Phase 2 – Objectives 1. Population estimation using mark...

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Trinity River Restoration Program Phase 2 – Objectives

1. Population estimation using mark-recapture data that provides proper measures of precision and can deal with “problems” such as missing or odd data 2. Estimates of run timing based on methods in (1) 3. Evaluate sampled-discharge methods in terms of

population estimates and run timing. 4. Methodology to assess program over many years using

(1), (2), and (3). All material is available at: http://www.stat.sfu.ca/~cschwarz/Consulting/Trinity/Phase

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Evaluation of long term trends

Power Power = Pr(detecting a change when it exists)

- power increases with size of difference - power increases with length of series - power decreases with increasing p+s error - power decreases with alpha decreasing

Aim for 80% power with alpha=.05.

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Evaluation of long term trends Condition – Overview

Data Availability

Site Fork-length Weight Health JC 1997-2004 - - PT 2003-2007 2006-2007 - WC 1993-2006 2004-2006 -

Metrics evaluated:

• Several evaluated, but only fork length has a sufficiently long time series

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Evaluation of long term trends: fork-length

• NC and AD-clipped fish collected and measured • AD-clipped mean length used to “extrapolate” in NC fish • Example from JC 2004 (top), WC 2005 (bottom)

Year=2004 Site=Junction City

nat_mean

30

40

50

60

70

80

90

100

110

120

130

jd

0 100 200 300 year=2005 Site=Willow Creek age=0

nat_mean

30

40

50

60

70

80

90

100

110

jd

60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250

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Change in mean fork-length at julian day 200 at WC

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Estimated power to detect trend in mean fork-length over time based on WC julian day 200 results.

5%

over study

10% over study

15% over study

20% over study

CH (base mean 84 mm; process + sampling std dev 3.7 mm)

5 years 0.08 0.17 0.32 0.49 10 years 0.15 0.43 0.76 0.94 15 years 0.21 0.64 0.93 1.00 20 years 0.28 0.78 0.98 1.00

ST (base mean 59 mm;

process + sampling std dev 3.2 mm) 5 years 0.07 0.13 0.23 0.36

10 years 0.11 0.31 0.59 0.83 15 years 0.16 0.47 0.81 0.96 20 years 0.2 0.61 0.92 0.99

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Evaluation of long term trends: abundance (W.YoY)

Imputed abundance (red) based on “parallel” movement among sources including discharge-sampled methods

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Evaluation of long term trends: abundance (W.YoY)

Estimated power (alpha=.05) to detect linear changes in mean log(abundance) based on imputed JC CH values.

Process + sampling standard deviation is 0.7. Percent change in abundance PER year. Yrs 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%

5 0.05 0.05 0.05 0.06 0.06 0.07 0.07 0.08 0.09 0.10 10 0.06 0.07 0.11 0.15 0.21 0.28 0.36 0.45 0.54 0.63 15 0.07 0.14 0.27 0.43 0.60 0.76 0.87 0.94 0.98 0.99 20 0.11 0.29 0.56 0.80 0.94 0.99 1.00 1.00 1.00 1.00

Yikes!! Huge process + sampling error

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Evaluation of long term trends: 50th percentile of run

Imputed abundance (red) based on “parallel” movement

among sources including discharge-sampled methods Are these changes artifacts of sampling protocol?

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Evaluation of long term trends: 50th percentile of run

Estimated power (alpha=.05) to detect linear changes in run timing based on imputed JC

CH values.

Julian week changes/year. [E.g. .07 julian weeks/year = 0.5 day/year]

50th Percentile

Process + sampling variation=1.4 weeks Yrs 0.07 0.14 0.21 0.28 0.35

5 0.06 0.07 0.12 0.15 0.20 10 0.22 0.35 0.79 0.88 0.97 15 0.63 0.86 1.00 1.00 1.00 20 0.95 1.00 1.00 1.00 1.00

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Evaluation of long term trends Summary

• Sampling variation vs. process variation. • What data sources are available? Can they be calibrated

against each other? Are the different sources measuring the same thing?

• What difference is biologically important?

