The role of selective extinction in promoting cooperation in a many demes model

This study investigates the evolution of cooperation in a deme-structured population where individuals interact via the Prisoner's Dilemma. Reproduction is payoff-dependent, and demes contribute to a global migrant pool proportionally to their fecundity. Deme extinction occurs with a baseline probability plus an additional probability term that is proportional to the fraction of defectors in the deme, modulated by a parameter α. Extinct demes are then repopulated from the migrant pool. A two-timescale analysis, valid in the limit of a large number of demes, reveals that the system's evolutionary dynamics are well-approximated by a continuous-time diffusion process. Using this diffusion approximation, we show that uniform extinction (α=0) suppresses cooperation. However, extinction targeting defector-dominated demes can significantly promote cooperation, establishing critical thresholds of α that determine when cooperation dominates. The study further explores how varying extinction rates and reproductive dynamics impact cooperation's persistence and evolutionary success in structured populations.