Emergence and maintenance of mutation rate variation in a gut commensal strain

To be able to study the evolution of new E. coli strains as they invade and colonise the mouse gut, we used a short-course antibiotic treatment (8 days with streptomycin), which perturbs microbiota composition and leads to a decrease in its species diversity (including killing native E. coli). With this setup, we colonised four mice with two commensal strains of E. coli (marked with two fluorescent markers: yellow fluorescent protein [YFP] and cyan fluorescent protein [CFP]; both streptomycin-resistant) and followed their dynamics for 190 days (approximately 3,600 generations, assuming 19 generations/day; Fig 1A) [38–40]. Both strains carry mutations that we previously showed to be adaptive in the mouse gut [38,39]. Mice 1 and 2 were co-colonised with a YFP-labelled strain with a 1-bp insertion in gatC and a CFP-labelled strain with the same gatC mutation and two other mutations: an IS2 insertion between yjjP and yjjQ and a 4bp insertion between yjjY and yjtD. Mice 3 and 4 were co-colonised with the same genetic backgrounds, with the single mutant expressing CFP and the triple mutant expressing YFP. All mice were co-colonised with the triple mutant at a lower starting frequency (10%), as this carries more beneficial mutations and has a higher fitness under the 7-day streptomycin treatment (S1 Fig). Throughout the entire experiment, both strains coexisted in all mice, and E. coli generally maintained a population size of >10⁷ colony-forming units (CFU)/g of faeces (S1 Fig), i.e., the typical size of its ecological niche in this host [41].

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Fig 1. Multiple clones with variable mutation rates (up to 1,000-fold higher than ancestral) emerge and coexist during long-term adaptation to the mouse gut.

(A) Scheme of the experimental design used to follow the long-term adaptation of E. coli to the mouse gut. (B) Screen for mutation rate variation shows that mutators emerged in mouse 1. A total of 83 to 90 clones, isolated from each mouse at day 190 post colonisation, were grown overnight and plated in nalidixic acid. The number of resistant colonies obtained for each clone is shown. The same procedure was carried for 96 replicates of the ancestral clones. (C) Large-scale variation for mutation rate emerges in mouse 1. Mutation rates (towards Nal^R), measured through fluctuation tests, for multiple clones randomly isolated at different time points from mouse 1. Each point corresponds to one clone. Error bars represent 95% CIs of 10 independent growths (nonoverlapping bars indicate significant differences). Blue and yellow points correspond to clones from the CFP and YFP backgrounds. Coloured areas indicate the mutation rate fold-change of a particular evolved clone relative to the ancestral (i.e., mutator strength). CFP, cyan fluorescent protein; CFU, colony-forming units; Nal^R, nalidixic acid resistance; YFP, yellow fluorescent protein.

https://doi.org/10.1371/journal.pbio.3000617.g001

As mutation rate is a key evolutionary parameter that can evolve, both in vitro and in vivo (e.g., [8,17,23–25,30]), we screened a sample of clones from each mouse (n ≈ 90 per mouse) for potential changes in mutation rate (Fig 1B). In one of the four mice, we detected clones with increased mutation rate. To understand the magnitude and dynamics of the mutation rate increase in this host, we performed Luria-Delbrück fluctuation assays for several clones sampled at days 45, 136, 148, and 190 and measured their mutation rate towards nalidixic acid resistance (n = 10 independent growths per clone; Fig 1C). At day 45, none of the clones exhibited a mutation rate (towards resistance) significantly different from that of the ancestral (5 × 10⁻¹⁰; per cell per generation; 95% CIs for all clones overlap with those of the ancestral). However, from day 136 onwards, mutation rate varied by three orders of magnitude, ranging between 4.7 × 10⁻¹⁰ and 6 × 10⁻⁷/cell/generation. Similar levels of mutation rate variation were observed at days 148 and 190 (range at day 148: 3.1 × 10⁻¹⁰ to 2.8 × 10⁻⁷; day 190: 1.2 × 10⁻¹⁰ to 4.5 × 10⁻⁷ per cell per generation). This indicates that multiple mutators emerged either simultaneously or sequentially and that nonmutator clones coexisted with both strong hypermutators (mutation rates up to 1,200-fold higher than the ancestral) and with intermediate hypermutators (10- to 100-fold increases in mutation rate). Coexistence between clones differing in mutation rate by less than 70-fold has been previously observed [42–45]. However, to the best of our knowledge, our results represent the first observation of long-term coexistence (>1,000 generations, i.e., >54 days) of clones differing in mutation rate by around 1,000-fold in the gut.

These observations raised two main questions: What is the genetic basis for the observed mutation rate increase? Under what evolutionary conditions could we expect the emergence of 1,000-fold mutators and the long-term maintenance of mutation rate polymorphism?

Mutations in the proofreading and catalytic subunits of DNA polymerase III cause hypermutability and improve mutator fitness, respectively

To determine the cause of the observed mutation rate variation, we carried out whole-genome sequencing of 18 clones, 13 mutators and 5 nonmutators, isolated from mouse 1 (all CFP), between day 136 and 190 post colonisation (Fig 2A). Mutator and nonmutator clones accumulated 164 to 658 and 4 to 5 mutations (respectively) and followed independent evolutionary paths (Fig 2A). Observing 4 to 5 mutations in nonmutator clones after 6 months is not unexpected, given that the nonmutators are competing with mutator clones and that previous experiments showed 1 to 4 adaptive mutations in nonmutator clones after 1 month of colonisation of the mouse gut (approximately 450 generations [38,39]). All mutator clones shared 45 mutations, none of which were present in the isolates that maintained the ancestral mutation rate (Fig 2A and S1 Table). Among these, we identified a single nonsynonymous mutation in the gene dnaQ, which could increase mutation rate by 1,000-fold. dnaQ encodes the proofreading (ε) subunit of DNA polymerase III [46], the main DNA polymerase in E. coli. Following their divergence, mutators accumulated mutations in several other genes that may affect mutation rate (S2 Fig; none of these genes were mutated in the nonmutators; S2 Table). Strikingly, these included several mutations in two different subunits of DNA polymerase III: the catalytic (α) subunit (encoded by dnaE; mutated in 11 clones) [47] and the θ subunit (holE; two clones) [48]. The α, ε, and θ subunits physically interact to form the core of DNA polymerase III (Fig 2B) [20,49]. Nonsynonymous mutations in dnaQ were previously shown to cause mutation rate increases up to >5,000-fold [19]. Mutations in dnaE and to a smaller extent in holE were also shown to have antimutator effects when linked to dnaQ mutations [50,51]. This led us to hypothesise that a mutation in dnaQ first raised the mutation rate, which was later reduced by subsequent mutations in dnaE, thus leading to the observed mutation rate polymorphism. To query whether the dnaQ mutation caused the hypermutator phenotype, and whether dnaE could act as a modifier, we engineered single and double mutants with the dnaQ mutation (L145P; CTC → CCC) and a mutation in dnaE (T771S; ACG → TCG) and measured their mutation rates. We generated approximately 20 clones carrying the DnaQ^L145P allele, as dnaQ hypermutators can exhibit high mutation rate variation, possibly because of the rapid emergence of suppressors [42,51]. The dnaQ clones indeed showed a very high mutation rate, reaching 3,000-fold increases for both nalidixic acid and rifampicin (Fig 2C). The distribution of mutation rate estimates is bimodal, with a group of clones showing approximately 200-fold increase in mutation rate, whereas another shows an increase of approximately 1,000-fold (none of the 95% CIs overlap with the ancestral; S3 Table). Given the observed mutation rate increase of about 1,000-fold for clones isolated from mice and that it is possible for mutation rate variation to emerge during the engineering process (because of suppressors; see [51]), we suggest that the dnaQ mutation is responsible for the approximately 1,000-fold mutation rate increase.

