fishbase.org). b. These parameters produced the approximate mean maximum weight cited in FishBase (www.fishbase.org). c. Hilborn and Mangel 1997. d. Arbitrarily assigned.  42  Figures  100 (a) 80  Derived compensation ratio  60  100 (b)  2 3 4  60  40  40  20  20  0  0 0.00  100 (c) 80 60  0.10  0.20  0.30  0.0 100 (d)  1 4 6  80 60  40  40  20  20  0  0 0.00  0.10  0.1 0.2 0.3  80  0.20  0.30  0.00  0.2  0.4  0.6  0.20  0.30  10 15 20  0.10  Leading UMSY Figure 2.1. Effect of different parameters on the relationship between leading productivity parameter UMSY and the derived compensation ratio, CR for a hypothetical species. Graphs show (a) age-at-50%-first-harvest, ah (years); (b)von Bertalanffy growth rate, κ (year-1); (c) age-at50%-maturity, amat (years); and (d) maximum age, amax (years) Parameter values are provided in Table 1. Note truncation of the y-axis at CR = 100 and different scales on the x-axes.  43  600  2.0  (a)  1.5  400  CPUE  Catch  500  (b)  300 200  1.0 0.5  100 0  0.0 1965  1975  1985  1965  1975  1985  Year  Figure 2.2. (a) Catch (thousands of tons) and (b) CPUE (tons per standardised trawler hour) for Namibian hake, used to fit the models. Data source: Hilborn and Mangel (1997).  44  Relative density  1.0  1.0  (a)  0.8  0.8  0.6  0.6  0.4  0.4  0.2  0.2  0.0  0.0 1000  1.0  4000  0  R0  Compensation ratio 1.0  (c)  0.8  0.8  0.6  0.6  0.4  0.4  0.2  0.2  0.0  0.0 150  (b)  250 MSY  350  50  100  (d)  0.15  0.30  0.45  U MS Y  Figure 2.3. Density plots showing relative posterior probability density distributions of R0, CR, MSY and UMSY for Model 1 (dashed line) and Model 2 (solid line). Plots obtained from MCMC sample of length 100,000 (burn-in: 10,000 cycles).  45  (a)  0.3  R0  U MS Y  0.4 0.2 0.1  (b)  250  CR  MSY  300  200  0.6  (c) M  M  (g)  0.4  (d)  0.25  (h)  0.20 σ  σ  (f)  0.2  0.2  0.20  (e)  0.3  0.3  0.25  120 100 80 60 40 20 0 0.5  0.5 0.4  6 5 4 3 2 1  0.15  0.15  0.10  0.10  Iterations (thousands) Figure 2.4. Trace plots of iterations vs sampled values for each estimated parameter indicating convergence of the estimates. Results are shown for Model 1: (a) UMSY, (b) MSY, (c) M and (d) σ; and Model 2: (e) R0 (thousands), (f) CR, g) M and h) σ.  46  Chapter 3. Extension of a meta-analysis of 54 fish stocks for evaluating effects of life history, selectivity and density dependence on optimal harvest rate UMSY Introduction With the widespread adoption of ecosystem-based fisheries management (EBFM) around the world (FAO 2003; Pikitch et al. 2004; Pitcher et al. in press), the discussion of sustainable harvesting has shifted to include a much broader range of species than previously. With this has come recognition of the need for new approaches and frameworks for risk assessment of datalimited species (e.g., Smith et al. 2007). A basic need for risk assessment for a fish population is an estimate of its productivity. Productivity is a general term that refers to mortality and growth of individuals and recruitment. Recruitment productivity is usually represented by a measure of the degree of density dependence in recruitment, i.e., improvement in juvenile survival rate as adult stock size is reduced (reviewed by Rose et al. 2001; Myers 2002). Commonly-used parameters representing density dependence in recruitment include α, the maximum juvenile survival rate of the Ricker (1954) and Beverton-Holt (1957) stock-recruitment functions; CR, the recruitment compensation ratio (Goodyear 1977; see Figure 1.2 and Chapter 2); and steepness, h (Mace and Doonan 1988). A key role of fisheries scientists is identification of thresholds of fishing mortality that should be avoided to prevent overfishing (reviewed by Caddy and Mahon 1995). Stocks are said to be subject to growth-overfishing if they are harvested while individuals are still in the rapid growth phase, implying that greater yields could be achieved if fish were allowed to grow larger before being harvested. Recruitment overfishing is a more serious, but less well-defined, biological issue that occurs when a stock’s ability to reproduce itself is compromised by fishing mortality rates that are too high. The fishing mortality rate that would produce maximum sustainable yield, FMSY, is, by definition, a valid limit reference point for growth-overfishing. Generally, the recruitment overfishing threshold is understood to be around double the growth overfishing threshold (Goodyear 1993; Mace 1994; 2001; Restrepo et al. 1998; but see Cook et al. 1997, Punt 2000 and NAFO 2003 for studies showing that fishing mortality thresholds for growth and 47  recruitment overfishing may be closer together for less productive species). A well-known recommendation is that fish stocks should be managed to avoid growth overfishing, as this will also prevent recruitment overfishing (Gulland 1971). A precautionary means of achieving this is to control selectivity (i.e., the age at which fish become vulnerable to fishing gear) and ensure that fish are given at least one chance to spawn before being harvested (Myers and Mertz 1998; Froese 2004; Froese et al. 2008). There is now a large body of literature studying the link between life history and FMSY in order to better estimate overfishing thresholds for data-limited fish stocks. Gulland (1971) expressed maximum sustainable yield as a function of the natural mortality rate, M, and unfished biomass, B0, where yield was equal to 0.5MB0. Kirkwood et al.(1994) suggested that, when density dependence in recruitment was accounted for, the proportion of unfished biomass was likely to be of the order of 0.1-0.3M. Beddington and Kirkwood (2005) presented a new method for estimating FMSY based on Beverton and Holt (1959) invariants and parameters describing growth, length at first capture and an estimate of steepness. Recently, meta-analysis has become popular as an approach for gaining insight about productivity from data-rich stocks, in order to derive general rules for estimation of productivity that can be applied to data-poor stocks. Meta-analysis has been used to estimate recruitment productivity parameters directly (e.g., Myers et al. 1999; Dorn 2002; Michielsens and McAllister 2004; Sadovy et al. 2007) and also to identify life history traits that correlate well with productivity. For example, there have been a number of recent papers that have correlated life history parameters with empirically observed changes in abundance after fishing (e.g., Jennings et al. 1998; 1999; Dulvy et al. 2004; 2005; Cheung et al. 2005; 2007). Patterson (1992) reviewed stock assessments for 28 pelagic fisheries and concluded that pelagic stocks have tended to collapse when fishing mortality has exceeded 60% of the natural mortality rate, M. This suggests that the commonly-used rule of thumb of F = M (Schaefer 1954; Gulland 1971) may be too incautious to avoid recruitment overfishing of pelagic stocks. Others have found correlations between life history and productivity parameters (including maximum population growth rate: Cortés 1998; Smith et al. 1998; Denney et al. 2002; steepness: Rose et al. 2001; and CR, the recruitment compensation ratio: Goodwin et al. 2006). Goodwin et al. (2006) used standardised unfished spawners per recruit (SPR0; Gabriel et al. 1989) as a composite life history parameter to test for relationships between life history and recruitment parameters. They found a strong negative correlation between lnSPR0 and lnα, and a 48  weaker positive correlation between lnSPR0 and lnCR. They suggested that stocks with low SPR0 (e.g., fast-turnover stocks like herring and anchovy) could be fished down, even at low harvest rates, but were resilient to extirpation because of high reproductive rates at low stock size. Alternatively, longer-lived, slower-growing and later-maturing stocks with high SPR0 (e.g., cod, halibut) could likely sustain higher harvest rates without being fished down due to strong recruitment compensation, but would be more vulnerable to extirpation if severely overfished. Chapter 2 (published as Forrest et al. 2008) quantified the relationship between measures of recruitment compensation (α and CR) and optimal harvest rate UMSY in an age-structured model, assuming Beverton-Holt recruitment. It showed that the relationship is strongly affected by certain life-history traits (especially growth rate and maximum age) and, especially, by the age at which species are first captured by the fishing gear (Chapter 2; Figure 2.1). Goodwin et al. (2006) suggested that conclusions about responses of fish stocks to different levels of fishing mortality could be made with an understanding of the compensation ratio, as predicted by SPR0. If this were the case, a logical extension of their work would be to show a predictive relationship between SPR0 and UMSY, which, if it existed, would be very useful for application to data-limited stocks. The analytical relationships between α, CR and UMSY developed in Chapter 2 presents a means of testing whether such a relationship exists, for stocks where life history and recruitment parameters are available. The parameters provided by Goodwin et al. (2006) provide a sufficiently complete dataset for testing this relationship. Therefore, using the model presented in Chapter 2, the work of Goodwin et al. (2006) is extended through calculation of UMSY for their 54 stocks, under assumptions of both Ricker (1954) and Beverton-Holt (Beverton and Holt 1957) recruitment, given the estimates of CR and life history and selectivity parameters they provided. Correlations between life history parameters and UMSY are then explored. The effect of age-at-recruitment to the fishery, which is under management control, is also evaluated. The work presented in Chapter 2 is extended in a number of ways. Firstly, bbecause Ricker recruitment was assumed by Goodwin et al. (2006), the relationship between α and UMSY for the Ricker model is derived. Secondly, relationships between life-history and selectivity parameters, density dependence in recruitment (measured by CR) and UMSY are examined more thoroughly. Thirdly, a graphic  49  approach is proposed for identification of stocks for which UMSY could be significantly increased through changes to the selectivity schedule and stocks for which it could not. Note that this study makes use of the parameter-estimates of Goodwin et al. (2006) in order to explore inter-relationships between life history, selectivity, density dependence and UMSY and, for tractability, makes a number of simplifying assumptions. The results presented here do not account for the many complexities of management of Atlantic fisheries and should not be considered a stock assessment for these populations.  Methods Deriving UMSY for 54 Atlantic stocks  Chapter 2 showed how the maximum juvenile survival rate, α, could be expressed as a function of UMSY when the Beverton-Holt stock-recruitment function was assumed. Goodwin et al. (2006) fitted Ricker curves to their stock-recruitment data and reported associated values of α and CR. Therefore, for comparative purposes, a Ricker version of the relationship between α and UMSY was derived. Note that α and CR are equivalent in both Ricker and Beverton-Holt stock recruitment functions (Myers et al. 1999), and the estimates of CR presented by Goodwin et al. (2006) can therefore be used to derive UMSY using both models. Derivation of the relationship between α and UMSY for the Ricker model was done following the steps in Appendix A to Chapter 2, replacing the Beverton and Holt recruitment function with the equilibrium version of the Ricker function, i.e.,  (3.1)  R=  ln(ϕ E α )  β ϕE  where R is equilibrium recruitment and φE is equilibrium eggs per recruit (Chapter 2, equation 2.2). Note that equation 3.1 was obtained by substituting E = RφE into the Ricker equation:  50  R = αEe-bE (Ricker 1954), where E is eggs, here assumed directly proportional to spawning stock biomass. As in Chapter 2, equilibrium yield is assumed to be given by (3.2)  Y = URφVB  where U is long term annual harvest rate and φVB is equilibrium vulnerable biomass per recruit. Substituting Equation 3.1 into Equation 3.2, taking the derivative and setting it to zero (thereby identifying the local maximum, or MSY), and solving for ln(α) gives:  (3.3)  ln (α ) =  − U MSY ϕVBMSY  ϕ EMSY ϕVBMSY + ϕ EMSY U MSY  ∂ϕ EMSY ∂U MSY  ∂ϕVBMSY ∂ϕ EMSY − ϕVBMSY U MSY ∂U MSY ∂U MSY  − ln (ϕ EMSY )  where φE and φVB are evaluated at UMSY. See Appendix A to Chapter 2 for solutions to and  ∂ϕ E ∂U MSY  ∂ϕVB . α is then obtained by taking the exponent of equation 3.3. α is a unit-dependent ∂U MSY  parameter and, therefore, not directly comparable among stocks, as different units may have been used to measure spawning stock biomass or eggs. Therefore, α was standardised across stocks by dividing by the unfished juvenile survival rate φE-1 to give the recruitment compensation ratio CR (Goodyear 1977; Myers et al. 1999; see Chapter 2), i.e., CR = αφE0 (see Figure 1.2). It is important to realise that the relationship between UMSY and CR is determined by a population’s individual life history and selectivity schedule and, given this relationship, there is a unique value of CR implied by each hypothesised value UMSY for a population. However, while CR can be calculated analytically, using equation 3.3, given a hypothesis for UMSY, there is no analytical solution for the reverse relationship (i.e., equation 3.3 cannot be re-arranged and solved for UMSY because φEMSY and φVBMSY are themselves recursive