Modeling count data of rare species: Some statistical issues

Most species abundance data show that a small number of species contribute the vast majority of individuals to a community. Thus, most taxa in a community are uncommon or rare. Yet such species will frequently be of ecological, conservation, or management interest. Data for uncommon or rare species will be presence/absence data or counts of abundance that contain a greater number of zero observations than would be predicted using standard, unimodal statistical distributions. Such data are generally referred to as zero-inflated data and require specialized methods for statistical analysis. Statistical approaches to modeling zero-inflated data include nonstandard mixture models; two-part, conditional models; and birth process models. In this paper, we briefly summarize two of these methods and illustrate the two-part, conditional approach to the problem of modeling count data with extra zeros. An advantage of this approach includes separate fits and separate interpretations of both components of count data; that is to say, the presence/absence component and the abundance component (given presence) can be analyzed separately. This can be valuable not only for simplicity, but also such a two-step method may assist ecological understanding in cases where the basis for species presence might be separated from the underlying reasons affecting the population size of that species at those sites where it is present. We present two case studies of the application of the two-part conditional model for modeling count data with extra zeros. One deals with modeling relationships between counts of the rare and endangered arboreal marsupial, Leadbeater's possum (Gymnobelideus leadbeateri) and habitat variables in the wet eucalypt forests of southeastern Australia. The other is an analysis of data obtained from a monitoring study of seabird nesting from the Coral Sea off northeastern Australia. Finally,, we briefly discuss some inferential and practical issues in developing designs and models for presence/absence data (which is the first component in the two-part conditional approach) when observed occurrences are low (e.g., < 5%).