Statistical mechanics and stability of a model eco-system

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.

💡 Research Summary

The paper presents a statistical‑mechanical analysis of a stylized ecosystem in which a set of species compete for a pool of resources while also interacting directly through a random coupling matrix. Each species i has a population variable (x_i) whose dynamics are governed by a generalized Lotka‑Volterra equation:
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