Figure 4. Simulations under the Wright-Fisher model with expiring fitness.

(A) Average frequency dynamics of immune escape mutations that are found to cross the frequency threshold ${\displaystyle x^{\ast }=0.5}$, for four different rates of fitness decay. If the growth advantage is lost rapidly (high ${\displaystyle \nu /s_0}$), the trajectories crossing ${\displaystyle x^{\ast }}$ have little inertia, while stable growth advantage (small ${\displaystyle \nu /s_0}$) leads to steadily increasing frequencies. (B, C, D) Ultimate probability of ${\displaystyle p_{fix}(x)}$ of trajectories found crossing frequency threshold ${\displaystyle x}$. Each panel corresponds to a different rate of emergence of immune escape variants, with four rates of fitness decay per panel. Increased clonal interference ${\displaystyle \rho /s_0}$ and fitness decay ${\displaystyle \nu /s_0}$ both result in a gradual loss of predictability. We use ${\displaystyle s_0=0.03}$. (E) Time to most recent common ancestor ${\displaystyle T_{MRCA}}$ for the simulated population, as a function of the prediction obtained using the random walk ${\displaystyle N_e=1/\rho ⟨{\beta }^2⟩}$. Points correspond to different choices of parameters ${\displaystyle \rho }$ and ${\displaystyle P_{\beta }}$, and a darker color indicates a higher probability of overlap as computed in Appendix 2.2.

Figure 4—figure supplement 1. Probability of fixation of mutation Probability of fixation of mutations ${\displaystyle p_{fix}(x)}$ of mutation frequency trajectories found crossing the frequency threshold ${\displaystyle x}$.

Fitness effects are exponentially distributed with fixed scale ${\displaystyle s_0=0.03}$. The blue to red gradient in colors corresponds to the increasing rate ${\displaystyle \rho }$ at which mutations are introduced. Strong clonal interference regime is obtained when ${\displaystyle \rho /s_0>1}$, in which case good mutations are introduced in close succession and compete for fixation. At low ${\displaystyle \rho /s_0}$, trajectories are very predictable and an increasing trajectory almost certainly fixes. Even for the highest ${\displaystyle \rho /s_0}$, ${\displaystyle p_{fix}(x)}$ remains significantly larger than ${\displaystyle x}$ and dynamics are visibly not neutral.