A stylized model of stochastic ecosystems with alternative stable states

Abstract

We construct a generic ecosystem model that features the basic mechanisms of alternative stable states as well as two different stochastic influences. In particular, we use a mean-reverting jump-diffusion process to model the evolution of the ecosystem state over time. We review key concepts of multistability theory and the simple heuristics commonly employed to illustrate them. We then provide mathematical definitions for these concepts in the model context. Our contribution to the literature is twofold: we improve the representation of stochasticity in, and clarify key concepts of, multistability theory. The simplicity of the model enables a number of applications, such as finding economically optimal management strategies, identifying criteria for sustainable ecosystem management in a stochastic viability framework, deriving the probability of a regime shift, or empirically identifying the factors which have caused a specific regime shift.