1412.1107Dec 2, 201440 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
Lotka Volterra in fluctuating environment or "how switching between beneficial environments can make survival harder"
Michel Benaïm, Claude Lobry
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.