Statistical mechanics and stability of a model eco-system

TL;DR

This paper models an ecosystem using disordered systems theory, analyzing how resource variability, interactions, and cooperation influence stability and diversity, and identifying conditions for optimal resource exploitation.

Contribution

It introduces a dynamical systems approach to analyze ecosystem stability, incorporating resource variability and species interactions, and maps the phase diagram of stability conditions.

Findings

Resources are exploited optimally only without co-operation pressure.

Increased direct interactions can destabilize the ecosystem.

The phase diagram delineates stable and unstable regimes.

Abstract

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally direct competitive or co-operative interaction between species may occur through a random coupling matrix. We compute the order parameters of the system in a fixed point regime, and identify the onset of instability and compute the phase diagram. We focus on the effects of variability of resources, direct interaction between species, co-operation pressure and dilution on the stability and the diversity of the ecosystem. It is shown that resources can be exploited optimally only in absence of co-operation pressure or direct interaction between species.