Using intransitive triads to determine final species richness of competition networks

It is well established that intransitive competition among species can promote their coexistence. A typical intransitive system involves a community of three competing species that satisfy a relationship similar to the popular rock-paper-scissors game. Such a community is said to form an intransitive triad. Theoretical and empirical evidence indicates that the rock-paper-scissor competition dynamics can lead to the indefinite coexistence of the three species if ecological processes such as dispersal, migration and interaction occur over small spatial scales. However, for communities containing four or more species, deciding how many species will survive the competition and, hence, determining the final species richness, remains a challenge even for the most intransitive communities. In this work, we explore the role played by the intransitive triads in the time evolution of a competition network. By creating dominance relations among the intransitive triads of a network, we are able to deduce its final species richness or to narrow it down to a few possibilities. For example, all competition networks in which one intransitive triad dominates every other triad will evolve to a three-species system composed of the species that make up the most dominant triad. Our results, stated as hypotheses, are tested using a Crank-Nicolson simulation of a simple reaction-diffusion system that models the spatio-temporal dynamics of the network.