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

We investigate the dispersal-driven instabilities that arise in a disc rete-time predator-prey model formulated as a system of integrodiffere nce equations. Integrodifference equations contain two components: (1) difference equations, which model growth and interactions during a se dentary 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 o rganisms. We derive a number of redistribution kernels from first prin ciples. Integrodifference equations generate pattern under a far broad er set of ecological conditions than do reaction-diffusion models. We delineate the necessary conditions for dispersal-driven instability fo r two-species systems and follow this with a detailed analysis of a pa rticular predator-prey model. (C) 1995 Academic Press, Inc.