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Fig 2. Mutations in DNA polymerase III both drive mutation rate increase by 1,000-fold (DnaQ^L145P; ε subunit) and rescue fitness of hypermutator clones (DnaE^T771S; α subunit).

(A) Phylogenetic tree of 18 clones from mouse 1 and the ancestral strain generated from whole-genome sequence data. Mutator and nonmutators have independent evolutionary histories, with all mutators sharing 45 mutations. Branch lengths and tip labels indicate the number of accumulated mutations. Tip point colours indicate the day post colonisation at which different clones were isolated. (B) Structure of the core DNA polymerase (“pol.”) III (PDB ID: 5M1S), with each subunit in a different colour and nonsynonymous mutations highlighted in red or black. (C) In vitro fluctuation tests were performed for the ancestral clone (“Anc”), the single mutant DnaQ^L145P, and the double mutant DnaQ^L145P+DnaE^T771S (21 and 5 independent clones were tested for each mutant, respectively). Each point shows the mutation rate fold-change of a particular evolved clone relative to the ancestral (i.e., in vitro mutator strength; 10 replicates per clone for ancestral and double mutant; 5 replicates per clone for DnaQ^L145P). For ease of visualisation, 95% CIs are only shown for the ancestral, but none of the 95% CIs of either mutant is overlapping with those of the ancestral (see S3 Fig for the mutation rate of DnaE^T771S and S3 Table for mutation rates and 95% CIs). (D) In vitro phenotypic growth capacity of the ancestral clone, the single mutant DnaQ^L145P, and the double mutant DnaQ^L145P+DnaE^T771S (spot assay; all inocula had the same OD_600nm; similar results were obtained for an extended number of clones, see S4 Fig). (E) In vivo dynamics and summary box plots of the mutation frequency fold-change relative to the average mutation frequency obtained for the ancestral strain (i.e., in vivo mutator strength; similar results were obtained when measuring mutation frequency towards Nal^R; S6 Fig); (F) In vivo dynamics and summary boxplots of E. coli CFU per gram of faeces. AA, amino acids; CFU, colony-forming units; Glu, glucose; LB, lysogeny broth; Nal^R, nalidixic acid resistance; ns, not significant; OD_600nm, optical density at 600 nm; PDB, Protein Data Bank; Rif^R, rifampicin resistance; Sor, sorbitol.

https://doi.org/10.1371/journal.pbio.3000617.g002

Contrary to our hypothesis, the DnaE^T771S mutation did not cause any significant change in the mutation rate on the ancestral or the DnaQ^L145P genetic backgrounds (Figs 2C and S3). This suggests that the dnaE mutation did not act to decrease mutation rate. However, the independent occurrence of different alleles in the α subunit of DNA polymerase III (Figs 2B and S2) strongly suggests that mutations in dnaE could be beneficial. Consistent with this hypothesis, we observed that DnaE^T771S strongly improves growth of the DnaQ^L145P mutant (Figs 2D and S4). Remarkably, the DnaQ^L145P mutation is lethal in minimal media with a single carbon source (either glucose or sorbitol). Its null fitness can be rescued by complementing minimal media with amino acids or in lysogeny broth (LB), which allows the DnaQ^L145P mutant clones to achieve slow but visible growth (Fig 2D). Furthermore, the double mutant (DnaQ^L145P+DnaE^T771S) grows to levels similar to the ancestral strain across all media.

As mutation rate and spectrum can depend on the environment (e.g., [52]), we sought to determine the mutation rate of the dnaQ and dnaQ+dnaE mutant strains in vivo. The classical Luria-Delbrück in vitro assay, designed to avoid selection, is inappropriate for estimating the mutation rate in the gut. However, we can use Haldane’s mutation-selection balance principle to estimate the in vivo mutation rate of these clones. We colonised mice with the ancestral strain, the dnaQ mutant, and the double dnaQ+dnaE mutant and measured the equilibrium frequency of rifampicin-resistant (Rif^R) clones (n = 3 mice for each genetic background). Under mutation-selection balance, the frequency of resistant mutants is directly proportional to the mutation rate [53]. Thus, the ratio of the Rif^R mutation frequency in the mutants, relative to the ancestral strain, provides an estimate of the fold-change in mutation rate (i.e., mutator strength). The mutation frequency (towards resistance) of either the single dnaQ mutant or the double dnaQ+dnaE mutant is about 1,000-fold higher than observed for the ancestral strain but not significantly different between mutants (Fig 2E, see also S5 Fig for comparison between mutation frequency in vivo and in an in vitro propagation; linear mixed model followed by Tukey test: clone effect: χ²₂ = 31.9, p < 0.0001; ancestral versus dnaQ: t = −12.8, df = 6, p < 0.0001; ancestral versus dnaQ+dnaE: t = −14.9, df = 6, p < 0.0001; dnaQ versus dnaQ+dnaE: t = −1.5, df = 6, p = 0.37). Similar results were obtained when using nalidixic acid as the selection marker (S6 Fig), which targets a different region of the genome [54,55]. When comparing the niche size that each strain occupies in the mouse gut, we find that the average abundance of the dnaQ mutant (10⁶ per gram of faeces) is significantly lower than that of the ancestral strain (>10⁸ per gram of faeces; linear mixed model followed by Tukey test: clone effect: χ²₂ = 10.2, p = 0.006; ancestral versus dnaQ: t = −3.7, df = 6, p = 0.022). Remarkably, the fitness defect of dnaQ is fully rescued by the dnaE mutation (Fig 2F), as the bacterial loads for the double mutant are similar to those for the ancestral strain (>10⁸ per gram of faeces; ancestral versus dnaQ+dnaE: t = 0.2, df = 6, p = 0.97; dnaQ versus dnaQ+dnaE: t = −3.5, df = 6, p = 0.029). These results are similar to those observed in vitro, when the strains grow in different nutrient sources. Taken together, our results establish that the dnaQ mutation massively increases mutation rate both in vitro and in vivo, albeit at a fitness cost. This cost can be recovered by a beneficial mutation in dnaE, without strong effects on mutation rate. The causes of mutation rate polymorphism are likely to be complex, as most mutator clones accumulated mutations in ≥3 genes that can affect mutation rates (e.g., a single clone can have mutations in dnaQ, dnaE, recF, katE, and sodB; S2 Fig). Interestingly, although clones with 1,000-fold increase in mutation rate (unknown genetic basis) have been observed in humans in the context of infection [17,56], to our knowledge, dnaQ mutators have not yet been reported in natural populations.