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Population Estimation using Mark-Recapture Overview

Objectives: - estimate total number of outgoing Chinook, Steelhead,

Coho - separate estimates for hatchery and wild fish - estimate characteristics such as percentiles of run timing - evaluate usefulness of “flow sampled” methods

Sampling Protocol:

- screw-traps are used to capture fish - a sample of fish is marked and transported above trap

and released - a portion of the marked fish are recaptured

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Population Estimation Data:

- marking changes weekly so unit of analysis is the (julian) week

- ni - number of fish marked and released in week i

- mij- number of marked fish released in week i and

recovered in week j. - u

i - number of unmarked fish captured in week i (may

include the ni). This can often be (partially) subdivided

in hatchery and wild fish. Hatchery Chinook are 25% ad-fin clipped; Hatchery Steelhead are 100% ad-fin clipped.

- Current program is basically diagonal recoveries, i.e. m

ij= 0for j>i.

Parameters:

- pi - recapture rate in week i - U

i - total outgoing population in week i.

- U = Ui

weeks

! - grand total outgoing population

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Population Estimation Key concept (of mark-recapture):

- recapture of marked fish provide estimate of screw-trap capture efficiency (e.g. the screw-trap is capturing 5% of the fish that pass the location)

- use the estimated recapture rate to expand the number of unmarked fish captured.

Methods: Complete Pooling Separate weekly

estimates Simple Petersen (Weekly) Stratified-

Petersen

U =

ui

weeks

!"#$%&'

ni

weeks

!"#$%&'

mii

weeks

!"#$%&'

U

i=uini

mii

;U = Ui

weeks

!

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Population Estimation Complete Pooling Separate weekly

estimates Comparison

Best possible precision BUT …

Weekly estimates may have poor precision but overall estimate has acceptable precision

Unable to estimate run timing.

Estimate run-timing

Handle missing marking weeks

No estimate if don’t mark in a week

Unable to deal with missing capture weeks

No estimate if don’t recapture in a week

Implicitly assumes homogeneous capture.

Est – small bias - whew

SE – large bias(!)

Allows for heterogeneous capture across weeks, but assumes homogeneity within weeks

“Odd” data has little effect

“Odd” data could lead to highly biased weekly estimates

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Population Estimation Proposed Spline-based Method

Intuitive Basis: - fit a “smooth” curve to the U

i (spline)

- allow pi to vary around a common mean (hierarchical model)

Advantages: - “borrows” information from other weeks for estimating

catchability and weekly run size. - gives weekly (and total) estimates - estimate run timing - if missing marking week, uses range of capture rates

seen in other weeks to “impute” range of possible capture rates for weeks with no marking done

- if missing unmarked fish in a week, uses spline to “interpolate” reasonable value for outgoing total based on variation of other weeks around smooth curve

- automatically adjusts for amount of heterogeneity in capture-rates across weeks. If small variation, estimates have precision similar to pooled-Petersen. If larger variation, estimates have realistic standard errors

- “odd” data easily handled (simply set to missing)

Disadvantage: - not amenable to hand computations - difficulty to fit – Bayesian methods useful

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- computer programs are “complex”

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Population Estimation Proposed Spline-based Method

Why not simply draw a smooth curve by hand to use as

estimation to avoid all of the problems in the data? This is the goal of the proposed methodology! BUT how do you compute estimates of se from the ad hoc

method? Are estimates of the se actually needed if process error is large?

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Population Estimation Example – JC 2003 Chinook

Julian Week n

i m

ii u

i

* Ui

9 0 0 9,616 ?? 10 1,465 51 9,168 263,367 11 1,106 121 2,557 23,372 12 229 25 655 6,000 13 20 0 308 ??

… 22 333 15 526 11,677 23 3,981 242 39,969 657,507 24 3,988 55 17,580 1,274,710

… 35 269 33 339 2,763 36 77 7 107 1,177 37 62 9 79 544 38 26 3 41 355 39 20 1 23 460 40 4,757 188 35,118 888,597 41 2,876 8 34,534 12,414,973 42 3,989 81 14,960 736,734

… Total 50,489 2,486 215,299 * Adjusted for less than 7 days sampling.

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Population Estimation Example – JC 2003 Chinook

Problems:

- some weeks with no marking - some weeks with very few recoveries - some weeks with odd data - heterogeneity in catchability

Plot of m2/n1 by julian week

Pooled Petersen: 4.2 (SE .081) million fish. Stratified-Petersen 16 (SE 3.7 ) million fish. Stratified-Petersen 5 (SE .21 ) million fish (ex j.w. 41)

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Population Estimation Example – JC 2003 Chinook - Spline Fit

- Allowed for 2 “jumps” when hatchery fish arrived.

