Fig. 2.

Mutants go extinct under a threshold proliferation advantage. The continuous lines show the size of the mutant (red) and wild-type (green) populations and their combined number (black) during the simulation. The dashed lines correspond to the theoretical mean population sizes in the quasi-stationary state. (A, Top) If the proliferation advantage of the mutant is below the threshold, the mutant will rapidly escape from the shallow quasi-stationary state and go extinct. (A, Bottom) The black $\times$ on the continuous approximation of the potential marks the quasi-stationary state. Parameters are $N^0=100$, $\beta =1$, and $r^{+}=0$, and $S_{\mathrm{m}}=0.2$ is below the threshold $S_{\mathrm{m}}^{*}=0.34$. (B, Top and Bottom) Increasing the compartment size to $N^0=400$, the potential well becomes deeper and the threshold proliferation advantage becomes correspondingly smaller $S_{\mathrm{m}}^{*}=0.17$, allowing a mutant with the same advantage of $S_{\mathrm{m}}=0.2$ to persist in the tissue during the individual’s lifetime.