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Quantitative Biology, Populations and Evolution, q-bio.PE
Abstract:
People tend to have their social interactions with members of their own
community. Such group-structured interactions can have a profound impact on the
behaviors that evolve. Group structure affects the way people cooperate, and
how they reciprocate each other's cooperative actions. Past work has shown that
population structure and reciprocity can both promote the evolution of
cooperation. Yet the impact of these mechanisms has been typically studied in
isolation. In this work, we study how the two mechanisms interact. Using a
game-theoretic model, we explore how people engage in reciprocal cooperation in
group-structured populations, compared to well-mixed populations of equal size.
To derive analytical results, we focus on two scenarios. In the first scenario,
we assume a complete separation of time scales. Mutations are rare compared to
between-group comparisons, which themselves are rare compared to within-group
comparisons. In the second scenario, there is a partial separation of time
scales, where mutations and between-group comparisons occur at a comparable
rate. In both scenarios, we find that the effect of population structure
depends on the benefit of cooperation. When this benefit is small,
group-structured populations are more cooperative. But when the benefit is
large, well-mixed populations result in more cooperation. Overall, our results
reveal how group structure can sometimes enhance and sometimes suppress the
evolution of cooperation.