Abstract
Some capture-recapture models for population estimation cannot easily be fitted by the usual methods (maximum likelihood and Markov-chain Monte Carlo). For example, there is no straightforward probability model for the capture of animals in traps that hold a maximum of one individual ('single-catch traps'), yet such data are commonly collected. It is usual to ignore the limit on individuals per trap and analyse with a competing-risk 'multi-catch' model that gives unbiased estimates of average density. However, that approach breaks down for models with varying density. Simulation and inverse prediction was suggested by Efford (2004) for estimating population density with data from single-catch traps, but the method has been little used, in part because the existing software allows only a narrow range of models. I describe a new R package that refines the method and extends it to include models with varying density, trap interference and other sources of non-independence among detection histories. The method depends on (i) a function of the data that generates a proxy for each parameter of interest and (ii) functions to simulate new datasets given values of the parameters. By simulating many datasets, it is possible to infer the relationship between proxies and parameters and, by inverting that relationship, to estimate the parameters from the observed data. The method is applied to data from a trapping study of brushtail possums Trichosurus vulpecula in New Zealand. A feature of these data is the high frequency of non-capture events that disabled traps (interference). Allowing for a time-varying interference process in a model fitted by simulation and inverse prediction increased the steepness of inferred year-on-year population decline. Drawbacks and possible extensions of the method are discussed.