Evolutionary dynamics on sequential temporal networks

Population structure is a well-known catalyst for the evolution of cooperation and has traditionally been considered to be static in the course of evolution. Conversely, real-world populations, such as microbiome communities and online social networks, frequently show a progression from tiny, active groups to huge, stable communities, which is insufficient to be captured by constant structures. Here, we propose sequential temporal networks to characterize growing networked populations, and we extend the theory of evolutionary games to these temporal networks with arbitrary structures and growth rules. We derive analytical rules under which a sequential temporal network has a higher fixation probability for cooperation than its static counterpart. Under neutral drift, the rule is simply a function of the increment of nodes and edges in each time step. But if the selection is weak, the rule is related to coalescence times on networks. In this case, we propose a mean-field approximation to calculate fixation probabilities and critical benefit-to-cost ratios with lower calculation complexity. Numerical simulations in empirical datasets also prove the cooperation-promoting effect of population growth. Our research stresses the significance of population growth in the real world and provides a high-accuracy approximation approach for analyzing the evolution in real-life systems.Author summary: The temporality of real-world populations often arises from the growth in the number of individuals and links. Such dynamical systems cannot be adequately represented by a single static network. Here, we use sequential temporal networks to characterize time-varying interactions in growing populations and propose a method for analyzing evolutionary dynamics over these networks with arbitrary structures and growth rules. We find that cooperation can be favored in sequential temporal networks under neutral drift when cooperators form clusters or become hub nodes before new intruders (defectors) enter the populations. These conditions ensure the smooth dissemination of cooperation among individuals. We also derive the corresponding condition under weak selection, which is related to coalescence times on networks. At the same time, we provide a mean-field approximation approach for measuring the cooperation-promoting effect of large-scale sequential temporal networks. Through numerical simulations in empirical datasets from different realistic contexts, we confirm that population growth is key to promoting cooperation.