Extinction statistics in N random interacting species

TL;DR

This paper studies how Gaussian multiplicative noise affects the extinction times in a complex system of randomly interacting species, revealing Gaussian distributions and nonmonotonic behaviors in extinction time statistics.

Contribution

It introduces an analysis of extinction time distributions in a stochastic Lotka-Volterra model with external noise, highlighting new statistical behaviors.

Findings

Extinction time distributions are Gaussian for various noise levels.

Mean extinction time varies monotonically with noise intensity.

Distribution width exhibits nonmonotonic behavior with noise.

Abstract

A randomly interacting N-species Lotka-Volterra system in the presence of a Gaussian multiplicative noise is analyzed. The investigation is focused on the role of this external noise into the statistical properties of the extinction times of the populations. The distributions show a Gaussian shape for each noise intensity value investigated. A monotonic behavior of the mean extinction time as a function of the noise intensity is found, while a nonmonotonic behavior of the width of the extinction time probability distribution characterizes the dynamical evolution.