Taylor Peter D, Day Troy, Wild Geoff
Department of Mathematics and Statistics, Queen's University Kingston, Ontario K7L 3N6, Canada.
Nature. 2007 May 24;447(7143):469-72. doi: 10.1038/nature05784.
Recent theoretical studies of selection in finite structured populations have worked with one of two measures of selective advantage of an allele: fixation probability and inclusive fitness. Each approach has its own analytical strengths, but given certain assumptions they provide equivalent results. In most instances the structure of the population can be specified by a network of nodes connected by edges (that is, a graph), and much of the work here has focused on a continuous-time model of evolution, first described by ref. 11. Working in this context, we provide an inclusive fitness analysis to derive a surprisingly simple analytical condition for the selective advantage of a cooperative allele in any graph for which the structure satisfies a general symmetry condition ('bi-transitivity'). Our results hold for a broad class of population structures, including most of those analysed previously, as well as some for which a direct calculation of fixation probability has appeared intractable. Notably, under some forms of population regulation, the ability of a cooperative allele to invade is seen to be independent of the nature of population structure (and in particular of how game partnerships are specified) and is identical to that for an unstructured population. For other types of population regulation our results reveal that cooperation can invade if players choose partners along relatively 'high-weight' edges.
固定概率和广义适合度。每种方法都有其自身的分析优势，但在某些假设下，它们会给出等效的结果。在大多数情况下，种群结构可以由通过边连接的节点网络（即图）来指定，并且这里的大部分工作都集中在一种连续时间进化模型上，该模型最早由参考文献11描述。在此背景下，我们进行了广义适合度分析，以得出一个令人惊讶的简单分析条件，用于确定在任何满足一般对称条件（“双传递性”）的图中合作等位基因的选择优势。我们的结果适用于广泛的种群结构类别，包括大多数先前分析过的结构，以及一些直接计算固定概率似乎很棘手的结构。值得注意的是，在某些形式的种群调节下，合作等位基因的入侵能力被认为与种群结构的性质无关（特别是与博弈伙伴关系的指定方式无关），并且与非结构化种群的情况相同。对于其他类型的种群调节，我们的结果表明，如果参与者沿着相对“权重高”的边选择伙伴，合作就可以入侵。
