A competitive network theory of species diversity

Abstract

Nonhierarchical competition between species has been proposed as a potential mechanism for biodiversity maintenance, but theoretical and empirical research has thus far concentrated on systems composed of relatively few species. Here we develop a theory of biodiversity based on a network representation of competition for systems with large numbers of competitors. All species pairs are connected by an arrow from the inferior to the superior. Using game theory, we show how the equilibrium density of all species can be derived from the structure of the network. We show that when species are limited by multiple factors, the coexistence of a large number of species is the most probable outcome and that habitat heterogeneity interacts with network structure to favor diversity.competitive exclusion | rock-paper-scissor | neutral theory | niche theory E cologists have long sought to explain how a wide diversity of species coexists in nature (1). Coexistence is a conundrum because if two species share the same niche, the competitive exclusion principle predicts the extinction of the inferior competitor (2). This foundational principle continues to motivate advances in niche and neutral theories (3-5) of coexistence, which use niche differences and species equivalence, respectively, to avoid competitive exclusion. However, each theory suffers shortcomings. Field evidence that classic resource-based niche differences are essential for coexistence is rare (6-8), whereas the species equivalence assumption of neutral theory is hard to reconcile with nature. These shortcomings justify the quantitative exploration of less conventional niche mechanisms of coexistence.Here, we ask how embedding pairs of superior and inferior species in a network of competitors alters the outcome of competition and influences patterns of relative abundance. We find that although the competitive exclusion principle certainly holds for any pair of competitors, when multiple factors determine the outcome of competition and species are embedded in competitive networks, a large number of species can coexist. The coexistence relies on the stabilizing effect of intransitivities (9-12) that emerge in these networks rather than more traditional pairwise niche differences. By combining a game theoretical framework with graph theory and dynamical systems (13, 14), we show how the equilibrium abundance of all species can be determined from the competitive network, how species diversity relates to the number of limiting factors, and how spatial heterogeneity combines with intransitivity to interactively favor diversity maintenance. ModelThe pairwise competitive relationships between species in a community can be expressed as a network, or more formally, a tournament, in which species are the nodes and arrows connect the competitive inferior to the superior competitor (Fig. 1A). In the simplest case, where all species in a system compete for a single limiting resource, their competitive abilities should be transitive: Species A beats all others, B beats all but...

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Evolution of restraint in a structured rock–paper–scissors community

“…This situation was reported in a grassland community in which grasses outcompete forb species but are disproportionately parasitized by a root hemiparasitic plant (20). More broadly, many studies have proposed that nontransitive relations may be more prevalent than currently appreciated in systems with frequency-dependent selection or ecological tradeoffs (49,52,53).…”

Intraspecific genetic variation and species coexistence in plant communities

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