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Extinction in the Lotka-Volterra model

2009; American Physical Society; Volume: 80; Issue: 2 Linguagem: Inglês

10.1103/physreve.80.021129

1550-2376

Matthew W. Parker, Alex Kamenev,

Evolution and Genetic Dynamics

Birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey interaction. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the system toward extinction of one or both species. We show that the corresponding extinction time scales as a certain power-law of the population sizes. This behavior should be contrasted with the extinction of models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.