PADE APPROXIMANTS AND EXACT TWO-LOCUS SAMPLING DISTRIBUTIONS

作者：Jenkins Paul A^*; Song Yun S

来源：Annals of Applied Probability, 2012, 22(2): 576-607.

DOI：10.1214/11-AAP780

• Population genetics
• recombination
• sampling distribution
• asymptotic expansion
• Pade approximants

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.

• 出版日期2012-4