Two modes of evolution shape bacterial strain diversity in the mammalian gut for thousands of generations

Ethical statement

This research project was ethically reviewed and approved by the Ethics Committee of the Instituto Gulbenkian de Ciência (license reference: A009.2018), and by the Portuguese National Entity that regulates the use of laboratory animals (DGAV – Direção Geral de Alimentação e Veterinária (license reference: 008958). All experiments conducted on animals followed the Portuguese (Decreto-Lei n° 113/2013) and European (Directive 2010/63/EU) legislations, concerning housing, husbandry and animal welfare.

Escherichia coli clones

The ancestral invader E. coli strain expresses a Yellow Fluorescent Protein (YFP), and carries streptomycin and ampicillin resistance markers for easiness of isolation from the mouse feces [galK::amp (pZ12)::PLlacO−1-YFP, strR (rpsl150), ΔlacIZYA::scar]. An E. coli strain used for the in vivo competition experiments is isogenic to the ancestral invader but expresses a Cyan Fluorescent Protein (CFP) and carries streptomycin and chloramphenicol resistance markers [galK::chlor (pZ12)::PLlacO−1-CFP, strR (rpsl150), ΔlacIZYA::scar]. The resident E. coli lineage was isolated from the feces along time using McConkey + 0.4% lactose medium, as previously described⁹. All the resident clones sampled from each mouse belong to E.coli phylogenetic group B⁹. The invader E. coli strains (YFP and CFP) derive from the K-12 MG1655 strain (DM08) and exhibit a gat negative phenotype, gatZ::IS1¹². The resident E. coli clone used for the competition experiments in the mouse gut expresses a mCherry fluorescent protein and a chloramphenicol resistance marker, allowing to distinguish the invader and resident strains in the mice feces.

E. coli clones were grown at 37 °C under aeration in liquid media Luria broth (LB) from SIGMA — or McConkey and LB agar plates. Media were supplemented with antibiotics streptomycin (100 µg/mL), ampicillin (100 µg/mL) or chloramphenicol (30 µg/mL) when specified.

Serial plating of 1X PBS dilutions of feces in LB agar plates supplemented with the appropriate antibiotics were incubated overnight and YFP, CFP or mCherry-labeled bacterial numbers were assessed by counting the fluorescent colonies using a fluorescent stereoscope (SteREO Lumar, Carl Zeiss). The detection limit for bacterial plating was ~300 CFU/g of feces⁹.

In vivo evolution and competition experiments

All mice (Mus musculus) used in this study were supplied by the Rodent Facility at Instituto Gulbenkian de Ciência (IGC) and were given ad libitum access to food (Rat and Mouse No.3 Breeding (Special Diets Services) and water. Mice were kept at 20-24 °C and 40-60% humidity with a 12-h light-dark cycle. For the in vivo evolution experiment we used the gut colonization model previously established⁹. Briefly, mice drank water with streptomycin (5 g/L) only for 24 h before a 4 h starvation period of food and water. The animals were then inoculated by gavage with 100 µL of an E. coli bacterial suspension of ~10⁸ colony-forming units (CFUs). Mice A2, B2, D2, E2, G2, H2 and I2 were successfully colonized with the invader E. coli, while mice C2 and F2 failed to be colonized. Six- to eight-week-old C57BL/6 J non-littermate female mice were kept in individually ventilated cages under specified pathogen-free (SPF) barrier conditions at the IGC animal facility. Fecal pellets were collected during more than one year (>400 days) and stored in 15% glycerol at −80 °C for later analysis. In the competition experiments between the invader ancestral E. coli and evolved populations, we colonized the mice using a 1:1 ratio of each genotype, with bacterial loads being assessed and frozen on a daily basis after gavage.

