Evaluating methods for setting catch limits for gag grouper: data- rich versus data-limited Skyler R. Sagarese 1,2 , John F. Walter III 2 , Meaghan D. Bryan 2 , and Thomas R. Carruthers 3 1 Cooperative Institute for Marine and Atmospheric Studies, RSMAS, Univ. of Miami; 2 Southeast Fisheries Science Center; 3 Univ. of British Columbia 30 th Lowell Wakefield Fisheries Symposium May 13, 2015 Anchorage, Alaska
Outline • Brief introduction • Stock assessments in the southeast US • Study species: shallow-water groupers • Objective • Methods • Data-rich • Data-limited • Results • Applicability to data-limited grouper stocks
Biodiversity in the southeast US • High biodiversity Table 1 from Fautin et al. (2010) Image : http://www.nmfs.noaa.gov /sfa / management/councils/ Reference : Fautin, D., P. Dalton, L.S. Incze, J.-A.C. Leong, C. Pautzke, A. Rosenberg, P. Sandifer, G. Sedberry, J.W. Tunnell Jr, and I. Abbott. 2010. An overview of marine biodiversity in United States waters. PLoS One 5:e11914. 10.1371/ journal.pone.0011914
Biodiversity in the southeast US • High biodiversity Table 1 from Fautin et al. (2010) Image : http://www.nmfs.noaa.gov /sfa / management/councils/ Reference : Fautin, D., P. Dalton, L.S. Incze, J.-A.C. Leong, C. Pautzke, A. Rosenberg, P. Sandifer, G. Sedberry, J.W. Tunnell Jr, and I. Abbott. 2010. An overview of marine biodiversity in United States waters. PLoS One 5:e11914. 10.1371/ journal.pone.0011914
Biodiversity in the southeast US • High biodiversity Table 1 from Fautin et al. (2010) Image : http://www.nmfs.noaa.gov /sfa / management/councils/ Reference : Fautin, D., P. Dalton, L.S. Incze, J.-A.C. Leong, C. Pautzke, A. Rosenberg, P. Sandifer, G. Sedberry, J.W. Tunnell Jr, and I. Abbott. 2010. An overview of marine biodiversity in United States waters. PLoS One 5:e11914. 10.1371/ journal.pone.0011914
Biodiversity in the southeast US • High biodiversity Table 1 from Fautin et al. (2010) Image : http://www.nmfs.noaa.gov /sfa / management/councils/ Reference : Fautin, D., P. Dalton, L.S. Incze, J.-A.C. Leong, C. Pautzke, A. Rosenberg, P. Sandifer, G. Sedberry, J.W. Tunnell Jr, and I. Abbott. 2010. An overview of marine biodiversity in United States waters. PLoS One 5:e11914. 10.1371/ journal.pone.0011914
Assessments in the southeast US • Most OFLs/ABCs set using data-poor methods (Newman et al. 2015) • GOM – 74% • South Atlantic – 77% • Caribbean – 100% • Atlantic HMS – 92% • OFLs are set with only minor scientific input
Shallow-water groupers (SWG) • Managed Complex Species Model as a Shallow-water gag Mycteroperca microlepis Integrated analysis species black M. bonaci Catch-at-age complex scamp M. phenax − yellowfin M. venenosa − • Assessed yellowmouth M. interstitialis − on a red Epinephelus morio Integrated analysis species red hind E. guttatus Data-limited basis rock hind E. adscensionis − Goliath E. itajara Catch-Free Nassau E. striatus − Images: http://safmc.net/fish-id-and-regs/regulations-species
SWG landings Red Grouper Gag Black Grouper Scamp Other SWG 5000 4000 Landings (t) 3000 2000 1000 0 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1998 1999 2000 2001 2002 2003 2004 2005 2006 2008 2009 2010 2011 2012 2013 1997 2007 Data source : http://www.st.nmfs.noaa.gov/commercial-fisheries/commercial-landings/annual-landings/
Objective Figure : Data inputs from Stock Synthesis model • Could we have achieved a similar assessment result for GOM gag with less data or with computationally less-intensive methods on aggregated data?