Survival of hypermutators indicates that deleterious mutations are of small effect

Clonal populations with very high genomic mutation rates can quickly accumulate many deleterious mutations and experience severe impediments on fixing adaptive mutations [57,58]. Because of the accumulating mutational load, such strong mutators may continuously decay in fitness (sensu Muller’s ratchet [59,60]) in a potentially inescapable path towards extinction [61,62]. However, we observe clones with 1,000-fold increase in mutation rate that coexist with nonmutators and intermediate mutators for >1,000 generations (Fig 1C) and a high variation in the number of accumulated mutations across mutator clones (Fig 2A). Furthermore, E. coli loads in mouse 1 are approximately 10-fold lower than in any other mouse (S1 Fig), specifically after the detection of mutators, which should lead to an even faster accumulation of mutational load. These observations raise two questions: Under which conditions can such strong mutators avoid a catastrophic fitness decline, caused by the accumulation of deleterious mutations [59,60]? And what conditions allow for coexistence between mutator and nonmutator clones?

To explore theoretical scenarios under which the above observations could be expected, we simulated clonal populations evolving under many mutation rate values and considered different assumptions for the fitness effects of mutations. We started by simulating the simplest model, assuming that all mutations are deleterious with a fixed and constant effect and ignoring neutral, lethal, compensatory, or beneficial mutations. We simulated populations of 10⁶ individuals (similar to E. coli’s population size in the gut; S1 Fig) under many combinations of mutation rate (U; per genome per generation) and the fitness effects of deleterious mutations (s_d; per generation). We then quantified mean fitness and the number of accumulated mutations after a time similar to that over which mutator maintenance was observed (1,000 and 2,000 generations). First, we consider fixed s_d values and show that for clones with a wild-type mutation rate (U = 0.001 per genome per generation), fitness remains at approximately 1 independently of s_d (Figs 3Ai and S7). However, when U > 0.1, fitness depends on s_d. At s_d values between 0.001 and 0.01, typical estimates from in vitro MA experiments with bacteria (which assume a constant s_d or estimate an average s_d) [31–35], the mean fitness of lineages with U > 0.5 declines to <0.68 within 1,000 generations (Fig 3Ai) and is even lower after 2,000 generations (see S7 Fig and S4 Table for a broader parameter space at 1,000 and 2,000 generations). Therefore the long-term persistence of such hypermutators is unlikely. In contrast, mean fitness remains high when s_d ≤ 0.0001, across mutation rates spanning three orders of magnitude, and the level of variation for the number of accumulated mutations in mutator populations is similar to what we observe in the evolution experiment (indicated by the boxed numbers in Fig 3Ai). Next, we assumed a fraction f_neut of neutral and 1 − f_neut of deleterious mutations with a fixed effect (Fig 3Aii and 3Aiii), since many mutations are expected to be neutral. Neutral mutations allow hypermutators to maintain high fitness across a wider range of s_d values. With f_neut = 0.9 (Fig 3Aiii), populations with high U may avoid extinction, for thousands of generations, even under s_d = 0.01. However, irrespectively of f_neut, when s_d ≤ 0.0001 mutator populations can maintain fitness at approximately 1 despite accumulating hundreds of mutations (Figs 3A and S7). These results suggest that coexistence between nonmutators and strong hypermutators is possible when s_d ≤ 0.0001 regardless of f_neut, or f_neut = 0.9, irrespectively of s_d. Simulations of populations with a 50:50 mixture of mutators (1,000-fold increase in mutation rate) and nonmutators competing for 1,000 generations (the minimum time over which mutators and nonmutators coexisted; Fig 1C) predict coexistence between mutator and nonmutator clones when s_d ≤ 0.0001 (Fig 3C) but not when s_d is 0.001 or 0.01. We note that lethal mutations are ignored in these simulations. These can be an important source of mutational load that could impair mutator persistence. Under a more realistic scenario, spontaneous mutations were assumed to follow an exponential distribution of deleterious effects (with mean effect s_d per generation). Under such conditions (Fig 3Bi and 3Di), we obtain results similar to those when s_d has a fixed and constant effect (Fig 3Ai and 3Ci).

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Fig 3. Strong, intermediate, and weak mutators can maintain high fitness and coexist if deleterious mutations have very weak effects.

(A-B) Simulations with a monoclonal population. Numbers indicate the mean number of mutations, and the colour gradient indicates mean fitness after 1,000 generations (initial fitness is 1). Numbers in bold and inside a box indicate the parameter space for which there is a fit between the observed and the simulated number of mutations (n = 10 simulations for panel Ai and n = 3 simulations for all others; see S4 and S5 Tables for the mean and standard deviation of fitness and the number of mutations). (C-D) Temporal dynamics of competition between two clones differing in mutation rate by 1,000-fold (U = 1 and U = 0.001 per genome per generation; equivalent to the DnaQ^L145P mutant and the ancestral, respectively; dynamics of 3 simulations per parameter combination are shown). All populations had 10⁶ individuals, which evolved under different distributions of the fitness effect of mutations. (A and C) Mutations were either all deleterious with a fixed fitness effect (panel i) or neutral, with a fraction of neutral mutations (f_neut) of 50% or 90% (panels ii-iii). (B and D) Either mutations were all deleterious (panel i), or a 1% fraction (f_ben) was beneficial. The fitness effects of deleterious and beneficial mutations were drawn from two independent exponential distributions, with mean effects being indicated in each panel (see S7, S8, S9, and S10 Figs for a broader exploration of the parameter space and S11, S12, S13, S14, and S15 Figs for N = 10⁵).

