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arXiv · 1605.07479

Communities as cliques

Yael Fried·David A. Kessler·Nadav M. Shnerb
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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.

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Yael Fried, David A. Kessler, Nadav M. Shnerb. 2016-05-24. Communities as cliques. https://arxiv.org/abs/1605.07479

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