functions of UMSY; see 51  equation 2.2 and 2.3). However, given the values of CR published by Goodwin et al. (2006), it was possible to obtain the corresponding estimate of UMSY for each stock, by calculating CR over a discrete, finely-resolved sequence of hypotheses for UMSY until the observed value of CR was reached. The UMSY hypothesis that produced the published value of CR was then the appropriate value of UMSY for that particular stock. This is illustrated in Figure 3.1. This procedure was done for the 54 stocks considered by Goodwin et al. (2006). For comparison, the analysis was repeated using the Beverton-Holt form of equation 3.3 (Chapter 2, equation 2A.6) and the Beverton-Holt stock-recruitment function (equation 2.1). In both cases, a plus group was used to account for unobserved older age classes and the correction to the derivative of survivorship with respect to UMSY, shown in equation 2A.10, was used. Equations 2A.6 and 3.3 show that the relationship between α and UMSY is insensitive to stock size and the model was therefore initialised at a baseline of B0 = 1. Life-history parameters and ages-at-recruitment were published by Goodwin et al. (2006). Parameters were missing for some species and were obtained from FishBase (Froese and Pauly 2008; see Table 3.1 for values). For species where W∞ was not provided, L∞ was first obtained from FishBase then converted to W∞ using length-weight parameters obtained from FishBase (Table 3.1). Goodwin et al. (2006) used direct estimates of the fecundity schedule. In the absence of this information, fecundity, fa, was here assumed to be directly proportional to weight at age, wa, through the relationship fa = wa Mata, where Mata is maturity-at-age, assumed to be described by a logistic maturity curve (see Chapter 2, Appendix B), with age-at-50%-maturity, amat, set to the value published by Goodwin et al. (2006) and the steepness parameter, σ, assumed to be 0.1amat, which assumes almost knife-edged maturity at amat. The natural mortality rate, M, was assumed constant across age classes and the natural survival rate, s, was assumed to equal e-M for all age classes (Beverton and Holt 1959). Note that all summations (i.e., the survivorship function, equation 2.3, and all parameters derived from it) were initiated at age-at-recruitment to the fishery, ah. This is because Goodwin et al. (2006) defined a recruit as a fish entering the fishery rather than the population.  52  Uncertainty in parameter values  Because of uncertainty in input parameters, 100 Monte Carlo simulations were used to obtain confidence intervals for the estimates of UMSY. Life history parameters that were treated as random variables were the von Bertalanffy growth rate, κ; the natural mortality rate, M; maximum weight, W∞; and amat. κ and M were assumed to be lognormally distributed with mean set to the natural logarithm of the published value and coefficient of variation (CV) of 20% of this mean. This was done to prevent drawing negative values of these parameters, as the mean value was already close to zero. W∞ and amat were assumed to be normally distributed with mean set to the published value and CV of 20% of this mean. The 20% CV was selected to enable uncertainty to be accounted for without departing too far from parameters characteristic of each stock. Correlations between life history and selectivity parameters and UMSY The input parameters and calculated values of UMSY provide a dataset that enabled testing for correlations between life history and selectivity parameters and UMSY. Goodwin et al. (2006) showed that lnSPR0 is a reasonable predictor of lnCR, suggesting that lnSPR0 might be a reasonable indicator of UMSY. The correlation between lnSPR0 and UMSY was also, therefore, tested. For all parameters, the Pearson’s correlation coefficient, r, between UMSY and the natural logarithm of the input parameters was calculated and tested for significance. Parameters were log transformed to reduce variance.  Effect of selectivity on UMSY  As in Goodwin et al. (2006), selectivity was assumed to be knife-edged (i.e., all individuals of an age-cohort are fully vulnerable to the fishing gear when they reach ah). Age-at-recruitment is an important determinant of UMSY and has a strong effect on the relationship between CR and UMSY (Chapter 2). This means that for a given level of recruitment compensation in a stock, increasing the age at which fish are first harvested increases the proportion of the remaining vulnerable stock that can be sustainably harvested. Many of the 54 stocks had reported ah of 0 or 1, suggesting that UMSY for these stocks could be limited by their current selectivity schedule. Therefore the analysis was repeated for a range of values of ah (0-6). 53  Results Derived estimates of UMSY  Mean derived estimates of UMSY (+ standard error) from the 100 Monte Carlo runs for each stock, under both Ricker and Beverton-Holt stock-recruitment assumptions, are shown in Figure 3.2. Overall, the Ricker model predicted higher UMSY than the Beverton-Holt model and, overall, the range of values of UMSY predicted by the Beverton-Holt model was much smaller than that predicted by the Ricker model. Mean predicted values of UMSY from the Ricker model ranged from 0.07 (Atlantic horse mackerel 1) to 0.68 (Atlantic cod 6), while mean UMSY ranged from 0.06 (Atlantic horse mackerel 1) to 0.46 (Whiting 3) under the Beverton-Holt stock-recruitment relationship. Linear regression of the predicted Ricker UMSY against the Beverton-Holt UMSY showed Ricker estimates to be, on average, 1.13 times higher than Beverton-Holt estimates (UMSY Ricker = 1.13UMSY BH + 0.11). Under Ricker recruitment, the three stocks with extremely high CR (Atlantic cod 6 and 7 and European anchovy; Table 3.1) also had the highest mean UMSY and the stock with the lowest CR (Atlantic horse mackerel 1) had the lowest mean UMSY. The correlation between lnCR and UMSY was positive and highly significant (Figure 3.3a; r = 0.72, P < 0.001, 52 df). Under BevertonHolt recruitment, however, while the stocks with the lowest predicted UMSY also had the lowest CR, the trend did not continue to stocks with the highest CR and the correlation between lnCR and UMSY was not significant (Figure 3.3b; r = 0.02, n.s., 52 df). The strong significant correlation between lnCR and UMSY in the Ricker model was mainly due to the three stocks with extreme estimates of CR (Figure 3.3a). Removal of these stocks resulted in a reduced correlation coefficient, although the relationship was still significant (r = 0.46, P < 0.01, 49 df). The relationship between CR and UMSY under the two different stock-recruitment functions is explored more fully in a later section. Correlations between UMSY and life history parameters Correlations between the mean estimate of UMSY from the 100 Monte Carlo simulations and mean logged values of M, amat, κ, W∞, amax and SPR0 are shown in Figures 3.4 and 3.5, with 54  correlation coefficients shown in Table 3.2. Under Ricker recruitment, none of the relationships were significant except for lnM, which was significantly positively correlated with UMSY (P < 0.05, df = 52). Under Beverton-Holt recruitment, the correlation between M and UMSY was highly significant (P < 0.001, df = 52). Correlations between lnκ (P < 0.001, df = 52) and lnamax (P < 0.001, df = 52) were also highly significant. The correlation between lnSPR0 and UMSY was non-significant in both models (Figure 3.4f and 3.5f).  Relationship between density dependence, SPR0 and UMSY  Because some of the life history parameters used in this study were different from those used by Goodwin et al. (2006), the relationship between their published values of SPR0 and the ones obtained in the present study was checked (Figure 3.6a). The correlation between the value of SPR0 obtained in the present study and the published value of CR was also checked for consistency with the results of Goodwin et al. (2006). Estimates of SPR0 from the present and previous studies were very strongly correlated (r = 0.94, P < 0.001, df = 52). The slope of the linear regression between the SPR0 estimates from the two studies was 1.16, implying that the current study had systematically overestimated SPR0 compared to the previous study. This may have been due to the different parameters used for some species or assumptions about the length weight relationship or the relationship between fecundity and weight. It can be noted, however, that a systematic overestimation of SPR0 would not affect subsequent correlations between SPR0, CR and UMSY. The correlation between the present value of lnSPR0 and published lnCR (Figure 3.6b) was also significant (r = 0.44; P < 0.01, df = 52) and very similar to that reported by the other authors (r = 0.48; P < 0.001; 52 df; note they reported the r2 value). Therefore the non-significant correlation between lnSPR0 and UMSY could not simply be attributed to different values of SPR0 used in the present study. The poor correlation between lnSPR0 and UMSY can be partly explained by considering the effects of life history parameters on the relationship between CR and UMSY. The value of SPR0 for a given stock is determined by the combined effect of several different life history parameters (see equations 2.2 and 2.3, where φE0 is the equivalent of SPR0). This is illustrated in Figure 3.7 for a hypothetical stock with parameters given in Table 3.3. In each case, SPR0 was calculated with all other parameters held constant while the parameter under consideration was varied. 55  Figure 3.7 shows that, all other parameters equal, W∞ and κ have a positive effect on SPR0, while amat and M have a negative effect. Because of these directional effects on the value of SPR0, and because there are trade-offs and correlations among certain parameters in nature (Jensen 1996; Winemiller 2005), the same value of SPR0 can be obtained under a number of different parameter-combinations. For example, a smaller species that matures early could have the same SPR0 as a larger, later-maturing species. Similarly, a small, fast-growing species could have the same SPR0 as a larger, slower-growing species, all other parameters equal. The composite parameter SPR0 has no power to distinguish the values of component parameters. Now consider the influences of these parameters on the relationship between UMSY and CR. Chapter 2 showed that the location of the curve describing the relationship between UMSY and CR (the UMSY-CR curve) is strongly affected by certain life history and selectivity parameters (Figure 2.1). For example, increasing κ causes the curve to become less steep and shift to the right, whilst changing W∞, has no influence. Effectively, this means that increasing κ allows a greater range of values of UMSY to be considered possible (where actual UMSY is unknown because CR is unknown). This is illustrated in Figure 3.8a, which shows UMSY-CR curves for five hypothetical stocks (Table 3.3) with very similar values of SPR0 (SPR0 ~ 9). Each stock has a different pair of values of κ and W∞ with all other parameters held constant (Table 3.3). Stock 1 represents a small, fast-growing species, while Stock 5 represents a larger, slower-growing species. W∞ has no effect on the location of the UMSY-CR curve and, therefore, the differences among location of the curves in Figure 3.8a are due to the effect of decreasing κ. The stock with the highest value of κ (Stock 1) has the rightmost curve and, therefore, the largest range of possible hypotheses for UMSY over the range of CR shown. Similarly, the stock with the lowest value of κ (Stock 5) has the smallest range of possible hypotheses for UMSY. Figure 3.8a shows that assuming the same value of CR for these five stocks would result in five different values of UMSY - despite them all having the same SPR0. Similar effects would be seen by varying amax, M and ah (Chapter 2; see next section for further discussion of the effect of ah). Given that there are several parameters contributing to the value of SPR0, it is easy to see that many different combinations of parameters could result in a similar value of SPR0. Therefore, since the contributing parameters have different effects on the relationship between UMSY and CR, knowledge of SPR0 alone is insufficient to predict UMSY. 56  Figure 3.8b shows the UMSY-CR curves for the same five hypothetical stocks under BevertonHolt recruitment (calculated using equation 2A.6). In this case, the same effect of κ on the location of the curves can be seen, but the shape of the curves is markedly different. Differences between the shapes of the Ricker and Beverton-Holt UMSY-CR curves are due to the different properties of equations 2A.6 (Beverton-Holt) and 3.3 (Ricker). A key difference between them is that the Beverton-Holt formulation, under many life-history and selectivity-parameter combinations, predicts UMSY to approach a vertical asymptote, beyond which α is undefined (i.e., predicted to be negative). This asymptote occurs at the value of UMSY for which the denominator of equation 2A.6 is equal to zero. It is therefore defined as the value of UMSY for which UMSY = k2-1 (where k2 =  ∂ϕVBMSY ϕVBMSY −1 ; see Chapter 2, Appendix A). Note that UMSY = - k2-1 cannot be ∂U MSY  solved analytically for UMSY because ϕVBMSY is a recursive function of UMSY (see equation 2.3). Truncation of the range of UMSY, due to this effect, explains the smaller range of UMSY estimates obtained for the 54 Atlantic stocks with the Beverton-Holt model compared with the Ricker model, which does not share this property (the limits of UMSY prevent equation 3.3 from becoming undefined).  