https://doi.org/10.1371/journal.pbio.3000617.g003

Next, we evaluated the impact of beneficial mutations. In vitro estimates suggest a fraction of beneficial mutations at 1% in E. coli (U_b = 10⁻⁵ per genome per generation) with average effect s_b = 0.01 (per generation; [63]). Moreover, strong-effect beneficial mutations have been inferred in the mouse gut (s_b between 0.02 and 0.12 per generation; [39,64]). Thus, we assumed different proportions of beneficial mutations (1% or 10%), with the fitness effects of deleterious and beneficial mutations drawn from two independent exponential distributions (with mean effect s_d or s_b per generation, respectively), which may or may not be symmetrical (we tested the following mean s_b: −s_d, −10s_d, 0.01, and 0.05). The occurrence of strong-effect beneficial mutations (s_b ≥ 0.01) leads to high variation in mean fitness under different U values, for large s_d (Figs 3Bii and 3Biii and S9 and S5 Table). Consistent with these results, coexistence between clones differing in mutation rate by 1,000-fold is short lived (<500 generations) across all s_d values when s_b ≥ 0.01 (Figs 3Dii and 3Diii and S10). Conversely, the number of observed mutations (Fig 2A) and the coexistence of clones with mutation rates differing by three orders of magnitude (for 1,000 generations) can be expected when s_b < 0.0001, but only if s_d ≤ 0.00001 (Figs 3Dii and 3Diii and S10; similar results were obtained with 10% of beneficial mutations).

The theoretical expectations, constrained by the experimental observations (in vivo accumulation of mutations and long-term maintenance of mutation rate polymorphism; Figs 1C, 2A, and 3), are consistent with low fitness effects of deleterious mutations. The same conclusion is reached under different distributions of the fitness effects of mutations and at two reasonable population sizes (see S11, S12, S13, S14, and S15 Figs for simulations under a population size of 10⁵). We note these simulations ignore temporal variation in the distribution of fitness effects of beneficial and deleterious mutations, which could affect the inferences. Thus, within the simplifying assumptions made in the simulations, the fitness effect of deleterious mutations in the mouse gut appears to be lower than what was previously inferred in vitro in rich media for E. coli from classical MA experiments (s_d ≈ 0.01 to 0.03, assuming a fixed effect; [31,32]) and closer to recent single-cell estimates (s_d ≈ 0.003; [35]).

To complement the inference from the simulations, we sought to experimentally compare the deleterious mutational load in vivo and in vitro. We tested clones with a large number of deleterious mutations, acquired under conditions of minimal selection, for their mutational load both in vitro and in the mouse gut. We used the double mutant DnaQ^L145P+DnaE^T771S, which should acquire about 1 new mutation per generation, to seed a short MA experiment. Two bacterial lineages were streaked on LB agar plates and allowed to grow from a single cell to 10⁸ cells, every 24 hours (i.e., approximately 25 generations per day). After 4 passages, we isolated clones (carrying a CFP marker) from the two independent MA lines (each line should have accumulated about 100 mutations) and competed these against the ancestral DnaQ^L145P+DnaE^T771S (carrying a YFP marker). As expected, fitness declined in all competitions (Fig 4A), but remarkably, the decline was much steeper in vitro than in vivo (Fig 4A and 4B). These data show that the same mutator lineage, loaded with deleterious mutations, will typically exhibit a lower mutational load in the gut than in rich LB media. Interestingly, one of the MA lines went extinct in vitro (it could not be detected in 3 of 4 replicates) but not in vivo. The combination of results indicates that levels of fitness decline are 10- and 4-fold lower for line 1 and 2 (respectively) in vivo than in vitro (linear mixed model: χ²₁ = 21.8, p < 0.0001). This difference between in vitro and in vivo is likely an underestimate, given that natural selection is not completely absent in MA experiments [34] and because we carried the MA and the in vitro competitions in LB.

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Fig 4. Competitive fitness assays demonstrate that the fitness effects of mutations are lower in the gut than in vitro.

A short MA experiment was performed, starting from a DnaQ^L145P+DnaE^T771S clone. Two lines were propagated for 4 passages (approximately 100 generations). These MA lines were propagated in conditions of nearly neutral evolution to accumulate many deleterious mutations. The evolved lines were then competed against the ancestral DnaQ^L145P+DnaE^T771S clone, either in vitro (for 1 day; approximately 10 generations) or in vivo, in the mouse gut (for 3 days; approximately 50 generations). (A) Temporal dynamics of the ratio between each evolved line and the ancestral, during 50 generations of competition. The natural logarithm of the ratio of the population sizes of the two genotypes is shown. Dashed line indicates the detection limit for colonies of the evolved lines. (B) Fitness decline for the two MA lines, when competing against the ancestral strain, both in vitro and in vivo. Fitness decline is estimated as the slope of the natural logarithm of the ratio between each evolved line and the ancestral. In 3 of the 4 in vitro replicates for line 1, we could not detect any colonies of the evolved clone. To estimate a fitness decline for these replicates, we assumed 1 colony for the evolved clone. We note that the values shown in Fig 4B are the fitness declines per generation of clones that have accumulated an unknown number of mutations and thus cannot be directly compared with the estimates of the fitness effect per deleterious mutation inferred in the simulations. MA, mutation accumulation.

https://doi.org/10.1371/journal.pbio.3000617.g004

The above experimental results concur with the inference from the simulations that the fitness effect of deleterious mutations is lower in vivo than in vitro. The estimated effects of deleterious, but nonlethal, mutations are compatible with the observed dynamics of mutators in a natural environment and close to typical estimates of the fitness effect of deleterious mutations obtained from analysis of natural polymorphism (e.g., for Drosophila, s_d ≈ 10⁻⁵ − 10⁻⁴ when estimated from natural polymorphism; [65,66]). Moreover, despite the gap in knowledge regarding the causes of polymorphism in commensal bacteria [67], the high level indicates that deleterious mutations should typically have small effects [68,69]. Remarkably, by analysing polymorphism patterns in species of the human gut microbiome (including E. coli), Garud and colleagues [5] recently estimated s_d/μ = 10⁵ (μ represents the mutation rate per site per generation). Given that our data indicate that the spontaneous mutation rate is similar in vitro and in vivo, if we take the mutation rate per site per generation estimated for E. coli from in vitro MA experiments (μ = 10⁻¹⁰ [70]), we obtain an s_d value of approximately 10⁻⁵, which is consistent with our results.

