Department of Mathematics, Harvard University, Cambridge, MA 02138.
Max Planck Research Group 'Dynamics of Social Behavior', Max Planck Institute for Evolutionary Biology, 24306, Plön, Germany.
Proc Natl Acad Sci U S A. 2023 May 16;120(20):e2221080120. doi: 10.1073/pnas.2221080120. Epub 2023 May 8.
Direct reciprocity is a powerful mechanism for the evolution of cooperation based on repeated interactions between the same individuals. But high levels of cooperation evolve only if the benefit-to-cost ratio exceeds a certain threshold that depends on memory length. For the best-explored case of one-round memory, that threshold is two. Here, we report that intermediate mutation rates lead to high levels of cooperation, even if the benefit-to-cost ratio is only marginally above one, and even if individuals only use a minimum of past information. This surprising observation is caused by two effects. First, mutation generates diversity which undermines the evolutionary stability of defectors. Second, mutation leads to diverse communities of cooperators that are more resilient than homogeneous ones. This finding is relevant because many real-world opportunities for cooperation have small benefit-to-cost ratios, which are between one and two, and we describe how direct reciprocity can attain cooperation in such settings. Our result can be interpreted as showing that diversity, rather than uniformity, promotes evolution of cooperation.
直接互惠是一种基于相同个体之间重复相互作用的合作进化的强大机制。但如果收益与成本的比值超过一定的阈值，合作水平才会提高，而这个阈值取决于记忆长度。对于研究最透彻的一轮记忆的情况，这个阈值是 2。在这里，我们报告说，中间突变率会导致高水平的合作，即使收益与成本的比值仅略高于 1，即使个体只使用最少的过去信息。这一惊人的观察结果是由两个效应引起的。首先，突变产生了多样性，从而破坏了缺陷者的进化稳定性。其次，突变导致了比同质群体更有弹性的多样化的合作者社区。这一发现很重要，因为许多现实世界的合作机会的收益与成本的比值都在 1 到 2 之间，我们描述了直接互惠如何在这种情况下实现合作。我们的结果可以解释为表明多样性而不是统一性促进了合作的进化。
