Mathematics – Probability
Scientific paper
2011-07-20
Mathematics
Probability
34 pages, 2 figures. To appear in the Annals of Applied Probability
Scientific paper
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 \rho 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 Pad\'e approximants) the exact two-locus sampling distribution as an analytic function of \rho; this function is exact for all values of \rho. It is also shown that the new computational framework presented here is flexible enough to incorporate natural selection.
Jenkins Paul A.
Song Yun S.
No associations
LandOfFree
Padé approximants and exact two-locus sampling distributions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Padé approximants and exact two-locus sampling distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Padé approximants and exact two-locus sampling distributions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-34384