Stochasticity, Selection, and the Evolution of Cooperation in a Two-Level Moran Model of the Snowdrift Game

Figure 7

Two-level Moran model with variation in r-values. Each panel represents simulation results for our model when groups in the metapopulation vary in their initial -values. The panels (a, e, c) show the results for , while the panels (b, d, f) show . Each panel represents summary results for 100 independent simulations with populations of 10 (a, b), 100 (c, d), and 1000 (e, f) individuals. In each simulation, there were 25 groups with an initial cooperator frequency of  .10, 500 group replication events, and 100 within-group generations. The red, black, and light blue (cyan) dots are the first, second, and third quartiles of the observed frequencies of cooperators in the metapopulation, respectively, while the thin black line is the mean frequency. The blue lines are the maximum and minimum observed frequency across 100 simulations. The dashed, horizontal line is the long-term, expected frequency of cooperation in the metapopulation assuming a null model given by (13). Note that the observed frequency of cooperators is greater than that predicted by the null models in all cases, sometimes substantially.

(a)

(b)

(c)

(d)

(e)

(f)