Species coexistence, intransitivity, and topological variation in competitive tournaments.

Competitive intransitivity occurs when species' competitive abilities cannot be listed in a strict hierarchy, but rather form competitive loops, as in the game 'Rock-Paper-Scissors'. Indices are useful for summarizing intransitivity in communities; however, as with most indices, a great deal of information is compressed into single number. So while recent ecological theory, experiments, and natural history observations demonstrate that competitive intransitivity can promote species coexistence, the consequence of variation in the 'topology' of competitive interactions that is not accounted for by intransitivity indices is much less well understood. We use a continuous analytical model and two complementary discrete lattice models (one spatially explicit, the other aspatial) to demonstrate that such variation does indeed greatly affect species coexistence. Specifically, we show that although intransitivity indices are good at capturing broad patterns of coexistence, communities with different levels of intransitivity can have equal coexistence, and communities with equal intransitivity can have different coexistence, due to underlying variation in competitive network topology.