Single-crossover recombination and ancestral recombination trees

  title={Single-crossover recombination and ancestral recombination trees},
  author={Ellen Baake and Ute Wangenheim},
  journal={Journal of Mathematical Biology},
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 recombination between them. We trace back the ancestry of single individuals from the present population. In the $$N \rightarrow \infty $$ 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… 
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A closed solution of the deterministic continuous-time system, for the important special case of single crossovers, is presented and an analogous deterministic discrete-time dynamics is provided, in terms of its generalised eigenvalues and a simple recursion for the corresponding coefficients.
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Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated and the stochastic process converges, in the infinite-population limit, to the deterministic dynamics, which turns out to be a good approximation already for populations of moderate size.
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This work considers a particular case of recombination in discrete time, allowing only for single crossovers, and transforms the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation.
Mutation and recombination with tight linkage
  • E. Baake
  • Mathematics
    Journal of mathematical biology
  • 2001
Abstract. An exact solution of the mutation-recombination equation in continuous time is presented, with linear ordering of the sites and at most one mutation or crossover event taking place at every
Recombination, gene conversion, and identity-by-descent at three loci.
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Properties of a neutral allele model with intragenic recombination.
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