Relative effects of selectivity  The above sections have treated age-at-recruitment to the fishery as a fixed parameter, when it is actually under management control, through measures such as mesh and hook size or spatial extent of the fishery. Table 3.4 shows predicted values of UMSY for the 54 stocks for an ascending sequence of values of ah. Four examples are shown in Figure 3.9, all of which show that predicted UMSY increases with ah. This is not a surprising result. It is noteworthy, however, that: i) the magnitude of difference between the highest and lowest predicted values of UMSY differs among stocks; and ii) while the Ricker recruitment model suggested that there were some values of ah for which it would be optimal to fish all of the vulnerable stock (UMSY = 1), this was rarely the case under the Beverton-Holt assumption. The large increase in UMSY with ah shown by many stocks implies that UMSY is strongly limited by selectivity for these stocks. For some stocks, however, where the increase in UMSY with ah 57  was small, UMSY was more strongly limited by life history or recruitment parameters than selectivity (i.e., increasing ah did not significantly increase UMSY). Two of the example stocks in Figure 3.9 (Haddock 5 and Atlantic herring 1) showed a large increase in predicted UMSY as ah increased, under both types of recruitment. The other two stocks (Atlantic horse mackerel 1 and Greenland halibut), however, showed very small increases in predicted UMSY with increasing ah. The effect was more pronounced under Beverton-Holt recruitment (i.e, less increase in UMSY with increasing ah). Plotting the relationship between CR and UMSY can be instructive for understanding these results. Figure 3.10 shows the UMSY-CR curves for the four stocks shown in Figure 3.9 under the seven values of ah. The value of CR reported for each stock in Goodwin et al. (2006) is shown on each graph as a horizontal dashed line. Understanding the relationship between selectivity, density dependence and UMSY is fairly straightforward for the first two stocks. The relationship between CR and UMSY is strongly affected by ah, with increasing ah shifting the UMSY-CR curve to the right. Therefore, as ah increases, there is a large increase in the value of UMSY predicted by the stock’s fixed value of CR (compare the values of UMSY at the intersections of the UMSY-CR curves and the horizontal CR line in Figure 3.10). For the other two stocks, increasing ah did not greatly increase predicted UMSY (Figure 3.9). However, the reasons differed slightly between the two stocks. Under Ricker recruitment, increasing ah for Atlantic horse mackerel 1 had quite a large effect on the location of the UMSY-CR curve, but the estimated value of CR was so low (CR = 4.7) that the realised effect of ah on UMSY was very small (Figure 3.10). Under Beverton-Holt recruitment for this stock, ah had a lesser effect on the location of the UMSY-CR curve. However, a larger range of values of UMSY could have still been realised with higher CR (Figure 3.10). Therefore, very low CR was the main factor limiting UMSY for this stock. For the final stock (Greenland halibut), CR was quite high (37.9) but the curves themselves were highly constrained by life history parameters (Figure 3.10), i.e., increasing ah had relatively little effect on the location of the curve and, therefore, the predicted value of UMSY was similar across ah. Therefore, life history traits were the main limiting factor of UMSY for this stock. Compared to most of the other stocks, Greenland halibut was long-lived and late-maturing (amax = 15; amat = 9.2) with a relatively low natural mortality rate (M = 0.15).  58  Curves for all 54 stocks are shown in the Appendix to Chapter 3. Stocks have been categorised into three categories, representing stocks for which mean predicted UMSY was ‘selectivitylimited’, ‘recruitment-limited’ and ‘life history-limited’. Recruitment-limited stocks were defined as those with CR < 10. This captures stocks such as Atlantic horse mackerel 1 (Figure 3.11), for which the range of UMSY was small, due mainly to the low value of CR. Stocks predicted to be recruitment limited are identified in Table 3.4 (graphs are shown in the Appendix to Chapter 3: Figure 3A.1 and 3A.2). Anomalies in this group were Norway pout and sandeel, which still had relative high UMSY despite very low CR (CR = 3.1 and 4.82 respectively). These species were both very short-lived (amax = 4) and therefore had very shallow, rightward UMSYCR curves and therefore intersected with the CR line at higher values of UMSY than the other stocks. Life history-limited stocks (e.g., Greenland halibut; Figure 3.11) were defined as having the range of predicted UMSY (across the tested values of ah) to be less than 0.15 and to have CR > 10. This captured stocks for which the effect of ah on the location of the UMSY-CR curve was small due to the constraining effect of certain life history parameters. Life history-limited stocks are identified in Table 3.4 and shown in Figure 3A.3. Note that there were no stocks that fell into the life history-limited category under Ricker recruitment. Remaining stocks were classified as selectivity-limited (i.e., CR > 10 and the range of UMSY > 0.15). These stocks are identified in Table 3.4 and are shown in Figures 3A.4 and 3A.5. The boundaries chosen for these categories were arbitrary, based on visual inspection of the graphs in the Appendix to Chapter 3. Obviously, life history, density dependence and selectivity all contribute to all stocks’ UMSY and the range of relative effects of these three factors is continuous in nature. For example, UMSY for some stocks was both recruitment and life history-limited (e.g., common sole 5 under Beverton-Holt recruitment; Figure 3A.2). The boundaries chosen were intended simply to capture apparent patterns in the current dataset and enable broad-brush observations to be made. Recruitment-limited stocks included both pelagic and demersal species (e.g., Atlantic horse mackerel 1; Herring 2 and 5, megrim 2 and common sole 5; Table 3.4) that tended towards early maturity and were relatively short-lived, although, they shared these traits with many species that were not classified as recruitment-limited. However, all recruitment-limited stocks had very low SPR0. For these stocks, the UMSY-CR curve was less important for prediction of UMSY and, 59  therefore, stocks for which UMSY is likely to be limited by very low recruitment compensation could be identified as having low SPR0. Life history-limited stocks (e.g., European plaice 2-6 and Greenland halibut; Table 3.4) tended to be longer-lived stocks with either slow growth, low natural mortality, or both. There was no obvious trend in SPR0 for these stocks. However, they could be easily identified by UMSY-CR curves close to the left of the plot (Figure 3A.3). Given that knowledge of recruitment parameters is not needed to calculate either SPR0 or the UMSY-CR curve, these two rules of thumb could be useful in a risk assessment framework for initial rapid identification of species with overfishing thresholds highly constrained by factors not under management control.  Discussion Density dependence in recruitment, due to intraspecific competition for resources, is one of the main determinants of the productivity of harvested stocks (Myers 2001; 2002). While a stock may have strong density dependence, however, it does not necessarily follow that it can withstand a high harvest rate, because UMSY is also governed by other factors, including growth rate, age at maturity, longevity and age at first harvest. The last is important because this factor is under management control, i.e., increasing the age at which fish are first harvested will increase UMSY. UMSY is a productivity parameter intrinsic to a fish stock, which reflects the magnitude of density dependence in recruitment, as well as aspects of its life history and the selectivity schedule imposed upon it (Schnute and Kronlund 1996; Chapter 2). UMSY also represents a valid harvest rate threshold for prevention of both growth and recruitment overfishing of single species (Gulland 1971; Mace 2001; see May et al. 1979 and Walters et al. 2005 for studies incorporating needs of predators and prey in calculation of MSY). Results of this study were dependent on a number of simplifying assumptions and the results presented should be considered for their illustrative value and not for management advice. For example, the model assumed knife-edge selectivity, a general logistic maturity curve for all stocks (although age-at-maturity was stock specific), and stationarity in life history parameters and the selectivity schedule. This last assumption is unlikely to be valid, and a number of studies have shown fishery-induced changes on life history parameters (e.g., Hutchings 2005; Olsen et 60  al. 2005; Rijnsdorp 2005). Most of these assumptions could be tested with slight modifications to the existing model framework and this would be an avenue for future extension of this work. Despite the limiting assumptions of the present study, the results have been instructive for quantifying and visualising the relative effects of different biological and management parameters on thresholds for overfishing. Results showed that, for most stocks, changing the selectivity schedule could have a significant impact on UMSY. This is a well known approach for precautionary management of fisheries (Gulland 1971; Myers and Mertz 1998; Froese 2004). However, there were some stocks for which UMSY was highly constrained by either life history or recruitment parameters and was little affected by selectivity. Stocks with UMSY mostly limited by life history parameters could be identified by inspection of the UMSY-CR curve, calculated over a range of hypothesised ages at recruitment to the fishery. Under Beverton-Holt recruitment, stocks with ‘life history-limited’ UMSY had characteristic curves that were far to the left of the x-axis, encompassing a small range of UMSY across all tested values of ah. Stocks with these types of curves tended to be longer-lived stocks with slower growth and/or lower natural mortality. Because predicted UMSY was affected very little by changes to the selectivity schedule, prevention of overfishing of these types of stocks may require more a careful management plan than simply controlling selectivity. The UMSY-CR curves can be constructed using only life history and selectivity parameters, suggesting they may be a useful tool for rapid assessment of stocks that fall into this category. For a few stocks, UMSY was highly constrained by the low density dependence estimated from stock-recruitment data (Goodwin et al. 2006). The UMSY-CR curve was not useful for identifying these ‘recruitment-limited’ stocks. However, these stocks were all characterised by very low SPR0, which can be calculated using only life history parameters. While the remaining stocks did not share any defining suite of characteristics, it is still possible to draw conclusions about the likely magnitude of UMSY for many stocks because there appear to be natural constraints on possible values of CR. Of the 700 teleost stocks analysed by Myers et al. (1999), mean estimated CR exceeded 50 for only three species and exceeded 100 for only one species. Apart from the three outlying stocks in the study of Goodwin et al. (2006), estimated values of CR fell into a similar range. Most of the Atlantic stocks considered in this study are harvested at a very young  61  age (0-2 years) and examination of their UMSY-CR curves for these ages at recruitment, under all hypotheses of CR < 100, indicates strong constraint in the possible value of UMSY. The predictions of the Ricker and Beverton-Holt models differed considerably. UMSY predicted by the Ricker model was higher than that obtained using the Beverton-Holt model and the range of values across all stocks was greater in the Ricker case. In particular, the Ricker model predicted UMSY = 1 for many stocks under high age at recruitment to the fishery. It is important to note that UMSY refers to the harvest rate on the vulnerable stock only and, therefore, if there are sufficient spawners and surviving recruits in the unfished population, it may be optimal to harvest all of the vulnerable stock. A value of UMSY = 1 implies that the stock cannot be growth overfished (see Myers and Mertz 1998), although environmental variability and extreme pitfalls in estimating stock-recruitment parameters precisely (Hilborn and Walters 1992) imply that this would be a very risk-prone management strategy. The Beverton-Holt model rarely predicted UMSY = 1 or even values of UMSY approaching 1. The reasons for the differences between the predictions of the two models can, again, be seen by looking at the shape of the curve describing the relationship between CR and UMSY. The Ricker curves tended to ascend less steeply than the Beverton-Holt curves and therefore predicted larger UMSY than the Beverton-Holt curve, given the same value of CR. It is probably not useful to try to find biological explanations for these observations as the Ricker and Beverton-Holt stock recruitment relationships are, themselves, statistical approximations of a range of biological processes occurring over a wide range of spatial and temporal scales (Hilborn and Walters 1992). However, the