Single-crossover recombination and ancestral recombination trees

Baake E, von Wangenheim U (2014)
Journal of Mathematical Biology 68(6): 1371-1402.

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Abstract
We consider the Wright-Fisher model for a population of 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 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.
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Baake E, von Wangenheim U. Single-crossover recombination and ancestral recombination trees. Journal of Mathematical Biology. 2014;68(6):1371-1402.
Baake, E., & von Wangenheim, U. (2014). Single-crossover recombination and ancestral recombination trees. Journal of Mathematical Biology, 68(6), 1371-1402. doi:10.1007/s00285-013-0662-x
Baake, E., and von Wangenheim, U. (2014). Single-crossover recombination and ancestral recombination trees. Journal of Mathematical Biology 68, 1371-1402.
Baake, E., & von Wangenheim, U., 2014. Single-crossover recombination and ancestral recombination trees. Journal of Mathematical Biology, 68(6), p 1371-1402.
E. Baake and U. von Wangenheim, “Single-crossover recombination and ancestral recombination trees”, Journal of Mathematical Biology, vol. 68, 2014, pp. 1371-1402.
Baake, E., von Wangenheim, U.: Single-crossover recombination and ancestral recombination trees. Journal of Mathematical Biology. 68, 1371-1402 (2014).
Baake, Ellen, and von Wangenheim, Ute. “Single-crossover recombination and ancestral recombination trees”. Journal of Mathematical Biology 68.6 (2014): 1371-1402.
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PMID: 23564407
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