Modelling the abundance of rare species: Statistical models for counts with extra zeros

We consider several statistical models for the analysis of the abundance of a rare species and these are illustrated in detail with data for the abundance of Leadbeater's Possum in montane ash forests of south-eastern Australia. These data are characterised by a discrete distribution with the zero class inflated. In many statistical problems the parameters of this distribution depend on covariates, such as the number of hollow bearing trees. We advocate a conditional model which is simple to interpret and readily fitted. We show how to obtain standard errors for the parameter estimates. We also show how to estimate the mean abundance of animals at a site. The methods outlined in this paper offer a powerful framework for the study of problems having a discrete response (like abundance) with the zero class inflated.