In vivo competition experiments in which the two modes of selection (directional and diversifying) were acting for a longer time period were performed using evolved invader E. coli populations colonizing mice D2, B2 and A2, H2. Here we used both male (n = 8) and female (n = 8) C57BL/6 J mice aged six- to eight-week-old treated with streptomycin during 3 days before gavage. E. coli populations evolving for short time periods do not allow for strong conclusions on which mode of selection is taking place. Evolved invader populations such as I2 or G2 were therefore not used for in vivo fitness assays. To assess the impact of the mouse resident E. coli in the competitive fitness of dgoR we performed one-to-one competitions between the invader ancestral and dgoR KO clones. We first homogenized the mice microbiotas by co-housing the animals during seven days. The animals (n = 6, female C57BL/6 J mice aged six- to eight-week-old) were then maintained under co-housing and given streptomycin-supplemented (5 g/L) water during seven days to break colonization resistance and eradicate their resident E. coli. At this point, the co-housed mice were removed from the antibiotic-supplemented water for two days. The following day, one group of mice was gavaged with an mCherry-expressing resident E. coli (n = 3 mice) while the other group (n = 3) was not, with all animals being individually caged from this point on and receiving normal water without antibiotic. The day after gavage, all mice were colonized with a mix (1:1) of the invader ancestral and the dgoR KO clones, and the bacterial loads were assessed and frozen on a daily basis.

Microbiota analysis

Fecal DNA was extracted with a QIAamp DNA Stool MiniKit (Qiagen), according to the manufacturer’s instructions and with an additional step of mechanical disruption³². 16 S rRNA gene amplification and sequencing was carried out at the Gene Expression Unit from Instituto Gulbenkian de Ciência, following the service protocol. For each sample, the V4 region of the 16 S rRNA gene was amplified in triplicate, using the primer pair F515/R806, under the following PCR cycling conditions: 94 °C for 3 min, 35 cycles of 94 °C for 60 s, 50 °C for 60 s, and 72 °C for 105 s, with an extension step of 72 °C for 10 min. Samples were then pair-end sequenced on an Illumina MiSeq Benchtop Sequencer, following Illumina recommendations. Sampling for microbiota analysis was performed until the microbiota composition stabilized (~1 year after the antibiotic perturbation).

QIIME2 version 2017.11³³ was used to analyze the 16 S rRNA sequences by following the authors’ online tutorials (https://docs.qiime2.org/2017.11/tutorials/). Briefly, the demultiplexed sequences were filtered using the “denoise-single” command of DADA2 version 1.14³⁴, and forward and reverse sequences were trimmed in the position in which the 25th percentile’s quality score got below 20. Diversity analysis was performed following the QIIME2 tutorial³⁵. Beta diversity distances were calculated through Unweighted Unifrac³⁶. For taxonomic analysis, OTU were picked by assigning operational taxonomic units at 97% similarity against the Greengenes database version 13 (Greengenes 13_8 99% OTUs (250 bp, V4 region 515 F/806 R))³⁷.

