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 I 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.