Time to fixation in the presence of recombination

Kavita Jain

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arXiv · 0905.3262

Time to fixation in the presence of recombination

Kavita Jain

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Abstract

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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Kavita Jain. 2009-10-22. Time to fixation in the presence of recombination. https://arxiv.org/abs/0905.3262

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