Dana Hanselman and Pete Hulson Alaska Fisheries Science Center Juneau, AK

1. Tradeoffs between bias, model fits, and using common sense about biology and fishing behaviors when choosing selectivity forms Dana Hanselman and Pete Hulson Alaska Fisheries Science Center Juneau, AK

2. Outline • Introduction • Biology and fleet behavior • Case study: GOA Pacific ocean perch • Precision and estimability • Case study: Alaska sablefish • Simulation tests • Preliminary Conclusions

3. Introduction • The slow creep of SS3 into AFSC • Paladins of parsimony • Highly parameterized models seem unstable • Can we use complicated models for research, but simpler models for management?

4. Double Domes and steep drops • WC Sablefish H&L BS Turbot Trawl fish. BS skate trawl fish. Ian-Stewart

5. Time varying everything • BS P. Cod T. Survey EBS Pollock Ian-Elli Ian-Taylor

6. GOA Pacific ocean perch • Strong catch-history, rebuilt • Variable recruitment, clustered cohorts • Age structured (AMAK-like) • Marginally good trawl survey • 1000 otoliths per survey/fishery year (odd/even)

7. Gulf of Alaska POP – Problems Survey q drifting upward each assessment Fishery selectivity was drifting domed but highly constrained q and selectivity interact Is it more likely that the survey q is changing in one direction or the fishery selectivity might have changed? Look for evidence of dome-shape selectivity in fishery

8. POP Fishery:Early Fishery versus Current

9. POP – Catch by depth

10. Fishery was catching greater than 25% over 25 years old in the 80’s

11. Fishery was catching a much higher proportion of older fish than survey in 80’s

12. The reverse has occurred recently

13. Fit selectivities to raw data by estimating selectivity curves and mortality Logistic looks pretty good for survey

14. Gamma fits about half as good, minimal dome suggested.

15. Logistic to the fishery fits acceptably except for pooled group…

16. But gamma has 20% of the residual error and fits pooled age well

17. POP – Final model New selectivity functions to describe fishing fleet Fit toward dome in three stages 1961 to 1976: the beginning and end of the foreign fishing fleets massive catches 1977 to 1995: The domestication of the fishery, but large factory trawlers still dominant 1996-Present: The emergence of catcher-boats, semi-pelagic trawling, fishing cooperatives, fishing shallower

18. Better fit to fishery ages, 9 less parameters, slightly better but similar fit overall

19. POP – Model Results Recommended model, new selectivity Substantially better fit to fishery age comps (25% reduction in fishery age –lnL) Survey catchability parameter reduced below 2 Fit data better with 9 less parameters

20. Alaska sablefish Long survey time series (36 annual LL, 13 trawls) High-value fish ($142 million in 2011, IFQ) Lots of data Split-sex 2 fishery (really at least 3) Huge area Mainly targeted

21. Alaska sablefish • Two sexes made selectivity difficult to estimate • Trawl survey and fishery should be descending (shallow) • Simplified selectivities for better estimation

22. Trawl fishery selectivity Exponential Logistic Gamma Females Females Males Males 6 parameters to 2 parameters

23. Trawl survey selectivity Exponential Logistic Power (1/ax) Females Females Males Males 6 parameters to 2 parameters

24. Selectivity: Precision

25. Model Evaluation • Parameter correlations greater than 0.4: • Model 1: 17 • Model 2: 14 • Model 3: 1 • Model 3 fits about the same as Model 1 but with 13 less parameters, better model stability and less parameter correlation.

26. Simulation – life history cases

27. Simulation – selectivity cases

28. Simulation – model

29. Operating/Estimation One fishery, one survey, one SEX Survey constrained to be logistic 6 x 6 x 100 (fixed q) 6 x 6 x 1000 (estimate q) Age comps only, no lengths Multinomial sample size of 200

30. Gamma (POP)

31. Double normal (POP)

32. Double normal (pollock, est. q)

33. Catchability (POP) (est. q)

34. LMR (POP, est. q)

35. Natural mortality (ATF)

36. Natural mortality (POP)

37. Ending SSB (POP)

38. Estimation/precision More parameters, more uncertainty, less convergence Even when biased, logistic and gamma are precise Models are more stable Correlations are lower

40. CVs –Double normal

41. CVs –Logistic and gamma Logistic Gamma

42. CV of OFL (pollock)

43. Multiplier at P*=0.25 (pollock, est. q)

44. Preliminary conclusions Forcing the logistic can create bias in M For fishery selectivity, logistic not necessarily conservative Double normal can fit most shapes but at a cost: Selectivity parameters are not precise Oddly, OFL and ending SSB are more precise (Hessian)

45. Preliminary conclusions Complicated selectivities are OK when: There is a rationale that a fisherman can understand The model can be reliably estimated with the number of selectivity parameters (e.g., easy convergence and CV<50%) Parameter correlations <0.5? Our simple simulations did not provide obvious results, selectivity IS complicated

46. IntroducingThe TWINCE model

47. Introducing The Triple-Weibull-Inverse-Negative-Cauchy-Exponential ONLY 19 parameters Can meet all your selectivity needs Flexible shapes (reversible, like overfished) Stable until you add real data Estimable until you turn on the parameters THANKS!