an:06289293
Zbl 1284.92063
Baake, Ellen; Von Wangenheim, Ute
Single-crossover recombination and ancestral recombination trees
EN
J. Math. Biol. 68, No. 6, 1371-1402 (2014).
0303-6812 1432-1416
2014
j
92D15 92D10 60J28 60F15
population genetics; segmentation processes; ancestral trees; subtree decompositions
Summary: We consider the Wright-Fisher model for a population of \(N\) individuals, each identified with a sequence of a finite number of sites, and single-crossover recombinations between them. We trace back the ancestry of single individuals from the present population. In the \(N\to\infty\) 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.