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

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?

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

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

Methods

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

Data for analysis Data for wild Chinook M.Y.s Wild steelhead: 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 C 0 fish for in-river SAR Used bootstrap output for annual sampling variance, except for C 0 -only analysis

Results

Forest plot of Chinook TIR, incl (C 1 )

Forest plot of Chinook TIR, without 2001

Forest plot of C 0 -only Chinook TIR

Forest plot of steelhead TIR, incl (C 1 )

Forest plot of steelhead TIR, without 2001

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

TIR findings summary 2001 highly influences Chinook B-Y var, if C 1 fish are used as in-river group that year Mean Ck TIR ~ sensitive to use of C 1 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

Forest Plot of wild Chinook D, incl (C 1 )

Forest Plot of wild Chinook D, without 2001

Forest Plot of wild steelhead D, incl (C 1 )

Forest Plot of wild steelhead D, without 2001

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

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

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 S R < Ck S R. Maximum transport strategies may not have maximized wild Chinook SAR Delayed transport mortality of wild Chinook Unclear if wild steelhead experience delayed transport mortality

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 S R

Questions?