The probability of spontaneous genetic mutations occurring during replication evolves among organisms. This mutation rate can also vary at a particular site in a particular genotype, dependent upon the environment.
The probability of spontaneous genetic mutations occurring during replication evolves among organisms . This mutation rate can also vary at a particular site in a particular genotype, dependent upon the environment . Specifically, mutation rate can increase with endogenous and exogenous factors . Indeed, any factor that affects the balance between mutagenesis and DNA repair can modify the mutation rate. These include intracellular nucleotide pools , organism age , and factors affecting the expression  and stochastic presence or absence  of low copy number repair proteins. Where such mutation/repair-balance factors depend on the environment, the result is mutation-rate plasticity. Plastic mutation rates have been most thoroughly addressed for stress-induced mutagenesis. This may involve the induction of error-prone polymerases, for instance, in the E. coli SOS response . We have recently identified a novel mode of mutation-rate plasticity in response to population density in E. coli. This plasticity does not have any very obvious association with stress—the densest populations, experiencing the most competition, show the lowest mutation rates .
Understanding mutation-rate plasticity is hampered by the difficulty of accurately measuring any mutation rate. Spontaneous mutation rates have long been estimated in microbes using counts of cells gaining a phenotypic marker of mutation in environments lacking selection for that marker: the “fluctuation test” created by Luria and Delbrück in 1943 . Alternative approaches to measuring rates of mutation in the absence of selection, such as accumulation of mutations through many population bottlenecks , directly comparing genome sequences of parents and offspring , or targeted population sequencing , are much more laborious and thus poorly suited to potentially dynamic responses. Therefore, well-conducted fluctuation tests , remain the most appropriate tool to assay environmental dependence in mutation rates.
Population density affects many traits, particularly in microbes . Its association with mutation rate has great potential to affect evolutionary trajectories  in ways relevant to the evolution of antimicrobial resistance . However, thus far, this plasticity associated with population density is poorly understood: Its prevalence across domains of life is unknown. Whether it varies among organisms, enabling its evolution, remains to be tested. A little is known about the relationship of mutation rate with density perception in 1 organism , but the required downstream mechanisms of mutation or repair remain uncharacterised. Here, we address each of these issues. We demonstrate that there is indeed density-associated mutation-rate plasticity (DAMP) across domains of life: high population density is associated with low mutation rates. DAMP differs between closely related organisms, indicating that this trait does indeed evolve. Strikingly, the same mutation avoidance mechanism is required to modulate mutation rate in response to population density in both prokaryotes and eukaryotes.
In order to test the nature and prevalence of mutation-rate plasticity, we considered over 70 years of published mutation rates estimated by fluctuation test. We collated 474 individual mutation-rate estimates from 68 independent studies that conducted fluctuation tests in organisms of 26 species from all domains of life and viruses, in which the final population density (D) an organism’s population reached was either reported or could be obtained from the original authors (Fig 1 and S1 Table).
Fig 1. Mutation rates published from 1943 to 2017 in relation to population density.
Colour indicates organism, and shape indicates domain: Archaea (circle), Bacteria (triangle), Eukaryota (square), and viruses/bacteriophage (diamond). Mutation rates were estimated using a wide variety of phenotypic markers (N = 70). The genetic basis and number of mutations giving each phenotype varies and is not known for all markers (i.e., different mutation rates may be generated from the same underlying per base-pair rate). Population densities are estimated by different techniques (cell counts, colony-, or plaque-forming units). See Results, Materials and Methods, and Model S-I in S1 Text for statistical analysis accounting for these and other differences. Note the logarithmic axes. Raw data is available in S1 Data.
There is a clear negative association between mutation rate and D (Spearman’s ρ = −0.66), spanning more than 6 orders of magnitude in both measures. This association potentially involves both between- and within-organism variation in mutation rate. We therefore analysed this relationship using a linear mixed-effects model (Model S-I in S1 Text), accounting for various features of the original experiments (organism, culture media, phenotypic marker, publication, and phylogenetic relationships among organisms). We find that, having taken all these factors into account, changes in D explain 93% of variation in published mutation-rate estimates (N = 474, LR1 = 22, P = 2.9×10−6; Model S-I in S1 Text). The model identifies substantial variation between-organisms in a negative within-organism association of mutation rate with D (slope varies from −0.46 to −0.98; S2 Fig). The average slope across organisms is −0.67 (−0.89 to −0.48 CI), meaning that mutation rate doubles with a 64% reduction in D (54% to 76% CI), quantitatively similar to the plasticity reported for E. coli B strains , in which the figure is 77% (61% to 96% CI).
