Figure 1.

The effect of the model parameters on the likelihood that cooperation evolves. The likelihood is measured as the proportion of 21 runs where the population becomes cooperative (here defined such that helping occurs in more than half of the interactions for at least 50 000 consecutive generations). A population is considered as non-cooperative if no long-lasting cooperation (i.e. lasting for at least 50 000 generations) evolved for 10⁶ generations. (a) The effect of group size for two values of benefit, b and two values of the expected number of interactions per individual, n/M. b; n/M values: (a) black squares, 3;40; red circles, 3;80; green triangles, 5;40; blue diamonds, 3;40. The blue-dashed line shows the case when the population was remixed three times in each generation and three games were played per generation. In all other cases, one game is played per generation. (b) The effects of the expected number of interactions per individual at two group sizes, M, and two benefit values, b. b; M values: (b) black circles, 3;10; red circles, 3;20; green circles, 5;10. (c) The effects of the benefit to cost ratio at two group sizes, M, and two expected numbers of interactions, n/M. n/M; M values: (c) black circles, 40;10; red circles, 40;20; green circles, 80;10. Note that cooperative populations already arise at benefit-to-cost ratios below 2 : 1. For all simulations: population size, N, is 1200 and cost of helping, c, is 1. Dots mark arithmetic means and vertical bars mark the 95% CI for binomial distributions.