for the two genotypes: $T_{1}$ shows an abrupt transition around the critical value $u=u_{1c} \approx 0.09$, whereas $T_{2}$ reaches the neutral regime around $u=u_{2c} \approx 0.30$. The mutation rate at which this transition occurs is known as the [*error threshold*]{} [@eigen].

![\[figure:fig4\] Overall probability of fixation as a function of mutation rate $u$. Circles correspond to the situation of two invading mutants ($s_{1}=0.1$, $s_{2}=0.5$, $\Delta t=100$, $N=1000$), and squares correspond to the situation of three invading mutants ($s_{1}=0.8$, $s_{2}=0.9$, $s_3=1.0$, $\Delta t = 20$). The solid line is the prediction according to diffusion theory, while the long-dashed line corresponds to the branching process. The short dashes indicate the fixation probability levels according to the neutral theory Eq. (\[neutral\]), for two or three mutants, respectively.](Figure5.eps){width="10cm"}

In Figure \[figure:fig4\] we can see the overall probability of fixation as a function of mutation rate for the case of two as well as three interfering mutants. Simulation results are again compared to the diffusion theory result Eq. (\[kimura-approx\]), but also to a prediction from branching process theory, Eq. (\[branchingmut2\]). For these simulations, we used $s_{1}=0.1$, $s_{2}=0.5$ and population size $N=1000$. We also chose a time interval $\Delta t =100$, which is smaller than the 