Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Wright-Fisher diffusion bridges

Tools
- Tools
+ Tools

Griffiths, Robert, Jenkins, Paul and Spanò, Dario (2018) Wright-Fisher diffusion bridges. Theoretical Population Biology, 122 . pp. 67-77. doi:10.1016/j.tpb.2017.09.005

[img]
Preview
PDF
WRAP-Wright-Fisher-diffusion-bridges-Jenkins-2017.pdf - Accepted Version - Requires a PDF viewer.
Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0.

Download (741Kb) | Preview
Official URL: https://doi.org/10.1016/j.tpb.2017.09.005

Request Changes to record.

Abstract

The trajectory of the frequency of an allele which begins at $x$ at time $0$ and is known to have frequency $z$ at time $T$ can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when $x=z=0$ are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time $T$. The coalescent genealogy back in time of a population in a neutral Wright-Fisher diffusion process is well understood. In this paper we obtain a new interpretation of the coalescent genealogy of the population in a bridge from a time $t\in (0,T)$. In a bridge with allele frequencies of 0 at times 0 and $T$ the coalescence structure is that the population coalesces in two directions from $t$ to $0$ and $t$ to $T$ such that there is just one lineage of the allele under consideration at times $0$ and $T$.
The genealogy in Wright-Fisher diffusion bridges with selection is more complex than in the neutral model, but still with the property of the population branching and coalescing in two directions from time $t\in (0,T)$. The density of the frequency of an allele at time $t$ is expressed in a way that shows coalescence in the two directions.
A new algorithm for exact simulation of a neutral Wright-Fisher bridge is derived. This follows from knowing the density of the frequency in a bridge and exact simulation from the Wright-Fisher diffusion. The genealogy of the neutral Wright-Fisher bridge is also modelled by branching P\'olya urns, extending a representation in a Wright-Fisher diffusion. This is a new very interesting representation that relates Wright-Fisher bridges to classical urn models in a Bayesian setting.

This paper is dedicated to the memory of Paul Joyce.

Item Type: Journal Article
Subjects: Q Science > QH Natural history
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Population biology -- Mathematical models
Journal or Publication Title: Theoretical Population Biology
Publisher: Academic Press
ISSN: 0040-5809
Official Date: July 2018
Dates:
DateEvent
July 2018Published
6 October 2017Available
26 September 2017Accepted
Volume: 122
Page Range: pp. 67-77
DOI: 10.1016/j.tpb.2017.09.005
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Open Access Version:
  • ArXiv

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us