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2022 Genealogies in bistable waves
Alison Etheridge, Sarah Penington
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Electron. J. Probab. 27: 1-99 (2022). DOI: 10.1214/22-EJP845


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’.

Funding Statement

SP is supported by a Royal Society University Research Fellowship.


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Alison Etheridge. Sarah Penington. "Genealogies in bistable waves." Electron. J. Probab. 27 1 - 99, 2022.


Received: 20 October 2021; Accepted: 30 August 2022; Published: 2022
First available in Project Euclid: 13 September 2022

Digital Object Identifier: 10.1214/22-EJP845

Primary: 60J27 , 60J90 , 92D10

Keywords: Coalescent process , selection , Travelling wave


Vol.27 • 2022
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