Closed-Form Two-Locus Sampling Distributions: Accuracy and Universality
Closed-Form Two-Locus Sampling Distributions: Accuracy and Universality
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DOI：
10.1534/genetics.109.107995
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发表时间：
2009-11-01
期刊：
影响因子：
3.3
通讯作者：
Song, Yun S.
中科院分区：
文献类型：
--
作者：
Jenkins, Paul A.;Song, Yun S.
抽样分布在群体遗传学分析中起着重要的作用，但封闭形式的抽样公式通常很难获得。在存在重组的情况下，没有已知的封闭形式的采样公式，适用于任意的重组率。然而，我们最近证明了这一点。当群体比例重组率p较大时，可以获得有用的封闭形式的采样公式。具体地说，在两位点无限等位基因模型的情形下，我们考虑了抽样公式的所有渐近展开式，并得到了展开式中前几项的封闭表达式.在这篇文章中，我们推广这一结果到所有任意有限等位基因突变模型，并表明，直到前几项的扩展，我们能够计算分析，函数形式的渐近抽样公式是共同的所有突变模型。我们进行，所有广泛的研究的两个位点的父母独立突变模型的渐近公式的准确性，并详细讨论了具体的应用背景下的复合似然方法。此外，利用我们的渐近抽样公式，我们建立了一个简单的充分条件为一个给定的两个轨迹的样本配置有一个有限的最大似然估计（MLE）的ρ。这个条件是第一个分析结果的分类的极大似然估计的p和即时检查在实践中，提供了一个位点的概率是已知的。
Sampling distributions play an important role in population genetics analyses, but closed-form sampling formulas are generally intractable to obtain. In the presence of recombination, there is no known closed-form sampling formula that holds for an arbitrary recombination rate. However, we recently showed that. it is possible to obtain useful closed-form sampling formulas when the population-scaled recombination rate p is large. Specifically, in die case of the two-locus infinite-alleles model, we considered all asymptotic expansion of die sampling formula in inverse powers of rho and obtained closed-form expressions for the first Few terms in the expansion. In this article, we generalize this result to all arbitrary finite-alleles mutation model and show that, till to the first few terms in the expansion that we are able to compute analytically, the functional form of the asymptotic sampling formula is common to all mutation models. We carry, out all extensive study of the accuracy of the asymptotic formula for the two-locus parent-independent Mutation model and discuss in detail a concrete application in the context of the composite-likelihood method. Furthermore, using our asymptotic sampling formula, we establish a simple sufficient condition fora given two-locus sample configuration to have a finite maximum-likelihood estimate (MLE) of rho. This condition is the first analytic result on the classification of the MLE of p and is instantaneous to check in practice, provided that one-locus probabilities are known.