Despite the striking association shown in Fig 1, the relationship could originate in various processes, including, but not limited to, mutation-rate plasticity. We consider several hypotheses: 1. Technical bias: (1a) The same estimate of final population size (Nt) is typically used to calculate both D and the mutation rate. Therefore, any error in Nt could itself lead to a negative association between mutation rate and D. (1b) Fluctuation tests typically assume that the phenotypic markers used are selectively neutral; however, in practice, this is not always the case. If cultures grown to higher D also, typically, go through more generations, a systematic tendency towards phenotypic markers being costly could lead to underestimated mutation rates, specifically at high D. 2. Reporting bias: there could be an underrepresentation of reported low mutation rates at low D and high mutation rates at high D. This is expected because standard volume microbial cultures with low D may not have sufficient mutational events at marker loci to achieve good estimates of low mutation rates. Similarly, in dense populations, high mutation rates can produce more mutants than it is practical to count. 3. DAMP: the relationship in Fig 1 is consistent with DAMP across domains of life. However, the data in Fig 1 comes from diverse studies using very different experimental and analytical set-ups. It remains for us to test the association at different marker loci in different organisms within a single experimental and analytical framework.
To test these hypotheses, we focused on the 2 most-diverged genetic model organisms in Fig 1: the bacterium E. coli (strain MG1655) and the eukaryotic yeast S. cerevisiae (strains S288C, BY4742 and Sigma1278b). Using fluctuation tests, we estimated mutation rates in batch cultures at 2 marker loci in each organism: rpoB and gyrA in E. coli and 25S ribosomal proteins and URA3 in S. cerevisiae (see Materials and Methods). These confer resistance to antibiotics rifampicin, nalidixic acid, hygromycin B, and 5-Fluoro-orotic acid (5-FOA), respectively. In each case, we varied culture volume and added nutrients to give different D (see Materials and Methods). To test hypothesis 1a (correlation of errors), we estimated Nt by 2 independent methods for each organism: an ATP-based luminescence assay and colony-forming units (CFU) for bacteria, haemocytometer cell counts (CC) and CFU for yeast. Using CFU to estimate mutation rate (typical in Fig 1) and any of the 3 methods to estimate D (Fig 2 and S4 Fig), we find significant variation of mutation rates with changing D: mutation rate varies from 5-fold to 23-fold across both loci in all organisms, where mutation rate is lower at high D (Fig 2). This refutes hypothesis 1a that the broad association between population density and mutation rate (Fig 1) is caused by a correlation of errors.
Fig 2. Density-associated mutation-rate plasticity (DAMP) in bacteria and yeast.
(A) Mutation rates to rifampicin (triangles) and nalidixic acid (circles) resistance in E. coliMG1655 (dark blue, N = 77) and P. aeruginosa PAO1 (light blue, N = 40); lines from Model S-II in S1 Text: Wald test t80 = 11; P = 1.7×10−18 that E. coli slope is 0; t80 = 1.2, P = 0.22 that P. aeruginosa slope is 0. Lines are plotted separately for the 2 E. colimarkers because there are more mutations conferring rifampicin resistance (in the rpoBgene) than nalidixic acid resistance (in the gyrA gene), resulting in different overall rates. (B) Mutation rates to hygromycin B (squares) and 5-Fluoro-orotic acid (5-FOA, diamonds) resistance in S. cerevisiae BY4742 (brown, N = 46), Sigma1278b (orange, N = 41), and S288C (red, N = 24); lines from Model S-III in S1 Text: t81 = 9.6; P =4.3×10−15 Wald test that average S. cerevisiae slope with D is 0; likelihood ratio test that slopes are equal among strains LR1 = 17, P = 4.1×10−5. Open shapes denote mutation-rate estimates that would typically be excluded because the estimated number of mutational events per culture, m, is either below 0.3 or above 30. Population densities estimated by ATP-based assay in (A) and direct cell counts in (B). See main text for the slope estimates of the given lines. Note the logarithmic axes. Raw data are available in S1 Data.
