1. Is down weighting composition data adequate to deal with model misspecification or do we need to fix the model? Sheng-Ping Wang, Mark N. Maunder National Taiwan Ocean University Inter-American Tropical Tuna Commission Center for the Advancement of Population Assessment Methodology

2. Data weighting is a common issue that arises when developing stock assessment models. Previous studies indicated that diverse stock assessment conclusions may result from different data weightings. The appropriate weighting of data sets in stock assessment models is an important component of model development.

3. In this study, we develop a simple age- structured population dynamics model for summer flounder in the U.S. mid-Atlantic to explore the influence of data weightings on model estimation using a simulation approach. A simulation analysis based on this model is conducted to examine whether data weighting can deal with misspecified steepness, natural mortality and selectivity.

4. Summer flounder fishery Summer flounder (Paralichthys dentatus) is one of the most important commercial and recreational species on the U.S. Atlantic coast. Total landings declined substantially during the late 1980s by 1990 and then has been relatively constant since the early 1990s.

5. Previous stock assessment Data used in previous assessments consists of – Catches for 6 fisheries – Indices for 3 surveys – Age-compositions for 6 fisheries and 3 surveys – Mean body weight for 1 fishery

6. Model used in this study To explore the influence of data weighting on model estimation, we develop a simple model, which includes data of – Catch for 1 fisheries (total catch) – Index for 1 surveys – Age-compositions for 1 fisheries and 1 surveys – Mean body weight for 1 fishery

7. Model used in this study We also change the sex-specific model into single sex model. Life history parameters: Life history parameterValue Steepness (h)0.85 Natural mortality (M)0.20 Length at maximum age (Linf)62.12 Growth coefficient (K)0.20 Coefficient of length-weight relationsip (a)2.44E-06 Exponent of length-weight relationsip (b)3.35 Length at 50% maturity (L 50 )28.10 Slope of maturity ogive-0.25 Recruitment deviation (σ R ) 0.60

8. Simulation procedure The model is developed using Stock Synthesis. 1)Fit actual data to the model to obtain estimates of parameters. 2)Generate simulated data based on SS bootstrap data by fixing parameters obtained from step 1), and also replacing recruitment deviation by random values. 3)Fit simulated data to the model without any misspecification to obtain the “true” estimates. 4)Fit simulated data to the model with assumed misspecification to obtain the estimates under model misspecification. 5)Repeat steps 2) to 4) for 100 times.

9. Scenarios We conduct 9 scenarios to explore the influence of misspecifications of model estimations. CaseMhSelectivity for fishery True0.20.85Dome-shaped and time-variant 10.2 0.85Dome-shaped and time-variant 21 30.15 40.3 5Asymptoic and time-variant 6Estimate 7 1 8 Asymptoic and time-variant 9 Dome-shaped and time- invariant

10. Scenarios We also conduct 5 weightings for age composition data to explore the influence of data weighting of model estimations. CaseFisherySurvey 1-F&S11 0.1-F&S0.1 10-F&S10 0.1-F0.11 10-F101

11. Misspecification of life history parameters generally leads to biased estimates. Biased estimates occurs when down or up weighting, even without any misspecification (case1). Down weighting could not significantly improve model estimates. Up weighting leads to obviously imprecise estimations. Results - Misspecification for life history parameter

12. Down or up weighting leads to biased estimates when selectivity is misspecified. Up weighting may somehow improve accuracy of estimates but substantially deteriorates the precision of estimates for most quantities. Results - Misspecification for selectivity

13. Although misspecification of h leads to systematically biased estimates, estimating M makes estimates more consistent whenever down or up weighting, even though selectivity is misspecified. Up weighting deteriorates the precision of estimates. Results - Estimating natural mortality

14. Estimate of M are not influenced when down or up weighting. Up weighting slightly deteriorates the precision of estimates. Results - Influence of weighting on estimate of M

15. Parameters of selectivity are less influenced when misspecifiying life history parameters or estimating M (most REs within 10%). Estimates of selectivity are less relevant to data weighting. Misspecifiying selectivity as time-invariant leads to systematically biased estimates of selectivity. Results - Influence of weighting on selectivity

