BRIEF INTRODUCTION TO

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BRIEF INTRODUCTION TO CLOSED CAPTURE-RECAPTURE
METHODS
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Workshop objectives

• Basic understanding of capture-recapture
• Estimators
• Sample designs
• Uses and assumptions

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Detectabilityand abundance estimation
N true abundance C catch p probability of
capture E(C) pN
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Incomplete capture Inference
Inferences about N require inferences about p
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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!

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Closed Population Estimation

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

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Commonly Used EstimatorsLincoln-Petersen/Schnabe
l/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

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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

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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

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Violations of Assumptions
All animals are not available for capture -
underestimate N - overestimate p
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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

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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

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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
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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

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Closed population estimators

• Definitions
• pt probability of first capture sampling
  occasion t
• ct probability of recapture sampling occasion
  t1 (dont confuse with big C)
• N population size
• Note there are t-1 estimates possible for c

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Closed population estimators

• Definitions
• If there is no effect of first capture on
  recapture probability
• - no trap happy
• - no trap shy, etc.
• pt1 ct

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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

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Capture (encounter) histories

• H1 111
• Verbal description individual was captured on
  all three occasions
• Mathematical depiction
• P(H1 111) p1c1c2

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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

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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
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Capture (encounter) histories
H 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-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
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Huggins version of CR estimator

•  

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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 2K Danger of over
parameterization (more parameters than data)
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Frequently encountered problem

• I dont 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
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Frequently encountered problem
Lake Sturgeon in Muskegon River, MI
Year 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) --- ---
Estimate (95 CL) modeled together f(soak time, size) 22 (16-45) 16 (12-37) 45 (14-247) 18 (16-39)
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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
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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

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BREAK! then ON TO MARK