Pooled Petersen: 4.2 (SE .081) million fish. Stratified-Petersen 5 (SE .21 ) million fish (ex j.w. 41) Spline est: 5.3 (SE .18 ) million fish

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- Notice range of catchability in j.w. 9 etc

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- Run timing (but may not be sensible for pooled wild and

hatchery fish) 0% 10% 30% 50% 70% 90% 100% Mean 9.0 19.4 24.3 26.3 40.7 42.7 47.0 Sd 0.0 4.0 0.1 0.7 0.1 0.1 0.0

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Population Estimation Example – JC 2003 Steelhead

Julian Week u

i

* ni m

ii U

i

9 58 0 0 ?? 10 359 0 0 ?? 11 720 0 0 ?? 12 5,493 999 5 915,500 13 6,354 1,707 13 775,188 14 4,752 1,947 39 231,422 15 3,201 2,109 7 844,264 16 1,777 972 1 864,511 17 1,167 687 0 802,896 18 84 0 0 ??

… (no marks released again!) 46 236 0 0 ??

Total 30,620 8,424 65 Marking very limited. Lots of missing data. Pooled Petersen: 3.9 (SE .40) million fish. Stratified-Petersen 4.4 (SE 2.2) million fish. BUT… are these sensible given missing data in many

weeks?

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Notice poor precision when no marking is done.

Pooled Petersen: 3.9 (SE .40) million fish. Stratified-Petersen 4.4 (SE 2.2) million fish. Spline method 6.5 (SE 1.9) million fish

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Notice poor precision when no marking is done.

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Population Estimation Example – JC 2003 - Spline Fit

Separating Wild and Hatchery fish Chinook

- 25% of hatchery fish are adipose fin clipped. - prior to first hatchery release, all wild - after first hatchery release, mixture of wild and hatchery;

need to “expand” the ad-clipped fish to account for hatchery non-clipped fish

- second hatchery release is all age 1+ Steelhead

- all hatchery fish are marked - separate into W.YoY, H.1+, W.1+

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Separating Wild and Hatchery YoY fish

W.YoY

(millions) H.YoY (millions)

Pooled Petersen* 0.74 (SE .02) 1.3 (SE .03) Stratified-Petersen 0.71 (SE .04) 2.3 (SE .17) Spline 0.87 (SD .11) 2.3 (SD .12)

Not adjusted for interpolation of ad-clipped.

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Separating Wild and Hatchery YoY fish Run Timing for Chinook YoY Wild 0% 10% 30% 50% 70% 90% 100% Mean 9.0 9.5 10.3 13.0 22.5 29.2 40.0 SD 0.0 0.2 0.3 2.1 2.0 0.6 0.0 Hatchery Mean 23.0 23.4 24.1 24.4 24.8 26.9 40.0 SD 0.0 0.1 0.3 0.1 0.1 0.2 0.0

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Example – JC 2003 - Spline Fit Separating Wild and Hatchery YoY fish

W.YoY

(millions) W.1+

(millions) H.1+

(millions) Petersen* .78 (SE .10) .68 (SE .08) 2.50 (SE .31) Strat-Petersen .01 (SE .01) .82 (SE .25) 3.62 (SE .90) Spline 1.27 (SD .40) 1.17 (SD .23) 3.59 (SD .50) * Not adjusted for interpolation of ad-clipped.

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Example – JC 2003 - Spline Fit Separating Wild and Hatchery fish

Run Timing for Steehead W.YoY, W.1+, and W.1+ YoY.W 0% 10% 30% 50% 70% 90% 100% Mean 9.0 26.2 29.5 31.1 33.8 37.8 47.0 Sd 0.0 0.7 0.5 0.6 1.1 2.7 0.0 1+.W Mean 9.0 11.0 12.4 14.4 16.1 19.8 47.0 Sd 0.0 0.4 0.4 0.9 0.4 1.5 0.0 1+.H Mean 12.0 12.4 13.1 14.0 15.6 17.0 47.0 Sd 0.0 0.1 0.3 0.6 0.4 0.3 0.0

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Population Estimation using Mark-Recapture Summary

Pooled-Petersen: - with complete data, est are likely unbiased, but se are

underreported - can deal with weeks with no marking - cannot deal with weeks with no recovery of unmarked

Stratified-Petersen - with complete data, est are unbiased, se are valid but

large because of sparse data - cannot deal with weeks with no marking or no unmarks

Spline-Methods

- “borrows” information from other weeks o spline forces estimates to follow “smoothish” curve o capture rates come from common distribution

- estimates available at weekly and total level - estimates available for wild vs hatchery groups - run timing estimates available - easy to interpolate for weeks with missing/odd data - model fitting complex – no hand computations

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Population Estimation using sampled discharge - Overview

Pinnix et al (2007) suggested using the proportion of the flow sampled by the traps as a measure of capture efficiency.

