CLOSED CAPTURE-RECAPTURE 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

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!

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 Tends to cause underestimation of p and overestimation of N 9

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

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

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

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

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

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 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

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 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)

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

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