BRIEF INTRODUCTION TO CLOSED CAPTURE-RECAPTURE METHODS

1. BRIEF INTRODUCTION TO CLOSED CAPTURE-RECAPTURE METHODS

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

3. Detectabilityand 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

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

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

12. 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

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 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

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

19. 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

20. Capture (encounter) histories

21. Capture (encounter) histories

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

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