Transitive and intransitive structures in competition-based ecological communities

Based on the classical idea that no two species can occupy the same niche, ecological communities are frequently assumed to be structured according to the rules of interspecific competition, based on the intuition provided by the Lotka/Volterra competition equations in two dimensions. It has been noted that when three or more species are involved, the usual tacit assumption that all competition is transitive may be violated. Intransitive loops change some of the emergent principles of the competition-based framework of community structure. Since the intransitivity is oscillatory, the convenient stable equilibrium approach to communities is altered and oscillatory behavior of the system needs to be acknowledged. It is likely that real communities, especially if they are relatively large, will contain one or more intransitive structures, along with normal transitivities. Here we examine some theoretical constructs that emanate from the joint consideration of intransitive and transitive structures co-occurring in an ecological community.