Genealogies in bistable waves

Alison Etheridge, Sarah Penington

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)


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 languageEnglish
Pages (from-to)1-99
JournalElectronic Journal of Probability
Early online date13 Sept 2022
Publication statusPublished - 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]


  • coalescent process
  • selection
  • travelling wave

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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