Biodiversity and robustness of large ecosystems

TL;DR

This paper analyzes the biodiversity and stability of large resource-competition ecosystems, providing estimates of biodiversity, stability conditions, and robustness, with implications for the predictability of ecosystem dynamics.

Contribution

It introduces new analytical estimates for biodiversity and robustness in resource competition models with extinctions and self-limitation, extending understanding of ecosystem stability.

Findings

Estimates of biodiversity based on model parameters.

Proof of global stability under certain conditions.

Explicit robustness estimates supporting the $R^*$ rule.

Abstract

We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the global stability of solutions for systems with extinctions and large turnover rate. We show that when the extinction threshold is distinct from zero, the large time dynamics of system is fundamentally non-predictable. In the last part of the paper we obtain explicit analytical estimates of ecosystem robustness with respect to variations of resource supply which support the $R^*$ rule for a system with random parameters.