Evaluation of the Statistical Propertie

recapture Estimators of Grand CanyoHumpback Chub Abundance and Tre

David Otis

USGS Iowa Cooperative Fish and W

Research Unit

Iowa State University

AcknowledgementsHadley Wickham, Jenny Loda, Dave Miller (ISU)Jeff Laake (NMFS)
Background

 Capture-recapture (CR) data collected since 1987 

sampling designs 

 Population estimation method depends on

 Sampling design used to collect the data Statistical model ( = assumptions, e.g., closure, de

 Bias and precision of an estimator depend on

 Validity of the demographic and temporal dynamic

underlie each design/model

 Quality and quantity of the data

 Computer simulation is a tool for investigation of 

performance of different estimators under differedemographic scenarios 
Project Objectives

 Use a Monte Carlo simulation mode

statistical performance of alternativdesigns and estimators for age-specsize, recruitment, and trend under dscenarios:

 Time frame Age-specific survival schedule Movement dynamics Capture effort 

→probability of capture

 Synthesize results and make recom
Simulation Model
Simulate Life History Vectors for All Individu
Simulate Capture History Vectors for Al

Sampling Months in 

Each Year

February

November

Locations of Each 

Sample Month

Is Individual Alive at 

Sampling Time and 

Present in Sampling 

Location?

Yes No

Captured Not Captured

Capture 

History 

Vector

Life 

History 

Vector

= 1 (LCR)

 2 (MS) = 0 = 0

Repeat 

Over 

Sample Months 

and Years

=

[ 1 2 0 0 0 2 ] (Designs 1,3,5)

[ 1 1 0 1 2 2 0 1] (Designs 2,4)

e.g. ,
Model and Design Performance

Simulated 

Mark-recapture 

Dataset

ASMR models

(vpa)

Population 

and trend 

estimates

Repeat 

Model and Design 

Performance 

Comparison

Closed models Open models (Jolly-Seber)

Bias

 Precision

Bias

 Precision

Bias

 Precision

Population 

and trend 

estimates

Population 

and trend 

estimates

Sampling Designs and Estimation 

 Designs

1. Spring concurrent, 3 trips2. Spring concurrent, 4 trips3. Fall concurrent, 3 trips4. Fall concurrent, 4 trips5. GCMRC: Spring and fall, LCR, 2 trips 

mainstem, 2 trips

 Estimation models

 3 ASMR 3 Closed 1 Jolly-Seber type open
Movement Dynamics
Colorado River Mainstem

(MS)

February
Colorado River Mainstem

(MS)

March
Colorado River Mainstem

(MS)

April
Colorado River Mainstem

(MS)

May
Colorado River Mainstem

(MS)

June-November
Colorado River Mainstem

(MS)

December-January
True Population Sizes

Year

0 1 2 3 4 5 6 7 8 

Total

6000700080009000

10000110001200013000140001500016000

nonvonnonvon
Results

 Reduction of the set of candidate es Comparison of estimators Comparison of sampling designs Miscellaneous

 Trend estimation Effect of reduced capture proba Effect of age misclassification
Reduction of the Set of Es
Comparison of ASMR Estimators

 Total Estimates 

Non-Parametric Survival Standard Capt

Design 1 ASMR Estim

Year

0 1 2 3 4 5 6 7 8 9 

Total

6000700080009000

100001100012000130001400015000

ASMR1ASMR2ASMR3
Comparison of Closed Estimators

 Total Estimates 

Non-Parametric Survival Standard Capt

Design 1 Closed Estim

Year

0 1 2 3 4 5 6 7 8 9 

Total

6000700080009000

100001100012000130001400015000

MMM
Reduction of the Set of Estimator

Conclusions

 3 ASMR estimators not much different, b

generally slightly better, so present only 



Mh generally much worse than Mo and Mt

 Proceed with ASMR2, Open, Mo and Mth
Comparison of Estimators
Percent Relative Bias

