%0 Journal Article %1 etheridge2022genealogies %A Etheridge, Alison %A Penington, Sarah %D 2022 %I Institute of Mathematical Statistics and Bernoulli Society %J Electronic Journal of Probability %K allee_effect coalescent_theory travelling_wave %N none %P 1 -- 99 %R 10.1214/22-EJP845 %T Genealogies in bistable waves %U https://doi.org/10.1214/22-EJP845 %V 27 %X 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’.

@article{etheridge2022genealogies, 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’.}, added-at = {2023-12-15T15:41:02.000+0100}, author = {Etheridge, Alison and Penington, Sarah}, biburl = {https://www.bibsonomy.org/bibtex/2bca86c14a03d07f5db6fba9b81deb117/peter.ralph}, doi = {10.1214/22-EJP845}, interhash = {c4645d828100b3b29a201f20afe7f8ac}, intrahash = {bca86c14a03d07f5db6fba9b81deb117}, journal = {Electronic Journal of Probability}, keywords = {allee_effect coalescent_theory travelling_wave}, number = {none}, pages = {1 -- 99}, publisher = {Institute of Mathematical Statistics and Bernoulli Society}, timestamp = {2023-12-15T15:41:02.000+0100}, title = {Genealogies in bistable waves}, url = {https://doi.org/10.1214/22-EJP845}, volume = 27, year = 2022 }