To test hypothesis 1b (costs of marker mutations) for the association between population density and mutation rate, we first considered the fitness effects of resistance mutations. Others have found small negative effects (12% on average in Pseudomonas aeruginosa ) and sometimes positive effects on fitness of mutations at the rpoB locus considered in Fig 2A[19,20]. Consistent with this, the fitness effects of mutations in our experiments are, on average, close to neutral (S5 Fig) and, where present, are similar across population densities (S6 Fig). Secondly, we reanalysed the data in Fig 2 assuming different average fitness effects of resistance mutations. We find that, even assuming large fitness costs (>50%), there is only a small flattening of the negative slope (S5 Fig). Thus, it is highly unlikely that the differential growth of resistant strains is responsible for the slopes seen in Fig 2, refuting hypothesis 1b that the association in Fig 1 may be accounted for by technical bias driven by differential growth of mutant strains.
Typically, mutation rates at which the estimated number of mutational events per culture (m) is either too low (<0.3) or too high (>30) are excluded and may not be reported . To test hypothesis 2 (reporting bias) we kept a close account of all estimates. Those 34 estimates that would typically be excluded are shown as open symbols in Fig 2. As expected, these points fall in either the lower left or upper right of the data. Nonetheless, the association between D and mutation rate is similar and highly significant with or without these data (−0.68 [−0.80 to −0.56 CI] versus −0.68 [−0.79 to −0.56 CI] in E. coli and, on average, −0.65 [−0.79 to −0.52 CI] versus −0.48 [−0.63 to −0.33] in S. cerevisiae), refuting hypothesis 2—that the negative association between population density and mutation rate in Fig 1 is caused by reporting bias. In contrast, our findings from different loci and different organisms within a single experimental and analytical framework are consistent with the pattern across the literature (Fig 1 and S7 Fig), strongly supporting hypothesis 3—that there is negative DAMP across the domains of life.
Our assays in S. cerevisiae identify significant variation in DAMP slope among strains (Fig 2B): the slope for S288C and Sigma1278b is −0.98 (−1.2 to −0.73 CI), whereas in BY4742, it is −0.32 (−0.40 to −0.25 CI). This limited difference in plasticity suggests that this trait may evolve. To investigate the extent of interorganism variation in DAMP, we tested another model organism, much more closely related to E. coli: P. aeruginosa PAO1 (both are gram-negative gamma Proteobacteria). We find P. aeruginosa has a greatly reduced DAMP slope relative to E. coli, not significantly different from 0 (Fig 2A and S4A Fig, slope estimate −0.15 [−0.40 to +0.095 CI], Model S-II in S1 Text). This indicates that, while DAMP is very widespread, it has evolved among closely related organisms.
Diverse mechanisms, some broadly conserved, could in principle be modulated to give DAMP. These include polymerases used for DNA replication and repair, some of which are more error-prone than others , and systems that repair mutational mismatches  or remove mutagenic nucleotides before they can be incorporated into DNA . To identify mechanisms by which the observed DAMP occurs, we tested E. coli strains deleted for genes involved in these processes (S2 Table). A strain lacking the error-prone polymerase Pol IV (encoded by dinB), implicated in stress-induced mutagenesis , displays DAMP (Fig 3; −1.1 [−1.3 to −1.00 CI]). E. coli’s methyl-directed DNA mismatch repair (MMR) system was hypothesised to be involved in DAMP . Despite >100-fold increases in mutation rates, strains lacking MMR proteins (MutH, MutL, and MutS) still display DAMP, albeit with a less steep slope (Fig 3; −0.20 [−0.30 to −0.11 CI]). We also considered other systems potentially associated with DAMP: a strain lacking MetI (Fig 3), a transporter protein responsible for feeding methionine to the activated methyl cycle, which was previously implicated in DAMP . Despite growing over only a relatively narrow range of densities, the metI deletant shows DAMP with a slope indistinguishable from the dinB deletant, as does a strain lacking Dam methylase, required for MMR to identify the ‘correct’ DNA strand (Fig 3). Finally, a strain lacking Endonuclease VIII (encoded by nei in E. coli) also shows DAMP, with the greatest slope among all these strains (Fig 3, −1.5 [−1.8 to −1.3 CI]).
Fig 3. Density-associated mutation-rate plasticity (DAMP) in strains of E. coli with deficiencies in various DNA repair and other systems.
