1. Gulf of Maine cod SCAA/ASPM vs ADAPT-VPA Doug Butterworth and Rebecca Rademeyer __________________________________________________________________ Marine Resource Assessment and Management Group, University of Cape Town

2. METHODS ADAPT-VPA - Backward calculation - Oldest-age F assumption - Catches-at-age exact SCAA/ASPM - Based on separability: F y,a = S a F y - Forward estimation, typically likelihood based - Errors in proportions-at-age SCAA - Statistical treatment of age data errors May include S/R relationship ASPM - Age-structured dynamics Must include S/R relationship Age data not necessary

3. ASPM methodology updates - M fixed (0.2) (not estimated) - Ricker-like not Beverton-Holt S/R relationship - MSY calculated internally - All S a ’s estimated (no functional form imposed) - Model to 11+, though fit to 7+ data - Fully Bayesian PI computations

4. VPA methodology - RC-VPA: as Mayo and Col (2006) – asymp. flat selectivity Fit either to ages 1-6 or 1-7+ MSY calculated externally - Alt-VPA (  =1): removes inconsistency in plus-group eqns - Alt-VPA (  =est): estimates  where

5. Data used Mayo and Col (2006) BUT Scaled to get

6. 2003 Results Gulf of Maine cod

7. Results RC-ASPM (M=0.2, Ricker) Shading shows 95% PIs

8. Abundance index fits RC-ASPM (M=0.2, Ricker)

9. Average age-proportion fits RC-ASPM (M=0.2, Ricker)

10. Selectivity estimates RC-ASPM (M=0.2, Ricker) Commercial, pre-1992 Commercial, post-1991

11. Selectivity estimates RC-ASPM (M=0.2, Ricker) Commercial, pre-1992 Commercial, post-1991 NEFSC-Spring NEFSC-Autumn

12. ASPM Stock-recruit relationships - l nL = -46.3 Ricker

13. ASPM Stock-recruit relationships - l nL = -46.3 RickerBeverton-Holt - l nL = -39.9 If estimate  parameter (  =1 for Ricker): 1.05 [0.54; 1.15]

14. ASPM Selectivity dome - l nL = -46.3 S 7 /S 6 =0.52 [0.41; 0.64] - l nL = -11.4 Asymp. flat selectivity

15. ASPM Past catch selectivity 1992-2004: Estimated 1981-1991: Estimated Pre-1982: Set equal to 1982-1991 Second order effect (Important assumption is unchanging survey selectivity) Per-recruit contribution to cohort biomass

16. ASPM Results

19. ADAPT-VPA comparisons VPA as Mayo and Col (2006)

20. ADAPT-VPA comparisons VPA as Mayo and Col (2006) RC-VPA

21. ADAPT-VPA comparisons VPA as Mayo and Col (2006) RC-VPA Alt-VPA,  =1

22. ADAPT-VPA comparisons VPA as Mayo and Col (2006) RC-VPA Alt-VPA,  =1 Alt-VPA,  =est

23. ADAPT-VPA comparisons VPA as Mayo and Col (2006) RC-VPA Alt-VPA,  =1 Alt-VPA,  =est ASPM – Data from 1982

24. ADAPT-VPA comparisons VPA as Mayo and Col (2006) RC-VPA Alt-VPA,  =1 Alt-VPA,  =est ASPM – Data from 1982 RC – ASPM

25. ADAPT-VPA comparisons VPA as Mayo and Col (2006) RC-VPA Alt-VPA,  =1 Alt-VPA,  =est ASPM – Data from 1982 RC – ASPM

26. ADAPT-VPA Selectivities RC-VPA

27. ADAPT-VPA Selectivities RC-VPA Alt-VPA,  =1

28. ADAPT-VPA Selectivities RC-VPA Alt-VPA,  =1 Alt-VPA,  =est

29. ADAPT-VPA Selectivities RC-VPA Alt-VPA,  =1 Alt-VPA,  =est ASPM – Data from 1982

30. ADAPT-VPA Selectivities RC-VPA Alt-VPA,  =1 Alt-VPA,  =est ASPM – Data from 1982 RC – ASPM

31. ADAPT-VPA Results

34. Conclusions General - Careful treatment of plus-group - Fully flexible S a parametrization - Take care with use of Beverton-Holt S/R relationship

35. Conclusions Gulf of Maine cod - 2003 difference as ADAPT-VPA imposed asymp. flat selectivity - Asymp. flat selectivity statistically inconsistent with data Independent evidence of mechanisms to give dome shape ? - close to and Robust to sensitivities - SCAA to be preferred Enables use of pre-1982 data Greater range of B sp Better precision of estimates M-S Act focus on MSY

36. Thank you for your attention