Beverton-Holt recruitment function is consistent with a generalised theory about foraging behaviour in young fish as a mechanism leading to density dependence (Walters and Juanes 1993; Walters and Korman 1999; Walters et al. 2000) and is likely to be appropriate for most fish stocks. Walters and Martell (2004) have discussed differences between the Ricker and Beverton-Holt models and shown how the Ricker model can result in lower estimates of α than the BevertonHolt model when extrapolating beyond the observed range of the stock-recruitment data. They state that, because of this, the Ricker model has often been advocated as a more precautionary model because its lower estimates of α would imply lower UMSY. This may appear contrary to the findings of the present analysis but it must be remembered that the present study did not estimate α from stock-recruitment data (this had already been done by Goodwin et al. 2006) and, 62  therefore, this bias does not apply. The idea that the Ricker model is more precautionary because it produces lower estimates of α is based on the assumption that the relationship between α and UMSY is similar in both models, which it is not. The present study suggests that the BevertonHolt model would predict much lower UMSY for a given α (standardised to CR), due to differences in the form of the relationship between α and UMSY between the two models. Standardised unfished spawners per recruit, SPR0, has been shown to be a useful composite parameter for predicting density dependence (Goodwin et al. 2006). Translating this predictive power to UMSY, however, requires consideration of whether the parameters that determine SPR0 also influence the relationship between UMSY and CR. This study showed that SPR0 had poor ability to predict UMSY (except for the recruitment-limited stocks discussed above), due to confounding of the effects of the different parameters comprising SPR0 and their individual effects on the relationship between UMSY and CR. Care therefore needs to be taken when interpreting indications of strong density dependence as evidence that a stock can withstand high rates of harvest. Goodwin et al. (2006) suggested that stocks with low SPR0 (high α, low CR; e.g., herring, anchovy) could be depleted even at low harvest rates but were resilient to extirpation because of high reproductive rates at low stock size. Alternatively, longer-lived, slower-growing and later-maturing stocks with high SPR0 (low α, high CR; e.g., cod, halibut) could likely sustain higher harvest rates without being fished down due to strong compensation, but would be more vulnerable to extirpation if severely overfished. The results of the present study suggest that stocks with the lowest CR tended to have lower UMSY than average, consistent with the arguments of Goodwin et al. (2006). However, for stocks with higher recruitment compensation (CR between ~ 20 and 100; excluding the three extreme cases), there was no relationship between UMSY and CR under the assumption of Beverton-Holt recruitment. This is because most stocks are currently harvested at very young ages (providing a strong constraint on UMSY) and also because, for some stocks, UMSY is strongly constrained by life history parameters such as the growth and natural mortality rates, regardless of the strength of recruitment compensation. It should be noted that the statements of Goodwin et al. (2006) refer mainly to the problem of recruitment overfishing and recovery from depletion (see also Denney et al. 2002). Note, though, that thresholds for growth and recruitment overfishing may be close together for low productivity species (Punt 2000; NAFO 2003).  63  It is noteworthy that, under the assumption of Beverton-Holt recruitment, UMSY was highly positively correlated with the natural mortality and growth rate and negatively correlated with maximum age, consistent with previous findings (e.g., Jennings et al. 1998; Dulvy et al. 2004) and demonstrated theory (Beverton and Holt 1957; Gulland 1971; Kirkwood et al. 1994). This implies that the first priority in data-limited situations should be to obtain: (i) a growth curve, from which one can obtain rough predictions of M and age-at-maturity (using, for example, Beverton-Holt invariants: Charnov 1993); and (ii) the selectivity schedule that would maximize yield without driving the stock size low enough for density dependence in recruitment to become important (C. Walters, UBC Fisheries Centre, pers. comm.). Therefore, when the size-selection regime can be regulated, a management priority should be to adjust it (Myers and Mertz 1998; Froese et al. 2008). Control of selectivity in fisheries remains one of the biggest challenges in fisheries today (Hall and Mainprize 2005). Mechanisms include regulated changes to mesh or hook size in trawl and line fisheries; and regulation of spatial extent of the fishery so that some age-classes are invulnerable to the fishing gear (to allow growth and/or recruitment to occur). Seasonal temporal closures are often also implemented to allow growth and reproduction before harvesting (e.g., Myers et al. 2000). Some of the most successfully-managed fisheries are highly regulated in all these respects (e.g. Pacific halibut: Clark and Hare 2004). Most species, however, especially those that are data-limited, are caught in multispecies fisheries (often as bycatch) where it is very difficult or impossible to control individual ages at recruitment of multiple species. In recent years, there has been much progress in devising methods to reduce bycatch that have included modifications to gear, such as escape panels in trawl nets, or modifications to the method of fishing, such as deeper setting of longlines to target specific pelagic species. Many of these solutions have been developed by members of the fishing industry or by partnerships between industry, government and scientists. For example, one such partnership has resulted in development of a net that selectively catches haddock, avoiding bycatch of cod and other unwanted groundfish species (Beutel et al. 2006). Another recent innovation uses magnets to deter sharks from longline hooks (see Gilman et al. 2007). There are, however, disincentives for selective fishing. In the past decade, many developed countries have shifted to individual quota systems (e.g., New Zealand, Iceland, Australia, Canada and the United States) and, while they 64  have been effective at reducing wasteful fishing effort, they have sometimes resulted in discarding of unwanted fish that exceed quota-limits or hold limits (Arnason 1994; 1996; Annala 1996). Unreported dumping of groundfish by boats fishing under the quota system is believed to have occurred in the years leading up to the collapse of the Newfoundland cod fishery (Angel et al.1994; Blades 1995) and is possibly part of the reason for the collapse (Walters and Maguire 1996; Myers et al. 1997). Coggins et al. (2007) discuss discarding as a cryptic source of fishing mortality and have demonstrated that discarding may undermine efforts to achieve sustainable harvest rates using length-based regulations, particularly when there are large recreational fisheries. Changes to the incentive structure in fisheries, e.g., through control of fishing effort and focus on more profitable fisheries, will be an important part of the solution (Grafton et al. 2006). Development of adaptive risk assessment approaches and management strategies that are flexible to changes in the fishery and new information are also necessary (Ludwig et al.1993). For example, Smith et al. (2007) have described recent developments in ecological risk assessment and harvest strategy frameworks for EBFM in Australian Commonwealth fisheries that vary according to the probable level of risk to each species and the amount of data available for assessment. These types of frameworks will require a suite of tools for assessing species with widely-varying amounts of available data (e.g., Mace and Sissenwine 1993; papers in Kruse et al. 2005; Sadovy et al. 2007). Presentation of the likely range of UMSY among stocks in multispecies fisheries can help managers visualise the effects of different levels of fishing effort on multiple stocks simultaneously and can be used to frame discussions of trade-offs inherent in managing non-selective fisheries.  Acknowledgements This work would not have been possible without the ideas and insightful advice of Carl Walters. Numerous discussions with Robert Ahrens were critical to the development of this paper. James Scandol, Steve Martell, Tony Pitcher and Wai Lung Cheung also gave valuable advice. This work was funded in part by the Charles Gilbert Heydon Travelling Fellowship in Biological Sciences, awarded to R.F. by the University of Sydney, Australia; and in part by a grant provided to the UBC Fisheries Centre by the NSW Department of Primary Industries, Australia. 65  66  Table 3.1. Input parameters used in the model. W∞ = maximum weight (kg); κ = growth rate (y-1); amat = age at 50% maturity (years); amax = maximum age (years); M = natural mortality rate (y-1); SPR0 = unfished spawning stock biomass = per recruit; CR = recruitment compensation ratio; ah = age at recruitment to the fishery. Parameters in italics were obtained from FishBase. All other parameters were taken from Goodwin et al. (2006). CS, Celtic Sea; BB, Bay of Biscay; Channel, English Channel; NS, North Sea.  Tables  67  68  Table 3.1 continued.  Table 3.2. Pearson’s correlation coefficient, r, for relationship between logged life history/selectivity parameters and mean UMSY for all stocks under Ricker and Beverton-Holt assumptions for the stock-recruitment relationship. Ln parameter Ricker Beverton-Holt  M 0.27* 0.85**  amat -0.01  n.s.  -0.22  κ 0.25  n.s.  0.63**  W∞ 0.15  n.s.  -0.14  amax  SPR0  n.s.  0.12  n.s.  -0.46**  -0.24  n.s.  -0.17  ** = P < 0.01; * = P < 0.05; n.s. = not significant, df = 52.  69  Table 3.3. Parameters used to make Figures 3.7 (Stock 3) and 3.8. Stock  κ  W∞  amat  amax  M  ah  SPR0  1  0.36  4.2  2.5  10  0.25  2  9.0  2  0.31  4.8  2.5  10  0.25  2  9.0  3  0.25  6  2.5  10  0.25  2  9.1  4  0.23  6.6  2.5  10  0.25  2  9.0  5  0.21  7.4  2.5  10  0.25  2  9.0  70  Table 3.4a. Mean values of UMSY obtained for the 54 stocks under a range of values of ah assuming Ricker recruitment. (see text for definition of the determinants of UMSY). Important: These values are illustrative and not appropriate for management recommendations. Stock Atlantic cod 1 Atlantic cod 2 Atlantic cod 3 Atlantic cod 4 Atlantic cod 5 Atlantic cod 6 Atlantic cod 7 Atlantic cod 8 Atlantic cod 9 Atlantic herring 1 Atlantic herring 2 Atlantic herring 3 Atlantic herring 4 Atlantic herring 5 Atlantic herring 6 Atlantic herring 7 Atlantic horse mackerel 1 Atlantic horse mackerel 2 Atlantic mackerel 1 Bluewhiting 1 Common sole 1 Common sole 2 Common sole 3 Common sole 4 Common sole 5 European anchovy 1 European hake 1 European hake 2 European pilchard 1 European plaice 1 European plaice 2 European plaice 3 European plaice 4 European plaice 5 European plaice 6 Fourspotted megrim 1 Greenland halibut 1 Haddock 1 Haddock 2 Haddock 3 Haddock 4 Haddock 5 Haddock 6 Megrim 1 Megrim 2 Norway pout 1 Pollock 1 Pollock 2 Pollock 3 Sandeel 1 Whiting 1 Whiting 2 Whiting 3 Whiting 4  0 0.25 0.21 0.18 0.22 0.21 0.49 0.44 0.31 0.29 0.21 0.11 0.15 0.29 0.13 0.28 0.31 0.07 0.21 0.14 0.13 0.16 0.17 0.14 0.15 0.08 0.41 0.16 0.14 0.34 0.19 0.18 0.14 0.13 0.20 0.17 0.19 0.15 0.24 0.21 0.23 0.26 0.24 0.26 0.17 0.09 0.24 0.21 0.16 0.21 0.28 0.18 0.30 0.37 0.18  1 0.32 0.24 0.21 0.27 0.26 0.56 0.56 0.40 0.36 0.27 0.13 0.17 0.40 0.15 0.38 0.42 0.08 0.25 0.17 0.15 0.19 0.20 0.16 0.17 0.09 0.55 0.18 0.16 0.50 0.22 0.21 0.16 0.15 0.23 0.19 0.23 0.16 0.29 0.25 0.28 0.33 0.29 0.33 0.19 0.10 0.48 0.24 0.18 0.25 0.43 0.21 0.41 0.59 0.22  2 0.45 0.30 0.26 0.35 0.35 0.67 0.73 0.56 0.51 0.37 0.17 0.21 0.65 0.18 0.58 0.67 0.09 0.32 0.20 0.18 0.23 0.24 0.19 0.20 0.10 0.96 0.23 0.19 0.92 0.27 0.25 0.18 0.17 0.28 0.23 0.30 0.18 0.37 0.31 0.34 0.44 0.39 0.45 0.23 0.13 0.95 0.29 0.22 0.30 0.87 0.26 0.62 0.98 0.28  3 0.72 0.39 0.32 0.49 0.50 0.78 0.93 0.90 0.82 0.53 0.21 0.26 0.98 0.22 0.94 1 0.10 0.41 0.26 0.22 0.29 0.30 0.23 0.24 0.12 1 0.29 0.24 1 0.35 0.30 0.22 0.20 0.35 0.30 0.40 0.21 0.52 0.40 0.42 0.68 0.56 0.69 0.29 0.15 0.98 0.35 0.26 0.38 1 0.34 1 1 0.36  4 0.98 0.54 0.40 0.71 0.70 0.92 1 1 1 0.73 0.26 0.33 1 0.27 1 1 0.12 0.59 0.32 0.28 0.37 0.38 0.28 0.31 0.13 1 0.38 0.30 1 0.47 0.38 0.27 0.24 0.47 0.38 0.54 0.24 0.79 0.58 0.56 0.98 0.87 1 0.37 0.19 0.98 0.46 0.33 0.51 1 0.46 1 1 0.49  5 1 0.77 0.55 1 0.94 1 1 1 1 0.94 0.32 0.42 1 0.36 1 1 0.15 0.88 0.40 0.34 0.48 0.50 0.35 0.38 0.16 1 0.51 0.41 1 0.64 0.51 0.34 0.29 0.65 0.50 0.73 0.28 1 0.87 0.71 1 1 1 0.49 0.24 0.98 0.66 0.44 0.74 1 0.63 1 1 0.67  6 1 1 0.77 1 1 1 1 1 1 1 0.38 0.50 1 0.43 1 1 0.17 1 0.47 0.40 0.62 0.66 0.44 0.47 0.18 1 0.65 0.52 1 0.86 0.69 0.43 0.36 0.92 0.63 0.95 0.33 1 1 0.92 1 1 1 0.64 0.30 1 0.91 0.58 0.96 1 0.85 1 1 0.90  Strongest determinant of UMSY Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity CR (recruitment) Selectivity Selectivity CR (recruitment) Selectivity Selectivity CR (recruitment) Selectivity CR (recruitment) CR (recruitment) Selectivity Selectivity Selectivity Selectivity CR (recruitment) Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity CR (recruitment) CR (recruitment) Selectivity Selectivity Selectivity CR (recruitment) Selectivity Selectivity Selectivity Selectivity  