Genealogies in bistable waves

Alison Etheridge; Sarah Penington

doi:10.1214/22-EJP845

Genealogies in bistable waves

Alison Etheridge, Sarah Penington

University of Oxford

Research output: Contribution to journal › Article › peer-review

4 Citations (SciVal)

Abstract

We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular gene appears in two forms (alleles) A and a, and that individuals carrying AA have a higher fitness than aa individuals, while Aa individuals have a lower fitness than both AA and aa individuals. The proportion of advantageous A alleles expands through the population approximately according to a travelling wave. We prove that on a suitable timescale, the genealogy of a sample of A alleles taken from near the wavefront converges to a Kingman coalescent as the population density goes to infinity. This contrasts with the case of directional selection in which the corresponding limit is thought to be the Bolthausen-Sznitman coalescent. The proof uses 'tracer dynamics'.

Original language	English
Pages (from-to)	1-99
Journal	Electronic Journal of Probability
Volume	27
Early online date	13 Sept 2022
DOIs	https://doi.org/10.1214/22-EJP845
Publication status	Published - 31 Dec 2022

Bibliographical note

Funding Information:
*SP is supported by a Royal Society University Research Fellowship. †Department of Statistics, University of Oxford, UK. E-mail: [email protected] ‡Department of Mathematical Sciences, University of Bath, UK. E-mail: [email protected]

Keywords

coalescent process
selection
travelling wave

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/22-EJP845Licence: CC BY

Cite this

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abstract = "We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular gene appears in two forms (alleles) A and a, and that individuals carrying AA have a higher fitness than aa individuals, while Aa individuals have a lower fitness than both AA and aa individuals. The proportion of advantageous A alleles expands through the population approximately according to a travelling wave. We prove that on a suitable timescale, the genealogy of a sample of A alleles taken from near the wavefront converges to a Kingman coalescent as the population density goes to infinity. This contrasts with the case of directional selection in which the corresponding limit is thought to be the Bolthausen-Sznitman coalescent. The proof uses 'tracer dynamics'.",

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AU - Penington, Sarah

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KW - travelling wave

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JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

ER -

Genealogies in bistable waves

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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