Communities as cliques

TL;DR

This paper models ecological communities as maximal cliques in a graph, revealing that stable uninvadable subsets grow subexponentially with species richness and exhibit different relaxation dynamics based on symmetry.

Contribution

It introduces a geometric graph approach to analyze stable community subsets, providing new insights into biodiversity maintenance and community dynamics.

Findings

Number of stable uninvadable subsets grows subexponentially with species richness

Symmetric systems rapidly relax to a stable state, remaining until a regime shift

Asymmetric systems have relaxation times that grow faster, indicating excitable dynamics

Abstract

High-diversity assemblages are very common in nature, and yet the factors allowing for the maintenance of biodiversity remain obscure. The competitive exclusion principle and May's complexity-diversity puzzle both suggest that a community can support only a small number of species, turning the spotlight at the dynamics of local patches or islands, where stable and uninvadable (SU) subsets of species play a crucial role. Here we map the community SUs question to the geometric problem of finding maximal cliques of the corresponding graph. We solve for the number of SUs as a function of the species richness in the regional pool, $N$, showing that this growth is subexponential, contrary to long-standing wisdom. We show that symmetric systems relax rapidly to an SU, where the system stays until a regime shift takes place. In asymmetric systems the relaxation time grows much faster with $N$, suggesting an excitable dynamics under noise.