Persistence and patchiness of predator-prey systems induced by discrete event population exchange mechanisms.

Abstract We consider a spatially distributed predator-prey system in which population exchange between cells can occur at only certain points in the predation cycle. Studying the characteristics of this discrete event model, by both analytic and simulation methods, we show that indefinite persistence of populations is possible over a wide range of parameter settings, even though the cells all tend to rapid extinction in isolation. The persistence is shown to take two forms: one in which a constant distribution of cells both in phase and space is maintained, and one in which this homogeneity of distribution is replaced by dynamically stable patterns of patches and waves. The former is shown to be neatly describable by the classical Lotka-Volterra equation. In contrast, persistence of locally unstable Lotka-Volterra predator-prey systems in both forms is shown to be impossible when the discrete population exchange mechanism is replaced by one of the continuous linear diffusion type.