Asymmetric effects of interaction and dispersal graphs on evolutionary dynamics

Abstract

Population structure is a critical factor in shaping evolutionary dynamics. It constrains not only who interacts with whom, but also who learns from whom. In many real-world cases, such spatial constraints can lead to asymmetric interaction and strategy dispersal. For example, individuals who are geographically and socially too distant to interact physically may still learn from each other through social media. Despite the ubiquity of the asymmetry, their impact on evolutionary outcomes, particularly in the presence of structural heterogeneity, is not well understood. In this paper, we investigate their influence on evolutionary dynamics. Our analytical and simulation results demonstrate that although population structure can lead to the formation of clusters of cooperators, disrupting the balance between the interaction and dispersal graphs can severely impede cooperation. Moreover, we find that increased network heterogeneity exacerbates the cooperation-inhibiting effects. We also examine the roles of the interaction and dispersal networks separately. By modifying the connections in each network, we find that altering the dispersal network has a more pronounced effect on cooperation compared to the interaction network. Our work emphasizes the importance of the correlation between interaction and strategy dispersal and highlights that modifying the paths of strategy or information dissemination can be a more effective way of promoting social prosperity than modifying the interaction networks.