16. Results - Mean relative error QuantityCase1-F&S0.1-F&S10-F&S0.1-F10-F R0R0 10.006.69-2.001.12-1.47 2-46.94-45.70-46.15-46.20-46.52 332.7445.4330.1834.4429.78 4-3.870.77-5.95-3.05-4.56 50.0512.54-7.041.03-1.88 60.146.262.091.88-1.92 7-47.38-47.43-45.71-48.17-45.92 8-2.668.46-6.08-0.21-5.07 95.7912.32-4.147.698.19 SB cur /SB 0 10.00-5.40-1.16-2.400.08 270.3063.0067.6965.6367.43 3-49.81-53.99-48.96-51.29-49.12 483.3985.3674.2080.3279.43 5-1.23-11.26-7.75-0.55-8.67 67.637.994.243.2713.44 763.6449.6464.8151.3969.24 825.7517.6217.5115.0931.68 9-9.92-8.47-40.37-8.15-13.70

17. Results - Mean relative error QuantityCase1-F&S0.1-F&S10-F&S0.1-F10-F MSY 10.003.40-1.570.67-1.61 2-37.34-36.62-36.33-36.64-36.86 361.7269.5059.6662.8357.92 4-30.45-29.22-31.70-30.06-31.05 54.7312.67-1.685.263.53 6-2.11-1.352.39-0.05-5.89 7-35.98-34.31-35.10-34.28-36.82 8-8.50-2.89-9.64-2.04-15.13 9-2.253.38-11.170.55-9.81 SB cur /SB MSY 10.00-4.82-1.47-1.990.72 2114.84108.78110.83109.93112.97 3-49.15-52.94-48.43-50.41-48.08 473.2677.8564.2770.7770.30 5-14.48-23.71-19.91-13.96-20.81 66.957.662.643.0712.59 7106.9892.72104.8894.24111.18 89.091.872.12-0.2714.31 9-12.09-10.02-41.78-12.55-7.34

18. Results - Root-Mean-Square Error (RMSE) QuantityCase1-F&S0.1-F&S10-F&S0.1-F10-F R0R0 10.003.355.891.432.00 24.254.604.344.254.39 36.2610.1513.977.146.28 43.474.785.073.413.93 52.314.357.492.653.01 65.856.9714.526.506.38 76.498.568.056.858.18 84.717.729.765.614.96 92.114.467.392.775.20 SB cur /SB 0 10.004.3915.481.814.29 28.7510.1228.018.7810.25 32.493.549.122.873.54 48.0211.5031.438.009.72 52.744.5717.773.235.40 621.2525.8238.7221.8328.36 732.2839.3942.8835.9037.85 826.4631.4339.6724.1831.91 92.664.4616.102.6612.71

19. Results - Root-Mean-Square Error (RMSE) QuantityCase1-F&S0.1-F&S10-F&S0.1-F10-F MSY 10.003.375.891.191.63 24.955.165.104.925.02 37.5811.1417.168.527.53 42.473.363.582.472.73 52.684.287.762.763.26 613.3914.8827.7114.3014.86 76.297.547.156.996.32 814.3918.9023.3215.4514.29 91.224.026.221.893.59 SB cur /SB MSY 10.004.7315.371.875.07 211.7213.1635.1611.9816.19 32.553.809.133.013.80 47.9410.9329.727.889.89 52.664.0115.643.015.03 620.1024.4336.3720.5326.58 730.2041.4644.1135.4634.60 823.3528.0834.7921.3228.07 92.704.8215.922.9413.63

20. Summary Biased estimates are generally obtained when misspecification occurs for either life history parameters or assumption of selectivity. Downing weighting composition data may lead to biased estimates for most quantities. Up weighting composition data may somewhat improve model estimates, but substantially deteriorates the precisions of model estimates.

21. Summary Either down or up weighting composition data leads to biased estimates when selectivity is misspecified. Estimates of M are not influenced by weighting for composition data. Estimates of Selectivity are also not influenced by weighting for composition data, except for misspecifying time-varying selectivity.

22. Future work Conduct simulation analysis by incorporating length-composition data. – Evaluate the impact of weighting to length- composition data on model estimates and growth. Evaluate the impact of data weightings on the results of full stock assessment model.

23. Thank you