Methods – Stock Synthesis “data-rich” • Integrated analysis (Wetzel and Methot 2013) 1. Population sub-model Statistical catch-at-age model • 2. Observational sub-model Uses a wide range of data types to calibrate model • 3. Statistical sub-model Quantifies the goodness of fit statistic between • values expected and observed • Highly flexible model structure SS3 freely available at: http://nft.nefsc.noaa.gov/Stock_Synthesis_3.htm
Methods – data-limited (DLM) • ‘DLMtool’ package in R (Carruthers et al. 2014) Method / Management Procedure Harvest Control Rules or Extensions Tested Catch Scalars - Geromont-Butterworth (GB) Constant catch, CPUE gradient rule Simple Bluefin Tuna (SBT1) - Depletion Fratio (DepF) - Depletion-Based Stock Reduction 40% depletion, 40-10, Mean Length Estimation Analysis (DBSRA) (ML) Depletion-Corrected Average Catch 40% depletion, 40-10, ML (DCAC) F MSY to M ratio (Fratio) 40% depletion, 40-10, ML Beddington and Kirkwood Life-History CC (Catch Curve Estimation), ML Analysis (BK) Delay-Difference (DD) 40-10 Demographic FMSY (Fdem) CC, ML Surplus Production MSY (SPMSY) - Surplus Production Stock Reduction ML Analysis (SPSRA) Yield Per Recruit (YPR) CC, ML ‘DLMtool’ available from: http://cran.r-project.org/web/packages/DLMtool/index.html
Model evaluation • Compared OFL distributions between SS (“truth”) and DLMs using relative absolute error (RAE) (Dick and MacCall 2011) : 𝑆𝐵𝐹 = ¡ |𝑛𝑓𝑒𝑗𝑏𝑜(𝑃𝐺𝑀) − ¡ 𝑃𝐺𝑀↓𝑏𝑡𝑡𝑓𝑡𝑡𝑛𝑓𝑜𝑢 |/𝑃𝐺𝑀↓𝑏𝑡𝑡𝑓𝑡𝑡𝑛𝑓𝑜𝑢 • Sensitivity analysis to determine which data inputs strongly influence quota recommendations
Management strategy evaluation • Explored the relative performance among potentially applicable DLM for gag grouper • Simulations: 200 • Repetitions: 100 • Duration: 30 years • Assessment interval: 5 years • Compared trade-offs between probability of overfishing, yield, and probability of the biomass dropping below B MSY
Results – quota comparison with SS SS: 3,192 t ± 204 SD Overfishing Limit (OFL, t) Methods Min Median Max RAE GB_slope 2,164 3,060 3,246 0.04 DCAC_ML 1,148 2,950 17,504 0.08 Fdem_ML 293 2,854 22,205 0.11 SPSRA 453 3,565 1,439,942 0.12
Data Inputs Results - Sensitivity BMSY_B0 FMSY_M MaxAge vbLinf steep Abun Mort vbt0 AvC LFC LFS CAA CAL Cref Bref Dep vbK AM wla wlb Cat Ind Dt Method AverC X • OFL quotas MCTen MCThree GB_CC X X • Sensitive to: GB_slope X X SBT1 X DepF X X X X • Natural mortality X X X X X DBSRA 40 X X X X • Catch 4010 X X X X ML X X X X • Abundance DCAC X X X X X 40 X X X X 4010 X X X X X • Depletion ML X X X X X X Fratio X X X • Steepness X X X CC 4010 X X X X ML X X X X X • Insensitive to: BK X X X CC X X X X ML X X X X X • Von Bertalanffy t0 DD X X X X 4010 X X X X X Fdem X X X X • Von Bertalanffy Linf X X X X X CC ML X X X X X X • Weight length a SPMSY X SPSRA X X X X ML X X YPR X X X X X CC X X X X ML - - - - - - - - - -
Results - MSE Probability of overfishing (POF) • Best performance: • Depletion Fratio, Fratio4010 • < 20% POF • Intermediate yield (55 – 60 t) • SS-matching methods: B < B MSY • SPSRA • < 40% of biomass dropping below B MSY • Intermediate yield (~50 t) • GB_slope • Low yield
Results - MSE Probability of overfishing (POF) • Best performance: • Depletion Fratio, Fratio4010 • < 20% POF • Intermediate yield (55 – 60 t) • SS-matching methods: B < B MSY • SPSRA • < 40% of biomass dropping below B MSY • Intermediate yield (~50 t) • GB_slope • Low yield
Summary • Most DLMs provide lower estimates of OFL compared to SS • Due to dome-shaped selectivity and “cryptic” biomass • DLMs assume asymptotic selectivity • Expect higher F • Could lead to precautionary advice
Summary • Quota recommendations influenced by data inputs • M, steepness, catch, current abundance, depletion • Setting management objectives • Sexes combined versus female only SSB models • DLM methods appear to produce similar results to sexes combined SS model • Methods producing results similar to SS: • DCAC_ML, Fdem_ML, GB_slope, SPSRA
Applicability to other SWG • Use depletion estimates for gag • “Robin Hood” approach (Punt et al. 2011) • DCAC_ML and Fdem_ML • If catch-at-length data is available • Easy to collect • Estimate F, can estimate current abundance or depletion • Importance of selectivity • Way to scale OFL based on degree of doming in selectivity?
Acknowledgments • Assessment analysts • J. Tetzlaff, A. Rios, S. Cass-Calay, C. Porch, M. Schirripa, M. Karnauskas, N. Cummings • Fisheries Statistics & Sustainable Fisheries Divisions • SEDAR participants • Funding: Gulf of Mexico IFQ cost-recovery program
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