Fig. 4: Strategy frequency as a function of population size N.

Error bars represent the standard deviation from 100 independent runs, and horizontal dashed lines represent reference outcomes from a large population (N = 2000²), as reported in ref. ³². The colours blue, orange, and green represent cooperators (C), defectors (D), and loners (L), respectively. The shaded region indicates the range of network sizes where mutation-induced outcomes align with those observed in large populations, effectively addressing finite-size effects. Synergy factors are set to r = 2.02 for (a) and (b), and r = 4.6 for (c) and (d). a and c show results without mutation, while (b) and (d) include mutation at a fixed rate of μ = 10⁻⁶.