tree reconstruction methods [@PageHolmes1998].

We studied the probability of fixation of beneficial mutations in the presence of other beneficial mutations that were introduced either earlier or later, and in the presence of other deleterious mutations, that is, we studied fixation in a non-equilibrium background. This problem has been addressed previously by [@barton95] using a deterministic approach, which was unfortunately limited to small selective advantages. Similarly, Johnson and Barton [-@johnson2002] studied the probability of fixation in a changing background, but they confined themselves mostly to the case where deleterious mutations accumulate in the background after a selective sweep.

We found that the probability of fixation is easily understood from an analytic point of view as long as the time interval between the introduction of mutants is larger than the fixation time of the least beneficial mutation. In the interference regime, where the population consists of clones of the wild type as well as both beneficial mutants, a phenomenological approach based on logistic growth is successful at describing the competition. In general, we find that the probability of fixation of the most beneficial mutant is reduced when it competes against a less beneficial mutant, and there is a sizable probability that the 