How competitive intransitivity and niche overlap affect spatial coexistence

Competitive intransitivity is mostly considered outside the main body of coexistence theories that rely primarily on the role of niche overlap and differentiation. How the interplay of competitive intransitivity and niche overlap jointly affects species coexistence has received little attention. Here, we consider a rock-paper-scissors competition system where interactions between species can represent the full spectra of transitive-intransitive continuum and niche overlap/differentiation under different levels of competition asymmetry. By comparing results from pair approximation that only considers interference competition between neighbouring cells in spatial lattices, with those under the mean-field assumption, we show that (1) species coexistence under transitive competition is only possible at high niche differentiation; (2) in communities with partial or pure intransitive interactions, high levels of niche overlap are not necessary to beget species extinction; and (3) strong spatial clustering can widen the condition for intransitive loops to facilitate species coexistence. The two mechanisms, competitive intransitivity and niche differentiation, can support species persistence and coexistence, either separately or in combination. Finally, the contribution of intransitive loops to species coexistence can be enhanced by strong local spatial correlations, modulated and maximised by moderate competition asymmetry. Our study, therefore, provides a bridge to link intransitive competition to other generic ecological theories of species coexistence.

Methods
This dataset contains the analyses of pair approximationthe (PA) model, codes of drawing Figure 3 and numerical solution datas. It is performed by Matlab R2014a.