Mutation rate in strains from the Keio collection  deleted for genes encoding deoxyadenosine methylase (Δdam, N = 23, yellow triangles), error-prone DNA polymerase Pol IV (ΔdinB, N = 25, pink triangles), methionine transporter MetI (ΔmetI, N = 10, light green triangles), endonuclease VIII (Δnei, N = 15, dark green triangles), and each protein of methyl-directed DNA mismatch repair (MMR), which comprises MutS (ΔmutS, N = 28, light blue circles) that binds mismatched DNA and MutL (ΔmutL, N = 27, dark blue circles) that interacts with MutS to activate endonuclease MutH (ΔmutH, N =24, medium blue circles). All lines result from Model S-VII in S1 Text. Wald tests that average slope for Δdam, ΔdinB, and ΔmetI is 0: t92 = 17; P = 4.2×10−30, that average slope for Δnei is 0: t91 = 13; P = 6.0×10−22, and that average slope for MMR strains is 0: t91 = 4.3; P = 5.1×10−5. See S2 Table for further strain details. Densities estimated by ATP-based luminescence assay. As in Fig 2, triangles and circles indicate mutation rates to rifampicin and nalidixic acid resistance, respectively. Note the logarithmic axes. Raw data are available in S1 Data.
In contrast to the systems tested above, mutT deletion removed the dependence of mutation rate on D (Fig 4A and S8A Fig, likelihood ratio test of slope N = 63, LR1 = 1.5; P = 0.22, Model S-VIII in S1 Text). MutT is the mutation-avoidance component of the 8-Hydroxyguanine (GO) system, protecting cells from mutagenic effects of damaged nucleotides . Specifically, the MutT Nudix hydrolase removes 8-oxo-dGTP from the free-nucleotide pool. This prevents AT to GC transversions, which occur when 8-oxo-dGTP is incorporated in place of a thymidine triphosphate nucleotide during DNA synthesis . The GO system also includes mutation-correction proteins MutM and MutY, which target 8-oxo-dGTP once incorporated in DNA . Strains lacking either protein display DAMP (Fig 4B and S8B Fig; Model S-X in S1 Text). Thus, while neither error-prone polymerase Pol IV nor the MMR system with Dam methylase is necessary (Fig 3), DAMP in E. coli (Fig 2A) requires scavenging the oxidised nucleotide 8-oxo-dGTP from the cellular pool.
Fig 4. Density-associated mutation-rate plasticity (DAMP) in cells lacking mutation-avoidance or -correction genes in E. coli and S. cerevisiae.
(A) Mutation rates to nalidixic acid resistance in 2 independent E. coli ΔmutT strains that share no secondary mutations (JW0097-1 and JW0097-3 S3 Table), dark and light blue, respectively (Model S-VIII in S1 Text) (B) Mutation rates to rifampicin resistance in E. coliΔmutM and ΔmutY strains (medium blue and light green, respectively), with equal slopes −1.1 (−1.2 to −1.04, CI) (N = 46, Model S-X in S1 Text) (C) Mutation rate to hygromycin B resistance in S. cerevisiae BY4742 and Sigma1278b PCD1-Δ strains (brown and orange, respectively, Model S-XII in S1 Text) (D) Mutation rate to 5-Fluoro-orotic acid (5-FOA) resistance in S. cerevisiae Sigma1278b MLH1-Δ (slope −1.22 [−1.44 to −1.01 CI], N = 26, Model S-XIV in S1 Text). Open shapes are as in Fig 2. Population density measured by ATP-based luminescence assay in (A) and (B) and via colony-forming unit (CFU) counts in (C) and (D). See also the main text for the slope estimates of the given lines. Note the logarithmic axes. Raw data are available in S1 Data.
Eukaryotes possess more, and more diverse, genes and systems for mutation avoidance and correction than bacteria. Nonetheless, the mutation-avoidance mechanism required for DAMP in E. coli is conserved across domains of life . PCD1 encodes the yeast 8-oxo-dGTPase functionally homologous to bacterial MutT . We tested PCD1-Δ strains in 2 different S. cerevisiae backgrounds (BY4742 and Sigma1278b). As in E. coli ΔmutT, mutation rates are greatly increased in PCD1-Δ, with no evidence of DAMP (Fig 4C and S8C Fig likelihood ratio test of slope N = 42, LR1 = 0.18, P = 0.67, Model S-XII in S1 Text). In contrast, MLH1, a yeast gene homologous to E. coli MMR gene mutL, displays DAMP (Fig 4D and S8D Fig; Model S-XIV in S1 Text). Therefore, DAMP not only occurs across domains of life, but, in the bacteria and eukaryotes tested, requires the same specific mutation-avoidance mechanism.