71  Table 3.4b. Mean values of UMSY obtained for the 54 stocks under a range of values of ah assuming Beverton-Holt recruitment (see text for definition of the determinants of UMSY). Stock Atlantic cod 1 Atlantic cod 2 Atlantic cod 3 Atlantic cod 4 Atlantic cod 5 Atlantic cod 6 Atlantic cod 7 Atlantic cod 8 Atlantic cod 9 Atlantic herring 1 Atlantic herring 2 Atlantic herring 3 Atlantic herring 4 Atlantic herring 5 Atlantic herring 6 Atlantic herring 7 Atlantic horse mackerel 1 Atlantic horse mackerel 2 Atlantic mackerel 1 Bluewhiting 1 Common sole 1 Common sole 2 Common sole 3 Common sole 4 Common sole 5 European anchovy 1 European hake 1 European hake 2 European pilchard 1 European plaice 1 European plaice 2 European plaice 3 European plaice 4 European plaice 5 European plaice 6 Fourspotted megrim 1 Greenland halibut 1 Haddock 1 Haddock 2 Haddock 3 Haddock 4 Haddock 5 Haddock 6 Megrim 1 Megrim 2 Norway pout 1 Pollock 1 Pollock 2 Pollock 3 Sandeel 1 Whiting 1 Whiting 2 Whiting 3 Whiting 4  0 0.13 0.10 0.09 0.11 0.12 0.12 0.13 0.13 0.13 0.12 0.09 0.08 0.15 0.09 0.14 0.15 0.05 0.09 0.09 0.09 0.08 0.08 0.07 0.07 0.06 0.13 0.10 0.09 0.19 0.09 0.07 0.08 0.07 0.08 0.08 0.11 0.07 0.11 0.11 0.12 0.12 0.12 0.12 0.09 0.07 0.34 0.09 0.09 0.10 0.21 0.10 0.14 0.24 0.11  1 0.17 0.12 0.11 0.14 0.14 0.14 0.16 0.16 0.15 0.15 0.10 0.09 0.19 0.10 0.18 0.19 0.06 0.11 0.10 0.10 0.09 0.09 0.08 0.08 0.06 0.16 0.11 0.10 0.27 0.10 0.08 0.09 0.07 0.09 0.10 0.13 0.08 0.14 0.13 0.14 0.14 0.15 0.15 0.10 0.08 0.44 0.10 0.10 0.11 0.32 0.12 0.18 0.39 0.12  2 0.23 0.14 0.12 0.17 0.18 0.17 0.21 0.21 0.20 0.19 0.13 0.11 0.28 0.12 0.26 0.27 0.07 0.13 0.12 0.12 0.11 0.10 0.10 0.09 0.07 0.22 0.14 0.12 0.44 0.12 0.09 0.10 0.08 0.10 0.11 0.17 0.09 0.17 0.15 0.18 0.18 0.19 0.19 0.12 0.10 0.93 0.12 0.12 0.13 0.65 0.15 0.26 0.82 0.15  3 0.32 0.17 0.15 0.22 0.24 0.22 0.30 0.28 0.27 0.26 0.16 0.13 0.43 0.15 0.38 0.40 0.08 0.16 0.15 0.15 0.13 0.12 0.11 0.11 0.08 0.32 0.17 0.15 0.68 0.15 0.11 0.11 0.09 0.12 0.14 0.22 0.11 0.22 0.19 0.23 0.24 0.25 0.26 0.15 0.12 0.96 0.14 0.14 0.16 0.93 0.19 0.38 1 0.20  4 0.44 0.22 0.18 0.29 0.31 0.29 0.43 0.40 0.38 0.34 0.20 0.16 0.58 0.18 0.52 0.57 0.10 0.20 0.18 0.18 0.16 0.14 0.14 0.13 0.09 0.53 0.22 0.19 0.94 0.18 0.13 0.14 0.11 0.14 0.17 0.29 0.12 0.30 0.25 0.29 0.32 0.34 0.35 0.18 0.14 0.98 0.17 0.18 0.20 0.95 0.25 0.54 1 0.26  5 0.57 0.28 0.23 0.40 0.40 0.40 0.65 0.57 0.53 0.42 0.24 0.19 0.74 0.23 0.67 0.76 0.11 0.25 0.22 0.21 0.19 0.17 0.16 0.15 0.10 0.53 0.29 0.25 1 0.23 0.16 0.17 0.13 0.17 0.20 0.38 0.14 0.40 0.33 0.38 0.43 0.47 0.47 0.22 0.18 0.98 0.21 0.22 0.25 0.93 0.33 0.75 1 0.34  6 0.71 0.36 0.29 0.58 0.51 0.56 0.96 0.80 0.74 0.51 0.28 0.23 0.85 0.27 0.78 0.91 0.13 0.32 0.26 0.25 0.24 0.21 0.20 0.18 0.12 0.53 0.36 0.31 1 0.29 0.20 0.21 0.14 0.21 0.25 0.50 0.16 0.52 0.43 0.52 0.57 0.64 0.60 0.28 0.22 0.97 0.26 0.28 0.32 0.94 0.46 0.75 1 0.48  Strongest determinant of UMSY Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity CR (recruitment) Life history Selectivity CR (recruitment) Selectivity Selectivity CR (recruitment) Selectivity CR (recruitment) CR (recruitment) Selectivity Life history Life history Life history CR (recruitment) Selectivity Selectivity Selectivity Selectivity Selectivity Life history Life history Life history Life history Life history Selectivity Life history Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity Selectivity CR (recruitment) CR (recruitment) Selectivity Selectivity Selectivity CR (recruitment) Selectivity Selectivity Selectivity Selectivity  72  Figures  60  Ricker Compensation Ratio  55 50 45 40 35 30 25 20 15 10 5 0 0  0.05  0.1  0.15  0.2  0.25  0.3  0.35  0.4  0.45  0.5  Umsy  Figure 3.1. Relationship between UMSY and CR for a hypothetical stock, with dashed lines showing a unique pair of UMSY and CR values.  73  0.9  Ricker  0.8  Beverton-Holt  0.7 0.6  U MSY  0.5 0.4 0.3 0.2 0.1 0.0 Horse mackerel 2  Plaice 1  Horse mackerel 1  Herring 4  Pilchard 1  Herring 7  Herring 3  Hake 2  Herring 6  Herring 2  Hake 1  Herring 5  Herring 1  Cod 9  Cod 8  Cod 7  Cod 6  Cod 5  Cod 4  Cod 3  Cod 2  Cod 1 0.9 0.8 0.7  UMSY  0.6 0.5 0.4 0.3 0.2 0.1 0.0 Plaice 6  Plaice 5  Plaice 4  Plaice 3  Plaice 2  Anchovy  Common sole 5  Common sole 4  Common sole 3  Common sole 2  Common sole 1  Blue whiting  Mackerel  Figure 3.2. Mean (+ s.e.) estimates of UMSY for the 54 stocks of Goodwin et al. (2006) under Ricker (grey bars) and Beverton-Holt (black bars) assumptions about the stock-recruitment relationship. UMSY values are the means of 100 Monte Carlo runs (see text). See Table 3.1 for description of stocks.  74  0.5  0.4  UMSY  0.9  0.8  0.7  0.6  0.3  0.2  0.1  0.0  Whiting 4 Whiting 3 Whiting 2 Whiting 1 Sandeel 1 Pollock 3 Pollock 2 Pollock 1 Norway pout Megrim 2 Megrim 1 Haddock 6 Haddock 5 Haddock 4 Haddock 3 Haddock 2 Haddock 1 Greenland halibut Fourspotted megrim  Figure 3.2 cont.  75  0.5  1.0  0.4  (b)  0.3  0.6  0.2  0.4  0.0  0.0  0.1  0.2  U M SY  0.8  (a)  5  10 20  50  200 CR  500  2000  5  10  20  50 100  500  2000  CR  Figure 3.3. Relationships between CR and UMSY under (a) Ricker and (b) Beverton-Holt recruitment. See text for correlation coefficients. Note logarithmic scale and differences in scale of y-axis.  76  1.0 0.8 0.6 0.2 0.0  0.0  0.2  0.5  1.0  2.0  5.0  1.0  (c)  2.0  5.0  10.0  t  0.8  (d)  0.4 0.2 0.0  0.0  0.10  0.20  0.50  1.00  2.00  5e-02  1.0  0.05  5e-01  5e+00  5e+01  (f)  0.8  (e)  0.0  0.0  0.2  0.2  0.4  0.4  0.6  0.6  0.8  1.0  1.0  0.6  0.6 0.4 0.2  U M SY  0.5  10.0  0.8  1.0  0.1  U M SY  (b)  0.4  0.6 0.4 0.2  U MSY  0.8  1.0  (a)  4  6  8  10  12  14  5e-03  5e-02  5e-01  5e+00  5e+01  Figure 3.4. Correlations between log life history parameters and UMSY for the Ricker model. Graphs show (a) M, (b) amat, (c) κ, (d) W∞, (e) amax and (f) SPR0. Correlation coefficients are given in Table 3.2. Note logarithmic scale.  77  0.5  0.5  0.4 0.2 0.1 0.0  0.0  0.2  0.5  1.0  2.0  5.0  2  5  (d)  0.2  0.2  0.3  0.3  0.4  0.4  (c)  0.0  0.0  0.1  0.1  U M SY  1 0.5  0.5  0.1  0.10  0.20  0.50  1.00  5e-02  0.5  0.5  0.05  5e-01  5e+00  5e+01  (f)  0.2  0.2  0.3  0.3  0.4  0.4  (e)  0.0  0.0  0.1  0.1  U M SY  (b)  0.3  0.3 0.2 0.1  UMSY  0.4  (a)  4  6  8  10  12  14 16  5e-03  5e-02  5e-01  5e+00  Figure 3.5. Correlations between log life history parameters and UMSY for the Beverton Holt model. Graphs show (a) M, (b) amat, (c) κ, (d) W∞, (e) amax and (f) SPR0 for the Beverton-Holt model. Correlation coefficients are given in Table 3.2. Note logarithmic scale.  78  1000 200  (b)  5 10  50  Compensation Ratio  5e+00 5e-01 5e-02 5e-03  Goodwin et al. (2006)  (a)  5e-03  5e-02  5e-01  Present Study  5e+00  5e+01  5e-03  5e-02  5e-01  5e+00  5e+01  Unfished SPR  Figure 3.6. Correlations between (a) SPR0 estimated by Goodwin et al. (2006) and SPR0 obtained in the present study; and (b) lnSPR0 (present study) and lnCR published by Goodwin et al. (2006). See text for correlation coefficients.  79  (a)  Unfished SPR  20  (b)  20  18  18  16  16  14  14  12  12  10  10  8  8  6  6  4  4  2  2 0  0 2  4  6  8  10  0  12  0.1  0.2  Unfished SPR  20  (c)  18  0.4  0.5  0.6  0.4  0.5  0.6  vbK  Winf  20  0.3  (d)  18  16  16  14  14  12  12  10  10  8  8  6  6  4  4  2  2 0  0 1  2  3 amat  4  5  0  0.1  0.2  0.3 M  Figure 3.7. Relationship of SPR0 to (a) W∞; (b) κ ; (c) amat; and (d) M, for a hypothetical fish stock. In each case all other parameters were held constant while the parameter under consideration was varied. See Table 3.3 (Stock 3) for baseline parameters used.  80  100  (a)  40  CR  60  80  Ricker  0  20  Stock 1 Stock 2 Stock 3 Stock 4 Stock 5  100  0.0  0.2  0.4  0.6  0.8  Beverton-Holt  0  20  40  CR  60  80  (b)  0.0  0.2  0.4  0.6  0.8  U MS Y  Figure 3.8. Relationship between UMSY and CR for five hypothetical stocks with SPR0 = 9, under (a) Ricker and (b) Beverton-Holt stock-recruitment assumptions. Each stock has a different pair of values of κ and W∞, but all other parameters are held constant (Table 3.4). Note truncation of the y-axis at CR=100, for readability.  81  Haddock 5 , published ah = 1  0.0  0.0  0.2  0.2  0.4  0.4  Umsy  Umsy  0.6  0.6  0.8  0.8  1.0  1.0  Haddock 5 , published ah = 1  Atlantic herring 1 , published ah = 1  0.0  0.0  0.2  0.2  0.4  0.4  Umsy  Umsy  0.6  0.6  0.8  0.8  1.0  1.0  Atlantic herring 1 , published ah = 1  Atlantic horse mackerel 1 , published ah = 0  0.0  0.0  0.2  0.2  0.4  0.4  Umsy  Umsy  0.6  0.6  0.8  0.8  1.0  1.0  UMSY  Atlantic horse mackerel 1 , published ah = 0  Greenland halibut , published ah = 5  0.0  0.0  0.2  0.2  0.4  0.4  Umsy  Umsy  0.6  0.6  0.8  0.8  1.0  1.0  Greenland halibut , published ah = 5  0  1  2  3  4  5  6  0  1  2  3  4  5  6  ah Figure 3.9. Predicted UMSY for four example stocks over a range of ages at first harvest under Ricker (left panel) and Beverton-Holt (right panel) assumptions for the stock-recruitment relationship.  82  0 1 2 3 4 5 6  Atlantic horse mackerel 1  0 1 2 3 4 5 6  Greenland halibut  0 1 2 3 4 5 6  100  Atlantic herring 1  0 1 2 3 4 5 6  Atlantic herring 1  0 1 2 3 4 5 6  Atlantic horse mackerel 1  0 1 2 3 4 5 6  Greenland halibut  0 1 2 3 4 5 6  60  60  CR  CR  40  40  20  20  60  80  100  0  0 100 80  CR  60  40  CR  20  40 20  60  80  100  0  0 100 80 0  100 80 0  20  20  40  40  CR  CR  60  60  80  100  0  0  20  20  40  40  CR  CR  60  CR  Haddock 5  80  100  0 1 2 3 4 5 6  80  Haddock 5  0.0  0.2  0.4  0.6 U MS Y  0.8  1.0  UMSY  0.0  0.2  0.4  0.6  0.8  1.0  U MS Y  Figure 3.10. Predicted UMSY-CR curves for the four example stocks in Figure 9, over a range of ages at first harvest under Ricker (left panel) and Beverton-Holt (right panel) assumptions for the stock-recruitment relationship. Published estimates of CR for each stock (Goodwin et al. 2006) are shown as horizontal dotted lines.  83  Chapter 4. Optimal harvest rate for long-lived, low-fecundity species: deepwater dogsharks of the continental slope of southeastern Australia  Introduction Chondrichthyans (sharks, skates, rays and chimaeras) are among the least productive species caught in fisheries, mainly due to life history traits that include low fecundity, late maturity and slow growth (Walker 1998). A number of authors have documented large declines in fished Chondrichthyan populations (e.g., Dulvy et al. 2000; Graham et al. 2001; Baum et al. 2003; Baum and Myers 2004, but see Burgess et al. 2005 and Baum et al. 2005) and, at the time of writing, 51 Chondrichthyan species were listed as Critically Endangered or Endangered in the IUCN Red List of Threatened Species (IUCN 2008). Sharks are frequently of low value in fisheries and tend to receive little management attention, as priority is usually given to maintaining harvest of more valuable and productive teleosts (Bonfil 2004). The difficult tradeoff between abundance of low-productivity species and catch of more productive species is inherent in multispecies fisheries, although it is seldom explicitly acknowledged (Hilborn et al. 2004; Walters and Martell 2004). However, with the shift towards more ecosystem-based fisheries management (EBFM) in many countries (FAO 2003; Pikitch et al. 2004) there may be a requirement for more explicit recognition and assessment of this trade-off. An important part of the assessment process is obtaining estimates of the relative productivities of species in fisheries. This can be problematic when good quality data are lacking. Lack of informative time series for sharks has led a number of authors to develop demographic methods for improving estimates of shark productivity using more readily-available life-history information (e.g., Smith et al. 1998; Cortés 1998; 2002; Heppell et al. 1999; McAllister et al. 2001; Dulvy and Reynolds 2002). Demographic approaches have provided valuable estimates of the range of harvesting pressures that can sustainably be applied to shark populations and, in some cases, maximum sustainable harvest rate, UMSY, has been found to be very low. For example, McAllister et al. (2001) used demographic approaches to obtain an informative prior for a surplus production model, applied to large coastal sharks on the US east coast. Their final 84  median estimate of UMSY was 0.035 (3.5% of the population could be sustainably fished per year), more than an order of magnitude lower than estimates obtained without incorporating demographic information. Cortés (1998) used a life table approach to estimate UMSY = 0.014 for dusky sharks (Carcharhinus obscurus) and UMSY = 0.022 for Atlantic sharpnose sharks (Rhizoprionodon terranovae) in the eastern USA. UMSY is the fixed annual harvest rate that maximises long-term yield of a fish population (see Chapter 2). It is a function of the intrinsic productivity of the population, determined by growth, mortality and density dependence in recruitment, as well as of the selectivity regime of the fishery. In sharks, density dependence in recruitment may occur through decreased rates of predation, competition or cannibalism as population size is reduced, realised through changes to the natural mortality rate in juvenile age groups. Walker (1994) showed evidence for density dependence in the survival rate of juvenile gummy sharks (Mustelus antarcticus) in Australia, although Walker (1998) suggested that, for many species, density dependence in survival of juveniles may be less important than density dependence in natural mortality and growth rate across all age classes in determining population size. This author noted that recruitment is commonly