Population Extinction on a Random Fitness Seascape

TL;DR

This paper investigates how stochastic environmental fluctuations, modeled as 'seascape' noise, influence population extinction, revealing novel critical behaviors and phase transitions in a mean-field framework.

Contribution

It introduces a mean-field model of population extinction under spatially and temporally varying fitness noise, connecting it to directed percolation and polymers in random media.

Findings

Extinction transition exhibits novel critical behavior with exponents depending on migration and noise ratio.

Probability distributions of population sizes can be computed self-consistently.

Model captures variants of directed percolation and polymers in random media within a mean-field approach.

Abstract

Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed population with logistic growth at each location, subject to "seascape" noise, wherein the population's fitness randomly varies with {\it location and time}. Despite its simplicity, the model actually incorporates variants of directed percolation, and directed polymers in random media, within a mean-field perspective. Probability distributions of the population can be computed self-consistently; and the extinction transition is shown to exhibit novel critical behavior with exponents dependent on the ratio of the strengths of migration and noise amplitudes. The results are compared and contrasted with the more conventional choice of demographic noise due to stochastic changes in reproduction.