1. CLOSED CAPTURE-RECAPTURE
BRIEF INTRODUCTION TO
CLOSED CAPTURE-RECAPTURE
METHODS

2. Workshop objectives Basic understanding of capture-recapture
Estimators
Sample designs
Uses and assumptions

3. Detectability and abundance estimation
N = true abundance
C = catch
p = probability of capture
E(C)= pN

4. Incomplete capture: Inference
Inferences about N require inferences about p

5. Estimating abundance with capture probability known = 0.5 (or 50%)
If you ignore p then C =2 is biased
Usually we have to collect other data to estimate p!

6. Closed Population Estimation
Parameters
Abundance
Capture probability
Population closed
No gains or losses in the study area
Replicate samples used to estimate N, p

7. 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

8. 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

9. 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
Tends to cause underestimation of p and overestimation of N 9

10. Violations of Assumptions
All animals are not available for capture
- underestimate N
- overestimate p
Tends to cause underestimation of p and overestimation of N 10

11. 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
Tends to cause underestimation of p and overestimation of N 11

12. Potential Violations of Assumptions
Tag loss
Lost between sampling periods
Underestimate p
Overestimate N
Overlooked or incorrectly recorded
Effect can be eliminated or minimized by double-tagging
Tends to cause underestimation of p and overestimation of N 12

13. 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

14. 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

15. 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

16. 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

17. Capture (encounter) histories
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

18. Capture (encounter) histories
Verbal description: individual was captured on all three occasions
Mathematical depiction:
P(H1 = 111) = p1c1c2

19. Capture (encounter) histories
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

20. 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

21. Capture (encounter) histories
Capture and recapture equal differ in time
Capture and recapture equal across time
100
p1(1-c1)(1-c2)
p1(1-p2)(1-p3)
p(1-p)2
010
(1-p1)p2(1-c2)
(1-p1)p2(1-p3)
(1-p)p(1-p) or p(1-p)2
001
(1-p1)(1-p2)p3
(1-p)2 p
110
p1c1(1-c2)
p1p2(1-p3)
p2(1-p)
101
p1(1-c1)c2
p1(1-p2)p3
p(1-p)p or p2(1-p)
011
(1-p1)p2c2
(1-p1)p2p3
(1-p)p2
111
p1c1c2
p1p2p3 p3

22. Huggins version of CR estimator

23. 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)

24. 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

25. 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 5
Schnabel Estimate (95% CL) each year seperate 24
(12-74)
(9-45)
---
Estimate (95% CL) modeled together
f(soak time, size) 22
(16-45) 16
(12-37) 45
(14-247) 18
(16-39)

26. Double Sampling
Disadvantages of capture recapture approaches: Can be labor/time intensive!!
But….double sampling can reduce effort:
Capture recapture
Normal sampling
Estimate p
and adjust
data

27. 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

28. BREAK!
then
ON TO MARK