assumed to be a linear function of adult stock size in sharks, based on knowledge of shark reproductive strategies (i.e, many sharks have mammal-like reproduction, with each individual producing few large, live young with a relatively high survival rate). This does not imply that stock-recruitment relationships such as the Beverton-Holt (1957) or Ricker (1954) function are inappropriate to use for sharks, as these functions approach linearity for low recruitment compensation (CR values approaching 1). Chapter 2 (Forrest et al. 2008) presented an analytical relationship between UMSY and CR for iteroparous species (see also Schnute and Richards 1998 and Martell et al. 2008). Chapter 2 showed that the relationship between UMSY and CR is affected by certain life history parameters, particularly growth rate and the age at which fish are first harvested. Chapter 3 further explored these relationships and showed that, for some stocks, UMSY was more strongly constrained by life history parameters than by either selectivity or the magnitude of recruitment compensation. These stocks tended to be longer-lived with lower natural mortality and slower growth. Graphic presentation of the relationship between CR and UMSY for these stocks showed that, under Beverton-Holt recruitment, UMSY had a maximum upper boundary that could not be exceeded, no 85  matter how strong the recruitment compensation response. The upper boundary could be found using only life history and selectivity information. Based on these findings, it was suggested in Chapters 2 and 3 that the model would be useful for finding the range of possible hypotheses for UMSY for long-lived, data-limited species. As these characteristics tend to apply to elasmobranchs, it may be possible to place fairly conservative constraints on the management parameter UMSY for these species, using only life history and selectivity information, despite uncertainty in recruitment parameters. More than 200 Chondrichthyan species occur in the Australian region (Cavanagh et al. (eds) 2003). As in most parts of the world (FAO 2000; Bonfil 2004) data for stock assessment of sharks is extremely limited in Australia. With the exception of a few important commercial species (M. antarcticus and Galeorhinus galeus: Punt et al. 2005) and charismatic threatened species (e.g., Carcharias taurus: Otway et al. 2003a,b), there have been few attempts to assess sharks in Australia (but see, e.g., Braccini et al. 2006a). Deepwater dogsharks (Order Squaliformes) are thought to be particularly vulnerable to overfishing due to life history strategies that place them at the lower end of the shark productivity spectrum (Daley et al. 2002). For example, Harrisson’s dogshark (Centrophorus harrissoni), known to be extremely depleted off the continental slope of southeastern Australia (Andrew et al. 1997; Graham et al. 1997; Graham et al. 2001) and listed as Critically Endangered on the IUCN Red List of Threatened Species (IUCN 2008; Cavanagh et al. (eds) 2003), does not reach maturity until close to its maximum length and has only 1-2 pups every two years (Daley et al. 2002). Like other deepwater dogsharks, it is ovoviviparous, giving birth to large pups that are potentially immediately vulnerable to fishing gear. Australian deepwater dogsharks are caught mostly as bycatch in multispecies trawl and line fisheries off the continental slope of southeastern Australia, and their flesh and livers have some commercial value (Daley et al. 2002). A number of dogshark species were recorded in surveys of the upper continental slope of NSW in 1976 (Gorman and Graham 1976; 1977), around the time that large-scale commercial trawling on the slope began. The surveys were repeated (partially) in 1979 (Gorman and Graham 1979; 1980a,b; 1981) and again in 1996 (Graham et al. 1997), resulting in a total of 361 tows in all three sets of surveys. The 1996 surveys found that most species of deepwater dogshark on the upper slope had undergone dramatic declines in the twenty 86  years since the first surveys, with some sites recording catch rates more than 99% below those in 1976 (Andrew et al. 1997; Graham et al. 2001). Three species (C. harrissoni; C. zeehaani and C. moluccensis) are currently under consideration for listing as Endangered under the Environment Protection and Biodiversity Conservation Act 1999. In this chapter, limitations on UMSY for Australian dogsharks are investigated. The model described by Forrest et al. (2008; Chapter 2) is systematically applied to show that, for certain growth, selectivity and reproductive schedules that tend to apply to dogsharks, the range of hypotheses for UMSY that can be considered possible may be very small indeed. The method is first systematically applied to hypothetical ‘species’ over a range of parameter-values representative of dogsharks; and then to 12 deepwater dogshark species from the continental shelf and slope of NSW. In the latter case, Monte Carlo simulations are used to account for uncertainty in life history parameters. Uncertainty in age-at-first-harvest is also considered. To test results for consistency with those from a previously published approach, a demographic model, described by McAllister et al. (2001), was used to estimate intrinsic rate of growth, r, for the 12 dogshark species. The intrinsic rate of growth represents the population production rate and also, therefore, the long-term harvest rate that could lead to extinction of the population, UMax. Both methods suggest that sustainable harvest rates for deepwater dogsharks are very low indeed. It is proposed that, despite lack of knowledge of recruitment parameters, there is more certainty about UMSY than might have been expected, given data-limitations. The results of this analysis can be used to inform policy for deepwater dogsharks and may be useful in the development of informative Bayesian priors for stock assessment models.  Methods Calculating the upper limit of UMSY  Equilibrium age-structured model - The age-structured model with UMSY as leading productivity parameter was described in detail in Chapter 2 (Forrest et al. 2008). The present model differs only in terms of calculation of fecundity at age, fa. In many fisheries models, fecundity is represented as a non-saturating function of weight. Sharks, however, tend to produce few large eggs or give birth to large live young and, for energetic and other reasons (e.g., in-utero 87  cannibalism), the number of pups produced is often consistent from year to year, regardless of the shark’s size. Population fecundity at age is therefore modelled as a saturating function of litter size and maturity-at-age, given by  (4.1)  1  f a = LS . 1+ e   −( a − amat )    σm    where LS is the maximum annual litter size, amat is age-at-50%-maturity (the age at which 50% of individuals are mature) and σm determines the steepness of a logistic maturity curve, with smaller values of σm resulting in a steeper ogive. Natural mortality is difficult to measure but may be empirically related to von Bertalanffy growth rate, κ (Beverton and Holt 1959); growth parameters and temperature (Pauly 1980); age at maturity (Jensen 1996); both growth rate and age at maturity (Chen and Watanabe 1989); or maximum age (Hoenig 1983). In a demographic study of two shark species, McAuley et al. (2007) compared five different methods to estimate natural mortality rate and obtained similar values for all methods. Here, it is assumed that M = 1.5κ (Beverton and Holt 1959). Calculating the upper limit of UMSY Chapter 2 presented the analytical relationship between α and UMSY (α = f(UMSY); equation 2A.6) and showed that the relationship is influenced by life history and selectivity parameters, notably growth rate, maximum age and the age at first harvest. Chapter 3 showed that, under the assumption of Beverton-Holt recruitment, for a large number of parameter combinations, UMSY approached an asymptotic maximum value (see the Appendix to Chapter 3). The asymptote (illustrated in Figure 4.1) is defined as the value of UMSY for which the denominator of f(UMSY) is predicted equal to zero (i.e., f(UMSY) is undefined at the asymptotic value of UMSY). This occurs when UMSY = - k2-1 (k2 =  ∂ϕVBMSY ϕVBMSY −1 ; see Chapter 2, Appendix A). UMSY = - k2-1 cannot be ∂U MSY  solved analytically for UMSY because ϕVBMSY is itself a recursive function of UMSY, through the effect of UMSY on survivorship (see equation 2.3). However, it is true that all values of UMSY  88  lower than the asymptotic limit will satisfy the inequality UMSY + k2-1 < 0. Therefore, the maximum possible hypothesis of UMSY can be identified by systematically calculating UMSY + k2-1 for a finely-scaled, discrete sequence of hypotheses of UMSY until the first value predicting UMSY + k2-1 > 0 is reached. This UMSY hypothesis is then discarded and the upper limit of UMSY is identified as the largest remaining UMSY hypothesis. Note that all UMSY hypotheses for which UMSY + k2-1 > 0 predict impossible, negative predictions of α. This is illustrated in Figure 4.1. The above rule can be applied to any fished species where Beverton-Holt recruitment is assumed. For sharks and similar species, however, there is further constraint on possible values of α, due to the way the stock-recruitment function is parameterised. Because sharks tend to produce large eggs or live young, the degree of certainty in the absolute number of eggs produced per female is usually high. This, and the relative independence of litter size and weight-at-age in sharks, make it appropriate to parameterise their stock-recruitment function in terms of numbers of eggs rather than spawning stock biomass (as is usually the case for teleosts). When the units of the dependent and independent variables of the stock-recruitment function are the same, α is literally the maximum survival rate from egg or pup to recruit and, therefore, cannot exceed unity. Another way of thinking about this is in terms of the recruitment compensation ratio CR, which is the ratio of α and unfished juvenile survival see Figure 1.2), or, rearranging, α = CR  R0 (equation 2.6; E0  R0 R . If, for example, 0 = 0.2 , then CR cannot exceed E0 E0  5, as this would give α > 1. This implies that, for sharks and similar species that produce few large eggs with high juvenile survival rates (where it is most appropriate to parameterise the x and y axis of the stock recruitment function in the same units), the interval over which CR is defined can be calculated from life history data. To obtain the upper limit of UMSY (UMSYLim) for each stock, the model was run iteratively over an ascending sequence of hypotheses of UMSY (0 to 1, step size 0.001), calculating α (equation 2.A6) and CR (equation 2.6) at each iteration. The results were then filtered to remove impossible values. At the first round of filtration, all values of UMSY that predicted UMSY + k2-1 > 0 were discarded. If any of the remaining UMSY hypotheses resulted in α > 1, these were also 89  discarded. The highest remaining value of UMSY then represented the maximum possible hypothesis for UMSY, i.e., UMSYLim.  Systematic exploration of the effects of life history and selectivity parameters on UMSYLim  To show the effects of life history parameters on UMSYLim, the algorithm was first systematically applied to hypothetical dogshark-like ‘species’, which were defined by combinations of life history parameters that could be reasonably applied to dogsharks (Table 4.1). Because UMSY is partly determined by selectivity, age-at-50%-first-harvest, ah, was also systematically varied. A logistic selectivity function (equation 2B.4) with fixed standard deviation was assumed (Table 4.1). For the present analysis, sensitivity to the form of the selectivity function (e.g., logistic vs dome-shaped) was not tested. The parameter values shown in Table 4.1 were systematically tested in a nested loop structure, thereby calculating UMSYLim for all parameter-combinations.  Application to deepwater dogsharks  Table 4.2 shows life history parameters for 12 species of dogshark caught on the continental shelf and slope of NSW. Most species are caught in deep water (> 300 m depth; Daley et al. 2002), although S. megalops also occurs in shallower water on the continental shelf (Braccini et al. 2006a). Parameters were missing for several species and, due to the difficulty of observing deepwater dogsharks, many of the available estimates were based on small-scale studies or opportunistic observations (Daley et al. 2002). It was therefore important to account for uncertainty in life history parameters and to test for sensitivity to important, but unavailable, selectivity parameters (i.e., age at recruitment). The algorithm described above was applied to each species in a Monte Carlo simulation framework, treating key parameters LS, κ, amax and amat as random variables. Note that the litter sizes shown in Table 4.2 were halved to account for the fact that most species are believed to give birth only once every two years (or less frequently; Daley et al. 2002). For simplicity, other parameters were fixed (see Table 4.2).  