BRIEF INTRODUCTION TO
CLOSED CAPTURE-RECAPTURE
METHODS
Workshop objectives

Basic understanding of capture-recapture

Estimators

Sample designs

Uses and assumptions
Detectability
and abundance estimation
N = true abundance
C = catch
p = probability of capture
E(C)= pN
Incomplete capture: Inference
Inferences about N require inferences about p
ˆ
N 
C
pˆ
Estimating abundance with capture
probability known = 0.5 (or 50%)
2
ˆ
N 
4
0 .5
• If you ignore p then C =2 is biased
• Usually we have to collect other data to
estimate p!
Closed Population Estimation
Parameters
• Abundance
• Capture probability
Population closed
• No gains or losses in the study area
Replicate samples used to estimate N, p
Commonly Used Estimators:
Lincoln-Petersen/Schnabel/etc.
Design
• Animals caught
• Unmarked animals in sample given (or have) unique marks
• Marks on any marked animals recorded
• Release marked animals into population
• Resample at subsequent occasions
• Minimum two sampling periods (capture and recapture)
• (Ideally) a relatively short interval between periods
Not during migration, harvest period, other period with
significant gains, losses, movement
• Must be long enough to generate recaptures
Closed Population Estimators
Key Assumptions
• Population is closed
(no birth/death/immigration/emigration)
• Animal captures are independent
• All animals are available for capture
• Marks are not lost or overlooked
• L-P and Schnabel
• assume equal p (never ever possible)
• Probability of recapture not affected by previous
capture
Violations of Assumptions
Closure violation
• Mortality or emigration during sampling
Unbiased estimate of N at first sample time
• Immigration or birth
Unbiased estimate of N at last sample time
• Both
Valid inferences not possible
Violations of Assumptions
All animals are not available for capture
- underestimate N
- overestimate p
Violations of Assumptions
Equal capture probability (when assumed)
• Differences (heterogeneity) among individuals
Underestimate abundance
• Trap response: “trap-shy”
Overestimate N
Underestimate p
•“Trap happy”
Underestimate N
Overestimate p
Potential Violations of Assumptions
Tag loss
• Lost between sampling periods
Underestimate p
Overestimate N
• Overlooked or incorrectly recorded
Underestimate p
Overestimate N
Effect can be eliminated or minimized by double-tagging
Variance of abundance estimate
Depends on
Variance in true N
Capture probability
Variance in estimated p
Affected by sample size
Sample size
Number of marked animals
Number of capture occasions
Rule of thumb


Number of animals captured each occasion
(C) determines precision of estimates of N
If capture probabilities low or true
abundance low:



More effort in fewer occasions
Increases occasion specific p
Increases C
Closed population estimators
Definitions
pt = probability of first capture sampling
occasion t
ct = probability of recapture sampling
occasion t+1 (don’t confuse with big
C)
N = population size
Note: there are t-1 estimates possible for c
Closed population estimators
Definitions
If there is no effect of first capture on
recapture probability
- no trap happy
- no trap shy, etc.
pt+1 = ct
Capture (encounter) histories
H1 = 101
Verbal description: individual was captured on
first and third sample occasion, not captured on
second occasion
Mathematical depiction:
P(H1 = 101) = p1(1-c1)c2
Capture (encounter) histories
H1 = 111
Verbal description: individual was captured on
all three occasions
Mathematical depiction:
P(H1 = 111) = p1c1c2
Capture (encounter) histories
H1 = 001
Verbal description: individual was captured on
first and third sample occasion, not captured on
second occasion
Mathematical depiction:
P(H1 = 001) = (1-p1)(1-p2)p3
Capture (encounter) histories
100
p1(1-c1)(1-c2)
010
(1-p1)p2(1-c2)
001
(1-p1)(1-p2)p3
110
p1c1(1-c2)
101
p1(1-c1)c2
011
(1-p1)p2c2
111
p1c1c2
Capture (encounter) histories
Capture and recapture
equal differ in time
Capture and recapture equal
across time
p(1-p)2
H
100
010
001
110
p1(1-c1)(1-c2)
(1-p1)p2(1-c2)
(1-p1)(1-p2)p3
p1c1(1-c2)
p1(1-p2)(1-p3)
(1-p1)p2(1-p3)
(1-p1)(1-p2)p3
p1p2(1-p3)
(1-p)p(1-p) or p(1-p)2
(1-p)2 p
p2(1-p)
101
011
111
p1(1-c1)c2
(1-p1)p2c2
p1c1c2
p1(1-p2)p3
(1-p1)p2p3
p1p2p3
p(1-p)p or p2(1-p)
(1-p)p2
p3
Huggins version of CR
estimator

Why Covariates?
Capture probability known to be related to:
species, body size, habitat characteristics
More efficient means of accounting for heterogeneity
e.g., assume p varies through time (5 time periods) due to
differences in stream discharge
Number of parameters time varying model = 5
Number parameters p in f(discharge) = 2
Effects model selection: AIC = -2LogL + 2*K
Danger of over parameterization (more parameters than data)
Frequently encountered problem
I don’t have enough marked and/or recaptured
individuals

Make sure closure assumption not violated

Include data from other years/locations to
estimate p for poor recapture year (Huggins)

Bayesian hierarchical approaches
p?
p1
p2
Frequently encountered problem
Lake Sturgeon in Muskegon River, MI
Year
Catch Statistic
1
2
3
4
Total Gill Net
Hours
3030
2250
1247
1852
Total marked
adults
13
10
8
15
Recaptured adults
8
5
1
2
Schnabel Estimate
(95% CL) each
year seperate
24
(12-74)
15
(9-45)
---
---
22
(16-45)
16
(12-37)
45
(14-247)
18
(16-39)
Estimate (95% CL)
modeled together
f(soak time, size)
Double Sampling
Disadvantages of capture recapture approaches: Can be labor/time
intensive!!
But….double sampling can reduce effort:
Capture recapture
Estimate p
and adjust
data
Normal sampling
Mark-resight
(will not cover in this course)

Estimate population size

Resighting marked and unmarked individuals
Requires known number of marks


But version available if marks unknown (not recommended)
Used terrestrial applications but potential fish uses



snorkeling: if marks detectable

weir or trap where unmarked fish returned unmarked
Marks
Batch marked

Individually identifiable


Open and closed versions
BREAK!
then
ON TO MARK