Modes of migration and multilevel selection in evolutionary multiplayer games

•We investigate four different modes of migration between groups.•For each mode we identify multiplayer games favoring the evolution of cooperation.•The number of games promoting the evolution of cooperation increases as individuals coordinate their migration behavior.•Weak altruism can evolve via any mode of migration.•Strong altruism evolves only under coordinated migration modes.

The evolution of cooperation in group-structured populations has received much attention, but little is known about the effects of different modes of migration of individuals between groups. Here, we have incorporated four different modes of migration that differ in the degree of coordination among the individuals. For each mode of migration, we identify the set of multiplayer games in which the cooperative strategy has higher fixation probability than defection. The comparison shows that the set of games under which cooperation may evolve generally expands depending upon the degree of coordination among the migrating individuals. Weak altruism can evolve under all modes of individual migration, provided that the benefit to cost ratio is high enough. Strong altruism, however, evolves only if the mode of migration involves coordination of individual actions. Depending upon the migration frequency and degree of coordination among individuals, conditions that allow selection to work at the level of groups can be established.