Stochastic Stability and Instability of Model Ecosystems

Abstract

In this work, we initiate a stability study of multispecies communities in stochastic environment by using Itô's differential equations as community models. By applying the direct method of Liapunov, we obtain sufficient conditions for stability and instability in the mean of the equilibrium populations. The conditions are expressed in terms of the dominant diagonal property of community matrices, which is a suitable mechanism for resolving the central problem of "complexity vs. stability" in model ecosystems. As a by-product of this analysis we exhibit important structural properties of the stochastic density-dependent models, and establish tolerance of community stability to a broad class of nonlinear time-varying perturbations.