Zhang Yanling, Liu Aizhi, Sun Changyin
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.
School of Automation, Southeast University, Nanjing 210096, China.
Sci Rep. 2016 Oct 21;6:35114. doi: 10.1038/srep35114.
For large quantities of spatial models, the multi-strategy selection under weak selection is the sum of two competition terms: the pairwise competition and the competition of multiple strategies with equal frequency. Two parameters σ and σ quantify the dependence of the multi-strategy selection on these two terms, respectively. Unlike previous studies, we here do not require large populations for calculating σ and σ, and perform the first quantitative analysis of the effect of migration on them in group-structured populations of any finite sizes. The Moran and the Wright-Fisher process have the following common findings. Compared with well-mixed populations, migration causes σ to change with the mutation probability from a decreasing curve to an inverted U-shaped curve and maintains the increase of σ. Migration (probability and range) leads to a significant change of σ but a negligible one of σ. The way that migration changes σ is qualitatively similar to its influence on the single parameter characterizing the two-strategy selection. The Moran process is more effective in increasing σ for most migration probabilities and the Wright-Fisher process is always more effective in increasing σ. Finally, our findings are used to study the evolution of cooperation under direct reciprocity.
对于大量的空间模型，弱选择下的多策略选择是两个竞争项的总和：成对竞争和等频率多策略竞争。两个参数σ和σ分别量化了多策略选择对这两个项的依赖性。与以往的研究不同，我们在此不需要大量种群来计算σ和σ，并对任意有限大小的群体结构种群中迁移对它们的影响进行了首次定量分析。莫兰过程和赖特 - 费希尔过程有以下共同发现。与充分混合的种群相比，迁移导致σ随突变概率从下降曲线变为倒U形曲线，并使σ持续增加。迁移（概率和范围）导致σ发生显著变化，但对σ的影响可忽略不计。迁移改变σ的方式在定性上类似于其对表征双策略选择的单个参数的影响。对于大多数迁移概率，莫兰过程在增加σ方面更有效，而赖特 - 费希尔过程在增加σ方面总是更有效。最后，我们的研究结果被用于研究直接互惠下的合作进化。
