Group-level events are catalysts in the evolution of cooperation

Group-level events, like fission and extinction, catalyze the evolution of cooperation in group-structured populations by creating new paths from uncooperative population states to more cooperative states. Group-level events allow cooperation to thrive under unfavorable conditions such as low intra-group assortment and moderate rates of migration, and can greatly speed up the evolution of cooperation when conditions are more favorable. The time-dependent effects of fission and extinction events are studied and illustrated here using a PDE model of a group-structured population based loosely on populations of hunter-gatherer tribes. By solving the PDE numerically we can compare models with and without group-level events, and explicitly calculate quantities associated with dynamics, like how long it takes a small population of cooperators to become a majority, as well as equilibrium population densities.