Trinity River Science Symposium
2009-01-14
Trinity River Restoration Program
Juvenile Salmonid Outmigrant Monitoring Program Evaluation
Carl James Schwarz (SFU)
Darcy Pickard (ESSA)
Keith Marine (North State Resources)
Simon J. Bonner (UBC)
cschwarz@stat.sfu.ca
1
Juvenile Salmonid Outmigrant Monitoring Program
Evaluation 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. Separate estimates for wild and hatchery fish.
4. Evaluate sampled-discharge methods in terms of
population estimates and run timing. (Pinnix talk)
5. Establish and evaluate metrics for fish condition.
6. Methodology to assess program over many years using
(1) … (5) (Read Report)
2
Population Estimation from Mark-recapture
Objectives:
- estimate total number of outgoing juveniles
- separate estimates for hatchery and wild fish
- estimate characteristics such as percentiles of run timing
Sampling Protocol:
- rotary 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 to estimate
capture efficiency
- unmarked fish are captured along with marked fish
3
Population Estimation
Data:
- marking may change 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.
- ui - 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% adfin clipped; Hatchery Steelhead are 100% ad-fin clipped.
- Current program is basically diagonal recoveries, i.e.
mij = 0 for j>i.
Parameters:
- pi - recapture rate in week i
- U i - total outgoing population in week i.
-U =
!U
i
- grand total outgoing population
weeks
4
Sample JC 2003 Chinook Data
Marked Fish
UnMarked Fish
AD
+NC
4,135
10,452
2,199
655
ni mii mi,i+1 mi,i+2
JW D
AD
NC
9 3
0
0
0
0
0 4,135
10 8 1,465
32 19
0
0 10,452
11 6 1,106 121
0
0
0 2,199
12 7
229
25
0
0
0
655
…
22 7
333
14
1
0
0
526
526
23 7 3,981 242
0
0 9,427 30,542 39,969
24 7 3,988
55
0
0 4,243 13,337 17,580
25 7 2,889 114
1
0 1,646 6,282 7,928
…
38 7
26
3
0
0
4
37
41
39 7
20
1
0
0
1
22
23
40 7 4,757 188
0
0 8,412 26,706 35,118
41 7 2,876
8
0
0 7,703 26,831 34,534
42 7 3,989
81
0
0 3,651 11,309 14,960
43 7 1,755
27
0
0
966 2,677 3,643
44 7 1,527
30
0
0
468 1,343 1,811
45 7
485
14
0
0
160
519
679
46 5
115
4
0
0
24
130
154
Total
50,489 2,459 26
0 41,084 168,911 209,995
5
lo
flo
6.
6.
7.
6.
7.
7.
7.
7.
6.
6.
6.
6.
5.
5.
5.
5.
5.
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
Simple Petersen
"
%"
%
$# ! ui '& $# ! ni '&
weeks
Û = weeks
"
%
$# ! mii '&
weeks
 Separate weekly
estimates
(Weekly) StratifiedPetersen
ui ni
Û i =
;Û = ! Û i
mii
weeks
JC 2003 Chinook Estimates
4.2 (SE .081) million
16 (SE 3.7 ) million
5 (SE .21 ) million
(ex JW 41)
6
Population Estimation
Example – JC 2003 Chinook
Julian
ni
Week
9
0
10 1,465
11 1,106
12
229
13
20
mii
ui*
Û i
0
9,616
??
51
9,168
263,367
121
2,557
23,372
25
655
6,000
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
…
Pooling 50,489 2,486 215,299 4.2 million
* Adjusted for less than 7 days sampling.
7
Population Estimation
 Separate weekly
estimates
Comparison
Best possible precision
Weekly estimates may
BUT …
have poor precision but
overall estimate has
acceptable precision
Complete Pooling
Unable to estimate run
timing easily
Estimate run-timing
Handle missing marking
weeks.
No estimate if don’t
mark in a week
Unable to deal with
missing capture of
unmarked fish weeks
No estimate if don’t
recapture in a week
Implicitly assumes
homogeneous capture.
Allows for
heterogeneous capture
across weeks, but
assumes homogeneity
within weeks
Est – small bias - whew
SE – large bias(!)
“Odd” data has little
effect
“Odd” data could lead
to highly biased
weekly estimates
8
Population Estimation – alternatives?
• 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
• Try pooling weeks that are “similar” (partially stratified)
- arbitrary
- how to estimate se properly?
- dealing with missing weeks esp. with no unmarked fish
9
Population Estimation
Proposed Spline & Hierarchical Model
Intuitive Basis:
a) fit a “smooth” curve to the Û i (spline) as the
underlying trend but allow variability about trend line
b) allow pi to vary around a common mean (hierarchical
model)
Notice very large pop estimate in JW 41
10
Population Estimation
Proposed Spline & Hierarchical Method
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
- computer programs are “complex”
11
Population Estimation
Proposed Spline & Hierarchical Model
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?
12
Population Estimation
JC 2003 Chinook - Spline Model
- 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
13
Capture Efficiency Estimation
JC 2003 Chinook - Hierarchical Model
- Notice range of catchability in j.w. 9, 41, etc
- Additional structure in p – use covariates such as log-flow?
14
Population Estimation
JC 2003 Steelhead Data
Julian
Week
9
10
11
12
13
14
15
16
17
18
46
Total
ui*
ni
mii
58
0
0
359
0
0
720
0
0
5,493
999
5
6,354
1,707
13
4,752
1,947
39
3,201
2,109
7
1,777
972
1
1,167
687
0
84
0
0
… (no marks released again!)
236
0
0
30,620
8,424
65
Û i
??
??
??
915,500
775,188
231,422
844,264
864,511
802,896
??
??
Marking very limited; but unmarked found in all weeks
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?
15
Population Estimation
JC 2003 Steelhead Spline Model
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
16
Capture Efficiency Estimation
JC 2003 Steelhead – Hierarchical Model
Notice poor precision when no marking is done.
17
Population Estimation
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+
18
Population Estimation
Separating Wild and Hatchery CH YOY Fish
JC 2003 - Spline Model
W.YOY
H.YOY
(millions)
(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)
*SE Not adjusted for interpolation of ad-clipped.
19
Population Estimation
Separating Wild and Hatchery YOY CH Fish
JC 2003 - Run Timing
Wild
Mean
SD
0% 10% 30% 50% 70% 90% 100%
9.0 9.5 10.3 13.0 22.5 29.2 40.0
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
20
Population Estimation
Separating Wild and Hatchery ST Fish
JC 2003 - Spline Model
W.YOY
W.1+
H.1+
(millions)
(millions)
(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)
* SE Not adjusted for interpolation of ad-clipped.
21
Population Estimation
Separating Wild and Hatchery ST Fish
JC 2003 – Run Timing
YOY.W
Mean
SD
0%
9.0
0.0
10%
26.2
0.7
30%
29.5
0.5
50%
31.1
0.6
70%
33.8
1.1
90% 100%
37.8 47.0
2.7 0.0
1+.W
Mean
SD
9.0
0.0
11.0
0.4
12.4
0.4
14.4
0.9
16.1
0.4
19.8 47.0
1.5 0.0
22
Summary - I
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
23
Summary - II
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 with
realistic se
- estimates available for wild vs hatchery groups with
realistic se
- run timing estimates available
- easy to interpolate for weeks with missing/odd data
- able to add covariates (e.g. log-flow for p) (not shown)
- model fitting complex – no hand computations
BTSPAS package in R.
- careful of interpolations before and after last sampling
- assumption that patterns visible = patterns hidden
- Allows some flexibility in sampling, e.g. every second
week
- 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.
24