Does local competition increase the coexistence of species in intransitive networks?

Competitive intransitivity, a situation in which species' competitive ranks cannot be listed in a strict hierarchy, promotes species coexistence through "enemy's enemy indirect facilitation." Theory suggests that intransitivity-mediated coexistence is enhanced when competitive interactions occur at local spatial scales, although this hypothesis has not been thoroughly tested. Here, we use a lattice model to investigate the effect of local vs. global competition on intransitivity-mediated coexistence across a range of species richness values and levels of intransitivity. Our simulations show that local competition can enhance intransitivity-mediated coexistence in the short-term, yet hinder it in the long-term, when compared to global competition. This occurs because local competition slows species disaggregation, allowing weaker competitors to persist longer in the shifting spatial refuges of intransitive networks, enhancing short-term coexistence. Conversely, our simulations show that, in the long-term, local competition traps disaggregated species in unfavorable areas of the competitive arena, where they are excluded by superior competitors. As a result, in the long-term, global intransitive competition allows a greater number of species to coexist than local intransitive competition.