Time to fixation in the presence of recombination

We study the evolutionary dynamics of a haploid population of infinite size recombining with a probability rr 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 TT to the fittest locus for various choices of epistasis. We find that: (1) for negative epistasis, TT decreases slowly for small rr but decays fast at larger rr; (2) for positive epistasis, TT increases linearly for small rr and mildly for large rr; (3) for compensatory mutation, TT 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.