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In this paper we study the long term dynamics of two prey species and onepredator species. In the deterministic setting, if we assume the interactionsare of Lotka-Volterra type (competition or predation), the long term behaviorof this system is well known. However, nature is usually not deterministic. Allecosystems experience some type of random environmental fluctuations. Weincorporate these into a natural framework as follows. Suppose the environmenthas two possible states. In each of the two environmental states the dynamicsis governed by a system of Lotka-Volterra ODE. The randomness comes fromspending an exponential amount of time in each environmental state and thenswitching to the other one. We show how this random switching can create veryinteresting phenomena. In some cases the randomness can facilitate thecoexistence of the three species even though coexistence is impossible in eachof the two environmental states. In other cases, even though there iscoexistence in each of the two environmental states, switching can lead to theloss of one or more species. We look into how predators and environmentalfluctuations can mediate coexistence among competing species.

Random switching in an ecosystem with two prey and one predator