PADE APPROXIMANTS AND EXACT TWO-LOCUS SAMPLING DISTRIBUTIONS
PADE APPROXIMANTS AND EXACT TWO-LOCUS SAMPLING DISTRIBUTIONS
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DOI：
10.1214/11-aap780
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发表时间：
2012-04-01
影响因子：
1.8
通讯作者：
Song, Yun S.
中科院分区：
文献类型：
--
作者：
Jenkins, Paul A.;Song, Yun S.
对于具有重组的群体遗传学模型，获得精确的、解析的抽样分布几十年来一直是一个具有挑战性的开放问题。最近，一种基于渐近级数的新视角被引入来研究这一问题。具体地说，当重组率p由中到大时，给出了双轨迹抽样分布渐近展开的前几项的闭合表达式。本文提出了一种求任意阶渐近展开式的新的计算方法。这种新方法的计算可以很容易地实现自动化。此外，本文还证明了用Pade近似的方法，只需在渐近展开式中用有限个数的项，就能将精确的两轨迹抽样分布恢复为Rho的解析函数，该函数对于Rho的所有值都是[0，无穷大)的元素是精确的。它还表明，这里提出的新的计算框架足够灵活，可以纳入自然选择。
For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to make progress on this problem. Specifically, closed-form expressions have been derived for the first few terms in an asymptotic expansion of the two-locus sampling distribution when the recombination rate p is moderate to large. In this paper, a new computational technique is developed for finding the asymptotic expansion to an arbitrary order. Computation in this new approach can be automated easily. Furthermore, it is proved here that only a finite number of terms in the asymptotic expansion is needed to recover (via the method of Pade approximants) the exact two-locus sampling distribution as an analytic function of rho; this function is exact for all values of rho is an element of [0, infinity). It is also shown that the new computational framework presented here is flexible enough to incorporate natural selection.