Constraint satisfaction mechanisms for marginal stability and criticality in large ecosystems

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.

arXiv commentUpdated version with references added. 6 pages, 2 figures

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• Effect of resource dynamics on species packing in diverse ecosystems
• Diverse communities behave like typical random ecosystems
• Free-then-freeze: transient learning degrees of freedom for introducing function in materials
• Constrained optimization as ecological dynamics with applications to random quadratic programming in high dimensions
• Well-mixed Lotka-Volterra model with random strongly competitive interactions
• Dynamically selected steady states and criticality in non-reciprocal networks
• Metabolic coordination and phase transitions in spatially distributed multi-cellular systems
• On the topology of solutions to random continuous constraint satisfaction problems
• Gradient descent dynamics and the jamming transition in infinite dimensions