Whole-genome sequencing and analysis pipeline

DNA was extracted³⁸ from E. coli populations (mixture of > 1000 clones) or a single clone growing in LB plates supplemented with antibiotic to avoid contamination. DNA concentration and purity were quantified using Qubit and NanoDrop, respectively. The DNA library construction and sequencing were carried out by the IGC genomics facility using the Illumina Miseq platform. Processing of raw reads and variants analysis was based on the previous work³⁹. Briefly, sequencing adapters were removed using fastp version 0.20.0⁴⁰ and raw reads were trimmed bidirectionally by 4 bp window sizes across which an average base quality of 20 was required to be retained. Further retention of reads required a minimum length of 100 bps per read containing at least 50% base pairs with phred scores at or above 20. BBsplit (part of BBMap version 38.9)⁴¹ was used to remove likely contaminating reads as explained previously³⁹. Separate reference genomes were used for the alignment of invader (K-12 (substrain MG1655; Accession Number: NC_000913.2)) and resident (Accession Number: SAMN15163749) E. coli genomes. Alignments were performed via three alignment approaches: BWA-sampe version 0.7.17⁴², MOSAIK version 2.7⁴³, and Breseq version 0.35.1^44,45. Final average alignment depths for invader and resident populations across time points equalled 302 (median = 236) and 253 (median = 235), respectively. While Breseq provides variant analysis in addition to alignment, other variant calling approaches were used to identify putative variation in the sequenced genomes, and to verify data from Breseq. A naïve pipeline³⁹ using the mpileup utility within SAMtools version 1.9⁴⁶ and a custom script written in python was employed. Only reads with a minimum mapping quality of 20 were considered for analysis, and variant calling was limited to bases with call qualities of at least 30. At these positions, a minimum of 5 quality reads had to support a putative variant on both strands (with strand bias, pos. strand / neg. strand, above 0.2 or below 5) for further consideration. Finally, mutations were retained if detected in more than one of the alignment approaches, and if they reached a minimum frequency of 5% at a minimum of one time point sampled. Further simple and complex small variants were considered from freebayes version 0.9.21⁴⁷ with similar thresholds, while insertion sequence movements and other mobile element activity was inferred via is mapper version 2⁴⁸ and panISa version 0.1.6⁴⁹, as well as Breseq, as previously described³⁹. All putative variants were verified manually in IGV version 2.7^50,51. Raw sequencing reads were deposited in the sequence read archive under bioproject PRJNA666769. Population dynamics of lineage-specific dynamics and the resulting Muller plots were inferred manually and are meant strictly as a means of presenting the data. In order to generate these plots, mutations were sorted by frequency (descending for each time point at which the population was sampled). The largest frequency mutations were considered major lineages within which minor frequency mutations occurred. Assuming that a mutation, which arises subsequent to a preexisting mutation (an already differentiated lineage) cannot exceed the frequency of that preexisting mutation at any point, and will fluctuate in frequency with the preexisting one, we assigned mutations to the lineages within each population. While this resolved the majority of high frequency and medium frequency mutations, low-frequency mutations within the Muller plots cannot be placed with high confidence, and are only included for completeness.

Prophage induction rate

To calculate the maximum prophage induction rate we grew E. coli lysogenic clones, starting with the same initial OD600 values: ~0.1 (Bioscreen C system, Oy Growth Curves Ab Ltd), with agitation at 37 °C in LB medium in the presence or absence of mitomycin C along time (5 µg/mL)⁹. The OD600 values were normalized by dividing the ones in the presence of mitomycin C by the ones in the absence of mitomycin C (sampling interval: 30 min). The LN of this ratios along time originates a lysis curve, where the maximum slope corresponds to the maximal prophage induction rate for each clone analyzed. We tested evolved clones from mouse A2, H2 and G2 against the ancestral clone which only carries the Nef and the KingRac prophages. We also tested clones of the resident strain that had evolved in the presence of the invader for more than 400 days (these clones were sampled from mouse A2).

E. coli growth rate, growth curves, cell aggregation, biofilm and motility capacity

To calculate the maximum bacterial growth rate, we grew E. coli lysogenic clones, starting with the same initial OD600 values: ~0.1 (Bioscreen C system, Oy Growth Curves Ab Ltd), with agitation at 37 °C in LB medium along time using reading intervals of 30 min. The LN of the OD600 values along time originates a growth curve, where the maximum slope corresponds to the maximum bacterial growth rate for each clone analyzed.

To test for metabolic differences of the psuK/fruA mutation, growth curves of evolved lysogenic E. coli clones, bearing the Nef and KingRac prophages, with or without the psuK/fruA mutation were performed with the same initial OD600 value (~0.03) for each clone. The clones were grown in glucose (0.4%) minimal medium (MM9-SIGMA) with or without pseudouridine (80 μM) and absorbance values were obtained using the Bioscreen C apparatus during 12 h.

