Communities as cliques

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.

References in corpus (6)

• Stability Criteria for Complex Ecosystems
• Neutral Theory and Relative Species Abundance in Ecology
• A phase transition between the niche and neutral regimes in ecology
• A generalized model of island biodiversity
• Statistical mechanics of ecosystem assembly
• Species abundances and lifetimes: from neutral to niche-stabilized communities