Impact of Colored Environmental Noise on the Extinction of a Long-Lived Stochastic Population: Role of the Allee Effect
Eitan Y. Levine, Baruch Meerson

TL;DR
This paper analyzes how colored environmental noise combined with demographic noise influences the extinction risk of populations with the Allee effect, providing new analytical insights into mean time to extinction under various noise conditions.
Contribution
It introduces a novel analytical framework using WKB approximation and Hamiltonian mechanics to study extinction dynamics under correlated environmental noise and the Allee effect.
Findings
Extinction risk increases significantly with stronger environmental noise.
The mean time to extinction shifts from exponential to negligible dependence as noise strength grows.
New analytic results for different noise correlation times and strengths are derived.
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 WKB 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 (MTE) is related to the mechanical action along this trajectory. We obtain new analytic results for…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
