Lotka Volterra in fluctuating environment or "how switching between beneficial environments can make survival harder"

Abstract

We consider two dimensional Lotka-Volterra systems in fluctuating environment. Relying on recent results on stochastic persistence and piecewise deterministic Markov processes, we show that random switching between two environments both favorable to the same species can lead to the extinction of this species or coexistence of the species.

40 pages, 8 figures. This is a revised version of a paper previously entitled Lotka Volterra in a fluctuating environment or "how good can be bad". 09/02/16: Reference to a recent paper by Malrieu and Zitt (http://arxiv.org/abs/1601.08151) has been added

References in corpus (4)

• Persistence in fluctuating environments
• Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments
• Sensitivity to switching rates in stochastically switched ODEs
• Regularity of invariant densities for 1D-systems with random switching

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• Large population asymptotics for a multitype stochastic SIS epidemic model in randomly switched environment
• Asymptotic expansion of the invariant measurefor Markov-modulated ODEs at high frequency