Nonlocal competition and the speciation transition on random networks.

A simple model for competition-induced speciation is presented and analyzed. Logistic growth with nonlocal interaction is studied on regular and random networks, and the large scale structure of the emerging genomic frequencies is examined. The neutrality assumption is violated if the network is random and the competition is nonlocal. Instead, "hubs" in the sequence space are suppressed by the competition more than nodes of a lower degree. Thus speciation is unavoidable for large-scale free networks. The emerging genetic mixture depends strongly on the initial conditions. The frequency of hubs is much greater in a population that evolved from a single nucleation event than in a population that recovered from a catastrophe.