Generalized Lotka-Volterra Systems with Time Correlated Stochastic Interactions

TL;DR

This paper analyzes stochastic ecological dynamics using a generalized Lotka-Volterra model with time-correlated interactions, revealing how environmental noise influences species coexistence and ecosystem stability.

Contribution

It introduces a dynamical mean field theory for GLV models with colored noise, providing analytical predictions that align with empirical data and enhance understanding of ecological stability.

Findings

Time-dependent interactions modeled as environmental noise.

Environmental noise promotes species coexistence.

Overcomes the complexity-stability paradox in ecosystems.

Abstract

In this work, we explore the dynamics of species abundances within ecological communities using the Generalized Lotka-Volterra (GLV) model. At variance with previous approaches, we present an analysis of stochastic GLV dynamics with temporal fluctuations in interaction strengths between species. We develop a dynamical mean field theory (DMFT) tailored for scenarios with annealed colored noise and simple functional responses. We show that time-dependent interactions can be effectively modeled as environmental noise in the DMFT and we obtain analytical predictions for the species abundance distribution that well matches empirical observations. Our results suggest that environmental noise favors species coexistence and allows to overcome the complexity-stability paradox, especially in comparison to dynamics with quenched disorder. This study offers new insights not only into the modeling of large ecosystem dynamics, but also proposes novel methodologies for examining ecological systems.