Incorporating the intraspecific occupancy-abundance relationship into zero-inflated models.

Zero-inflated versions of standard distributions for count data are often required in order to account for excess zeros when modeling the abundance of organisms. Such distributions typically have as parameters lambda, the mean of the count distribution, and pi, the probability of an excess zero. Implementations of zero-inflated models in ecology typically model lambda using a set of predictor variables, and pi is fit either as a constant or with its own separate model. Neither of these approaches makes use of any relationship that might exist between pi and lambda. However, for many species, the rate of occupancy is closely and positively related to its average abundance. Here, this relationship was incorporated into the model for zero inflation by functionally linking pi to lambda, and was demonstrated in a study of snapper (Pagrus auratus) in and around a marine reserve. This approach has several potential practical advantages, including better computational performance and more straightforward model interpretation. It is concluded that, where appropriate, directly linking pi to lambda can produce more ecologically accurate and parsimonious statistical models of species abundance data.