Fig 1. Examples of graphs with proper two-colorings: a, cycle; b, complete, symmetric bipartite graph; c, square lattice (von Neumann neighborhood); d, hexagonal lattice; e, complete, asymmetric bipartite graph; and f, star (an extreme case of e).
If the fitness of A and B are aG and bG on a green site and aR and bR on a red site, respectively, then on each of these graphs we can explicitly calculate the probability that one type replaces the other (Theorem 1).