Stochastic Ecology Models for Two Interacting Populations

Abstract

The interaction of two species can be considered to be either mutually competitive, the "co-predator" case, or dominated by one species, the "predator-prey" model. The study of stochastic versions of these models has been impeded by the occurrence of nonlinear expressions in the characterization of the resulting probability structure. Generating function methods are used to study the bivariate and conditional probability distributions and their moments. The results are illustrated using a Laplace transform technique for obtaining numerical values. These methods can be used in the development of ecological prediction techniques and can be extended easily to the bivariate logistic model.