Adaptive mutations target metabolism and stress resistance

Whereas weak-effect deleterious mutations can explain the observed molecular evolution patterns, they cannot explain mutator invasion. In in vitro evolution experiments, mutators have been observed to invade through hitchhiking with beneficial mutations (i.e., mutations causing the mutator phenotype increase in frequency because these occur in the same genotype as a beneficial mutation; [24,71,72]). Given the fitness defect of the dnaQ mutation described above (in vitro and in vivo), and because beneficial mutations can rapidly emerge during adaptation to the mouse gut [38–40,73], we propose that hitchhiking is also the most likely route driving the observed increase in mutation rate. Thus, we sought to find signatures of adaptation in the mutator clones. First, we computed the ratio of the rates of nonsynonymous to synonymous mutations, dN/dS, to detect whether there was evidence of either purifying (dN/dS < 1) or positive selection (dN/dS > 1) [74]. Consistent with the above modelling inference, in which a large number of very slightly deleterious mutations, or even neutral mutations, accumulated in the mutators, dN/dS showed a weak signal of purifying selection (dN/dS < 1 in 3/13 clones; p < 0.05; S16 Fig). Furthermore, no signs of positive selection could be detected using this statistic (a well-known difficulty for clonal populations).

Because of the power of our experimental design, in which the same colonising lineages evolve independently in genetically identical animals under the same diet, one can identify beneficial mutations through mutational parallelism. We isolated 3 to 4 clones per mouse (from the remaining 3 mice) 190 days post colonisation and carried out whole-genome sequencing. We then identified genes or operons that had been repeatedly mutated across hosts (i.e., parallelism; S17 Fig) as likely targets of natural selection. Using this approach, we identified 12 targets, 8 of which were also mutated in the mutator clones. Of these, ptsP, frlR, and dgoR were mutated in all mutators (i.e., in the mutator common ancestor), whereas 5 other targets were mutated in at least two mutator clones (Fig 5).

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Fig 5. Multiple adaptive mutations accumulate in mutator and nonmutator clones without fixing, highlighting the importance of negative frequency–dependent selection.

(A) Clustering of clones depending on which candidate targets of adaptation are mutated. (B) Candidate mutational targets of adaptation that are mutated in each clone (different colours indicate different alleles). All targets that showed parallelism across mice are included, plus dnaE and rho, which were identified from parallelism across mutator clones and for which we have independent evidence of adaptation. Thirty-nine additional targets were identified through parallelism across mutator clones (S6 Table). (C) Number of mutations accumulated per clone. (D) Negative frequency–dependent selection can maintain stable coexistence for 1,000 generations between two clones differing in mutation rate (U) by 1,000-fold. A population of 10⁶ individuals, composed by a 50:50 mixture of two clones with U = 1 and U = 0.001 (per genome per generation), was simulated for 1,000 generations, while accumulating deleterious mutations of fixed effect s_d = 10⁻⁵. The genotypes of these clones include a locus that is under negative frequency–dependent selection of strength 0.1. Darker tones of grey indicate larger numbers of mutations; shades of blue oscillate every 10 accumulated mutations. The subpopulation with U = 1 rapidly accumulates many deleterious mutations, reaching about 1,000 mutations by the end of the simulation. In contrast, the majority of the subpopulation with U = 0.001 remains without any mutations until about 400 generations and has accumulated only up to 3 mutations by generation 1,000. IS, insertion sequence; non-syn., non-synonymous; SNP, single nucleotide polymorphism.

https://doi.org/10.1371/journal.pbio.3000617.g005

Most parallel targets in the mutators have a metabolic function, and some have been previously observed in other mouse gut colonisation experiments. Specifically, whereas ptsP is a novel target of adaptation, frlR and dgoR have been previously identified as targets of adaptation to the gut of streptomycin-treated immunocompromised or wild-type hosts, respectively [40,73]. frlR and dgoR are negative regulators of the frl and dgo operons [73,75,76], which are involved in carbon metabolism, namely of fructoselysine and galactonate (respectively). ptsP encodes a phosphoenolpyruvate-protein phosphotransferase, which is thought to be involved in the response to nitrogen availability and to several stresses (e.g., salt, pH) [77–79], both important pressures in the gut [80–82]. Of the three targets, dgoR is the most likely candidate for the adaptive mutation with which the dnaQ mutator allele could have hitchhiked, since dgoR is mutated in clones from all other mice, but only in the mutator clones from mouse 1. Furthermore, dgoR is the main target of adaptation when a uropathogenic E. coli colonises laboratory mice of a different genetic background [73]. This suggests that mutations in dgoR are strongly adaptive and such adaptation transcends the specific E. coli–mouse strain combinations. Interestingly, the mutations targeting dgoR and frlR (in this and in previous studies) often involve IS insertions, indels, or nonsense mutations. These are likely to lead to loss of function of the negative regulators and, thus, overexpression of the regulated operons. Such adaptive mutations are expected if galactonate and fructoselysine are present in the gut as limiting resources for E. coli. This form of adaptation has been previously shown to occur in the case of galactitol [64].

After divergence from their common ancestor, the mutators acquired potentially adaptive mutations in the cad operon, ycbC, atoC, psuK/fruA and fruB, and tdcA/tdcR. Of these targets, mutations in the last two have previously been observed during adaptation of E. coli to the gut of immune-competent or immunocompromised mice [40,41]. Many of the adaptive targets are functionally important for regulating carbon (dgoR, frlR, atoC, and, potentially, the cad operon) [77,83–85] or nitrogen metabolism (ptsP and tdcA/tdcR) [79,86,87], stress resistance (ptsP, cad operon, ycbC, and, potentially, atoC), and peptidoglycan biogenesis (ycbC) [77,83–85]. Interestingly, ptsP, atoC, and the cad operon appear to be involved in regulating both nutritional competence and stress resistance, which suggests that such mutations may modulate a potential trade-off between nutritional competence and stress resistance, which is well described in in vitro experiments and which is also thought to be important in vivo [81,82,88]. Together with dgoR, the cad operon is the only other mutational target that occurs in all other mice but is specific of mutator clones in mouse 1.

As the mutator clones have largely independent evolutionary histories (long terminal branches in Fig 2A), the concept of parallel evolution can also be used to identify adaptive targets that were specific to the mutator lineages. However, as the mutation rate is extremely high, parallel mutations can occur just by chance. Thus, we used simulations and conservative filters to identify genes for which the observed number of nonsynonymous single nucleotide polymorphisms (SNPs) is significantly higher than what would be expected if the observed mutations were randomly distributed (see Methods; [89]). Forty-one genes were identified with this method. Among these, we found dnaE and cadC, which had been identified as adaptive via direct experiments or through parallelism across hosts. Moreover, rho was also identified as a parallel target among mutators and is also mutated in one nonmutator clone, as well as during adaptation of adherent-invasive E. coli to the mouse gut [90]. These results suggest that this method is capable of identifying beneficial mutations. Of the identified genes, >50% were annotated to the following cluster of orthologous genes (COG) categories: energy production/conversion (5 genes), amino acid transport/metabolism (5 genes), signal transduction (5), and transcription (4). Among the latter two categories, most genes were involved in regulating carbon or amino acid metabolism (S6 Table). This indicates that a large fraction of mutator-specific adaptive mutations are also involved in nitrogen or carbon metabolism, which is in line with the above results.

