  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.
