title: Spread of pedigree versus genetic ancestry in spatially distributed populations.
abstract: Ancestral processes are fundamental to modern population genetics and spatial structure has been the subject of intense interest for many years. Despite this interest, almost nothing is known about the distribution of the locations of pedigree or genetic ancestors. Using both spatially continuous and stepping-stone models, we show that the distribution of pedigree ancestors approaches a travelling wave, for which we develop two alternative approximations. The speed and width of the wave are sensitive to the local details of the model. After a short time, genetic ancestors spread far more slowly than pedigree ancestors, ultimately diffusing out with radius ∼ t rather than spreading at constant speed. In contrast to the wave of pedigree ancestors, the spread of genetic ancestry is insensitive to the local details of the models.
authors.affiliation: Wellcome Trust Centre for Human Genetics, University of Oxford, Roosevelt Drive, Oxford OX3 7BN, UK. Electronic address: jerome.kelleher@well.ox.ac.uk.
authors.forename: J
authors.initials: J
authors.lastname: Kelleher
authors.affiliation: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK. Electronic address: etheridg@stats.ox.ac.uk.
authors.forename: A M
authors.initials: AM
authors.lastname: Etheridge
authors.affiliation: Centre de Mathématiques Appliquées, École Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France. Electronic address: amandine.veber@cmap.polytechnique.fr.
authors.forename: A
authors.initials: A
authors.lastname: Véber
authors.affiliation: Institute of Science and Technology, Am Campus I, A-3400 Klosterneuberg, Austria. Electronic address: n.barton@ist.ac.at.
authors.forename: N H
authors.initials: NH
authors.lastname: Barton
mesh_terms: D005828:Genetics, Population; D006801:Humans; D008957:Models, Genetic; D010375:Pedigree; D013997:Time Factors
keywords: Ancestral wave; Coalescent simulation; Fisher–KPP wave; Pedigree ancestry