Population response to environmental change: A model with an alternate stable state

Abstract

In ecology, the theory of alternative stable states predicts that ecosystems can exist under multiple "states". Ecosystems may transition from one stable state to another, in what is known as a state shift. Typically such shifts are considered as instantaneous and isolated non-interacting events resulting from environmental shocks, whose dynamics resemble the dynamics of a ball in a "potential well". More often however, ecological systems are subject to continuous variation due to environmental drivers such as rainfall, temperature, among others, and these interact with the ecosystem dynamics to alter the potential well. Such drivers are known to impact intra-species interactions. We explore a single species population model with logistic-like growth and a variable crowding parameter that measures the strength of the intra-species interaction. The crowding parameter is treated as a state-variable whose dynamics is described via a potential function subject to external environmental drivers.