title: The existence and abundance of ghost ancestors in biparental populations.
abstract: In a randomly-mating biparental population of size N there are, with high probability, individuals who are genealogical ancestors of every extant individual within approximately log2(N) generations into the past. We use this result of J. Chang to prove a curious corollary under standard models of recombination: there exist, with high probability, individuals within a constant multiple of log2(N) generations into the past who are simultaneously (i) genealogical ancestors of each of the individuals at the present, and (ii) genetic ancestors to none of the individuals at the present. Such ancestral individuals-ancestors of everyone today that left no genetic trace-represent 'ghost' ancestors in a strong sense. In this short note, we use simple analytical argument and simulations to estimate how many such individuals exist in finite Wright-Fisher populations.
authors.affiliation: Genome Quebec Innovation Centre, Department of Human Genetics, McGill University, 740 Dr Penfield, Montreal, Quebec, H3A 0G1, Canada. Electronic address: simon.gravel@mcgill.ca.
authors.forename: Simon
authors.initials: S
authors.lastname: Gravel
authors.affiliation: Biomathematics Research Centre, University of Canterbury, New Zealand.
authors.forename: Mike
authors.initials: M
authors.lastname: Steel
mesh_terms: D003198:Computer Simulation; D005789:Genealogy and Heraldry; D040961:Genetic Drift; D005828:Genetics, Population; D006801:Humans; D008957:Models, Genetic; D010290:Parents; D010375:Pedigree; D010802:Phylogeny
keywords: Genealogy; Genetic drift; Recombination; Wright–Fisher model