Partial selective sweeps structure the high polymorphism of a commensal strain evolving in the mouse gut

Among the tens of adaptive mutations that we identified, none reached fixation. Indeed, even after 190 days of evolution (approximately 3,600 generations), no complete sweep could be observed, neither of a single mutation (hard sweep) nor of multiple, functionally equivalent lineages (soft sweep). This indicates that most beneficial mutations in this ecosystem are only conditionally beneficial. Thus, a more complex form of selection is likely causing the observed polymorphism. This could be mediated by strong clonal interference or spatial or metabolic structuring of niches within the gut and/or caused by forces such as temporally fluctuating or negative frequency–dependent selection (NFDS) (in which the fitness of a genotype increases as its relative abundance decreases). Despite the simplicity of the simulations (Fig 3), these suggest that strong clonal interference is probably not a main mechanism, as simulations with s_b ≥ 0.01 always lead to fixation of one of the competing clones (Figs 3D and S10 and S15), although coexistence is possible when s_b ≤ 0.001 (and s_d ≤ 0.0001). However, such low s_b values are at odds with the observation of strong mutational parallelism across the four animals and with previous estimates of the fitness effects of beneficial mutations in the mouse gut (which ranged from 2% to 12%, with an average of 5% [38–40,64]). A stronger candidate mechanism that could lead to coexistence under a wide range of effects of deleterious mutations is NFDS, which we have previously shown to be operating in the mouse gut [39,64]. To query whether NFDS plays a role in the observed dynamics, we tested whether loss of function of dgoR would be under this form of selection (dgoR is a strong candidate for the driver mutation leading mutators to increase in frequency). When performing in vivo competitions between a dgoR knock-out mutant and the ancestral strain, at two different starting frequencies, we find a signature of NFDS. The dgoR mutant decreases in frequency when it is inoculated at a high frequency but remains at about 10% when inoculated from a low frequency (S18 Fig). As mutations in dgoR are highly parallel across mice (and even across different E. coli–mouse combinations), such mutations must be advantageous when rare. An important role for NFDS is also in complete agreement with three observations: lack of fixation of adaptive mutations (Figs 5 and S17), long-term maintenance of polymorphism for mutation rate (Fig 1), and maintenance of variation at a neutral locus (YFP/CFP; S1 Fig). These are not expected under a regime in which adaptive mutations are unconditionally beneficial but are consistent with a regime in which adaptive mutations are advantageous at low frequency but disadvantageous at high frequency.

To evaluate how NFDS could lead to stable coexistence between two clones with markedly different rates of molecular evolution, we simulated a population with two clones, differing in mutation rate by 1,000-fold (U = 1 and U = 0.001), whose genotypes include a locus that is under NFDS of strength 0.1. These clones further acquire recurrent deleterious mutations of effect s_d = 10⁻⁵. Under these conditions, the two clones can coexist for at least 1,000 generations at a stable relative frequency of approximately 50% (Fig 5D; coexistence was unstable in the absence of NFDS; Fig 3Ai) and with markedly different patterns of molecular evolution, similar to those observed experimentally (Fig 5C). However, we note that a signature of negative frequency–dependent dynamics may also be caused by mechanisms such as temporally fluctuating selection or different metabolic or spatial niches within the gut [26,91,92], beyond the form of NFDS that we simulated (in which fitness of a genotype depends on the relative abundance of another). For example, if there are two independent metabolic niches with different carrying capacities, the dynamics of two genotypes occupying those niches can appear to be under NFDS but may actually be determined by the absolute density of each genotype (as we have previously seen in [64]). A similar argument could be made for spatial niches, as the mammalian gut is inherently spatially structured. The relevance of these mechanisms for maintaining diversity will depend on the rate at which bacterial strains transition between such niches. Thus, further work will be needed in order to understand the relevance of different ecological and evolutionary mechanisms and how the distribution of beneficial and deleterious mutations may change along time, for determining the genetic structure of microbial populations evolving within the gut.

Conclusions

The emergence and temporal dynamics of mutator populations can provide information on key evolutionary parameters when direct experimental measures may be difficult to obtain. Of key relevance, these can allow the fitness effects of deleterious mutations to be inferred [31–35]. Here, we studied the emergence of multiple mutator lineages during colonisation of the mouse gut, including a hypermutator with up to 1,000-fold increase in mutation rate. Under simplifying assumptions for the distribution of fitness effects of mutations, we found the pattern of molecular evolution to be consistent with effects of deleterious mutations < 10⁻⁴, smaller than in vitro estimates [31–35]. Competitions of MA lines, in vitro and in vivo, also indicate a lower mutational load in the mouse gut than in rich laboratory medium. The mammalian gut is a complex environment that may temporally fluctuate (e.g., variable diet or time of feeding), which could result in temporal variation of the effect of deleterious mutations, with a small time-averaged fitness effect. Indeed, we show in Fig 2D that the availability of particular resources might buffer the fitness effects of deleterious mutations. Moreover, in vitro experiments have shown that the presence of environmental stressors can lead to a reduction in the fitness effect of deleterious mutations [93]. Another mechanism for reducing the effects of deleterious mutations is revealed by the nature of the adaptive mutations. As previously observed, adaptation of E. coli to the mouse gut involved mutations linked to carbohydrate metabolism, which appear to be under NFDS, likely created by niche segregation of the different mutants [39,64]. This segregation may reduce competition between lineages and therefore buffer the effect of deleterious mutations.

The low effect of deleterious mutations should lead to weak purifying selection, which we detect in the form of a genome-wide dN/dS ≈ 1 (S16 Fig). Analysis of human metagenomics data also shows a dN/dS ≈ 1 for closely related strains with a dS ≈ 10⁻⁵, similar to the dS for the mutator clones studied here. However, as is typical for bacteria [94], dN/dS declines with increasing dS, reaching dN/dS of approximately 0.1 at dS ≈ 0.01, indicating strong purifying selection for divergent strains. This might suggest that different forces are affecting the genetic composition of populations on short versus long time scales. Transmission is a key force that is expected to become more important as time passes. Transmission could intensify genetic drift but also increase the strength of purifying selection. For example, deleterious mutations could be lost when transmitted across hosts if their effects are stronger in a new host (relative to the host where these emerged) or if they are hitchhiking with host-specific advantageous mutations [5,8]. More generally, understanding the effects of deleterious mutations may be of relevance for a variety of processes both within the gut microbiota (e.g., evolution of antibiotic resistance) and beyond this ecosystem (e.g., cancer evolution). As an example, it has recently been shown that tumour mutational load can be a predictor of survival for some, but not all, types of cancer [95]. Our work suggests that determining the fitness effect of deleterious mutations may be key to understand these differences.

