The Annals of Applied Probability

Lotka–Volterra with randomly fluctuating environments or “how switching between beneficial environments can make survival harder”

Michel Benaïm and Claude Lobry

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

Article information

Ann. Appl. Probab., Volume 26, Number 6 (2016), 3754-3785.

Received: October 2015
Revised: February 2016
First available in Project Euclid: 15 December 2016

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Zentralblatt MATH identifier

Primary: 60J99: None of the above, but in this section 34A60: Differential inclusions [See also 49J21, 49K21]

Population dynamics persistence piecewise deterministic processes competitive exclusion Markov processes


Benaïm, Michel; Lobry, Claude. Lotka–Volterra with randomly fluctuating environments or “how switching between beneficial environments can make survival harder”. Ann. Appl. Probab. 26 (2016), no. 6, 3754--3785. doi:10.1214/16-AAP1192.

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