time required for fixation of mutant $1$, to ensure that the dynamics takes place in the clonal interference regime. Above the error threshold, the probability of fixation is known to be $1/N$ for a single mutation ($2/N$ and $3/N$ for two or three mutants, respectively). Because the branching process description assumes infinite population size, it predicts zero probability of fixation above the error threshold. Diffusion theory, on the other hand, describes this regime adequately, while being less accurate at small mutation rates. The abrupt change between the ordered and disordered regime predicted by both theories is not present in the numerical data because the simulated system is finite.

Finally, we tested the prediction that the mean number of fixations in the population is larger when the mutant with the smaller selective advantage is introduced first, even though the mean fitness increase is smaller. Figure \[figure:figNmutants\]a shows the results for the expected increase in fitness as a function of the time interval $\Delta t$ as defined in Eq. (\[expectedinc\]), as well as the solution of Eq. (\[expectedinc\]) using a sigmoidal [*ansatz*]{} for the probabilities $\pi_{1}$ and $\pi_{2}$, as defined in Eq. (\[tanh-ansatz\]). As expected, the mean fitness gain decreases as $\Delta 