Vortices and strings in a model ecosystem

Abstract

We study the spatial pattern formation in a model ecosystem by the position-fixed reaction method. This ecosystem contains three biospecies whose competing powers are cyclic. It is well known that this system is self-organized into a quasistationary state, and that the mean-field approximation (MFA) never predicts such a pattern formation. Recently, several authors applied the pair approximation (PA), and obtained considerable improvements. However, applying PA to our ecosystem fails to yield such an improvement as revealed by computer simulations. The failures of MFA and PA may be attributed to the fact that both approximations neglect a long-range correlation. Thus we introduce the concept of topological defects, such as ``vortices'' or ``strings,'' and demonstrate that the dynamics of these defects can at least qualitatively account for the observed pattern formation dynamics.