Effects of periodic bottlenecks on the dynamics of adaptive evolution in microbial populations

Abstract Population bottlenecks can impact the rate of adaptation in evolving populations. On the one hand, each bottleneck reduces the genetic variation that fuels adaptation. On the other hand, each founder that survives a bottleneck can undergo more generations and leave more descendants in a resource-limited environment, which allows surviving beneficial mutations to spread more quickly. A theoretical model predicted that the rate of fitness gains should be maximized using ~8-fold dilutions. Here we investigate the impact of repeated bottlenecks on the dynamics of adaptation using numerical simulations and experimental populations of Escherichia coli. Our simulations confirm the model’s prediction when populations evolve in a regime where beneficial mutations are rare and waiting times between successful mutations are long. However, more extreme dilutions maximize fitness gains in simulations when beneficial mutations are common and clonal interference prevents most of them from fixing. To examine these predictions, we propagated 48 E. coli populations with 2-, 8-, 100-, and 1000-fold dilutions for 150 days. Adaptation began earlier and fitness gains were greater with 100- and 1000-fold dilutions than with 8-fold dilutions, consistent with the simulations when beneficial mutations are common. However, the selection pressures in the 2-fold treatment were qualitatively different from the other treatments, violating a critical assumption of the model and simulations. Thus, varying the dilution factor during periodic bottlenecks can have multiple effects on the dynamics of adaptation caused by differential losses of diversity, different numbers of generations, and altered selection.

For the growth phase between transfers, we simulate a fixed number of timesteps based on the dilution factor, D. During each timestep, the growth rate of a genotype is determined by its fitness.The number of timesteps is such that the total population size approximately doubles in each timestep, except for the final one.The program calculates the duration of the timesteps, such that the length of each timestep (except the last one) is scaled inversely to the population mean fitness.This scaling allows those genotypes with above-average fitness to more than double during that timestep, while genotypes with below-average fitness increase less than two-fold.The last timestep in each transfer cycle is implemented differently, such that the total population grows only enough to reach the fixed final size (rather than double).
Beneficial mutations can occur during any timestep.The expected number of mutations equals the product of the beneficial mutation rate, μB, and number of individuals produced in that timestep, with sampling from a Poisson distribution [1].The mutations are randomly distributed among the genotypes, with the expected numbers proportional to their relative abundances.Each mutation creates a newly tracked genotype with fitness Wnew.Following the model of Wiser et al. [2], Wnew = W (1 + s), where W is the fitness of the parent genotype relative to the ancestor, and s is the effect size of the new mutation.The fitness effects are drawn from an exponential distribution, αe −αs , that is unique to each genotype and has  !=  !"# as its initial mean.This distribution is updated for the new genotype as follows:  $%# =  $ (1 +  ×  $%# ), where  $%# is the selection coefficient of the  + 1 mutation and g determines the strength of the diminishing-returns epistasis.generations (E-H) for 10,000 populations evolving under the SSWM regime with four dilution treatments.Most trajectories are flat lines (i.e., no fitness increase), because most populations in this regime had no beneficial mutations (Table S1).Note the steeper trajectories leading to similar fitness gains at the higher dilutions when plotted against transfers, but not when plotted against generations.Trajectories for the grand means are shown in Figure 2 (main text).

Fig. S9.
Impact of changing the effect size of beneficial mutations on the dilution factor that maximizes fitness gains.The parameter s0 represents the average effect size of a beneficial mutation in the ancestral genetic background.Figure 3 (main text) shows the grand mean fitness trajectory from 100 simulations for each of 10 dilution factors when s0 = 0.012, which is the estimate based on the LTEE.The upper left and right panels show comparable trajectories when s0 is reduced by 10-fold and 3-fold, respectively.The lower left and right panels show comparable trajectories when s0 is increased by 3-fold and 10fold, respectively.

