DISPERSAL AND PATTERN-FORMATION IN A DISCRETE-TIME PREDATOR-PREY MODEL

We investigate the dispersal-driven instabilities that arise in a discrete-time predator-prey model formulated as a system of integrodifference equations. Integrodifference equations contain two components: (1) difference equations, which model growth and interactions during a sedentary stage, and (2) redistribution kernels, which characterize the distribution of dispersal distances that arise during a vagile stage. Redistribution kernels have been measured for a tremendous number of organisms. We derive a number of redistribution kernels from first principles. Integrodifference equations generate pattern under a far broader set of ecological conditions than do reaction-diffusion models. We delineate the necessary conditions for dispersal-driven instability for two-species systems and follow this with a detailed analysis of a particular predator-prey model. (C) 1995 Academic Press, Inc.