Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2009-05-20
Theo. Pop. Biol. 77, 23 (2010)
Biology
Quantitative Biology
Populations and Evolution
Corrected definition of linkage disequilibrium, new Section 5 added; Version to appear in Theo. Pop. Biol
Scientific paper
We study the evolutionary dynamics of a haploid population of infinite size recombining with a probability $r$ in a two locus model. Starting from a low fitness locus, the population is evolved under mutation, selection and recombination until a finite fraction of the population reaches the fittest locus. An analytical method is developed to calculate the fixation time $T$ to the fittest locus for various choices of epistasis. We find that (1) for negative epistasis, $T$ decreases slowly for small $r$ but decays fast at larger $r$ (2) for positive epistasis, $T$ increases linearly for small $r$ and mildly for large $r$ (3) for compensatory mutation, $T$ diverges as a power law with logarithmic corrections as the recombination fraction approaches a critical value. Our calculations are seen to be in good agreement with the exact numerical results.
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