Single-crossover recombination in discrete time

von Wangenheim U, Baake E, Baake M (2010)
JOURNAL OF MATHEMATICAL BIOLOGY 60(5): 727-760.

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Abstract
Modelling the process of recombination leads to a large coupled nonlinear dynamical system. Here, we consider a particular case of recombination in discrete time, allowing only for single crossovers. While the analogous dynamics in continuous time admits a closed solution (Baake and Baake in Can J Math 55:3-41, 2003), this no longer works for discrete time. A more general model (i.e. without the restriction to single crossovers) has been studied before (Bennett in Ann Hum Genet 18:311-317, 1954; Dawson in Theor Popul Biol 58:1-20, 2000; Linear Algebra Appl 348:115-137, 2002) and was solved algorithmically by means of Haldane linearisation. Using the special formalism introduced by Baake and Baake (Can J Math 55:3-41, 2003), we obtain further insight into the single-crossover dynamics and the particular difficulties that arise in discrete time. We then transform the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation. Still, the coefficients of the second step must be determined in a recursive manner, but once this is done for a given system, they allow for an explicit solution valid for all times.
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von Wangenheim U, Baake E, Baake M. Single-crossover recombination in discrete time. JOURNAL OF MATHEMATICAL BIOLOGY. 2010;60(5):727-760.
von Wangenheim, U., Baake, E., & Baake, M. (2010). Single-crossover recombination in discrete time. JOURNAL OF MATHEMATICAL BIOLOGY, 60(5), 727-760.
von Wangenheim, U., Baake, E., and Baake, M. (2010). Single-crossover recombination in discrete time. JOURNAL OF MATHEMATICAL BIOLOGY 60, 727-760.
von Wangenheim, U., Baake, E., & Baake, M., 2010. Single-crossover recombination in discrete time. JOURNAL OF MATHEMATICAL BIOLOGY, 60(5), p 727-760.
U. von Wangenheim, E. Baake, and M. Baake, “Single-crossover recombination in discrete time”, JOURNAL OF MATHEMATICAL BIOLOGY, vol. 60, 2010, pp. 727-760.
von Wangenheim, U., Baake, E., Baake, M.: Single-crossover recombination in discrete time. JOURNAL OF MATHEMATICAL BIOLOGY. 60, 727-760 (2010).
von Wangenheim, Ute, Baake, Ellen, and Baake, Michael. “Single-crossover recombination in discrete time”. JOURNAL OF MATHEMATICAL BIOLOGY 60.5 (2010): 727-760.
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Single-crossover recombination and ancestral recombination trees.
Baake E, von Wangenheim U., J Math Biol 68(6), 2014
PMID: 23564407

18 References

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