Frozen stocks of E. coli clones were used to seed tubes with 5 mL of liquid LB. These were incubated overnight at 37 °C under static conditions to assess the formation of cell flocks/clumps, observable to the naked eye, in order to evaluate the formation of cell aggregates. Biofilm was tested according a previously published protocol⁵² and to evaluate the motility capacity we adapted the protocol from Croze and colleagues⁵³. Briefly, overnight E. coli clonal cultures grown with agitation at 37 °C in 5 mL LB medium supplemented with streptomycin (100 ug/mL) were adjusted to the same absorbance and a 3uL volume was dropped on top of soft agar (0.25%). Plates were incubated at 37 °C and photos were taken at day 1, 2 and 5 post-inoculation to assess swarming motility phenotype.

Number of E. coli generations during mouse gut colonization

To estimate the number of generations of E. coli in the mouse gut, we used a previously described protocol to measure the fluorescent intensity of a probe specific to E. coli 23 S rRNA (as a measure of ribosomal content) that correlates with the growth rate of the bacterial cells⁵⁴. We measured the number of generations of the ancestral E. coli clone while colonizing the gut of 2 mice, treated during 24 h with streptomycin (5 g/L) before gavage, during 25 days.

Plasmid DNA extraction and PCR detection of ~69Kb (repA) and ~109Kb (repB) plasmids

Plasmid DNA was extracted from overnight cultures using a Plasmid Mini Kit (Qiagen), according to the manufacturer’s guidelines. Specific primers for the amplification of repA and repB genes, were used to determine the frequency of the 68935 bp (~69 Kb) and 108557 bp (~109 Kb) plasmids, respectively, in the invader E. coli population.

The primers used for repA gene were:

repA-Forward: 5’-CAGTCCCCTAAAGAATCGCCCC-3’ and repA-Reverse: 5’-TGACCAGGAGCGGCACAATCGC-3’.

For repB the primer sequences were:

repB-Forward: 5’-GTGGATAAGTCGTCCGGTGAGC-3’ and repB-Reverse: 5’-GTTCAAACAGGCGGGGATCGGC3’.

PCR amplification of plasmid-specific genes was performed in 12 isolated random clones from mouse A2 at days 104 and 493. PCR reactions were performed in a total volume of 25 μL, containing 1 μL of plasmid DNA, 1X Taq polymerase buffer, 200 μM dNTPs, 0.2 μM of each primer and 1.25 U Taq polymerase. PCR reaction conditions: 95 °C for 3 min, followed by 35 cycles of 95 °C for 30 s, 65 °C for 30 s and 72 °C for 30 s, finalizing with 5 min at 72 °C. DNA was visualized on a 2% agarose gel stained with GelRed and run at 160 V for 60 min.

Construction of the dgoR KO mutant

P1 transduction was used to construct a ΔdgoR mutant (dgoR KO). This KO strain was created by replacing the wild-type dgoR in the invader ancestral YFP-expressing genetic background by the respective knock-out from the KEIO collection, strain JW5627⁵⁵, in which the dgoR sequence is replaced by a kanamycin resistance cassette. The presence of the cassette was confirmed by PCR using primers dgoK-F: GCGATGTAGCGAGCTGTC, and yidX-R: GGGAATAAACCGGCAGCC. PCR reactions were performed in a total volume of 25 μL, containing 1 μL of DNA, 1X Taq polymerase buffer, 200 μM dNTPs, 0.2 μM of each primer and 1.25 U Taq polymerase. PCR reaction conditions: 95 °C for 3 min, followed by 35 cycles of 95 °C for 30 s, 65 °C for 30 s and 72 °C for 30 s, finalizing with 5 min at 72 °C. DNA was visualized in a 2% agarose gel stained with GelRed and run at 160 V for 60 min.

