Expanding spatial domains and transient scaling regimes in populations with local cyclic competition

Abstract

We investigate a six-species class of May-Leonard models leading to formation two types of competing spatial domains, each one inhabited by three-species with their own internal cyclic rock-paper-scissors dynamics. We study the resulting population dynamics using stochastic numerical simulations in two-dimensional space. We find that as three-species domains shrink, there is an increasing probability of extinction of two of the species inhabiting the domain, with the consequent creation of one-species domains. We determine the critical initial radius beyond which these one-species spatial domains are expected to expand. We further show that a transient scaling regime, with a slower average growth rate of the characteristic length scale $L$ of the spatial domains with time $t$, takes place before the transition to a standard $L \propto t^{1/2}$ scaling law, resulting in an extended period of coexistence.