1. Evolutionary Biology
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Selection on mutators is not frequency-dependent

  1. Yevgeniy Raynes  Is a corresponding author
  2. Daniel Weinreich
  1. Brown University, United States
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Cite this article as: eLife 2019;8:e51177 doi: 10.7554/eLife.51177
4 figures and 1 additional file

Figures

Figure 1 with 1 supplement
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, Udel = 10−4, Uben = 10−6, constant sben = 0.1, constant sdel = -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 x0, showing that selection favors mutators independent of frequency. Average mutator frequency always eventually reaches the expected Pfixx0 (dashed horizontal lines) calculated in Figure 2. Mutator frequencies averaged across 106 simulation runs at x0= 10−7 and x0= 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—source data 1

Numerical data represented in Figure 1.

Data set includes mutator frequencies in randomly-chosen individual realizationss and mutator frequencies averaged across all realizations.

https://cdn.elifesciences.org/articles/51177/elife-51177-fig1-data1-v3.csv
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 sben = 0.1 and sdel = −0.1 respectively.

Figure 1—figure supplement 1—source data 1

Numerical data represented in Figure 1—figure supplement 1.

Data set includes mutator frequencies in randomly-chosen individual realizationss and mutator frequencies averaged across all realizations.

https://cdn.elifesciences.org/articles/51177/elife-51177-fig1-figsupp1-data1-v3.csv
Mutator fixation probability is not frequency-dependent.

Fixation probability,  Pfixx0, of a mutator initiated at frequency x0 (circles: orange for x0=1/N, purple for x0>1/N). Data from simulations in Figure 1. Pfixx0 scales with but never crosses the fixation probability of a neutral mutation (x0; black dashed line). Thus, mutators are favored at all starting frequencies. The expected fixation probability Pfixx0  (solid orange line), calculated from the fixation probability of a single mutator, Pfixx0=1/N = 5.6×10−4 (orange point) using Equation 1 is indistinguishable from the Pfixx0 observed in simulations, demonstrating that the per-capita fixation probability at every frequency is independent of x0 and equal to Pfixx0=1/N.

Figure 2—source data 1

Numerical data represented in Figure 2.

Data set includes fixation probabilities of a mutator allele at each initial frequency shown.

https://cdn.elifesciences.org/articles/51177/elife-51177-fig2-data1-v3.csv
Frequency threshold in dynamics of fitness-affecting mutations.

(A) Individual realizations of a simulation initiated with a directly beneficial mutation of size sben = 0.01 at a starting frequency x0. Population size, N = 107. Inset: Fixation probability of a beneficial mutation of size sben =0.01 at N = 107. Dashed line is given by Pfixbenx0=1-e-2sbenNx01-e-2sbenN (Kimura, 1962), while circles are values of Pfixbenx0 measured in simulations (averaged across 105 runs). (B) Average frequency trajectories of a beneficial mutation of size sben = 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.

Figure 3—source data 1

Numerical data represented in Figure 3.

Data set includes frequencies of a beneficial mutation and a frequncy-dependent mutation in randomly-chosen individual realizations and averaged across all replicate realizations.

https://cdn.elifesciences.org/articles/51177/elife-51177-fig3-data1-v3.csv
Author response image 1

Data availability

Simulation code is available at https://github.com/yraynes/Mutator-Frequency (copy archived at https://github.com/elifesciences-publications/Mutator-Frequency).

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