Abstract
High-diversity species 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 on the dynamics of local patches or islands, where stable and uninvadable (SU) subsets of species play a crucial role. Here we map the question of the number of different possible SUs a community can support to the geometric problem of finding maximal cliques of the corresponding graph. This enables us to solve for the number of SUs as a function of the species richness in the regional pool, N, showing that the growth of this number is subexponential in N, contrary to long-standing wisdom. To understand the dynamics under noise we examine the relaxation time to an SU. Symmetric systems relax rapidly, whereas in asymmetric systems the relaxation time grows much faster with N, suggesting an excitable dynamics under noise.
Highlights
High-diversity species assemblages are very common in nature, and yet the factors allowing for the maintenance of biodiversity remain obscure
Theory, experiments and field studies focusing on the possibility of alternative steady states play a central role in contemporary community dynamics literature[19,20]
Community dynamics is the arena on which the evolutionary process unfolds
Summary
High-diversity species assemblages are very common in nature, and yet the factors allowing for the maintenance of biodiversity remain obscure. May’s complexity-diversity analysis[3,4] presents another level of difficulty; it states that, even when the number of resources is large enough, a substantial niche-overlap between species makes the chance of stable coexistence exponentially small in N, the species richness of the community These long standing puzzles have received a lot of attention over the last decades, with many mechanisms suggested to circumvent the mathematical constraints and many works that have tried to provide empirical support to these theories[9]. The dynamics takes place in local habitat patches, connected to each other by migration Different realizations of this scenario, ranging from the McArthur-Wilson mainland-island model (a single and relatively small patch is coupled to a well-mixed large system)[10,11] to the conceptual framework of metapopulations and metacommunities (a system of many, diffusively coupled, local patches)[12,13] have been considered in the literature. Theory, experiments and field studies focusing on the possibility of alternative steady states (and the theory of catastrophic shifts associated with this scenario) play a central role in contemporary community dynamics literature[19,20]
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