Genealogies in bistable waves
Consider a diploid population living in one spatial dimension. 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. We can 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. Joint work with Alison Etheridge.