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### Estimating closed population size from capture-recapture data

This page provides R functions to fit some
models of capture heterogeneity to estimate *N*, the size of a
closed population, from capture-recapture data. This is joint work
with
Byron Morgan.

In the most general model that we consider, captures are modelled as a mixture of binomial and beta-binomial counts. This generalises the beta-binomial model considered, for example, by Dorazio and Royle [Ref 1] and the (two-component form of) finite mixture model considered, for example, by Pledger [Ref 2]. Our new model is described in Refs [3] and [4] below, which also provide other references to the existing literature.

There are important issues of identifiability in models of capture
heterogeneity, see for example [Ref 5]. Our model does not resolve these
problems, but it does offer a broad and flexible class of models within which
to investigate and compare estimates of *N*.

A user guide explains how to use the software and gives details about computational methods. You need to download the file estimateN.R into a suitable directory on your computer. This contains all the functions needed to fit the models. You should not need to look at this code unless you want to see the details of what's going on. The code should work in R 2.6.1 onwards.

These files illustrate the use of the software:

All the data sets used in Refs [3] and [4] are in this file.

#### References

[1] Dorazio, R.M. and Royle, J.A. (2003). Mixture
models for estimating the size
of a closed population when capture rates vary among individuals.
*Biometrics*, **59**, 351-364.

[2] Pledger, S. (2000). Unified maximum likelihood estimates
for closed capture-recapture
models using mixtures.
*Biometrics*, **56**, 434-442.

[3]
Morgan, B.J.T. and Ridout, M.S. (2008)
A new mixture model for capture heterogeneity.
*Applied Statistics*, **57**, 433-446.
[
journal link]

[4]
Morgan, B.J.T. and Ridout, M.S. (2008) Estimating N: a robust approach to
capture heterogeneity. In: Thomson, D.L. and Cooch, E.G. and Conroy, M.J., eds.
Modelling Demographic Processes in Marked Populations. *Environmental and Ecological Statistics*.
Springer, New York, pp. 1069-1080. ISBN 978-0-387-78150-1.
[journal
link]

[5]
Link, W.A. (2003). Nonindentifiability of population size from capture-recapture data with
heterogeneous detection probabilities.
*Biometrics*, **59**, 1123-1130.