Fig. S10.
Trajectories for relative fitness (top), average number of beneficial mutations (middle), and log2 marker ratio of three illustrative runs of the SSSM simulations with D = 100.They show selective sweeps driven by a single beneficial mutation (solid lines), two beneficial mutations (dashed lines), and three beneficial mutations (dot-dash lines).The trajectories for each run are truncated when log2 (Marker ratio) < -18 in order to better visualize the average number of beneficial mutations on the sweeping lineage.Table S4 provides summary data for the average number of beneficial mutations in 100 runs at each of four dilution factors.We simulated 10,000 populations for each dilution treatment.We scored runs as having surviving beneficial mutations if the population's mean fitness was greater than unity at the end of the run.
We compared the grand mean fitness of each treatment with the adjacent treatments (above and below) using two-tailed Welch's t-tests.All comparisons between adjacent treatments were significant (p < 0.05) after a table-wide sequential Bonferroni correction.Overall, mean fitness was highest with 8-fold dilutions, followed closely by the 16-and 4-fold dilutions, and it declined monontonically at both lower and higher dilution factors.For each dilution treatment, we show the number of simulated populations out of 100 that had as many mutations on average as shown in the left-hand column when the losing marker state was nearly extinct.The last row shows the maximum number observed for each treatment.Figure S10 shows exemplary runs with 1, 2, and 3 beneficial mutations in the sweepig lineage.We competed each member of a founding clone pair against the reciprocally marked ancestor, and the competition assays were paired.We calculated the relative fitness of a founding pair as the ratio of each clone's fitness relative to the ancestor.We replicated the paired competitions 22 times for each clone pair.We ran two-tailed paired t-tests on the ln-transformed fitnesses.Each comparison is highly significant and in the direction consistent with the initial divergence in the marker ratios (Fig. 4).We simulated 100 populations for each dilution factor.The mean time to divergence, TD, is shown as the number of transfers.We compared the mean TD for each treatment with the adjacent treatments (above and below) using two-tailed Mann-Whitney tests.All tests were significant (p < 0.05) after a table-wide sequential Bonferroni correction except for the comparisons between 300and 1000-fold and between 1000-and 10 4 -fold.We calculated the absolute value of the log2-transformed change in the ratio of the two marked strains for the first 7 consecutive sample pairs (3-day intervals through day 21) for 10 populations in the 4 dilution treatments (excluding the two aberrant populations in each treatment).By day 24, some populations exhibited systematic divergence in marker ratios caused by selective sweeps, which thus set the limit of the data used in this analysis.The grand mean and standard deviation of these 280 early fluctuations were 0.1986 and 0.1479, respectively.The ANOVA shows no significant effect of the dilution treatment on the magnitude of the fluctuations.We isolated clones at the end of the 150-transfer experiment from populations in the four dilution treatments.Each evolved clone competed against the reciprocally marked ancestral strain using both the same dilution treatment in which it evolved and the common 100-fold dilution treatment.
We ran paired t-tests to compare the mean ln-transformed fitness values in the two environments.
The tests were one-tailed in all cases except the 100-fold treatment, given the expectation that fitness would be higher in the environment where a population had evolved than in the common environment; the environments are identical for the 100-fold treatment, and so that test was twotailed.Note that the reported p-value is high for the 1000-fold treatment because the difference was opposite to the expectation.

Fig. S1 .
Fig. S1.Progression of mean relative fitness over time in the SSWM regime as a function of the dilution factor D. Data are from the same simulations shown in Figure 2 (main text), but they are presented here with time running from the bottom (100 transfers) to the top (1500 transfers).Over time, the profile stabilizes with the maximum fitness gains for D = 8 (i.e., log2 D = 3).

Fig. S2 .
Fig. S2.Extended simulations showing trajectories of relative fitness for populations evolving under the SSWM regime with dilution factors ranging from 2-fold to 10 5 -fold.Each trajectory shows the grand mean of 10,000 runs for 100,000 transfers.

Fig. S3 .
Fig. S3.Progression of mean relative fitness over time in the SSWM regime as a function of the dilution factor D. Data are from the same simulations shown in Figure S2, but they are presented here with time running from bottom (10,000 transfers) to top (100,000 transfers), thus extending the analysis shown in Fig. S1.The profile has clearly stabilized with the maximum fitness gains for D = 8 (i.e., log2 D = 3).

