Extinction in neutrally stable stochastic Lotka-Volterra models

TL;DR

This paper studies how intrinsic noise causes extinction in neutrally stable stochastic Lotka-Volterra models, revealing that noise destroys species coexistence over time proportional to population size.

Contribution

It introduces a stochastic averaging method to analytically understand extinction dynamics in symmetric models, extending to complex cases numerically.

Findings

Extinction time scales linearly with population size.

Analytical extinction probabilities match simulations.

Method applicable to complex stochastic ecological models.

Abstract

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. In this paper, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: it destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.