Altruism Displays a Harmonic Signature in Structured Societies

Several parameters combine to govern the nature of agent interactions in evolutionary social simulations. Previous work has suggested that these parameters may have complex interplay that is obscured when they are not analyzed separately. Here we focus specifically on how three population-level parameters, which govern agent interactions, affect levels of altruism in a population. Specifically we vary how frequently agents interact in a generation, how far along a network they may interact, and the size of the population. We show that the frequency with which an agent interacts with its neighbors during a generation has a strong effect on levels of evolved altruism – provided that those pairings are stochastic. When agents interact equally with all of their neighbors, regardless of how often, minimal levels of altruism evolve. We further report a curious harmonic signature in the level of altruism resulting from the interplay of the benefit-cost ratio of an altruistic act and the number of agent interactions per generation. While the level of altruism is generally an increasing function of the number of pairings per generation, at each instance where pairings equals a multiple of the benefit-cost ratio a sharp discontinuity occurs, precipitating a drop onto a lower-value function. We explore the nature of these discontinuities by examining the temporal dynamics and spatial configuration of agents. Finally, we show that rules for the evolution of cooperation that are based on network density may be inadvertently missing effects that are due to the frequency of interactions and whether those interactions are symmetrical among neighbors.