Evolution of altruistic punishment in heterogeneous populations

Evolutionary models for altruistic behavior typically make the assumption of homogeneity: each individual has the same costs and benefits associated with cooperating with each other and punishing for selfish behavior. In this paper, we relax this assumption by separating the population into heterogeneous classes, such that individuals from different classes differ in their ability to punish for selfishness. We compare the effects of introducing heterogeneity this way across two population models, that each represents a different type of population: the infinite and well-mixed population describes the way workers of social insects such as ants are organized, while a spatially structured population is more related to the way social norms evolve and are maintained in a social network. We find that heterogeneity in the effectiveness of punishment by itself has little to no effect on whether or not altruistic behavior will stabilize in a population. In contrast, heterogeneity in the cost that individuals pay to punish for selfish behavior allows altruistic behavior to be maintained more easily. Fewer punishers are needed to deter selfish behavior, and the individuals that punish will mostly belong to the class that pays a lower cost to do so. This effect is amplified when individuals that pay a lower cost for punishing inflict a higher punishment. The two population models differ when individuals that pay a low cost for punishing also inflict a lower punishment. In this situation, altruistic behavior becomes harder to maintain in an infinite and well-mixed population. However, this effect does not occur when the population is spatially structured.