---
_id: '4253'
abstract:
- lang: eng
text: We consider a single genetic locus which carries two alleles, labelled P and
Q. This locus experiences selection and mutation. It is linked to a second neutral
locus with recombination rate r. If r = 0, this reduces to the study of a single
selected locus. Assuming a Moran model for the population dynamics, we pass to
a diffusion approximation and, assuming that the allele frequencies at the selected
locus have reached stationarity, establish the joint generating function for the
genealogy of a sample from the population and the frequency of the P allele. In
essence this is the joint generating function for a coalescent and the random
background in which it evolves. We use this to characterize, for the diffusion
approximation, the probability of identity in state at the neutral locus of a
sample of two individuals (whose type at the selected locus is known) as solutions
to a system of ordinary differential equations. The only subtlety is to find the
boundary conditions for this system. Finally, numerical examples are presented
that illustrate the accuracy and predictions of the diffusion approximation. In
particular, a comparison is made between this approach and one in which the frequencies
at the selected locus are estimated by their value in the absence of fluctuations
and a classical structured coalescent model is used.
author:
- first_name: Nicholas H
full_name: Nicholas Barton
id: 4880FE40-F248-11E8-B48F-1D18A9856A87
last_name: Barton
orcid: 0000-0002-8548-5240
- first_name: Alison
full_name: Etheridge, Alison M
last_name: Etheridge
- first_name: Anja
full_name: Sturm, Anja K
last_name: Sturm
citation:
ama: Barton NH, Etheridge A, Sturm A. Coalescence in a Random Background. *Annals
of Applied Probability*. 2004;14(2):754-785.
apa: Barton, N. H., Etheridge, A., & Sturm, A. (2004). Coalescence in a Random
Background. *Annals of Applied Probability*. Institute of Mathematical Statistics.
chicago: Barton, Nicholas H, Alison Etheridge, and Anja Sturm. “Coalescence in a
Random Background.” *Annals of Applied Probability*. Institute of Mathematical
Statistics, 2004.
ieee: N. H. Barton, A. Etheridge, and A. Sturm, “Coalescence in a Random Background,”
*Annals of Applied Probability*, vol. 14, no. 2. Institute of Mathematical
Statistics, pp. 754–785, 2004.
ista: Barton NH, Etheridge A, Sturm A. 2004. Coalescence in a Random Background.
Annals of Applied Probability. 14(2), 754–785.
mla: Barton, Nicholas H., et al. “Coalescence in a Random Background.” *Annals
of Applied Probability*, vol. 14, no. 2, Institute of Mathematical Statistics,
2004, pp. 754–85.
short: N.H. Barton, A. Etheridge, A. Sturm, Annals of Applied Probability 14 (2004)
754–785.
date_created: 2018-12-11T12:07:52Z
date_published: 2004-05-01T00:00:00Z
date_updated: 2021-01-12T07:55:38Z
day: '01'
extern: 1
intvolume: ' 14'
issue: '2'
main_file_link:
- open_access: '0'
url: http://www.jstor.org/stable/4140427
month: '05'
page: 754 - 785
publication: Annals of Applied Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '1842'
quality_controlled: 0
status: public
title: Coalescence in a Random Background
type: journal_article
volume: 14
year: '2004'
...