Overall, our work suggests that the evolutionary dynamics of gut commensals may be strongly shaped by beneficial mutations, which increase in frequency but do not fix (partial sweeps), and slightly deleterious mutations that can remain in the population for long periods of time. The combination of these two effects could allow strains of the same species to coexist within the gut microbiota for extended periods with complex temporal dynamics. Novel data on temporal dynamics of genetic polymorphism in species of human gut commensals are starting to confirm this prediction, at least for some species [5–8]. As genetic diversity can impact community composition [96], more time-series data (similar to the data obtained here) are needed for a full understanding of the selective mechanisms that shape microbiota eco-evolutionary dynamics [97,98].

Ethics statement

This research project was ethically reviewed and approved by both the Ethics Committee and the Animal Welfare Body of the Instituto Gulbenkian de Ciência (licence references: A009.2010 and A009.2018) and by the Portuguese National Entity that regulates the use of laboratory animals (Direção Geral de Alimentação e Veterinária [DGAV], licence reference: 009676). 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.

Bacterial strains

Strains used in this manuscript derive from the commensal E. coli K12, substrain MG1655 [99], and are named JB19-YFP, JB18-CFP, RR03-YFP, and RR04-CFP. JB19-YFP and JB18-CFP were previously described in [39]. The four strains carry a streptomycin-resistance mutation RpsL^K43R, a deletion of the lac operon (ΔlacIZYA), and a fluorescent protein (YFP or CFP) linked to either a chloramphenicol (JB18 and JB19) or ampicillin (RR03 and RR04) resistance cassette that is inserted at the galK locus. Additionally, all strains carry mutations that were previously shown to be adaptive in the mouse gut [38,39]. JB18 and JB19 carry a 1-bp frameshift insertion in gatC. RR03 and RR04 carry the same 1-bp frameshift insertion in gatC, an IS2 insertion, and a 4-bp insertion in the intergenic regions between yjjP and yjjQ and between yjjY and yjtD (respectively). The mutations yjjP/yjjQ::IS2 and yjjY/yjtD::4 bp were acquired after adapting strain JB19-YFP to the mouse gut for 24 days [39]. P1 transductions [100] were then used to replace the construct with YFP and the chloramphenicol resistance cassette by an ampicillin resistance cassette coupled with either YFP or CFP, thus creating strains RR03-YFP and RR04-CFP.

Mice

All experiments were carried using 6- to 8-week-old C57BL/6J male mice raised in specific pathogen-free conditions.

In vivo experimental evolution

To simulate a perturbation of the mouse gut microbiota and allow its invasion by E. coli, we provided mice with streptomycin-treated water (5 g/L) [38,82] for 24 hours before gavage with E. coli and during 1 week post colonisation (Fig 1A). After this period, mice were given normal water until day 190 post colonisation. On the day of gavage, food and water were removed from the cage for 4 hours. Following this period, mice were gavaged with 10⁸ E. coli (suspended in 100 μl PBS). Four mice were used in this experiment, two of which were gavaged with a mixture of RR03-YFP and JB18-CFP and the other two with a mixture of RR04-CFP and JB19-YFP. Clones RR03/RR04 represented 10% of the cells in the inoculum, whereas clones JB18/JB19 represented 90%. These inocula were prepared by growing each clone separately in brain heart infusion (BHI) medium to OD_600nm = 2 (at 37°C on an orbital shaker). After gavage, animals were separated into individual cages, and water and food were returned to them. Colonisation of each mouse was then followed for 190 days. We estimated that 190 days of evolution in the mouse gut correspond to approximately 3,600 generations, assuming 19 generations/day, which was the generation time that we previously measured in streptomycin-treated mice [40]. In this experiment, mice are under streptomycin treatment for 1 week, which reduces microbiota diversity [28,40]. Since mice are individually caged and housing conditions impose a high level of sterility, restoration of the microbiota to a high diversity state, which would lead to increases in generation time [101], does not occur.

At each sampling point, faecal pellets were collected, weighed, and dissolved in PBS, with the remaining volume being stored at −80°C in 15% glycerol. Dilutions were made for plating in LB agar with streptomycin (100 μg/ml; or streptomycin [100 μg/ml] + ampicillin [100 μg/ml]/streptomycin [100 μg/ml] + chloramphenicol [30 μg/ml]) and plates incubated overnight at 37°C. CFP and YFP colonies were then counted on a fluorescent stereoscope (SteREO Lumar, Carl Zeiss) to estimate total numbers of E. coli and the frequency of YFP and CFP clones (S1 Fig).

Mutator screen and fluctuation tests to estimate mutation rate

Whole-genome sequencing and analysis

Allelic reconstructions and P1 transductions

The mutations DnaQ^L145P (CTC→CCC) and DnaE^T771S (ACG→TCG) were constructed by pORTMAGE recombineering [123] in the ancestral (RR04-CFP) background, with the pORTMAGE-3 plasmid (carrying the kanamycin resistance cassette; oligomers are listed in S7 Table). The double mutant was constructed with the same method, by inserting the DnaQ^L145P mutation in the dnaE background. The presence of these mutations was confirmed by PCR and Sanger sequencing. Subsequently, we grew each clone in LB to lose the pORTMAGE plasmid (this was confirmed by streaking the clones in LB agar plates with or without kanamycin, 100 μg/ml). P1 transductions were used to construct the following clones: a YFP-expressing DnaQ^L145P+DnaE^T771S mutant and a ΔdgoR mutant. The YFP-expressing DnaQ^L145P+DnaE^T771S strain was created by replacing the CFP and ampicillin resistance cassette by a chloramphenicol resistance cassette coupled with YFP. The ΔdgoR strain was created by replacing the wild-type dgoR in RR04-CFP by the respective knock-out from the KEIO collection (strain JW5627; [124]), in which the dgoR sequence is replaced by a kanamycin resistance cassette.

In vivo and in vitro mutation frequency temporal dynamics

To measure the in vivo mutation frequency (Fig 2E and 2F), we inoculated different mice with one of three different clones: ancestral (RR04), a DnaQ^L145P single mutant (dnaQ; randomly chosen from the clones with highest mutation rate), and a DnaQ^L145P + DnaE^T771S double mutant (dnaQ+dnaE; chosen as for single dnaQ clone). All clones carry the CFP marker.

