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arXiv · 0905.3728

Extinction in Lotka-Volterra model

Matthew Parker·Alex Kamenev
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Abstract

Competitive 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 competition. 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.

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Matthew Parker, Alex Kamenev. 2009-05-22. Extinction in Lotka-Volterra model. https://doi.org/10.1103/physreve.80.021129

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