the overall probability of fixation $\pi=\pi_1+\pi_2$, for $u=0$. We see that the probability $\pi_1$ is constant for $\Delta t<0$, and starts to increase as soon as $\Delta t$ turns positive. Eventually, $\pi_1$ levels off again. We observe the opposite behavior for the probability $\pi_{2}$. For $\Delta
t<0$, $\pi_{2}$ is constant, but decreases rapidly in the same range of $\Delta t$ in which $\pi_{1}$ increases. Finally, $\pi_2$ levels off as well.

![\[figure:fig2\] Probability of fixation as a function of time interval $\Delta t$ ($N=1000$, $s_{1}=0.1$, $s_{2}=0.5$, $u=0.05$). Solid lines represent the prediction according to the logistic growth model Eq. (\[tanh-ansatz\]). a: Probability of fixation of genotype $1$, $\pi_{1}$. b: Probability of fixation of genotype $2$, $\pi_{2}$. c: Overall probability of fixation, $\pi$.](Figure2-new.eps){width="8cm"}

The overall probability of fixation $\pi$ is approximately constant for all values of $\Delta t$. The solid lines in Fig. \[figure:fig1\]a and b correspond to Eq. (\[tanh-ansatz\]), and the solid line in Fig. \[figure:fig1\]c is $\pi_1(-\infty)+\pi_2(-\infty)$. We find that our phenomenological description Eq. (\[tanh-ansatz\]) performs very well for intermediate $\Delta t$.

In Fig. \[figure:fig2\] we plot the same quantities as those shown in Figure $1$, but now with a positive mutation rate $u=0.05$. We observe that the two probabilities 