increased by the additional time it takes for mutant 1 to disappear again. This additional time will typically be one or two generations, which is in agreement with the height of the spike. ($T_1$ on the top of the spike is actually approximately half a generation larger than before the spike.) The limiting values for $\pi_{1}$ and $\pi_{2}$ when $\Delta t
\rightarrow -\infty$ and $\Delta t\rightarrow -\infty$ were estimated by means of branching process theory which provides very good accuracy, especially for low mutation values.

![\[figure:fig3\] Time to fixation as a function of the mutation probability $u$ ($s_{1}=0.1$ and $s_{2}=0.5$, $\Delta t=100$, $N=1000$). Solid line: the time $T_{1}$ to fixation for the less beneficial mutant, dashed line: time to fixation of more beneficial mutant $T_{2}$.](Figure4.eps){width="9cm"}

In Figure \[figure:fig3\] we show the fixation times $T_{1}$ and $T_{2}$ as a function of mutation rate obtained from simulations, and compared to the prediction from diffusion theory, Eq. (\[Time-Kimura\]). As we increase the mutation rate $u$, the population moves from a strong selection regime, characterized by a short time to fixation, to a neutral regime, where $T \approx 2N$. We also observe that the transition between these two regimes occurs at different mutation rates 