论文标题
Kingman的模型具有随机突变概率：收敛和凝结I
Kingman's model with random mutation probabilities: convergence and condensation I
论文作者
论文摘要
对于具有离散代的单位单倍体无限人群，著名的金曼的模型描述了在选择和突变的竞争中，适应性分布的演变具有恒定的突变概率。让突变概率随代的几代有所不同，反映了随机环境的影响。本文通过使用I.I.D.的序列来概括金曼的模型随机突变概率。对于序列的任何分布，证明了适应性分布的弱收敛性与任何初始适应性分布的全球稳定平衡。我们将随机模型的凝结定义为几乎肯定是人口的正比例在最大的健身价值上传播并凝结。当选择比突变更有利时，可能会发生凝结。给出标准以说明凝结是否发生。
For a one-locus haploid infinite population with discrete generations, the celebrated Kingman's model describes the evolution of fitness distributions under the competition of selection and mutation, with a constant mutation probability. Letting mutation probabilities vary on generations reflects the influence of a random environment. This paper generalises Kingman's model by using a sequence of i.i.d. random mutation probabilities. For any distribution of the sequence, the weak convergence of fitness distributions to the globally stable equilibrium for any initial fitness distribution is proved. We define the condensation of the random model as that almost surely a positive proportion of the population travels to and condensates on the largest fitness value. The condensation may occur when selection is more favoured than mutation. A criterion is given to tell whether the condensation occurs or not.
