平衡状态下链对称突变模型比例突变参数的最大似然（ML）估计
Maximum likelihood (ML) estimators for scaled mutation parameters with a strand symmetric mutation model in equilibrium
摘要：
在多等位基因亲本独立突变漂移模型中，等位基因的平衡比例服从狄利克雷分布。一个特殊的情况是双等位基因模型，其中比例是β分布的。然后，从这些模型中提取的样本分别是狄利克雷多项分布或贝塔二项分布。双等位基因亲本独立突变模型的突变参数的最大似然（ML）估计可通过期望最大化算法获得。假设小规模的突变率，大小为$M$的样本的分布可以在一阶泰勒级数中展开。然后，双等位基因模型中的两个参数的ML估计可以使用站点频谱来表示。在这篇文章中，我们超越了父母独立的突变，并分析了链对称突变模型与六个缩放的突变参数，偏离父母独立的突变，一般来说，从详细的平衡。假设突变漂移平衡和小规模突变率，我们推导出这六个参数的ML估计。这是第一次，ML估计提供了一个突变模型比父母独立的突变更复杂。
英文摘要：
With the multiallelic parent-independent mutation-drift model, the equilibrium proportions of alleles are known to be Dirichlet distributed. A special case is the biallelic model, in which the proportions are beta distributed. A sample taken from these models is then Dirichlet-multinomially or beta-binomially distributed, respectively. Maximum likelihood (ML) estimators for the mutation parameters of the biallelic parent-independent mutation model are available via an expectation maximization algorithm. Assuming small scaled mutation rates, the distribution of a sample of size $M$ can be expanded in a Taylor series of first order. Then the ML estimators for the two parameters in the biallelic model can be expressed using the site frequency spectrum. In this article, we go beyond parent-independent mutation and analyse a strand-symmetric mutation model with six scaled mutation parameters that deviates from parent independent mutation and, generally, from detailed balance. We derive ML estimators for these six parameters assuming mutation-drift equilibrium and small scaled mutation rates. This is the first time that ML estimators are provided for a mutation model more complex than parent-independent mutation.
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