The effects of intransitive competition on coexistence.

Coexistence theory has been developed with an almost exclusive focus on interactions between two species, often ignoring more complex and indirect interactions, such as intransitive loops, that can emerge in competition networks. In fact, intransitive competition has typically been studied in isolation from other pairwise stabilising processes, and thus little is known about how intransitivity interacts with more traditional drivers of species coexistence such as niche partitioning. To integrate intransitivity into traditional coexistence theory, we developed a metric of growth rate when rare, Δri¯, to identify and quantify the impact of intransitive competition against a backdrop of pairwise stabilising niche differences. Using this index with simulations of community dynamics, we demonstrate that intransitive loops can both stabilise or destabilise species coexistence, but the strength and importance of intransitive interactions are significantly affected by the length and the topology of these loops. We conclude by showing how Δri¯ can be used to evaluate effects of intransitivity in empirical studies. Our results emphasise the need to integrate complex mechanisms emerging from diverse interactions into our understanding of species coexistence.