Fig. 2.

Effect of clonal interference on fitness trajectory for different types of macroscopic epistasis. a) Within the diminishing returns model where the mean fitness effect of beneficial mutations decreases with fitness but the beneficial mutation rate stays the same, the functional form of the fitness trajectory stays the same. The upper panels show the fitness trajectories as a function of actual time t with (red) and without (blue) clonal interference. The solid lines are obtained from solving Equations (4) and (9), while the dashed lines (pink) are individual replicates from simulations. The lower panels compare trajectories (blue and red solid lines in the upper panel) after rescaling time $\tilde{t}=At$ for the case with clonal interference, with A being a constant chosen such that both trajectories have the same derivative at $\tilde{t}=0$. [Landscape parameters: $\alpha (F)=20F^5,\hspace{0.17em}{\mu }_b={\mu }_{b0}$] b) With the House-of-Cards/uncorrelated landscape where the mean fitness effects of beneficial mutations stays the same but the beneficial mutation rate decreases with fitness, the presence of clonal interference speeds up the functional form of the fitness trajectory. [Landscape parameters: $\alpha (F)=100F,\hspace{0.17em}{\mu }_b={\mu }_{b0}{e}^{-(F-1)}$] c) With a mutation-releasing landscape where the beneficial mutation rate increases with fitness, the presence of clonal interference slows down the functional form of the fitness trajectory. [Landscape parameters: $\alpha (F)=50e^{F-1},\hspace{0.17em}{\mu }_b={\mu }_{b0}{e}^{F-1}$.] [Other parameters in a–c): $N={10}^6,\hspace{0.17em}{\mu }_{b0}=1·{10}^{-5}$.]