Random switching in an ecosystem with two prey and one predator

TL;DR

This paper investigates how random environmental switching affects the long-term coexistence of two prey and one predator species, revealing that stochastic switching can both promote and hinder species coexistence.

Contribution

It introduces a stochastic model with environmental switching in a three-species ecosystem, showing novel effects on species coexistence not seen in deterministic models.

Findings

Random switching can enable coexistence of all three species.

Switching can cause the loss of species even when coexistence is stable in each environment.

Environmental fluctuations can mediate species coexistence in complex ways.

Abstract

In this paper we study the long term dynamics of two prey species and one predator species. In the deterministic setting, if we assume the interactions are of Lotka-Volterra type (competition or predation), the long term behavior of this system is well known. However, nature is usually not deterministic. All ecosystems experience some type of random environmental fluctuations. We incorporate these into a natural framework as follows. Suppose the environment has two possible states. In each of the two environmental states the dynamics is governed by a system of Lotka-Volterra ODE. The randomness comes from spending an exponential amount of time in each environmental state and then switching to the other one. We show how this random switching can create very interesting phenomena. In some cases the randomness can facilitate the coexistence of the three species even though coexistence is impossible in each of the two environmental states. In other cases, even though there is coexistence in each of the two environmental states, switching can lead to the loss of one or more species. We look into how predators and environmental fluctuations can mediate coexistence among competing species.