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The HoneyComb Paradigm for Research on Collective Human Behavior
Published on: January 19, 2019
The role of selective extinction in promoting cooperation in a many demes model
1Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia.
Abstract:
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.
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