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Lotka-Volterra with randomly fluctuating environments or “how switching between beneficial environments can make survival harder”. (English) Zbl 1358.92075
Summary: 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.

MSC:
92D25 Population dynamics (general)
92D40 Ecology
60J75 Jump processes (MSC2010)
60J25 Continuous-time Markov processes on general state spaces
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