The negative association between published mutation rates and population density (D, Fig 1) is remarkably tight. Much of the between-organism variation in microbial mutation rate is associated with variation in genome size, in which larger genomes tend to have smaller per-base-pair mutation rates . We account for this in our analysis of the data in Fig 1 by allowing mutation rates to vary among organisms and accounting for their phylogeny (explicitly including a typical genome size for each organism makes little difference to this analysis, Model S-I in S1 Text). However, the within-organism variation in mutation rate associated with D is strong enough to explain radical differences in mutation-rate estimates for the same organism within and between laboratories, without assuming any inconsistency in the fluctuation test itself. For instance, the estimates for Salmonella at the bottom of Fig 1 vary by over an order of magnitude but diverge little from a negatively sloping straight line. This suggests that, once population density is taken into account, fluctuation tests can give a more precise estimate of mutation rate than previously believed.
Fluctuation tests, however, have drawbacks, such as the possibility of unanticipated selection on mutant cells in a supposedly nonselective environment . We avoided that specific issue here by using short incubation times and making estimates at multiple loci. The more general drawback of using fluctuation tests for considering environmental correlates (shared with most other methods for estimating mutation rates) is that they average across the time-varying environment of batch culture. Thus almost any environmental variable, including population density, has no fixed value and is itself associated with many other characteristics of the culture, both environmental and organismal (e.g., times spent in different phases of the culture cycle). Thus, while we have demonstrated an association of mutation rate with final population density D (Fig 2) and the dependence of that association on a downstream mechanism (Fig 4), the link between 8-oxo-dGTPase and D remains unclear. Nonetheless, 2 important things can be said about this link. First, DAMP is observed across a wide range of environmental conditions and organisms (Fig 1 and Fig 2), which argues that features of particular environments, such as the starting nutrient concentration, as manipulated here, are unlikely to provide a general link between D and mutation rate. Second, we have previously demonstrated that in 1 organism, E. coli, cell–cell interactions are involved in DAMP and deletion of a quorum-sensing gene (luxS) breaks the association between D and mutation rate , demonstrating that population interactions can be important for DAMP. Such quorum-sensing mechanisms occur widely (even in some phages ). Future work, therefore, needs to focus on asking whether DAMP is associated with particular environmental molecules.
Mutation rate is a central population genetic parameter. Across organisms, it is negatively associated with the other central population genetic parameter, effective population size (Ne) . In our experiments, despite 2 orders of magnitude variation in each measure, we find no consistent association between mutation rate and Ne (S9 Fig). This is unsurprising because the proposed reason for the negative association across organisms is that selection for replication fidelity is more efficient at higher Ne, meaning that, over the long term, average mutation rates evolve to be lower at higher Ne . In our short-term experiments, there is little opportunity for such evolutionary change to occur, so we do not see this association. Nonetheless, this reinforces the clear distinction between within-organism plasticity and among-organism variation in mutation rate. Both have shaped mutation rates in the published literature (Fig 1), and we are able to separate the 2, both statistically and by focused experiments (Fig 2). There may be links between the causes of among-organism variation and within-organism plasticity in mutation rate, for instance, in the differing opportunities for selection on replication fidelity in polymerases expressed in common or rare environmental conditions . However, the evolutionary causes and effects of within-organism plasticity in mutation rate in general, and DAMP in particular, need further investigation.
The evolutionary causes of plasticity in mutation rates need not be adaptive . Nonetheless, mutation is an evolutionary mechanism, so any plastic variation in mutation rates will have consequences for evolutionary trajectories . What the evolutionary consequences might be depend on how mutation rate associates with the environment. For evolutionary computing, in which mutation rate is controlled, understanding the effect of that control is an important area of research . In biology, constitutively high mutation rates can evolve under specific circumstances [33,34], but incur the costs of many, typically deleterious, mutations. If plasticity is such that mutation rate is inversely related to absolute organismal fitness, then organisms may benefit from a high mutation-supply rate without paying the full evolutionary cost of a constitutively raised mutation rate, as seen in mathematical studies of evolutionary systems  and population genetic models . In some circumstances, DAMP can result in such a negative association of mutation rate with fitness , but the evolutionary effects of this remain to be tested.