Spring Concurrent S

Nonparametric Surviva

1 2 3 4 

Percent Relative Bias

-0.20-0.15-0.10-0.05

0.000.050.100.150.20

Spring Concurrent Sampling (Feb-Apr) Recruitment Estimates

Nonparametric Survival Standard Capture Probability

Year

1 2 3 4 5 6 7 8 9 10

Percent Relative Bias

-0.20-0.15-0.10-0.05

0.000.050.100.150.20

OpenASMR2 MoMth

Spring Concurrent Sampling (Feb-Apr) Recruitment Estimates

Nonparametric Survival Standard Capture Probability

Year

12345

Percent Relative Bias

-0.20-0.15-0.10-0.05

0.000.050.100.150.20

OpenASMR2 MoMth

Spring Concurrent S

Nonparametric Surviva

12

Percent Relative Bias

-0.20-0.15-0.10-0.05

0.000.050.100.150.20
Precision

Spring Concurrent Sampling (Feb-Apr) Recruitment Estimates

Nonparametric Survival Standard Capture Probability

Year

1 2 3 4 5 6 7 8 9 10

Standard deviation

0

100200300400

OpenASMR2 MoMth

Spring C

Nonparame

1 

Standard deviation

0

100200300400

Spring Concurrent Sampling (Feb-Apr) Recruitment Estimates

Nonparametric Survival Standard Capture Probability

Year

12345

Standard deviation

0

100200300400

OpenASMR2 MoMth

Spring Con

Nonparametr

Standard deviation

0

100200300400
Comparison of Estimators

Conclusions

 2 closed models are poor Both ASMR and Open have PRB < 1

less biased in Design 1

 ASMR more precise for Y = 5, and O

for Y = 10 in Design 1

 ASMR less biased in Design 3, espe

and performs better with von B surv
Comparison of Designs
Percent Relative Bias

 Perce

S

01

Percent Relative Bias

-0.20-0.15-0.10-0.05

0.000.050.100.150.20

 Percent Relative Bias (Estimates of Recruitment) 

Non-Parametric Survival

Standard Capture Probabilities

Year

0 1 2 3 4 5 6 7 8 9 10 11

Percent Relative Bias

-0.20-0.15-0.10-0.05

0.000.050.100.150.200.250.30

 Percen

St

0 1 2 

Percent Relative Bias

-0.20-0.15-0.10-0.05

0.000.050.100.150.20

 Percent Relative Bias (Estimates of Recruitment) 

Non-Parametric Survival

Standard Capture Probabilities

Year

0123456

Percent Relative Bias

-0.20-0.15-0.10-0.05

0.000.050.100.150.200.250.30

ASMR2-1ASMR2-2ASMR2-3ASMR2-4ASMR2-5OPEN-1OPEN-2OPEN-3 OPEN-4 OPEN-5 
Precision

 Standard deviation (Estimates of Recruitment)

Non-Parametric Survival

Standard Capture Probabilities

Year

0123456

Standard deviation

0

50

100150200250

ASMR2-1ASMR2-2ASMR2-3ASMR2-4ASMR2-5OPEN-1OPEN-2OPEN-3 OPEN-4 OPEN-5 

 Stand

St

01

Standard deviation

0

50

100150200250

Standard deviation (Estimates of Recruitment)

Non-Parametric Survival

Standard Capture Probabilities

Year

0 1 2 3 4 5 6 7 8 9 10 11

Standard deviation

0

50

100150200250

Stan

S

0 1 2 

Standard deviation

0

50

100150200250
Comparison of Designs

Conclusions

 Four trips produce marginal increas

relative to 3 trips, but no change in 

 Bias generally less than 10% for all 

Design 5, which produces larger bia

 Precision is very good for all Design No difference in relative performanc

respect to survival assumptions
Miscellaneous 
Estimation of Trend

 Estimates of log-linear trend in both recr

total population size have minimal bias aprecision (

± 1-2%) for both ASMR and O
Effect of Decrease in Capture Pro

LCR

(Based on a Single Simulation)

 Minimal effect on PRB Causes relatively large decrease in precis

for Open model, but precision still genera
Effect of Age Misclassification

(Based on Nonparametric Surviva

 Misclassified age at first capture

Scenario 1 Scenario 2

P[ correct ] = .6 P[ correct ] = .5

P[ 

± 1 ageclass ] = .3 P[ + 1 ageclass ] = 

P{ 

± 2 ageclass ] = .1 P{ + 2 ageclass ] = 

 No important effect on bias or precision
Summary Statistical Conclusions

 Spring concurrent sampling with 3 trips is the b Both ASMR and an Open Jolly-Seber type estim

results, except for significant bias with GCMRC 

 Good performance of estimators due to large ca No large, consistent superiority in performance 

model

 Open model has other advantages

 Fewer restrictive assumptions about capture prob

structure and hence probably more robust to vio

 Can utilize formal model selection theory Straightforward variance estimation