Fig. 2.
The critical benefit-to-cost ratio, b/c, for which cooperators and defectors fixate with the same probability is shown for a fixed group size, n = 10 (a) and for a fixed number of groups, m = 10 (b). The numerical simulations for q = 10−3 (circles) agree perfectly with the theory for weak selection and q ≪ 1 given by b/c > 1+ n/(m − 2); see Eq. 24 in Supporting Text. Simulations for q = 1.0 (triangles) show that the critical b/c is even smaller when q is larger: More frequent group splitting favors cooperators. All simulations are performed for weak selection, w = 0.1.