90  Parameter distributions Sampled distributions of parameters for each species are shown in the Appendix to Chapter 4. Literature estimates of the growth parameter κ were only available for five species, but were all low and of a similar magnitude (Table 4.2). It was therefore assumed that a common probability distribution of κ was shared by all 12 species. A lognormal probability distribution was assumed, which allowed for a longer right-hand tail while preventing values too close to zero. The mean of the distribution for all species was set to ln( κ ), where κ is the mean of the literature estimates of  κ for the species for which estimates were available. The standard deviation was set to 0.2, an arbitrary value that allowed uncertainty to be considered, while remaining in a range appropriate for these sharks. All other parameters were drawn from uniform distributions. Estimates of maximum age, amax, were not available for seven species. In these cases, if possible, the same amax as congenerics was assumed. D. licha and E. granulosus were assumed to have the same maximum age as D. calcea. The upper and lower bounds of the uniform distribution were then set to 5 + amax and amax - 5, respectively. Although estimates of amat were only available for four species, estimates of lengthat-maturity Lmat were available for all species (Table 4.2). For species without literature estimates of amat, deterministic amat was set to the age corresponding to La = Lmat, predicted by the von Bertalanffy growth equation (equation 2B.1), using κ , L∞ and a0 (where an independent estimate of a0 was not available, it was set so that the model predicted a newborn pup size that corresponded to the value given in Table 4.2). Note that L∞ was approximated from 1.2Lmax (Table 4.2). Parameters to convert length to weight were taken from Daley et al. (2002). The upper and lower bounds of the uniform distribution were then set to 5 + amat and amat - 5. Because litter size, LS, was already extremely low for a number of stocks (0.5 y-1), the lower boundary of the uniform distribution was set to the literature estimate (Table 4.2). The upper limit was set to the literature estimate + 4. Boundaries of all distributions were arbitrarily set to allow the effects of parameter uncertainty to be seen without deviating too far from values characteristic of these sharks. No selectivity data are available for these stocks. Selectivity-at-age was assumed to follow a steep logistic function, with σ = 0.1ah (equation 2B.4). Effects of ah on UMSYLim for each species were evaluated by running the model over a sequence of values of ah ranging from ah = 1 to ah = 91  15, with step size 2 years. UMSYLim was calculated for each species using the algorithm described in the previous section. For each species, for each value of ah, 100 Monte Carlo simulations were done, with parameters drawn at random from their respective distributions.  Demographic analysis  A demographic model (McAllister et al. 2001) was used to estimate intrinsic rate of growth, r, for the 12 dogshark species, given uncertainty in the input parameters described above. The intrinsic rate of growth represents the harvest rate that would lead to extinction of the population, UMax (Hilborn and Walters 1992). Therefore estimates of UMSYLim obtained in the previous section would be expected to be lower than estimates of r, although it is important to note that the demographic model directly estimates r, while the approach above estimates the upper limit of UMSY. For these reasons, the results from the two approaches are not directly comparable, but are expected to give results of similar magnitude. Note that r is often used to obtain approximate estimates of UMSY = r/2 (e.g., McAllister et al. 2001) but this rule only holds under the assumptions of the logistic surplus production model (Schaefer 1954). In the demographic approach, an age-structured model (without explicit representation of density dependent recruitment) was used to obtain r, which was defined as the ratio of abundance between one time-step and the previous, after stabilisation of the age-structure in the model. The model was initialised by (4.3)  Na,0 = 1000la  where N is female numbers at age a at time t = 0 and la is unfished survivorship at age (equation 2.3). For subsequent time-steps, the number of age 0 females was calculated as  (4.4)  ∞  N 0,t +1 = ∑ f a N a ,t . a =0  92  For a > 0, female numbers at age were calculated by (4.5)  N a ,t +1 = s a −1 N a −1,t  where sa is natural survival rate at age, given by e-M. The model was run until the age-structure stabilised. Stabilisation was determined by monitoring the average percent-change in proportions at age between each time step, given by  (4.6)   N a ,t N a ,t −1  − Pt −1 1 amax  Pt ∆ t = 100 ∑  N a ,t −1 a max a =0  Pt −1          where  (4.7)  amax  Pt = ∑ N a ,t . a =0  When ∆t becomes very small (∆t < 0.0001%) the age structure is considered stable and r can be approximated by  (4.8)   P  r = ln t  (McAllister et al. 2001).  Pt −1   One thousand Monte Carlo simulations were used to sample from probability distributions of the input parameters described above.  93  Results Systematic calculation of maximum possible UMSY  This analysis systematically evaluated the effects of fecundity, longevity, maturity, growth rate and selectivity on the maximum possible hypothesis for UMSY (i.e., UMSYLim) for species with life-history attributes characteristic of deepwater dogsharks. Results are presented as contour plots of UMSYLim, plotted against ah and κ, allowing the effects of growth and selectivity on UMSYLim to be seen simultaneously (Figure 4.2). Contour plots are presented in panels to show the effects of amat and LS. The contours in Figure 4.2 represent the degree of uncertainty in UMSY that can be calculated for a given stock prior to any formal stock assessment. It is important to note that contour values represent the maximum possible hypothesis for UMSY and actual values of UMSY will be in the range 0-UMSYLim, depending on the species’ (unknown) value of α. In general, uncertainty in UMSY was low over the range of parameter-values considered. Exceptions were more fecund, early-maturing cases with late ah (Figure 4.2 c,d). In these cases, UMSYLim reached values approaching or equal to 1, implying the existence of possible hypotheses for UMSY where all vulnerable individuals are harvested. Such a situation could exist if a large enough proportion of the mature stock was invulnerable to the fishery (e.g., due to the existence of spatial refugia) and there was sufficient recruitment compensation to replace the harvested stock. For later ages at maturity and smaller litter sizes, UMSYLim tended to be low (< 0.1) for all values of ah and κ, becoming extremely low (<0.05) for species with very late maturity and/or very small litters (Figure 4.2 e, f, i-l). Some generalisations can be made about the contribution of individual parameters to the value of UMSYLim . Over the parameter-ranges considered here results were almost completely insensitive to the value of amax and very sensitive to the value of amat for some litter sizes (Figure 4.2). In all cases, there was a positive relationship between UMSYLim and ah, indicated by higher-valued contour lines to the right of every plot. Increasing litter size, LS, also had a positive effect on UMSYLim, indicated by the trend towards higher-valued contour plots from left to right in Figure 4.2. The relationship between κ and UMSYLim was complex, as its effect was mitigated by the values of other parameters, particularly amat and LS. For amat = 5 (Figure 4.2 b,c,d), increasing κ 94  had a positive effect on UMSYLim (Figure 4.2 a-d). For amat = 20, however, the relationship was negative (Figure 4.2 i-l). The transition from positive to negative effect of κ on UMSYLim can be seen in plots g and h of Figure 4.2, where the contours of UMSYLim curve back on themselves as κ increases. This was caused by the effect of increased natural mortality rate M that occurred with increasing κ (through the relationship M = 1.5κ assumed here). As M increased, weight at age, which determines fishery yield, increased, but survivorship-at-age decreased, resulting in few surviving individuals in older age classes. Low survivorship coupled with late maturity (and low fecundity) resulted in few mature individuals and low egg-production (and therefore high unfished juvenile survival relative to α). Therefore, as κ was increased, the constraint on UMSY imposed by α ≤ 1 was reached at successively lower values of UMSY (see Figure 4.2 plots e,f, il). In general, for the same reasons, UMSYLim tended to decrease with increasing amat, although the magnitude of the effect varied.  Dogshark results  The mean and modal values of UMSYLim obtained from the Monte Carlo simulations were, in general, very low for all 12 species of dogshark, especially when age at first harvest was low (Table 4.3). Box plots of Monte Carlo results show the range of estimates of UMSYLim for each tested value of ah, with the median represented as a black bar inside the box showing the interquartile range, IQR (Figure 4.3). Whiskers represent the range of the results within 1.5IQR, with outliers represented as dots. Estimates of UMSYLim were especially low for species in the genus Centrophorus, for which mean UMSYLim ≤ 0.1 was obtained for all values of ah tested (Table 4.3). Similarly low values of UMSYLim across all ah were obtained for D. quadrispinosa and C. crepidater. For earlier age at first harvest (ah ≤ 5), mean UMSYLim was less than 0.05 for these species and less than 0.07 for all species. Low values of UMSYLim can be attributed to late maturity and low fecundity coupled with early age at harvest. For all species, increasing ah had the effect of increasing both the mean and variance of UMSYLim, shown by the larger boxes and whiskers (Figure 4.3). Species with the highest mean estimates of UMSYLim were D. calcea, E. granulosus, S. megalops and S. mitsukurii (Figure 4.3.; Table 4.3). 95  Many population models are parameterised in terms of biological productivity parameters such as CR rather than UMSY and limitations on these parameters are therefore also of interest. The unfished juvenile survival rate,  R0 is the inverse of unfished eggs per recruit, φE0, which can be E0  calculated using only life history parameters. The unfished juvenile survival rate provides a natural constraint on CR when the stock-recruit function is parameterised in terms of numbers of R eggs rather than spawning stock biomass, i.e., CR cannot exceed 0 E0  −1  , otherwise α would  exceed 1. Probability densities of unfished juvenile survival and the implied upper limit of CR (CRLim) resulting from the Monte Carlo simulations are shown in Figure 4.4. Mean CRLim was conservative for most species (~ 20), and very conservative for Centrophorus spp. (~ 5), reflecting severe limits on CR implied by very high unfished juvenile survival rates (Figure 4.4).  Demographic analysis  Mean and modal values of r ranged from 0.06 - 0.17 (Figure 4.5, Table 4.4). While r and UMSYLim are not comparable, estimates of r from the demographic analysis, representing UMax,  were, in general, consistent with trends in the estimates of UMSYLim from the previous section. The least productive species were found to be Centrophorus spp. and D. quadrispinosa, which had mean estimates of r = 0.06 - 0.08. The UMSYLim analysis also found these to be the least productive species for all selectivities tested (Table 4.3). Similarly, the most productive species were found in both studies to be D. calcea and E. granulosus. In both analyses, modal values were lower than mean values, reflecting slightly skewed probability densities (Figures 4.3 and 4.5). There were highly significant positive correlations between the mean values of r and UMSYLim across species, for all tested values of ah (P < 0.001; 10 df; see Table 4.5). The slope of  the relationship between mean r and mean UMSYLim increased as ah increased. The value of the slope ranged from 0.23 (ah = 1) to 2.03 (ah = 15), with slope equal to 1 for ah = 11 (i.e, r and UMSYLim approximately equal). See Table 4.5 and Figure 4.6.  96  Discussion Demographic approaches (e.g., Smith et al. 1998; Heppell et al. 1999; Cortés 1998; 2002; McAllister et al. 2001; Dulvy and Reynolds 2002; McAuley et al. 2007) have been very useful for estimating productivity of sharks and shark-like species. In one of the first studies applying demographic approaches to estimation of shark productivity, Smith et al. (1998) reported spiny dogfish (Squalus acanthias) to have the lowest intrinsic productivity of the 26 species they examined. Braccini et al. (2006a) reported similarly low values for S. megalops in Australia. Cortés (2002) found S. megalops and S. mitsukurii to have the lowest productivity of 38 species considered. While demographic approaches are instructive, they may be limited because they do not fully account for density dependence in recruitment (Heppell et al. 1999) and effects of selectivity on limits to UMSY. This study has demonstrated that an upper boundary to the range of possible hypotheses of UMSY is estimable for dogsharks and similar species using information only about life-history and selectivity; and that the upper possible hypothesis for UMSY may be very small indeed in some cases. Examinations of limitations imposed on UMSY by limits to the defined range of recruitment parameters proved a useful means of constraining estimates of UMSY, using prior life history information. Results can be used in construction of informative  priors for formal Bayesian stock assessment (e.g., McAllister et al. 2001) or directly, for species with very low UMSYLim, to inform fisheries policy and harvest control rules (e.g., Braccini et al. 2006a). Systematic exploration of combinations of different parameter on the upper limit of UMSY implied that there is more certainty in UMSY as populations tend towards more extreme life history strategies that include later maturity, slower growth and lower fecundity. The systematic analysis highlighted the complexity of the contribution of different parameters to UMSY, which optimises growth, mortality, survivorship and recruitment over a highly non-linear parameter space. It was beyond the scope of this study to conduct an exhaustive analysis of all the effects of individual parameters on UMSYLim, as this would require measurement of the rates of change of multiple variables in at least a five-dimensional parameter space, for a much larger range of values than considered here. However, within the parameter-space considered, some general patterns can be discussed.  