The probability of a particular mutational event occurring (e.g., the emergence of spontaneous antibiotic resistance) might be expected to increase with D, as denser populations, containing more cells, will have had more opportunity for mutation. But for the DAMP described here, this increase is offset by a reduction in the mutation rate. This offsetting means that for organisms with DAMP, numbers of mutational events per space and time vary much less with Nt than expected from a fixed mutation rate per generation (S10 Fig). Population genetic models typically consider mutations per replication to be constant for an organism. However, we find that the approximate constant is the number of mutational events per space and time (S10 Fig). This is consistent with observations of invariant numbers of mutations per time in Mycobacterium infections  and, indeed, in human somatic  and germ cells .
Both the occurrence across domains of life (Fig 2) and the conserved mutation avoidance mechanism required (Fig 4) point to an ancient evolutionary origin for DAMP. Furthermore, Fig 1 suggests that DAMP also occurs in viruses and bacteriophage. Any variation in mutation rates in viruses and phage lacking mutation-avoidance or -correction mechanisms must be mediated by the host environment. Consistent with this, we see different mutation rates, but similar DAMP, for the same RNA virus in different host cells (S11 Fig reanalysed from ). DAMP itself, therefore, seems closely related to basic processes of replication common to all organisms. Nonetheless, our findings are limited to organisms in which it is possible to assay mutation rate by fluctuation tests. This excludes multicellular eukaryotes, so how our findings might apply to them is unclear. Recent findings of variation in mitochondrial mutation rates at different population sizes and densities of the nematode Caenorhabditis elegans highlight the challenge of separating out what population density could mean at the organism, tissue, cellular, and subcellular (e.g., mitochondrial) levels . Even so, if it were possible to manipulate microbial DAMP clinically as well as genetically (Fig 4), for instance as a strategy to slow the rate at which antibiotic resistance arises , that could be applicable across the breadth of microbes, including pathogenic viruses.
We used MilliQ water for all media. Tetrazolium arabinose agar (TA), Davis minimal medium (DM), and M9 minimal medium were prepared according to . Luria-Bertani medium (LB), yeast extract peptone medium (YP), and yeast nitrogen base (YNB) were prepared according to manufacturers’ instructions. Magnesium sulphate heptahydrate, thiamine hydrochloride, carbon source (3 g/l L-arabinose or various concentrations of D-glucose), and 2,3,5-triphenyltetrazolium chloride (Sigma T8877) were sterile filtered and added to a cooled medium. Selective TA medium was supplemented with freshly prepared rifampicin (50 μg/ml) or nalidixic acid (30 μg/ml). Selective YP medium was supplemented with freshly prepared 5-FOA (1,000 μg/ml) or hygromycin B (300 μg/ml). For all cell dilutions, sterile saline (8.5 g/l NaCl) was used. All media were solidified as necessary with 15 g/l of agar (Difco).
We did fluctuation tests with E. coli and P. aeruginosa as explained in . In short, strains were first inoculated from frozen stock and grown in liquid LB medium at 37°C and then transferred to nonselective liquid DM (for E. coli) or M9 (for P. aeruginosa), supplemented with a particular concentration of glucose (25–300 mgl−1), and allowed to grow overnight shaking at 37°C. E. coli and P. aeruginosa were again diluted into fresh DM or M9 medium, respectively, giving the initial population size (N0) of around 10,000 (range 2.5×102 to 1.3×105) and 5,000 (range 2.5×103 to 1.2×104), respectively. Various volumes (0.5–10 ml) of parallel cultures were grown to saturation for 24 hours at 37°C in 96-deep-well plates or 50 ml falcon tubes. The position of each culture on a 96-well plate was chosen randomly. Nt of each culture was determined by 2 independent techniques. Nt was determined by CFU in which appropriate dilution was plated on a solid nonselective TA medium. Estimates of Nt using net luminescence were determined using a Promega GloMax luminometer and the Promega Bac-Titer Glo kit, according to manufacturer’s instructions. We measured the luminescence of each culture 0.5 seconds and 510 seconds after adding the Bac-Titer Glo reagent and calculated net luminescence as LUM = LUM510s − LUM0.5s. Each estimate of Nt is an average of 3 cultures. Evaporation (routinely monitored by weighing the plate before and after 24 hours of incubation) was accounted for in the Nt value determined by CFU and was also used in statistical modelling as a variance covariate. We obtained the observed number of mutants resistant to rifampicin or nalidixic acid, r, by plating the entirety of remaining cultures onto solid selective TA medium that allows spontaneous mutants to form colonies. Plates were incubated at 37°C, and mutants were counted at the earliest possible time after plating. For rifampicin plates, this was 44–48 hours, when nalidixic acid was used, the incubation time was 68–72 hours.
