CRITICAL SLOWING-DOWN IN TIME-TO-EXTINCTION - AN EXAMPLE OF CRITICAL PHENOMENA IN ECOLOGY

We study a model for two competing species that explicitly accounts fo r effects due to discreteness, stochasticity and spatial extension of populations. The two species are equally preferred by the environment and do better when surrounded by others of the same species. We observ e that the final outcome depends on the initial densities (uniformly d istributed in space) of the two species. The observed phase transition is a continuous one and key macroscopic quantities like the correlati on length of clusters and the time-to-extinction diverge at a critical point. Away from the critical point, the dynamics can be described by a mean-field approximation. Close to the critical point, however, the re is a crossover to power-law behavior because of the gross mismatch between the largest and smallest scales in the system. We have develop ed a theory based on surface effects, which is in good agreement with the observed behavior. The course-grained reaction-diffusion system ob tained from the mean-field dynamics agrees well with the particle syst em. (C) 1998 Academic Press Limited.