RNA extraction, DNAse treatment, RT-PCR and qPCR

The Qiagen RNeasy Mini Kit was used for RNA extraction. RNA concentration and quality were evaluated in the Nanodrop 2000 and by gel-electrophoresis. DNase treatment was performed with the RQ1 DNase (Promega) by adding 0.5 μl of DNase to 1 μg of RNA and 1 μl buffer in a final volume of 15 ul, followed by incubation 30 min at 37 °C. Afterwards, 1 ul of stop solution was added and incubation for 15 min at 65 °C was performed to inactivate the DNase. As a control for complete DNA digest a PCR was performed on the reactions including positive controls. Reverse transcription was performed with M-MLV RT[-H] (Promega) by mixing 1 μg of RNA with 0.5 μl random primers (Promega) and nuclease free water to a volume of 15 μl, incubation at 70 °C for 5 min and a quick cool down on ice. Afterwards the reverse transcription was accomplished by adding 5 μl of RT buffer, 0.5 μl RT enzyme and 2 μl dNTP mix, followed by incubation for 10 min at 25 °C, 50 min at 50 °C and 10 min at 70 °C. The resulting cDNA was diluted 100-fold in nuclease free water before changes in gene expression were detected using the The QuantStudio 7Flex (Applied Biosystems) with iTaq Universal SYBR Green Supermix (BioRad) and the following cycling protocol: Hold stage: 2 min at 50 °C, 10 min at 95 °C. PCR stage (40 cycles): 15 s at 95 °C, 30 s at 58 °C, 30 s at 60 °C. Melt curve stage: 15 s at 95 °C, 1 min at 50 °C then increments of 0.05 °C/s until 95 °C. Melt curve analysis was performed to verify product homogeneity. All reactions included six biological and three technical replicates for each sample. A relative quantification method of analysis with normalization against the endogenous control rrsA and employing the primer specific efficiencies was used according to the Pfaffl method (add reference). The primers used were designed with PrimerQuest (idt). The used primer sequences were: psuK – TGCGTTAGCAGCGATTGA, AATTTACGCCTGGTGGAGTAG; arcA – GATTCATGGTACGGGACAGTAG, CCGTGACAACGAAGTCGATAA; yjtD – CGCACATGGATCTGGTGATA, GGCGTGGCGTAGTAATGATA and rrsR – GTCAGCTCGTGTTGTGAAATG, CCCACCTTCCTCCAGTTTATC.

Statistics and reproducibility

Correlation between microbiota diversity measures and E. coli loads (CFU) or persistence (1-presence or 0-absence) was performed in R using the statistical package rmcorr (version 0.5.2)⁵⁶ and lme4 (version 1.1-10)⁵⁷, respectively. The rate of accumulation of new ISs in vivo was compared using Wilcoxon paired signed ranked test for expected and observed insertions, while the rate of selective sweeps correlation was performed using the Spearman Correlation test. Selective sweeps were taken to be mutations or HGT events that reached > 95% frequency in the population and kept high frequency until the end of the colonization. Statistical analysis of prophage induction as well as biofilm levels was performed using the Mann-Whitney test in GraphPad Prism (version 8.4.3). A single sample T-Test was used test if the growth rate of evolved invader clones deviates from the mean of the ancestral. A Wilcoxon rank sum test with continuity correction was used to compare the relative expression levels of the evolved clones with the ancestral. P values of < 0.05 were considered significant.

Pearson correlation tests between the frequency and the change in frequency of a mutation were performed to search for evidence of negative frequency-dependent selection. These were conducted for every mutation that showed parallelism and for each mouse, provided that the mutation was detected in at least four time points. The correlations were calculated in R with cor.test, used for the association between paired samples.

Linear mixed models (R package nlme, v3.1⁵⁸) were used to analyze the temporal dynamics of the dgoR KO mutant frequency in the presence or absence of the resident E. coli. The frequency of the dgoR KO mutant was log10 transformed to meet the assumptions of parametric statistics.

