MODELING THE ABUNDANCE OF RARE SPECIES - STATISTICAL-MODELS FOR COUNTS WITH EXTRA ZEROS

We consider several statistical models for the analysis of the abundan ce 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 distribu tion with the zero class inflated. In many statistical problems the pa rameters of this distribution depend on covariates, such as the number of hollow bearing trees. We advocate a conditional model which is sim ple to interpret and readily fitted. We show how to obtain standard er rors for the parameter estimates. We also show how to estimate the mea n abundance of animals at a site. The methods outlined in this paper o ffer a powerful framework for the study of problems having a discrete response (like abundance) with the zero class inflated.