Figure 4. Hybrid scoring requires a critical population size to stabilize cooperation under adverse conditions.

Cooperators essentially compete to segregate from defectors before being completely wiped out. The lower the value of r (main panel) and p (inset), the larger the population size needed for cooperation to be stabilized. Note that for a sufficiently small population size (see legend), there exist sudden drops to zero cooperation levels at critical values of r and p. Shown is the stationary fraction of cooperators in dependence on r (main) and p (inset), as obtained for different numbers of groups forming the population (see legend). Parameter values are: p = 0.01 (main) and r = 1.1 (inset).