Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems.

Abstract

We discuss a resource-competition model, which takes MacArthur's model as a platform, to unveil interesting connections with glassy features and jamming in high dimensions. This model, as first studied by Tikhonov and Monasson, presents two qualitatively different phases: a shielded phase, where a collective, 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 analysis in terms of the computation of the leading eigenvalue of the Hessian matrix of the associated Lyapunov function. 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.