Demographic noise in complex ecological communities

TL;DR

This paper introduces an individual-based ecological model with random interactions, showing how demographic noise causes species extinctions and how community complexity influences stability.

Contribution

It demonstrates how demographic noise affects species survival in complex communities and reveals that increased interaction complexity generally reduces noise-driven extinctions.

Findings

Demographic noise can lead to species extinction even when deterministic models predict survival.

Complex communities tend to be more resilient to demographic noise.

Predator-prey systems are particularly vulnerable to fluctuations despite deterministic stability.

Abstract

We introduce an individual-based model of a complex ecological community with random interactions. The model contains a large number of species, each with a finite population of individuals, subject to discrete reproduction and death events. The interaction coefficients determining the rates of these events is chosen from an ensemble of random matrices, and is kept fixed in time. The set-up is such that the model reduces to the known generalised Lotka-Volterra equations with random interaction coefficients in the limit of an infinite population for each species. Demographic noise in the individual-based model means that species which would survive in the Lotka-Volterra model can become extinct. These noise-driven extinctions are the focus of the paper. We find that, for increasing complexity of interactions, ecological communities generally become less prone to extinctions induced by demographic noise. An exception are systems composed entirely of predator-prey pairs. These systems are known to be stable in deterministic Lotka-Volterra models with random interactions, but, as we show, they are nevertheless particularly vulnerable to fluctuations.