We did fluctuation tests with yeast in a similar way to fluctuation tests with bacteria (see above). Strains were inoculated from frozen stock in liquid YP medium with 20 mg/ml of glucose at 30°C (200 rpm) and then transferred to nonselective liquid YNB medium supplemented with a particular percentage of YP (v/v) and glucose, except for S288C in which YP was not added. We then allowed cultures to grow overnight at 30°C (200 rpm). Overnight cultures were again diluted into fresh medium giving N0 of around 5,000 per parallel culture (range 5×102 to 5.1×104). Various volumes of parallel cultures (0.35–10 ml) were grown in yeast nitrogen base with 25–8,000 mgl−1 glucose and 0%–7% v/v YP in 96-deep-well plates or in 50 ml falcon tubes to saturation for 48 or 72 hours at 30°C (200 rpm). We positioned each culture on the plate randomly. Nt was determined by CFU, in which an appropriate dilution was plated on solid nonselective YP medium. Nt determined with haemocytometer (Cellometer Auto M10 –Nexcelom) (CC) was done according to manufacturer’s instructions. Nt was calculated with 3 cultures per mutation-rate estimate, in which for each culture, CFU and CC were determined. Evaporation was accounted for in the Nt value determined by CFU and also used in statistical modelling as a variance covariate. We obtained the observed number of mutants resistant to 5-FOA or hygromycin B, r, by plating the entirety of remaining cultures onto solid selective YP medium. Plates were incubated at 30°C, and mutants were counted at the earliest possible time after plating, for both markers that was 68–72 hours.
For Figs 2A, 2B, 3, 4A, 4B, 4C and 4D, we used 21, 14, 14, 8, 5, 5, and 3 independent experimental blocks, respectively, carried out on different days. Within an experimental block, multiple 96-well plates, or groups of falcon tubes, were used. Any individual mutation-rate estimate requires multiple parallel cultures, which were all carried out on a particular plate, or group of falcon tubes. For Figs 2A, 2B, 3, 4A, 4B, 4C and 4D, the median number of parallel cultures used (with interquartile range) was 16 (15–16), 16 (16–16), 16 (16–16), 16 (16–16), 16 (16–16), 16 (16–16), and 16 (15–16), respectively.
To calculate m from the observed number of mutants, we employed the Ma-Sandri-Sarkar maximum-likelihood method implemented by the FALCOR web tool  or rSalvador [43,44]. The mutation rate per cell per generation is calculated as m divided by Nt. The median (with interquartile range) of the coefficient of variation for Nt estimated with CFU and ATP-based luminescence assay is 15.9% (9.6%–24.8%) and 10.9% (6.9%–18.4%), respectively. Ne is calculated as the harmonic mean of the population size across generations.
All statistical analysis was executed in R v3.2.4 and v3.3.1, respectively, when using spaMM v 1.7.2 (Model S-I, S1 Text) and nlme v3.1 (Model S-II to S-XVIII, S1 Text) packages for linear mixed effects modelling [45, 46]. This enabled the inclusion within the same model of experimental factors (fixed effects), blocking effects (random effects), and factors affecting variance (heteroscedasticity) as described in S1 Text. In all cases, the log2 mutation rate was used. Raw data (S1 Data, described in S4 Table) and R code (S1 Code) are provided, sufficient to reproduce Figs 1–4, S1, S3 and S4 Figs, S6 Fig and S8–S11 Figs.
