The feasibility of equilibria in large ecosystems: a primary but neglected concept in the complexity-stability debate

TL;DR

This paper investigates whether feasible equilibria exist in large ecosystems, revealing that such equilibria often vanish as species richness increases, challenging traditional stability assumptions and emphasizing the importance of interaction strength and network structure.

Contribution

The study provides analytical and simulation evidence that equilibrium feasibility diminishes in species-rich ecosystems, highlighting the need to consider interaction structure and strength.

Findings

Feasible equilibria vanish in highly diverse ecosystems.

Weak interactions can ensure stability regardless of species richness.

Ecosystem architecture influences dynamical behavior significantly.

Abstract

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture.