Figure 3. Frequency threshold in dynamics of fitness-affecting mutations.

(A) Individual realizations of a simulation initiated with a directly beneficial mutation of size $s_{ben}$ = 0.01 at a starting frequency $x_0$. Population size, N = 10⁷. Inset: Fixation probability of a beneficial mutation of size $s_{ben}$ =0.01 at N = 10⁷. Dashed line is given by $P_{fix}^{ben}\left(x_0\right)=\frac{1-e^{-2s_{ben}N{x}_0}}{1-e^{-2s_{ben}N}}$ (Kimura, 1962), while circles are values of $P_{fix}^{ben}\left(x_0\right)$ measured in simulations (averaged across 10⁵ runs). (B) Average frequency trajectories of a beneficial mutation of size $s_{ben}$ = 0.01 in (A) averaged across all 10⁵ runs of simulation. (C) Individual realizations of a simulation initiated with a mutation under frequency dependent selection, with the selection coefficient s(x) = b + mx, where x is the frequency, b = -0.02, and m = 0.1, at N = 10⁷. (D) Average frequency trajectories of the frequency-dependent mutation in (C) averaged across all 10⁵ runs of simulation. All panels are on a log-log scale for clarity.