Closed‐population capture–recapture modeling of samples drawn one at a time

Barker, Richard J.; Schofield, Matthew; Wright, Janine; Frantz, Alain C.; Stevens, Chris

doi:10.1111/biom.12241

Cited by 12 publications

(22 citation statements)

References 25 publications

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“…(2014) (although their model is for abundance rather than density and does not include both time and space). However, the fact that single‐catch traps induce a dependence between individuals complicates matters and means that a high‐dimensional integral would need to be solved.…”

Section: Methodsmentioning

confidence: 99%

A spatially explicit capture–recapture estimator for single‐catch traps

Distiller

Borchers

2015

Ecology and Evolution

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Single‐catch traps are frequently used in live‐trapping studies of small mammals. Thus far, a likelihood for single‐catch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capture–recapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. We build on a recently developed continuous‐time model for SECR to derive a likelihood for single‐catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height of the detection function. By contrast, the single‐catch estimators of density, distribution, and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constant over the survey region, then the multicatch estimator performs well with single‐catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single‐catch estimator when trap saturation is above about 60%. The estimator's performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single‐catch likelihood with unknown capture times remains intractable for now, researchers using single‐catch traps should aim to incorporate timing devices with their traps.

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Section: Methodsmentioning

confidence: 99%

A spatially explicit capture–recapture estimator for single‐catch traps

Distiller

Borchers

2015

Ecology and Evolution

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“…Assuming independence between individuals, a probability model for the observed times of captures is

\begin{matrix} right f (boldt | boldλ, N) & center = \frac{N!}{(N - n)! \prod_{j = 1}^{T} f_{j}!} \prod_{i = 1}^{N} e^{- ν_{i}} \prod_{i = 1}^{n} \prod_{j = 1}^{c_{i}} λ_{i} (t_{italicij}) & left \end{matrix}

where

ν_{i} = \int_{0}^{τ} λ_{i} false(u false) italicdu

can be thought of as a study‐wide measure of catchability for individual i . This expression is similar to that in Barker et al (), the only difference is the combinatorial term due to the ordering of

boldt

we use here.…”

Section: Introductionmentioning

confidence: 72%

“…The first factorization is given in Barker et al () and expresses the joint model for

boldt

in terms of a model for the number of captures of each individual and a model for the times of capture conditional on number of captures,

f false(t false| λ, N false) = \underset{f false(c false| ν, N false)}{\underset{true⏟}{\frac{N!}{(N - n)! \prod_{j = 1}^{T} f_{j}!} \prod_{i = 1}^{N} \frac{e^{- ν_{i}} ν_{i}^{c_{i}}}{c_{i}!}}} \underset{f false(t false| c, λ false)}{\underset{true⏟}{\prod_{i = 1}^{n} ({}, c_{i}! \prod_{j = 1}^{c_{i}} \frac{λ_{i} false(t_{ij} false)}{ν_{i}})}} .

…”

Section: Factoring the Modelmentioning

confidence: 99%

“…We are able to avoid specification of

λ_{i} false(t false)

under broad conditions. Provided

λ_{i} false(t false)

does not depend on N , then

f false(t false| c, λ false)

in provides no information when making inference about the parameter N ; a result due to S‐ancillarity of

t false| c

(Barker et al, ; Schofield and Barker, ). To understand this result better, consider a reparameterization where

λ_{i} false(t false)

is replaced by

δ_{i} false(t false) = λ_{i} false(t false) / ν_{i},

with the constraint

\int_{0}^{τ} δ_{i} false(u false) italicdu = 1

.…”

Section: Factoring the Modelmentioning

confidence: 99%

“…Barker et al () showed that under broad conditions, continuous‐time models can be expressed in terms of commonly used probability distributions. They went on to use these results in an example where the analysis was complicated due to uncertain identities.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Continuous-time Capture–Recapture in Closed Populations

2017

Self Cite

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The standard approach to fitting capture-recapture data collected in continuous time involves arbitrarily forcing the data into a series of distinct discrete capture sessions. We show how continuous-time models can be fitted as easily as discrete-time alternatives. The likelihood is factored so that efficient Markov chain Monte Carlo algorithms can be implemented for Bayesian estimation, available online in the R package ctime. We consider goodness-of-fit tests for behavior and heterogeneity effects as well as implementing models that allow for such effects.

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Capture-Recapture: Frequentist Methods

Seber,

Schofield

2023

Statistics for Biology and Health

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Closed‐population capture–recapture modeling of samples drawn one at a time

Cited by 12 publications

References 25 publications

A spatially explicit capture–recapture estimator for single‐catch traps

A spatially explicit capture–recapture estimator for single‐catch traps

Continuous-time Capture–Recapture in Closed Populations

Capture-Recapture: Frequentist Methods

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