AI 中文总结
该研究在有限单倍体种群的周期表型空间中，通过结合溯祖理论与随机游走谱表示，推导合作演化的 benefit-to-cost 阈值，揭示表型突变的非单调效应及周期模型与无界格点模型的差异。
AI 中文摘要
我们研究有限单倍体种群中合作的演化，该种群的个体在有限周期空间中同时携带策略和表型。合作者的帮助概率随表型距离呈指数衰减，产生依赖表型距离的分级 assortation。在弱选择和大种群突变标度下，我们结合溯祖理论与离散环面上随机游走的谱表示，推导了合作在静态丰度中受青睐的明确 benefit-to-cost 阈值。更强的表型辨别力和更高的表型空间维度会严格降低该阈值，而策略突变会提高阈值。相比之下，表型突变具有非单调效应：对于极罕见和极快速的表型突变，阈值均会发散，因此在中间速率下至少达到一个最小值。高突变抑制源于有限表型空间上的混合，这将周期模型与其无界格点对应模型区分开来。
英文摘要
We study the evolution of cooperation in a finite haploid population whose individuals carry both a strategy and a phenotype on a finite periodic space. Cooperators help with a probability that decays exponentially with phenotypic distance, generating graded phenotype-dependent assortment. Under weak selection and a large-population mutation scaling, we combine coalescent arguments with the spectral representation of a random walk on the discrete torus to derive an explicit benefit-to-cost threshold for cooperation to be favored in stationary abundance. Stronger phenotypic discrimination and higher phenotype-space dimension strictly lower this threshold, whereas strategy mutation raises it. In contrast, phenotype mutation has a nonmonotone effect: the threshold diverges for both very rare and very rapid phenotype mutation and therefore attains at least one minimum at an intermediate rate. The high-mutation inhibition results from mixing on the finite phenotype space and distinguishes the periodic model from its unbounded-lattice counterpart.
Comments24 pages with 5 figures