Mice were provided with streptomycin-treated water (5 g/L) for 7 days before gavage with E. coli. Four hours before gavage, food and water were removed from the cages. After gavage, animals were separated into individual cages, and food and normal water (without streptomycin) were returned to them. To prepare the inoculum for these experiments, we defrosted each clone into PBS and plated in LB agar plates. After overnight incubation at 37°C, colonies were scrapped into PBS and OD_600nm adjusted to 2. One hundred microlitres of this suspension was then used to inoculate each mouse (i.e., 10⁸ E. coli). Independent replicate inocula were used to colonise independent mice. This procedure for preparing the inocula is different from the above because we wanted to minimise the strength of selection for compensatory mutations. These could reduce the mutation rate and/or the growth effects of the mutations (growth in liquid media, in which competition is global, is known to lead to more rapid adaptation than in solid media, in which competition is local; [125]). Faecal samples were then obtained at 6 hours and every 24 hours after gavage for 4 days and suspended in PBS. These were directly plated in LB agar plates with streptomycin and rifampicin to quantify the number of de novo Rif^R mutants, and dilutions were made to plate in LB agar plates with streptomycin to quantify the total number of E. coli (all clones are streptomycin-resistant). These two numbers were then used to estimate the equilibrium mutation frequency, which is proportional to mutation rate (as described in the Results section). Three mice were inoculated with each of the three clones to measure the mutation frequency towards rifampicin (Fig 2E and 2F). This experiment was repeated with two mice per clone, in order to measure the mutation frequency towards nalidixic acid (S6 Fig).

As we had estimated mutation rate in vitro with fluctuation tests, we carried a control experiment to understand if the equilibrium mutation frequency was similar between the in vitro and in vivo conditions. For this, we prepared the inocula of the three different clones as described above but started cultures with 10⁶ E. coli in 3 ml liquid LB (in 15-ml tubes). Cultures were incubated for 24 hours at 37°C in an orbital shaker. Every 24 hours, cultures were diluted 1,000-fold and allowed to grow until saturation (population size ≈ 3 to 5 × 10⁹; 10 generations per day). This procedure was repeated for 4 passages. Every day, the cells were plated as described for the in vivo experiment. The results of this experiment showed that the mutation frequency for all mutants was similar between the in vitro and the in vivo conditions (S5 Fig).

We used linear mixed models (with the R package nlme, v3.1 [126]) to analyse the temporal dynamics of mutation frequency and bacterial density, with replicate as a random effect. Both mutation frequency and bacterial density were log₁₀ transformed in order to meet the assumptions made by parametric statistics.

In vitro growth assays in different media

Bacteria were defrosted into 150 μl of liquid LB, grown overnight in a 96-well plate, and incubated at 37°C in a plate shaker (at 800 rpm). OD_600nm was then adjusted to 0.01, cultures were diluted 1:100, and 5 μl was spotted in agar plates and incubated at 37°C for 48 hours. After incubation, growth of each clone was imaged on a fluorescent stereoscope (SteREO Lumar, Carl Zeiss). The same inocula were tested across all media. The media used were LB and M9 minimal media with 0.4% glucose, 0.4% sorbitol, and 0.4% glucose plus the 20 proteinogenic amino acids (each at 0.05 mM) (Fig 2D).

MA coupled with in vitro and in vivo competitions

In vivo competitions to test for NFDS on ΔdgoR

Mice received streptomycin-treated water for 7 days before gavage and were gavaged as described above. Inocula for gavage were prepared by mixing the ΔdgoR mutant with the ancestral (RR03-YFP) at a ratio of 9:1 or 1:9.

Statistical analysis

All analyses were performed in R, version 3.5.1 [127], using the statistical methods described in the previous sections.

Simulations of evolving populations

Simulations were written in Mathematica [128] or C++. The annotated simulation codes are freely available online from Figshare at https://doi.org/10.6084/m9.figshare.10048427.v1.

Simulations of evolving clonal populations that can acquire deleterious mutations of fixed effects were implemented similar to those in [61]. Beginning with a mutation-free population of 10⁵ or 10⁶ individuals, at each generation mutations were drawn from a Poisson distribution with parameter U (mutation rate). The fitness of each individual was computed as w_i = (1 − s_d)ⁱ, where i is the number of mutations carried, and s_d > 0 is the deleterious selection coefficient. The next generation of the population was obtained by sampling 10⁶ individuals from the current population according to probabilities weighed by the individuals' absolute fitness. After 1,000 and 2,000 generations, respectively, we recorded the minimum number of mutations accumulated within the population (i.e., number of mutations in the least-loaded class), the mean and standard deviation of the number of mutations carried across the whole population, and the mean and standard deviation of fitness within the population.

For the model that includes neutral mutations, we performed the same simulations with two classes of mutations, a deleterious class with mutation rate U*(1 − f_neut) and selection coefficient s_d and a neutral class with mutation rate U*f_neut and selection coefficient 0.

For the model with a continuous distribution of fitness effects (Figs 3B and 3D and S8, S9, S10, S12, S13, and S15), upon mutation, an individual fitness effect per mutation was drawn from an exponential distribution with mean s_d. When including a proportion of beneficial mutations, these were drawn from an exponential distribution with mean s_b. As described for the model with neutral mutation, the simulation was performed with two classes of mutations, and the total fitness was computed as the product of the individual fitnesses 1 + s_b,i and 1 + s_d,i of all beneficial and deleterious mutations an individual carried, respectively.

For any parameter combination, we considered that the number of mutations in the simulations fitted those in the experiments if the number of mutations in the simulations was contained within the range of the number of observed mutations across clones (Figs 3A and 3B and S7, S8, S9, S11, S12, and S13).

For simulations of two subpopulations with different mutation rates (Figs 3C and 3D and S10, S14, and S15), a marker locus was implemented that determines the mutation rate within the subpopulation built by its carriers. The number of individuals of subpopulation 1 in the next generation was sampled from a binomial distribution with parameters N = 10⁶ and , where W_k is the total fitness of subpopulation k at generation t (i.e., the sum of all current individual fitnesses in this subpopulation). The number of individuals in subpopulation 2 was then determined as . These simulations were performed both for fixed-effect deleterious mutations (with or without neutral mutations) and for an exponential distribution of fitness effects.

Finally, for simulations with NFDS (Fig 5D), the number of individuals of subpopulation 1 in the next generation was sampled from a binomial distribution with parameters N = 10⁶ and where s_freq = 0.1.