Single-crossover dynamics: Finite versus infinite populations

Baake E, Herms I (2008)
BULLETIN OF MATHEMATICAL BIOLOGY 70(2): 603-624.

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Abstract
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarize and adapt a deterministic approach, as valid for infinite populations, which assumes continuous time and single crossover events. The corresponding nonlinear system of differential equations permits a closed solution, both in terms of the type frequencies and via linkage disequilibria of all orders. To include stochastic effects, we then consider the corresponding finite-population model, the Moran model with single crossovers, and examine it both analytically and by means of simulations. Particular emphasis is on the connection with the deterministic solution. If there is only recombination and every pair of recombined offspring replaces their pair of parents (i.e., there is no resampling), then the expected type frequencies in the finite population, of arbitrary size, equal the type frequencies in the infinite population. If resampling is included, 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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Baake E, Herms I. Single-crossover dynamics: Finite versus infinite populations. BULLETIN OF MATHEMATICAL BIOLOGY. 2008;70(2):603-624.
Baake, E., & Herms, I. (2008). Single-crossover dynamics: Finite versus infinite populations. BULLETIN OF MATHEMATICAL BIOLOGY, 70(2), 603-624.
Baake, E., and Herms, I. (2008). Single-crossover dynamics: Finite versus infinite populations. BULLETIN OF MATHEMATICAL BIOLOGY 70, 603-624.
Baake, E., & Herms, I., 2008. Single-crossover dynamics: Finite versus infinite populations. BULLETIN OF MATHEMATICAL BIOLOGY, 70(2), p 603-624.
E. Baake and I. Herms, “Single-crossover dynamics: Finite versus infinite populations”, BULLETIN OF MATHEMATICAL BIOLOGY, vol. 70, 2008, pp. 603-624.
Baake, E., Herms, I.: Single-crossover dynamics: Finite versus infinite populations. BULLETIN OF MATHEMATICAL BIOLOGY. 70, 603-624 (2008).
Baake, Ellen, and Herms, Inke. “Single-crossover dynamics: Finite versus infinite populations”. BULLETIN OF MATHEMATICAL BIOLOGY 70.2 (2008): 603-624.
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Inferring genome-wide recombination landscapes from advanced intercross lines: application to yeast crosses.
Illingworth CJ, Parts L, Bergstrom A, Liti G, Mustonen V., PLoS ONE 8(5), 2013
PMID: 23658715
Single-crossover recombination in discrete time.
von Wangenheim U, Baake E, Baake M., J Math Biol 60(5), 2010
PMID: 19636557

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