1. Estimation of selectivity in Stock Synthesis: lessons learned from the tuna stock assessment Shigehide Iwata* 1 Toshihde Kitakado* 2 Yukio Takeuchi* 1 *1 National Research Institute of far seas fisheries *2 Tokyo University of Marine Science and Technology

2.  Estimation of size selectivity has a large impact on results of stock assessment  However, size composition data are sometimes complex (e.g. bimodal, trimodal…)  As a result, the estimation of size selectivity has difficulty That was the case in the Pacific Bluefin Tuna assessment Background (1)

3.  In the case of Pacific Bluefin Tuna (PBFT) assessment, estimation of size selectivity was one of key issues because of some difficulty with many fleets to be considered and complicated size distribution data  By these difficulty, we were not able to get reasonable estimates of selectivity parameters in a normal estimation procedure (i.e. estimation using parametric functional forms, estimation of all the parameters once) Background (2)

4. Background (3) For the size composition data in PBFT assessment Circle size indicate the amount of sample size  Fleet4 (Tuna Purse Seine) There are bimodal distributions in the observation data at several year

5. . We will introduce some LESSONS learned from the Pacific Bluefin Tuna assessment with focusing on 1. Functional form (non-parametric or parametric) 2. An iterative estimation procedure (an extension of a method used in the IATTC yellow fin stock assessment) Purpose of this talk

6. Non-parametric selectivity functional form

7. Definitions of parameters

8.  Non-parametric selectivity functional forms are strong tools for estimation of selectivity curve (It is expected to achieve more flexible fit)  We hope to have a better fit to size composition data by using non-parametric functional form with same or least number of parameters. Method (1) Functional form

9.  As non-parametric functional form, cubic spline implemented in the Stock Synthesis 3 Method (2) Cubic Spline Number of parameter is AT LEAST 4.

10. Runs explanation Parametric.sso ： Ｆｌｅｅｔ４： Double normal function 4 parameters node3.sso, node5.sso and node9.sso ： Ｆｌｅｅｔ４： Cubic Spline (non-parametric) 1+x parameters (x=3,5 and 9)

11. Results (1) CPUE fit There is no significant change to the CPUE fit by increasing of # of nodes. Survey 2 Survey 3 Survey 5Survey 9 Survey 1 the confidence interval the observed CPUE

12. Results (2) fit to size composition data Fleet1 Fleet2 Fleet3 Fleet4 Fleet5 Fleet6 Fleet7 Fleet8 Fleet9 Fleet10 Fleet11 Fleet12 Fleet13 Fleet14 The fit to the size composition data except for fleet 4 does not change by using cubic spline. So the size compositions except for fleet4 are expected to give the big impact on θ ・・・ Observed data

13. Results (3) fit to the size composition data － By using cubic spline curves, the fit to size composition would be improved － However, there was no significant change in the fit to size composition data by increasing of # of nodes Estimated selectivity curve Fit to the size composition data ・・・ Observed data

14. Results (4) The dynamics of SSB and Recruitment There is no significant change in the dynamics of SSB and Recruitment SSB Recruitment

15. Results (5) likelihood change In the case of sable fish stock assessment (example in yesterday’s talk), the node numbers are 4 or 5 To be better Total Negative Log Likelihood

16. Summary of non-parametric functional form By using the non-parametric selectivity functional form － Total likelihood do not improve even if # of nodes are 3 or 5. － Total likelihood will be improved If the # of nodes are 9. However the SSB and Recruitment dynamics did not significantly change. In the case of sable fish stock assessment (example in yesterday’s talk), the number of nodes is 4 or 5. So 9 nodes are too much.

17. An iteratively-fixing method

18. Definitions of parameters (again)

19. “Joint likelihood” “Partial likelihood” contributed by CPUEs “Residual likelihood” contributed by size comps Method (1) General formation

20.  A two-step method was employed in the Yellow fin stock assessment in 2012  HOWEVER, the initially fixed selectivity parameters may not necessarily be the possible best option because those parameters  may be revised by maximizing the residual likelihood (L 2 ) given better estimates of   If the further treatment above would produce the better  then  should be updated again Method (2) Procedures

21. An iteratively-fixing method using two separated-likelihood functions Set initial parameter values (arbitrary) This time, we used estimates based on the joint likelihood as in YFT tuna stock assessment way, Then, continue iterative processes as follows

22.  The results tend to CONVERGE (especially estimated SSB, recruitment and selectivity) within the odd or even times  To get better parameters The points to accept this method or not are… Next, we shows the results after 40 iterative (80 runs, 1 iterative have odd and even run).

23. Results (1) Fleet 1 Before iterative run After 40 iterative run the confidence interval the observed CPUE

24. Results (2) Fleet 11 Before iterative run After 40 iterative run the confidence interval the observed CPUE

25. Results (3) CPUE fit all Before iterative run After 40 iterative run Survey 5 Survey 9 the confidence interval the observed CPUE Survey 2 Survey 3 Survey 1

26. Results (4) size selectivity fit Before iterative run After 40 iterative run In the almost fishery, we can get better size selectivity curve. Fleet1 Fleet2 Fleet3 Fleet4 Fleet5 Fleet6 Fleet7 Fleet8 Fleet9 Fleet10 Fleet11 Fleet12 Fleet13 Fleet14

27. Results (6) Convergence For the odd iteration run for SPB Increasing of iteration For the odd iteration run for Recruitment Increasing of iteration Each line indicates the SSB or REC ratio at same year during stock assessment period By the Raabe's convergence test, we can conclude the SSB and Recruitment will be converge

28. Results (7) SSB and recruitment Before iterative run After 40 iterative run After the iterations, series of SSB and recruitment are converged. However the levels of SSB are different between two runs Hope this change is “improvement”, but it is necessary to conduct a comprehensive simulation study for more valid conclusion

29. There was no impact on SSB and Recruitment by increase the number of nodes in PBFT The total likelihood dramatically changed only if number of nodes is 9. So, there is no improvement by the introduction of non-parametric functional forms and these were not suitable for the PBF stock assessment. The iterative method aimed at providing better estimation of population dynamics. Although the method is not perfect in terms of fitting, but some improvement was observed in the CPUE and size composition (good sign ??) Need more practice and investigation on this method Summary

30. Background (4) For the size composition data in PBFT assessment  Fleet12 (Tuna Purse Seine in EPO) - Highly temporal fluctuation 1955 1960 1965 1970 1975 1980 1980 1985 1990 1995 2000 2005 2010