Sample size in animal experiments was chosen according to institutional directives and in accordance with the guiding principles underpinning humane use of animals in scientific research. No data were excluded from the analysis. The experiments were randomized with animals being assigned arbitrarily to each experiment. The investigators were not blind towards the animal experiments.

Statistics of time-resolved mutation frequency trajectories

The following statistics are designed to infer the prevalent type of selection from time-resolved mutant frequency data. Specifically, we use such data to discriminate adaptive evolution under directional selection, which can take place by periodic sweeps or by clonal interference, and adaptation under diversifying selection (to be defined below).

We use two test statistics for frequency trajectories of established mutants (i.e., mutants that have overcome genetic drift):

• the frequency propagator G(x), defined as the probability that a trajectory reaches frequency x,

• the sojourn time T(x), defined as the time between origination at a threshold frequency x₀ and the first occurrence at frequency x, averaged over all trajectories reaching frequency x. In terms of the underlying coalescent, T(x) is the time to the last common ancestor for a genetic clade of frequency x.

These observables discriminate the following modes of adaptive evolution:

• Periodic selective sweeps under uniform directional selection. This mode is characteristic of simple adaptive processes in small populations or populations with low mutational inputs, where adaptive mutations are rare enough to fix independently^59,60,61. Almost all established adaptive mutations reach fixation, and sojourn times to an intermediate frequency x>x₀ are of order of their inverse selection coefficient (up to logarithmic corrections):

  $${{{{{rm{G}}}}}}left(xright)approx 1,{{{{{rm{T}}}}}}left(xright)sim frac{1}{s}.$$

  (1)

• Clonal interference under uniform directional selection. This mode occurs in asexual populations when adaptive mutations become frequent enough to interfere with one another^59,60,61. Only a fraction of the established adaptive mutations reaches fixation; sojourn times to intermediate frequencies are set by a global coalescence rate (widetilde{sigma }) that is higher than the typical selection coefficient of individual mutations⁶²:

Details of these dynamics depend on the spectrum of selection coefficients and on the overall mutation rate, which set the strength of clonal interference. For moderate interference, where a few concurrent beneficial mutations compete for fixation, we expect a roughly exponential drop of the frequency propagator, (Gleft(xright)sim {{exp }}left(-lambda xright)), reflecting the probability that a trajectory reaches frequency x without interference by a stronger competing clade. Moderate interference generates an effective neutrality for weaker beneficial mutations and at higher frequencies⁶³. This regime has been mapped for influenza⁶⁴. In the asymptotic regime of a travelling fitness wave, where many beneficial mutations are simultaneously present, the fate of a mutation is settled in the range of small frequencies; that is, at the tip of the wave⁶⁵. In this regime, emergent neutrality affects the vast majority of beneficial mutations and most of the frequency regime⁶⁶. Hence, the frequency propagator rapidly drops to its asymptotic value (Gleft(x=1right)ll 1.)

• Adaptation under diversifying selection. More complex selection scenarios involve selection within and between ecotypes, i.e., subpopulations occupying distinct ecological niches^67,68. An important factor generating niches and ecotypes is the differential use of food and other environmental resources. In this mode, ecotype-specific, conditionally beneficial mutations reach intermediate frequencies after a time given by their within-ecotype selection coefficients, but fixation can be slowed down or suppressed by diversifying (negative frequency-dependent) cross-ecotype selection¹⁸,

The details depend on the details of the eco-evolutionary model (synergistic vs. antagonistic interactions, carrying capacities, amount of resource competition vs. explicitly frequency-dependent selection). In a model with directional selection within ecotypes, conditionally beneficial mutations rapidly fix within ecotypes, but lead only to finite shifts of the ecotype frequencies. In the simplest case, the resulting dynamics of ecotype frequencies is diffusive, resulting in an effectively neutral turnover of ecotypes¹⁸. Given negative frequency-dependent selection between ecotypes, fixations become even rarer and can be completely suppressed; that is, ecotypes can become stable on the time scales of observation. The separation of time and selection scales between intra- and cross-ecotype frequency changes is expected to be a robust feature of ecotype-dependent selection: sojourn of adaptive alleles to intermediate frequencies is fast, fixation is slower and rarer. In other words, ecotype-dependent selection is characterized by two regimes of coalescence times T(x).