97  Decreasing fecundity (litter size) had a strong negative effect on the maximum possible UMSY. All other parameters equal, decreasing litter size decreases the predicted unfished eggs per recruit ϕ E 0 and, therefore, must increase unfished juvenile survival, because it is the inverse of  ϕ E 0 . In other words, sharks with small litters must have high unfished juvenile survival rates. The biological interpretation is that, for a population with very small litters to be able to sustain itself in its unfished state, the survival rate of the few eggs produced must be very high. Modal estimates of the unfished juvenile survival rate in this study ranged from approximately 0.02 to 0.3, much higher than might be expected for most teleosts. The low values of CR found for the dogsharks in this study are consistent with the common assumption of near-linear stockrecruitment relationships for sharks, where recruitment is directly dependent on adult stock size (Bonfil 1994; Walker 1998). Note that Goodwin et al. (2006) analysed stock-recruit data for 54 Atlantic teleost stocks and found that CR was higher in stocks that were longer-lived and slower growing, contrary to the findings presented here. The argument of Goodwin et al. (2006), however, applies to teleosts, which grow continuously and for which there is a strong relationship between age, body size and fecundity. In evolutionary terms, long-lived teleosts can afford low rates of unfished juvenile survival because they are able to spread their reproductive potential over many lifetime spawnings (Heppell et al. 1999). This is not generally the strategy for sharks, which tend to produce few pups with a high chance of survival. Chapter 2 reported a relatively minor effect of age at maturity on maximum UMSY and a larger effect of maximum age, amax. Very little to no effect of amax was found in the present study, although it is important to note that fecundity in the model used in Chapter 2 was a function of weight and therefore there was no need to constrain UMSY hypotheses to those that predicted α ≤ 1. In addition, the hypothetical stock considered Chapter 2 was relatively short-lived (15 y). For the given growth, survivorship and maturity schedule, increasing maximum age made a larger relative difference to potential yield than reducing age at maturity. For the longer-lived species considered here, however, survivorship of older age-classes was very low (extremely low for high M cases). Increases in potential yield were therefore better achieved when age at maturity was lower than by increasing the number of age classes, because mature older age classes contributed less to the reproductive output of the stock than younger age classes. This effect was increased by the fact that egg-production was very low, further decreasing the contribution of older age classes. 98  In general, the range of possible values of UMSY for the real dogsharks was estimated to be very small. For most species, under the lowest age-at-first-harvest scenarios (ah ≤ 7), the mean upper limit of UMSY was less than 0.1. For Centrophorus spp. the mean upper limit to UMSY was less than 0.06 for all ah ≤ 7 and, even under the highest age-at-first-harvest scenario (ah = 15), maximum possible UMSY was 0.08 for C. zeehaani. Under higher age-at-first-harvest scenarios, for some species (D. calcea, E. granulosus, S. megalops and S. mitsukurii) the mean value increased to values greater than 0.2 at ah = 15. Etmopterus granulosus had larger litters than most other species (Table 2.1). The other species had small litters, but, on average, had earlier maturity than other species (Appendix to Chapter 4). The species with the largest litters, C. plunketi (19 pups) also had late maturity, hence a more conservative range of UMSYLim than might  be expected from large litters alone. It should be remembered that the values presented here represent the maximum hypothesis for UMSY that could be admitted in a formal stock assessment, i.e., 0 < UMSY ≤ UMSYLim. The results compared favourably with those from the demographic approach, although the quantities estimated are not directly comparable. The demographic model predicted low mean r (< 0.13) for all species. This represents the harvest rate (on the entire stock) that would cause eventual extinction of the stock, UMax, i.e., harvest rates greater than r exceed the rate at which the population is able to replace itself (Hilborn and Walters 1992). There were significant positive correlations between the mean values of r and UMSYLim across species, for all tested values of ah. The slope of the relationship between mean r and mean UMSYLim increased noticeably as ah increased. Again, it should be remembered that UMSYLim represents an upper threshold to UMSY implied by life history and selectivity parameters and that the true value of UMSY lays in the region 0 < UMSY < UMSYLim. Therefore, for values of ah where the slope was  found to be greater than 1 (i.e., UMSYLim > r), it should not be interpreted as an indication that UMSY is greater than r, which is illogical. It should also be noted that demographic approaches  such as the one used here are limited by the fact that they do not account for density dependence in recruitment (Heppel et al. 1999). It is therefore perhaps not advisable to search for predictive relationships between r and UMSYLim, which differ in their interpretations and assumptions. Rather, they should be considered as separate sources of advice. For example, in cases where extinction risk is more of a concern than multispecies considerations, it may be more appropriate 99  to report r directly, as this directly represents the fishing mortality that would cause eventual extinction of the stock. Estimates of r (i.e., UMax) are important for management of multispecies fisheries where it is not possible to maintain all stocks at UMSY simultaneously. ‘Sustainable overfishing’, where UMSY < U < UMax, may be an acceptable policy that addresses the need for compromise between fishing  of important food species and conservation of less productive species (Hilborn 2007a). Punt (2000) reported that the relationship between Fτ (the instantaneous, age-structured equivalent of UMax) and FMSY was a function of the productivity of the stock, and that Fτ and FMSY could be  reasonably close in value for low productivity stocks such as sharks. Myers and Mertz (1998) showed that a precautionary approach for moving these reference points further apart (i.e., FMSY >> Fτ) is to increase the age at which individuals become vulnerable to fishing gear and to allow at least one spawning before allowing individuals to become vulnerable to capture (see also Froese 2004; Froese et al. 2008). Identification of successful tactics for achieving sustainable fishing limits for dogsharks in southeastern Australia will be challenging. Dogsharks are born relatively large and are potentially immediately vulnerable to hooks and trawl nets and also appear to mature late in life (Daley et al. 2002). These authors suggested that spatial closures might be one of the best ways to reduce harvest rates on these species. Recently, three deepwater spatial closures have been announced off NSW, off South Australia and in Bass Strait, aimed at protecting populations of C. moluccenis, C. zeehaani and C. harrissoni respectively (R. Daley, CSIRO, pers. comm.). The  NSW area is located over undersea fibre optic cables and was not targeted at any specific dogshark population, although the wider region is known to be inhabited by C. moluccenis. The other two locations were selected after observations of aggregations of dogsharks in these areas. All three locations were identified and implemented with collaboration and support from the fishing industry. The success of spatial refugia as a harvest control measure depends upon spatial distribution and movement of the population (Gerber and Heppell 2004; Gerber et al. 2005). Very little is known about Australian deepwater dogsharks in these respects, although limited surveys and commercial observations provide some information. There have been no formal tagging studies of deepwater dogsharks in southeastern Australia. Studies in New Zealand have suggested that migration may be extensive in some dogsharks (Clarke and King 1989; 100  Wetherbee 2000) and this could have important seasonal effects on selectivity. Survey data from NSW and southern Australian waters, and observations from commercial fishing vessels, suggest there is separation of males and females of many species (Andrew et al. 1997; Graham et al. 1997; Daley et al. 2002). This implies that some movement would be necessary for mating and, therefore, that sharks may move outside the closures. The same sources also provide evidence for spatial separation of adults and juveniles of most species, suggesting that strategic avoidance of certain age classes could be possible. There may be natural refugia for some species. Several species (e.g., C. zeehaani; C. harrissoni) are known to occur in untrawlable canyoned areas (Daley et al. 2002), although they are accessible by longliners targeting teleosts pink ling (Genypterus blacodes) and blue-eye (Hyperoglyphe antarctica). Walker (1998) discussed effects of size-selectivity in gillnets for sharks but noted that there have been few selectivity studies of sharks in trawl nets. Bycatch reduction devices (BRDs), such as escape panels and grids, have been very effective in reducing bycatch of fish in prawn trawls (Kennelly and Broadhurst 2002; Eayrs 2007) and a number of these devices have been shown to be effective at reducing catches of sharks in particular (Brewer et al. 1998). Gilman et al. (2008) interviewed fishers and compiled fishery data and literature on 12 pelagic longline fisheries, in eight countries, to assess interactions between sharks and longlining. Fishers employed a range of methods to: (i) increase efficiency in catching target non-shark species; and (ii) decrease shark catches. Both of these methods could be effective at reducing unwanted shark catches, but the latter tended to only be employed when there were disincentives to catch sharks (e.g., legal shark retention limits and large fines). Sharks are often patchily distributed and one of the main methods employed by the fishers to reduce shark catch was to move away from areas with high catch rates. Avoidance of topographic or oceanographic features known to be favoured by sharks, and vessel-to-vessel communication of shark ‘hotspots’ to avoid were also effective. Shark-repellent technologies, involving magnets or chemicals, are being developed to deter sharks from longline hooks but are currently still in testing phases (Gilman et al. 2008; see also www.smartgear.org). The trade-off between catch of productive commercial species and abundance of lowproductivity, low-value species such as sharks is unavoidable in most, if not all, multispecies fisheries. Society’s interests are measured by a broad range of objectives that includes 101  profitability of primary industries and maintenance of fresh seafood as well as conservation of vulnerable species. Different stakeholders value these objectives differently and good governance, therefore, requires evaluation of costs and benefits of different management strategies, in terms meeting a suite of management objectives, so that acceptable compromises can be negotiated (Fulton et al. 2007a; Hilborn 2007a,b). In jurisdictions where protection of vulnerable species is mandated, estimates of the range of harvest rates that can be considered sustainable, even if species are technically overfished, is an important part of the evaluation of trade-offs. The low values of UMSY and UMax reported in this study suggest that trade-offs to prevent overfishing of deepwater dogsharks may be severe. There is limited evidence for spatial structuring of dogshark populations in southeastern Australia, suggesting that incentives to encourage avoidance of dogsharks (e.g., Gilman et al. 2008) could be important strategies for controlling harvest rates on dogsharks. However, recent expansion of the automatic longline fishery into canyoned areas, and the efficiency with which dogsharks are caught by this gear (R. Daley, CSIRO, pers. comm.), suggests that spatial closures, such as the ones recently implemented, will also be a necessary management tool.  102  Acknowledgements This work was greatly advanced by the advice and assistance of Ross Daley and Ken Graham, who generously shared their resources and extensive knowledge of dogsharks. Lengthy discussions with both of them inspired this work. Matias Braccini generously provided life history parameters for dogsha