Then use this estimate of capture efficiency to inflate the ui

in the usual fashion. Process:

- flow measurements (rev/minute) taken at up to 6 points on each screw trap

- check for and remove outliers based on pairwise plots (e.g. rev<1000 or rev>6000)

- average remaining flow measurements - convert from rev/min -> feet/second - interpolate 5ft and 8ft screw traps if data missing when

both traps running (few observations) - assume trap ½ in water -> convert to cfs - add over days in week = Weekly Discharge Sampled - get gauge measurements (cfs) at nearest gauge station - add over days in week = Total River Volume

- piflow

=WeeklyDisSampledi

TotalRiverVoli

- Ui

flow=

ui

piflow

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Population Estimation using sampled discharge

Weekly discharge sampled vs total river flow JC/PT/WC Left=actual units; right=log scale (all years pooled on same plot)

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Population Estimation using sampled discharge

piflow vs. p

i

mr for JC/PT/WC Chinook; All years pooled on same plot

Left actual units; right on logit scale

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Population Estimation using sampled discharge Spline vs Flow based est of Chinook population size

Wild + Hatchery

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Wild + Hatchery

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Wild + Hatchery

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Wild + Hatchery

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Population Estimation using sampled discharge Wild + Hatchery

Site Year

Chinook Flow-based

(millions)

Chinook Spline-based

(millions)

Ratio flow-based/

spline-based JC 2003 2.4 5.3 .46 JC 2004 1.2 8.7 .14 PT 2005 .45 5.7 .08 PT 2006 .28 1.1 .24 PT 2007 .69 3.0 .23 WC 2002 .73 2.0 .37 WC 2003 .52 1.1 .45 WC 2004 .26 1.3 .20 WC 2005 1.58 3.6 .45 *Estimates cover same set of julian weeks.

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Population Estimation using sampled discharge Wild Only

Site Year

Chinook Flow-based

(millions)

Chinook Spline-based

(millions)

Ratio flow-based/

spline-based JC 2003 .55 .87 .64 JC 2004 .53 .59 .73 PT 2005 .21 2.38 .09 PT 2006 .18 .59 .31 PT 2007 .50 1.84 .27 WC 2002 .48 1.11 .43 WC 2003 .30 .43 .70 WC 2004 .16 .74 .21 WC 2005 1.32 2.83 .47 *Estimates cover same set of julian weeks.

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Population Estimation using sampled discharge Run Timing Wild Only

0% 10% 30% 50% 70% 90% WC 2002 spline 11 19.4 24.1 25.3 27.0 41.8 WC 2002 flow 11 18.2 21.6 24.6 26.1 29.9 WC 2003 spline 10 18.8 26.0 27.5 35.9 42.4 WC 2003 flow 10 11.5 17.9 25.5 27.4 29.3 * WC 2004 spline 12 18.5 27.7 30.8 41.4 42.5 WC 2004 flow 12 14.5 22.5 27.4 31.0 42.0 WC 2005 spline 10 13.0 16.0 22.8 24.5 28 WC 2005 flow 10 14.3 17.8 22.6 24.2 27 * * Missing one or more weeks early in the season

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Population Estimation using sampled discharge Applying to earlier years

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Population Estimation using sampled discharge – summary

• Estimates follows same general shape as spline methods, but seem to underestimate consistently.

• High variability among years at same site – can we

interpolate to past years? - process vs sampling variation (see earlier slides)

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Overview Summary

• Spline-based methods provide defensible estimates (and precision) of overall population size, individual weekly estimates, and run timing. • Spline-based methods able to deal with a variety of data problems in a consistent, defensible manner. • Sampled discharge methods may provide a (somewhat) reliable INDEX to population size to enable past years data to be integrated with current data. Estimates of run timing appears to be sensible. • Process error often overwhelms sampling error across years making it difficult to detect changes without longer time series. Aim for consistent sampling methods over time to reduce process error.

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