Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems

TL;DR

This paper explores a resource-competition model inspired by MacArthur's model, revealing two phases of ecosystem stability and connecting them to glassy phenomena and constraint satisfaction problems in high dimensions.

Contribution

It introduces a novel phase analysis of large ecosystems using constraint satisfaction and eigenvalue computations, linking ecological stability to glassy physics.

Findings

Identification of 'shielded' and 'vulnerable' phases in ecosystem models

Connection between ecosystem stability and glassy phenomena

Efficient phase distinction via Hessian eigenvalue analysis

Abstract

We discuss a resource-competition model, which takes the MacArthur's model as a platform, to unveil interesting connections with glassy features and jamming in high dimension. This model presents two qualitatively different phases: a "shielded" phase, where a collective and self-sustained behavior emerges, and a "vulnerable" phase, where a small perturbation can destabilize the system and contribute to population extinction. We first present our perspective based on a strong similarity with continuous constraint satisfaction problems in their convex regime. Then, we discuss the stability in terms of the computation of the leading eigenvalue of the Hessian matrix of the free energy in the replica space. This computation allows us to efficiently distinguish between the two aforementioned phases and to relate high-dimensional critical ecosystems to glassy phenomena in the low-temperature regime.