Department of Mathematics, Emmanuel College, Boston, Massachusetts, USA.
Program for Evolutionary Dynamics, Harvard University, Cambridge, Massachusetts, USA.
Nature. 2017 Apr 13;544(7649):227-230. doi: 10.1038/nature21723. Epub 2017 Mar 29.
Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve. Understanding evolutionary game dynamics in structured populations remains difficult. Mathematical results are known for special structures in which all individuals have the same number of neighbours. The general case, in which the number of neighbours can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class that suggests there is no efficient algorithm. Whether a simple solution for weak selection exists has remained unanswered. Here we provide a solution for weak selection that applies to any graph or network. Our method relies on calculating the coalescence times of random walks. We evaluate large numbers of diverse population structures for their propensity to favour cooperation. We study how small changes in population structure-graph surgery-affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.
进化发生在具有繁殖能力的个体的种群中。种群的结构可以影响哪些特征进化。理解结构化种群中的进化博弈动态仍然很困难。在所有个体具有相同数量邻居的特殊结构中，已经有了数学结果。在邻居数量可以变化的一般情况下，这个问题仍然没有解决。对于任意选择强度，这个问题属于计算复杂度类，表明没有有效的算法。对于弱选择是否存在简单的解决方案，这个问题仍然没有答案。在这里，我们提供了一种适用于任何图或网络的弱选择解决方案。我们的方法依赖于计算随机游走的合并时间。我们评估了大量不同的种群结构，以了解它们促进合作的倾向。我们研究了种群结构的微小变化（图手术）如何影响进化结果。我们发现，基于强对结对关系的社会最有利于合作的发展。
