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

Presenter: Paul Wilson CSS Annual Meeting Apr 2nd

2010

Chapter 5 ObjectivesMany 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 analysisData for wild Chinook 1994-2006 M.Y.sWild steelhead: 1997-2006 M.Y.sBoth 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

Results

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

Year1994199519961997199819992000200120022003200420052006

Summary

TIR1.620.951.920.740.871.140.608.960.651.061.092.140.79___ 1.17

0.5 1.5 2.5 3.5 4.5 6.5 8.5 11.5

TIR

Forest plot of Chinook TIR, without 2001

Year199419951996199719981999200020022003200420052006

Summary

TIR1.620.951.920.740.871.140.600.651.061.092.140.79___ 0.99

0.5 1.5 2.5 3.5 4.5 5.5 7.5 9.5 12.5

TIR

Forest plot of C0-only Chinook TIR

Year1994199519961997199819992000200120022003200420052006

Summary

TIR1.620.951.920.740.871.140.602.960.651.061.093.160.79____0.94

0.5 1.5 2.5 3.5 4.5 6.5 8.5 11.5

TIR

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

Year1997199819992000200120022003200420052006

Summary

TIR2.200.202.281.4537 4.254.4114.34.880.98___ 3.26

0.1 1.0 2.0 3.0 5.0 8.012.0 19.029.044.0

TIR

Forest plot of steelhead TIR, without 2001

Year199719981999200020022003200420052006

Summary

TIR2.200.202.281.454.254.4114.34.880.98___ 2.61

0.1 1.0 2.0 3.0 5.0 7.0 11.0 17.0 26.039.0

TIR

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

0.1

1.0

10.0

100.0

Ck w/ 2001 Ck w/o 2001 Ck C0 only SH w/ 2001 SH w/o 2001

TIR

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

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

Year1994199519961997199819992000200120022003200420052006

Summary

D0.36 0.42 0.92 0.40 0.55 0.72 0.32 2.16 0.44 0.68 0.45 1.07 0.48 ___ 0.593

0.2 1.2 2.2 3.2 4.2

D

Forest Plot of wild Chinook D, without 2001

Year199419951996199719981999200020022003200420052006

Summary

D0.36 0.42 0.92 0.40 0.55 0.72 0.32 0.44 0.68 0.45 1.07 0.48 ___ 0.552

0.2 1.2 2.2 3.2 4.2

D

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

Year1997199819992000200120022003200420052006

Summary

D1.180.111.070.501.462.241.752.691.300.60___ 1.12

0.02 1.00 2.00 3.00 5.00

D

Forest Plot of wild steelhead D, without 2001

Year199719981999200020022003200420052006

Summary

D1.180.111.070.502.241.752.691.300.60___ 1.09

0.02 1.00 2.00 3.00 5.00

D

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

0.1

1.0

10.0

Ck w/ 2001 Ck w/o 2001 SH w/ 2001 SH w/o 2001

D

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

ConclusionsBetter 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

Caveats & ExtensionsSARs 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

Questions?