Frequency propagators and the coalescence time spectra expected under these evolutionary modes are qualitatively sketched in Supplementary Fig. 11. For periodic sweeps under directional selection (dark green, left column), G(x) depends weakly on x and T(x) is set by rapid sweeps for all x. For clonal interference under directional selection (green, center column), G(x) decreases substantially with increasing x and T(x) becomes uniformly shorter. Under negative frequency-dependent selection (brown, right column), G(x) decreases substantially with increasing x, while T(x) substantially increases for large x and diverges in case of strong frequency-dependent selection generating stable ecotypes (dashed lines). (see Supplementary Fig. 11 for the results of simulations assuming a model of direction selection or assuming a resource competition model where ecotype formation occurs³¹.

The ({{{{{boldsymbol{p}}}}}})–({{{{{boldsymbol{tau }}}}}}) selection test

This test is based on qualitative characteristics of the functions G(x), T(x) and does not depend on details of the evolutionary process. We evaluate G(x) and T(x) for host-specific families of frequency trajectories; sojourn times are counted from an initial frequency x₀=0.01. Origination times at this frequency are inferred by backward extrapolation of the first observed trajectory segment; the reported results are robust under variations of the threshold x₀ and the extrapolation procedure. We then compute two summary statistics: the probability (p) that a mutation established at an intermediate frequency x_m reaches near-fixation at a frequency x_f,

and the corresponding fraction of sojourn times,

Here we use x_m=0.3 and x_f=0.95 to limit the uncertainties of empirical trajectories at low and high frequency; however, the selection test is robust under variation of these frequencies. We find evidence for different modes of evolution:

• The long-term frequency trajectories of mice B2, D2 and E2 are consistent with predominantly frequency-dependent selection (Fig. 2, Fig. 4a–c). The propagator G(x) is a strongly decreasing function of x, resulting in fixation probabilities (p) < 0.5. Sojourn times T(x) show two regimes with a stronger increase in the frequency range x>0.6, as measured by time ratios τ > 3.

• The trajectories of mice A2, G2, and I2 show a signature of recurrent selective sweeps and clonal interference under uniform directional selection (Fig. 4a–c). The propagator G(x) is a decreasing function of x, resulting in fixation probabilities (p=0.2-0.8), depending on the strength of clonal interference. Fixation times are short, giving time ratios (tau lesssim 2).

• The shorter trajectory of mouse H2 signals periodic sweeps under uniform directional selection (Fig. 3, Fig. 4a–c). The origination rate of mutations is lower than in the longer trajectories, and G(x) shows a weak decrease with (p=1.) Sojourn times T(x) are short and grow uniformly with x, resulting in a time ratio τ=2.25. This pattern is expected under directional selection in the low mutation regime: (Tleft(xright)={{log }}left[x/(1-x)right]/{s}) for individual mutations with a uniform selection coefficient s, leading to τ=2.0 for x_m=0.3 and x_f=0.95 (this value is marked as a dashed line in Fig. 4c).

• The trajectories of non-mutator lines in the long-term in vitro evolution experiment of Good et al¹, evaluated over the first 7500 generations, show an overall signal of clonal interference under uniform directional selection (Fig. 4c, Supplementary Fig. 12). The frequency propagators G(x) are strongly decreasing functions of x and sojourn times T(x) grow uniformly with x. We find (p=0.2-0.8) and (tau lesssim 2), similar to the pattern in mice A2, G2, and I2.

Code for Selection tests

The code for selection tests from the mutation frequency trajectories can be found in the Supplementary Information file.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

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