A Synthesis of Annual Estimates of TIR and D for Wild Populations

1. A Synthesis of Annual Estimates of TIR and D for Wild Populations Presenter: Paul Wilson CSS Annual Meeting Apr 2nd 2010

2. Chapter 5 Objectives • Many years, CIs of TIRs & Ds wide and/or contain 1—how can we determine if TIR or D is generally > or < 1? • Can we detect a  in mean TIR or D due to altered management? • Inter-annual variation in TIR and D of interest for modeling viability & effects of management. Can we get a good estimate?

3. Synthesizing multi-study data In various fields, incl. ecology, information from multiple studies is combined using “meta-analysis” Goal is to increase power to detect effects, by estimating “summary effect” from individual effect size estimates Treat each migration year as a “study” and use meta-analysis techniques

4. Kinds of meta-analysis “Fixed-effect”: all studies assumed to share same true effect—variation in estimates due solely to experimental error “Random-effects”: true effect size varies from study to study—summary effect estimates the mean of distribution of effect sizes Annual TIR & D values surely vary, so we use random effects formulas

5. Methods

6. RE Meta-analysis on TIR & D TIR and D = “response ratios”. Use ln(TIR) & ln(D) to linearize & normalize Need to estimate “between-study” variance: variance in true effect size between years Individual years weighted by inverse of (annual sampling variance + between-year variance) Estimate mean, CI of mean, & variance of distributions of TIR and D for years included

7. Data for analysis Data for wild Chinook 1994-2006 M.Y.s Wild steelhead: 1997-2006 M.Y.s Both species, did two analyses for TIR & D: 1) including 2001 M.Y., 2) omitting 2001 For Chinook TIR only, also did analysis using only C0 fish for in-river SAR Used bootstrap output for annual sampling variance, except for C0-only analysis

8. Results

9. Forest plot of Chinook TIR, incl. 2001 (C1)

10. Forest plot of Chinook TIR, without 2001

11. Forest plot of C0-only Chinook TIR

12. Forest plot of steelhead TIR, incl. 2001 (C1)

13. Forest plot of steelhead TIR, without 2001

14. Summary mean TIR (center lines), 90% CIs of summary mean (boxes), and 90% prediction limits of summary TIR (whiskers).

15. TIR findings summary 2001 highly influences Chinook B-Y var, if C1 fish are used as in-river group that year Mean Ck TIR ~ sensitive to use of C1 fish and inclusion of 2001, but all C.I.s include 1 SH B-Y var much > than Ck B-Y var; ~ sens. to 2001 Mean SH TIR >> 1 & C.I.s > 1,  benefit from transporting

16. Forest Plot of wild Chinook D, incl. 2001 (C1)

17. Forest Plot of wild Chinook D, without 2001

18. Forest Plot of wild steelhead D, incl. 2001 (C1)

19. Forest Plot of wild steelhead D, without 2001

20. Summary mean D (center lines), 90% CIs of summary mean (boxes), and 90% prediction limits of summary D (whiskers).

21. D findings summary 2001 strongly influences Chinook B-Y var Mean Ck D slightly sensitive to inclusion of 2001 Mean Ck D << 1, and both C.I.s < 1  delayed transportation mortality SH B-Y var much > than Ck B-Y var; not sens. to 2001 SH mean D not sens. to 2001; C.I.s include 1

22. Conclusions Better estimates of mean than unweighted Strong evidence that wild steelhead TIR > 1, under operations prior to 2007, but benefit is highly variable. SH TIR > Ck TIR both because SH D > Ck D and SH SR < Ck SR. Maximum transport strategies may not have maximized wild Chinook SAR Delayed transport mortality of wild Chinook Unclear if wild steelhead experience delayed transport mortality

23. Caveats & Extensions SARs of adjacent year classes not independent-but only ratios of SARs analyzed Dependence means CIs too narrow. Likely doesn’t change main conclusions Marking more steelhead marking could help narrow CIs Could use “meta-regression” to further investigate relation of TIR to SR

24. Questions?