Figure 1. The sharp transition between fixation and loss in mutator dynamics at different starting frequencies is due to limited sampling.

(A) Changes in the ratio of the mutator and the wild-type alleles of the E. coli mutT locus over time in continuous chemostat cultures. (Figure 1 from Chao and Cox, 1983). (B) In simulations, mutator trajectories in individual realizations initiated at different starting frequencies recapitulate the experimental observation of the frequency-threshold for mutator hitchhiking. Parameter values used are typical of microbial experimental populations (Raynes et al., 2018): N = 10⁷, U_del = 10⁻⁴, U_ben = 10⁻⁶, constant s_ben = 0.1, constant s_del = -0.1. Mutators mutate 100× faster than non-mutators. (C) Average mutator trajectories across realizations do not show evidence of the frequency-threshold. On average, mutators increase in frequency at all $x_0$, showing that selection favors mutators independent of frequency. Average mutator frequency always eventually reaches the expected $P_{fix}\left(x_0\right)$ (dashed horizontal lines) calculated in Figure 2. Mutator frequencies averaged across 10⁶ simulation runs at $x_0$= 10⁻⁷ and $x_0$= 3×10⁻⁷, and across 10⁵ simulation runs for all other starting frequencies. For simulations with exponentially distributed selection coefficients see Figure 1—figure supplement 1.

© 1983 John Wiley and Sons. All Rights Reserved

Figure 1 reproduced from Chao and Cox, 1983 with permission.

Figure 1—figure supplement 1. Simulations with exponentially distributed selection coefficients confirm that the frequency-dependent threshold in mutator dynamics is due to limited sampling.

(A) Mutator trajectories in individual realizations. (B) Average mutator trajectories across realizations. Mutator frequencies averaged across 10⁵ simulation runs. Parameter values as in Figure 1 except N = 10⁶, and beneficial and deleterious mutations are now randomly drawn from an exponential distribution with the mean s_ben = 0.1 and s_del = −0.1 respectively.