title: PADÉ APPROXIMANTS AND EXACT TWO-LOCUS SAMPLING DISTRIBUTIONS.
abstract: 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 rateρis moderate to large. In this paper, a new computational technique is developed for finding the asymptotic expansion to anarbitrary 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 Padé approximants) theexacttwo-locus sampling distribution as an analytic function ofρ; this function is exact for all values ofρ∈ [0, ∞). It is also shown that the new computational framework presented here is flexible enough to incorporate natural selection.
authors.affiliation: Computer Science Division, University of California, Berkeley, Berkeley, CA 94720, Berkeley USA.
authors.forename: Paul A
authors.initials: PA
authors.lastname: Jenkins
authors.forename: Yun S
authors.initials: YS
authors.lastname: Song
keywords: Padé approximants; asymptotic expansion; population genetics; recombination; sampling distribution