E. coli genomes were sequenced with the Illumina HiSeq2500 platform using 2 x 250 bp paired-end reads. Sequencing and initial read quality checking were provided by MicrobesNG (http://www.microbesng.uk) and deposited at the European Nucleotide Archive (accession number ERP024110, http://www.ebi.ac.uk/ena/data/view/ERP024110). Strains derived from MG1655 and from the Keio collection were aligned to the E. coli str. K-12 substr. MG1655 (NC_000913.3) and E. coli BW25113 (NZ_CP009273.1) genomes, respectively. Mutations (i.e., single nucleotide substitutions, small and large indels, and copy number variants) were predicted using breseq-0.27.2 using the default settings .
We identified studies that used Luria-Delbrück fluctuation tests for estimating mutation rates. We considered all papers citing the original reference  and further searched the Google Scholar and Web of Science databases with keywords “mutation rate”, “Luria Delbruck”, “fluctuation test”, and “fluctuation assay”; we also considered papers cited by papers identified in this way. We collected mutation rate estimations from studies spanning over 70 years, starting with Luria and Delbrück’s pioneering paper in 1943 outlining the fluctuation test . In all, we collected 474 mutation rate estimations from 68 separate studies, covering 26 different organisms from across domains of life (Archaea, Bacteria, Eukaryota) and viruses. From these studies, we recorded the mutation rate estimation, the estimator used for calculating mutation rate, the D of parallel cultures, identity of the nonselective medium, the organism studied, the selective marker used and its concentration, and the study the estimate came from. We excluded estimates that (i) involved microorganisms cultured in intentionally selective conditions, (ii) used genetically manipulated or mutator strains, or (iii) did not plate the entire culture volume onto the selective media. Any of this information that was not included in the published article was collected via a direct communication with the corresponding author.
Where the number of observed mutants per plate was available and the estimator was not the Ma-Sandri-Sarkar maximum-likelihood method, we recalculated the mutation rate using this method implemented by the FALCOR web tool . When only the proportion of plates without mutants was available, we recalculated the mutation rate using the P0 method , implemented by equation −ln(P0)/Nt in which P0 is the proportion of plates containing no mutant colonies. For viral mutation rates, we recorded the mutation rate as substitutions per strand copying. Where the published mutation rates were not in this format, these were converted using equation 10 in . All these points are highlighted in the column ‘recalculation’ as ‘yes’ in S1 Data (see S4 Table).
To take account of the fact that organisms may show similarity (including in mutation rates) through common ancestry, we accounted for phylogenetic relatedness using a correlation matrix within our Model S-I (S1 Text). This matrix was derived from a phylogeny (S1 Fig) constructed from a combination of 3 published phylogenies. All the bacteria and archaea came from the ‘All-Species Living Tree’ Project (LTP)  version LTPs123, and this phylogeny was used to add other organisms. S. cerevisiae was taken from , and viruses were taken from . Branch lengths for S. cerevisiae and the viruses were scaled to correspond to those in the LTP tree as follows. For S. cerevisiae, average branch lengths from the tips to the last common ancestor of the archaea Halobacterium and Sulfolobus were compared for the LTP and Lane and Darst  trees. The ratio between them was applied to the branch length of S. cerevisiaein Lane and Darst phylogeny  before adding it to the LTP tree at the branch point of the bacteria and archaea. For the viruses, 4 common tips from both trees (P. aeruginosa, Thermus thermophilus, S. cerevisiae, and Halobacterium) were selected, and the distance of each to a shared common ancestor (P. aeruginosa with T. thermophilus and S. cerevisiae with Halobacterium) were plotted against each other. A straight line was then fitted through the origin, and the gradient of that line was used to correct the branch length of the viruses in the Nasir and Caetano-Anollés tree  before being added to the combined LTP/S. cerevisiae tree at the branch point of the 3 domains.
Some organisms in our analysis were not present in these phylogenies. These were as follows: separate serovars of Salmonella enterica (serovars Typhimurium and Enteritidis), which we treated as subspecies of S. enterica (indica and enterica, present in the tree); Vesicular stomatitis virus and Measles virus, which were combined into their common order of Mononegavirales; and Bacteriophage ΦX174, which was positioned at Bacteriophage M13.
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The probability of spontaneous genetic mutations occurring during replication evolves among organisms. This mutation rate can also vary at a particular site in a particular genotype, dependent upon the environment.