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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