Defensive alliances in spatial models of cyclical population interactions

As a generalization of the 3-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated and a neutral interacting partner. Depending on their interaction topologies, these systems can be classified into four (isomorphic) groups exhibiting significantly different behaviors as a function of mutation rate. On three out of four cases three (or four) species form defensive alliances which maintain themselves in a self-organizing polydomain structure via cyclic invasions. Varying the mutation rate this mechanism results in an ordering phenomenon analogous to that of magnetic Ising model.