dorsal/arxiv
View SchemaSingle-crossover dynamics: finite versus infinite populations
| Authors | Ellen Baake, Inke Herms |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0612024 |
| URL | https://arxiv.org/abs/q-bio/0612024 |
| Journal | Bull. Math. Biol. 70 (2008), 603-624 |
Abstract
Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise 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 {\em 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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"abstract": "Populations evolving under the joint influence of recombination and\nresampling (traditionally known as genetic drift) are investigated. First, we\nsummarise and adapt a deterministic approach, as valid for infinite\npopulations, which assumes continuous time and single crossover events. The\ncorresponding nonlinear system of differential equations permits a closed\nsolution, both in terms of the type frequencies and via linkage disequilibria\nof all orders. To include stochastic effects, we then consider the\ncorresponding finite-population model, the Moran model with single crossovers,\nand examine it both analytically and by means of simulations. Particular\nemphasis is on the connection with the deterministic solution. If there is only\nrecombination and every pair of recombined offspring replaces their pair of\nparents (i.e., there is no resampling), then the {\\em expected} type\nfrequencies in the finite population, of arbitrary size, equal the type\nfrequencies in the infinite population. If resampling is included, the\nstochastic process converges, in the infinite-population limit, to the\ndeterministic dynamics, which turns out to be a good approximation already for\npopulations of moderate size.",
"arxiv_id": "q-bio/0612024",
"authors": [
"Ellen Baake",
"Inke Herms"
],
"categories": [
"q-bio.PE",
"math.PR"
],
"journal_ref": "Bull. Math. Biol. 70 (2008), 603-624",
"title": "Single-crossover dynamics: finite versus infinite populations",
"url": "https://arxiv.org/abs/q-bio/0612024"
},
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