Fig. S4 .
Fig. S4.Simulated relative-fitness trajectories with time shown for 1500 transfers (A-D) or 1500 generations (E-H) for 10,000 populations evolving under the SSWM regime with four dilution treatments.Most trajectories are flat lines (i.e., no fitness increase), because most populations in this regime had no beneficial mutations (TableS1).Note the steeper trajectories leading to similar fitness gains at the higher dilutions when plotted against transfers, but not when plotted against generations.Trajectories for the grand means are shown in Figure2(main text).

Fig. S5 .
Fig. S5.Simulated fitness trajectories for 100 populations evolving under the SSSM regime with dilution factors ranging from 2-fold to 10 5 -fold.Figure 3 (main text) shows the grand means.Figs.S6 and S7 show high-resolution trajectories for the early transfers.

Fig. S6 .
Fig. S6.High-resolution graph of the early phase of the simulated mean fitness trajectories for populations evolving under the SSSM regime with dilution factors from 2-fold to 10 5 -fold.Each trajectory shows the grand mean of 100 runs for the first 150 transfers only.

Fig. S8 .
Fig. S8.Progression of mean relative fitness over time in the SSSM regime as a function of the dilution factor D. Data are from the same simulations shown in Figure 3 (main text), but they are presented here with time running from bottom (100 transfers) to top (1500 transfers).By 200 transfers, the profile has stabilized with the maximum fitness gains for D = 100 (i.e., log2 D = 6.64).

Fig. S11 .
Fig.S11.Bacteria that evolved in the 100-fold dilution treatment were more fit than those that evolved in the 8-fold treatment.(A) Comparison of ln-transformed fitness values for bacteria that evolved in these two treatments, when both sets competed against marked ancestors with 8-fold dilutions.Black and gray symbols show means and replicate assays, respectively; error bars are 95% confidence intervals.The bacteria that evolved with 100fold dilutions were more fit than those that evolved with 8-fold dilutions, even in the 8-fold treatment (p = 0.0195, two-tailed Wilcoxon's signed-ranks test).(B) Correlation of fitness values measured with 8-fold and 100-fold dilutions for bacteria that evolved in those two treatments.The overall correlation is strong and highly significant (r = 0.8218, p < 0.0001).

Table S2 . Mean fitness in simulated populations evolved under the SSSM regime after 1500 transfers with ten dilution treatments.
We simulated 100 populations for each dilution treatment.We compared each treatment with the adjacent treatments (above and below) using two-tailed Mann-Whitney tests.All tests were significant (p < 0.05) after a table-wide sequential Bonferroni correction.

Table S3 . Change in mean fitness between transfers 1000 and 1500 in simulated populations with ten dilution treatments under the SSSM regime.
We simulated 100 populations for each dilution treatment.We compared each treatment with the adjacent treatments (above and below) using two-tailed Mann-Whitney tests.None of the comparisons were significant after a table-wide sequential Bonferroni correction.

Table S6 . Comparison of times to divergence between the four dilution treatments in the experiment with bacteria.
We performed two-tailed Wilcoxon's signed-ranks tests to compare the times to divergence in the four dilution treatments.As explained in the text, two aberrant trajectories were excluded in each treatment; these tests are based on the remaining 10 trajectories in each treatment.All of the comparisons are significant even after a table-wide sequential Bonferroni correction (p < 0.05).

Table S10 . Comparison of final fitness of bacteria that evolved for 150 transfers under the 8-, 100-, and 1000-fold dilution treatments.
We competed evolved clones against reciprocally marked ancestors in the common environment (i.e., 100-fold dilution treatment), with 5-fold replication.We calculated the mean ln-transformed fitness value for each population, and we ran two-tailed t-tests to compare those values for the treatments shown.

Table S11 . Comparison of fitness changes between transfers 90 and 150 in bacteria that evolved in the 8-, 100-, and 1000-fold dilution treatments.
We ran two-tailed Wilcoxon signed-ranks tests to compare the changes in mean ln-transformed fitness values from 90 to 150 transfers for the treatments shown.