Jenkins, Paul and Song, Yun S. (2012) Padé approximants and exact two-locus sampling distributions. Annals of Applied Probability, Vol.22 (No.2). pp. 576-607. doi:10.1214/11-AAP780

Research output not available from this repository, contact author.

Request Changes to record.

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 rate ρ 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 Padé approximants) the exact two-locus sampling distribution as an analytic function of ρ; this function is exact for all values of ρ ∈ [0, ∞). It is also shown that the new computational framework presented here is flexible enough to incorporate natural selection.

Item Type:	Journal Article
Divisions:	Faculty of Science > Statistics
Journal or Publication Title:	Annals of Applied Probability
Publisher:	Institute of Mathematical Statistics
ISSN:	1050-5164
Official Date:	April 2012
Dates:	Date Event April 2012 Published
Volume:	Vol.22
Number:	No.2
Page Range:	pp. 576-607
DOI:	10.1214/11-AAP780
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

Request changes or add full text files to a record

Repository staff actions (login required)

View Item