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 have a higher fitness than individuals, while individuals have a lower fitness than both and 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’.
SP is supported by a Royal Society University Research Fellowship.
"Genealogies in bistable waves." Electron. J. Probab. 27 1 - 99, 2022. https://doi.org/10.1214/22-EJP845