title: Single-crossover recombination and ancestral recombination trees.
abstract: We consider the Wright-Fisher model for a population of [Formula: see text] individuals, each identified with a sequence of a finite number of sites, and single-crossover recombination between them. We trace back the ancestry of single individuals from the present population. In the [Formula: see text] limit without rescaling of parameters or time, this ancestral process is described by a random tree, whose branching events correspond to the splitting of the sequence due to recombination. With the help of a decomposition of the trees into subtrees, we calculate the probabilities of the topologies of the ancestral trees. At the same time, these probabilities lead to a semi-explicit solution of the deterministic single-crossover equation. The latter is a discrete-time dynamical system that emerges from the Wright-Fisher model via a law of large numbers and has been waiting for a solution for many decades.
authors.affiliation: Faculty of Technology, Bielefeld University, 33594 , Bielefeld, Germany, ebaake@techfak.uni-bielefeld.de.
authors.forename: Ellen
authors.initials: E
authors.lastname: Baake
authors.forename: Ute
authors.initials: U
authors.lastname: von Wangenheim
mesh_terms: D003434:Crossing Over, Genetic / Q000235:genetics*; D005828:Genetics, Population; D008390:Markov Chains; D008957:Models, Genetic; D010802:Phylogeny
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