brief introduction to closed capture-recapture methods

BRIEF INTRODUCTION TOBRIEF INTRODUCTION TOCLOSED CAPTURE-RECAPTURE CLOSED CAPTURE-RECAPTURE

METHODS METHODS

Workshop objectives

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

N = true abundance C = catchp = probability of capture

E(C)= pN

DetectabilityDetectabilityand abundance estimationand abundance estimation

Inferences about N require inferences about p

p

CN

ˆˆ

Incomplete capture: Incomplete capture: InferenceInference

Estimating abundance with Estimating abundance with capture probability known = 0.5 capture probability known = 0.5

(or 50%)(or 50%)

45.0

2ˆ N

• If you ignore p then C =2 is biased

• Usually we have to collect other data to estimate p!

Closed Population Closed Population EstimationEstimation

Parameters• Abundance • Capture probability

Population closed • No gains or losses in the study area

Replicate samples used to estimate N, p

Commonly Used Estimators:Commonly Used Estimators:Lincoln-Petersen/Schnabel/etLincoln-Petersen/Schnabel/et

c.c.

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 AssumptionsViolations 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 AssumptionsViolations of Assumptions

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

Equal capture probability (when assumed)• Differences (heterogeneity) among individuals

Underestimate abundance

• Trap response: “trap-shy” Overestimate NUnderestimate p

•“Trap happy” Underestimate N Overestimate p

Violations of AssumptionsViolations 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

Potential Violations of Potential Violations of AssumptionsAssumptions

Variance of abundance estimate

Depends onVariance in true NCapture probabilityVariance in estimated pAffected by sample size

Sample size Number of marked

animalsNumber 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

Definitionspt = probability of first capture sampling occasion tct = 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

DefinitionsIf 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

HCapture and recapture

equal differ in timeCapture 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 p110 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 dischargeNumber of parameters time varying model = 5Number parameters p in f(discharge) = 2

Effects model selection: AIC = -2LogL + 2*KDanger 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

YearCatch 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)

--- ---

Lake Sturgeon in Muskegon River, MI

Estimate (95% CL) modeled togetherf(soak time, size)

22 (16-45)

16 (12-37)

45 (14-247)

18 (16-39)

But….double sampling can reduce effort:

Double Sampling

Disadvantages of capture recapture approaches: Can be labor/time intensive!!

Capture recaptureNormal sampling

Estimate pand adjustdata

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

MarksBatch markedIndividually identifiable

Open and closed versions

BREAK!then

ON TO MARK