PADE APPROXIMANTS AND EXACT TWO-LOCUS SAMPLING DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Jenkins, Paul A.; Song, Yun S.
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Berkeley; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP780
• 发表日期: 2012
• 页码: 576-607
• 关键词: linkage disequilibrium; formulas; recombination; coalescent

摘要

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.