The brave leader game and the timing of altruism among nonkin

The evolution of cooperation among nonkin remains a puzzle, and almost no theoretical work has examined the timing of altruism, that is, when a behavior that benefits others at one's own fitness expense should be expressed in time. We present an evolutionary dynamic-game model to address the question of when, if ever, an altruist would voluntarily emerge in time in groups of nonrelatives. Our model shows that when the benefit of having an altruistic leader decays with time, leaders will eventually emerge and will emerge later (i) in larger groups, (ii) when the cost of leadership increases, and (iii) when the assessment interval increases. The model applies to diverse situations in which time-decaying group benefits are obtained only after a group member assumes a leadership role at some cost to itself, including leader roles in foraging flocks and migration groups in birds and spiny lobsters and in high-risk foraging in desert ants.