Impact of colored environmental noise on the extinction of a long-lived stochastic population: Role of the Allee effect

Eitan Y. Levine*, Baruch Meerson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We study the combined impact of a colored environmental noise and demographic noise on the extinction risk of a long-lived and well-mixed isolated stochastic population which exhibits the Allee effect. The environmental noise modulates the population birth and death rates. Assuming that the Allee effect is strong, and the environmental noise is positively correlated and Gaussian, we derive a Fokker-Planck equation for the joint probability distribution of the population sizes and environmental fluctuations. In the Wentzel-Kramers- Brillouin approximation this equation reduces to an effective two-dimensional Hamiltonian mechanics, where the most likely path to extinction and the most likely environmental fluctuation are encoded in an instanton-like trajectory in the phase space. The mean time to extinction τ is related to the mechanical action along this trajectory. We obtain new analytic results for short-correlated, long-correlated and relatively weak environmental noise. The population-size dependence of τ changes from exponential for weak environmental noise to no dependence for strong noise, implying a greatly increased extinction risk. The theory is readily extendable to population switches between different metastable states, and to stochastic population explosion, due to a combined action of demographic and environmental noise.

Original languageAmerican English
Article number032127
JournalPhysical Review E
Volume87
Issue number3
DOIs
StatePublished - 13 Mar 2013

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