The elimination of hierarchy in a completely cyclic competition system

Interactions among competing units are crucial to maintaining biodiversity, and non-hierarchical interactions can promote biodiversity in cyclic competing systems. In the present study, we explore the role of hierarchical interactions, existing ubiquitously in reality, in the co-evolution of a cyclic competing system. In systems composed of cyclic competing species with hierarchy interactions in which one predator species has more than one prey, we find that hierarchy disappears in a rather short evolving time. In the process of co-evolution, a hierarchical competing system tends to transit to a cyclic non-hierarchical competing system described by the rock–paper–scissors game. In other words, the cyclic competing interactions appear to eradicate hierarchy. This conclusion is analyzed by a mean-field approach and is tested by stochastic simulations.