RIKEN Center for Computational Science, Kobe, Hyogo, 650-0047, Japan.
Max Planck Research Group 'Dynamics of Social Behavior', Max Planck Institute for Evolutionary Biology, Plön, Germany.
Sci Rep. 2022 Nov 4;12(1):18645. doi: 10.1038/s41598-022-23467-4.
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. In this model, the population is subdivided into groups. Individuals engage in pairwise interactions within groups while they also have chances to imitate strategies outside the groups. 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.
人们往往更倾向于与自己所在社区的成员进行社交互动。这种群体结构的互动会对演化出的行为产生深远的影响。群体结构影响着人们的合作方式，以及他们如何相互回报彼此的合作行为。过去的研究表明，群体结构和互惠性都可以促进合作的演化。然而，这些机制的影响通常是孤立地进行研究的。在这项工作中，我们研究了这两种机制是如何相互作用的。我们使用博弈论模型，研究了在群体结构的人群中，与同等大小的均匀混合人群相比，人们如何进行互惠合作。在这个模型中，人口被细分为群体。个体在群体内部进行成对的相互作用，同时也有机会模仿群体外部的策略。为了得出分析结果，我们关注了两种情况。在第一种情况下，我们假设时间尺度完全分离。与群体间比较相比，突变是罕见的，而群体间比较本身也比群体内比较罕见。在第二种情况下，时间尺度存在部分分离，突变和群体间比较以相当的速度发生。在这两种情况下，我们发现群体结构的影响取决于合作的好处。当这种好处较小时，群体结构的人群会更加合作。但当好处较大时，均匀混合的人群会导致更多的合作。总的来说，我们的结果揭示了群体结构如何有时增强、有时抑制合作的演化。
