Extinctions of coupled populations, and rare-event dynamics under non-Gaussian noise

TL;DR

This paper develops a hybrid theoretical framework to analyze rare extinction events in coupled populations under non-Gaussian environmental noise, revealing novel extinction phase transitions and counterintuitive effects of population sinks.

Contribution

It introduces a new hybrid method combining saddle-point and Donsker-Varadhan formalisms to study rare events in non-Gaussian noise systems, applied to population extinction dynamics.

Findings

Rare extinction paths are not dominated by a single trajectory.

A novel phase transition in extinction behavior is identified.

A sink patch can reduce extinction probability despite lowering population size.

Abstract

The survival of natural populations may be greatly affected by environmental conditions that vary in space and time. We look at a population residing in two locations (patches) coupled by migration, in which the local conditions fluctuate in time. We report on two findings. First, we find that unlike rare events in many other systems, here the histories leading to a rare extinction event are not dominated by a single path. We develop the appropriate framework, which turns out to be a hybrid of the standard saddle-point method, and the Donsker-Varadhan formalism which treats rare events of atypical averages over a long time. It provides a detailed description of the statistics of histories leading to the rare event. The framework applies to rare events in a broad class of systems driven by non-Gaussian noise. Secondly, applying this framework to the population-dynamics model, we find a novel phase transition in its extinction behavior. Strikingly, a patch which is a sink (where individuals die more than are born), can nonetheless reduce the probability of extinction, even if it normally lowers the population's size and growth rate.