论文标题
Kingman的模型具有随机突变概率：收敛和凝结II
Kingman's model with random mutation probabilities: convergence and condensation II
论文作者
论文摘要
金曼（Kingman）的模型描述了在选择和突变的竞争中，单位单位单倍体人群的无限大小和离散世代的演变。在先前的论文中已经进行了随机概括，该论文假设所有突变概率为i.i.d。如果几乎肯定的人口中的积极比例几乎肯定是由于选择优于突变而占主导地位，那么凝结就会发生。给出了凝结标准，该标准依赖于平衡，其显式表达尚不清楚。本文根据发现随机模型的矩阵表示，解决了这些问题。获得平衡的明确表达，并且可以估算缩合标准中的关键量。此外，我们研究了金曼模型中随机性的设计如何通过比较不同模型之间的均衡水平。发现的事实是在其他更复杂的模型中持有的。
Kingman's model describes the evolution of a one-locus haploid population of infinite size and discrete generations under the competition of selection and mutation. A random generalisation has been made in a previous paper which assumes all mutation probabilities to be i.i.d.. The weak convergence of fitness distributions to a globally stable equilibrium for any initial distribution was proved. A condensation occurs if almost surely a positive proportion of the population travels to and condensates on the largest fitness value due to the dominance of selection over mutation. A criterion of condensation was given which relies on the equilibrium whose explicit expression is however unknown. This paper tackles these problems based on the discovery of a matrix representation of the random model. An explicit expression of the equilibrium is obtained and the key quantity in the condensation criterion can be estimated. Moreover we examine how the design of randomness in Kingman's model affects the fitness level of the equilibrium by comparisons between different models. The discovered facts are conjectured to hold in other more sophisticated models.
