Table 1.

Fit and simulation data characterizing the invasion of cooperators for two different initial cluster sizes and two cost-to-benefit ratios. The number of cooperators n_c(t) increases according to n_c(t) = a_it^d_I,where i refers to the first and second growth phase (cf. Fig. 1b). T indicates the number of generations until the first cooperator reaches the boundary on a 1000² lattice (averaged over 100 runs). The estimated and simulated equilibrium fractions of cooperators are given by $f_c^{\text{theory}}$ (see Eq. (3)) and $f_c^{\text{sims}}$ respectively.

c/b	initial cluster size	a1	d1	a2	d2	T	$f_c^{\text{theory}}$	$f_c^{\text{sims}}$
0.02	3 × 3	3.34	1.17	0.14	2.07	1683	0.849	0.932
0.02	30 × 30	51.14	0.80	0.36	1.95	1625	0.848	0.932
0.12	3 × 3	1.11	1.03	0.01	2.06	6515	0.519	0.578
0.12	30 × 30	44.51	0.43	0.02	1.94	6280	0.514	0.578