Dissecting the role of transitivity and intransitivity on coexistence in competing species networks

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It is well established that intransitively assembled interaction networks can support the coexistence of competing species, while transitively assembled (hierarchical) networks are prone to species loss through competitive exclusion. However, as the number of species grows, the complexity of ecological interaction networks grows disproportionately, and species can get involved simultaneously in transitive and intransitive groups of interactions. In such complex networks, the effects of intransitivity on species persistence are not straightforward. Dissecting networks into intransitive/transitive components can help us to understand the complex role that intransitivity may play in supporting species diversity. We show through simulations that those species participating in the largest group of intransitive interactions (the core of the network) have high probabilities of persisting in the long term. However, participation in a group of intransitive interactions other than the core does not always improve persistence. Likewise, participating in transitive interactions does not always decrease persistence because certain species (the satellites) transitively linked to the core have also a high persistence probability. Therefore, when networks contain transitive and intransitive structures, as it can be expected in real ecological networks, the existence of a large intransitive core of species can have a disproportionate positive effect on species richness.