  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.
