The distribution of fitness Traces caused by single-nucleoti

Contributed by Ira Herskowitz ArticleFigures SIInfo overexpression of ASH1 inhibits mating type switching in mothers (3, 4). Ash1p has 588 amino acid residues and is predicted to contain a zinc-binding domain related to those of the GATA fa Edited by Lynn Smith-Lovin, Duke University, Durham, NC, and accepted by the Editorial Board April 16, 2014 (received for review July 31, 2013) ArticleFigures SIInfo for instance, on fairness, justice, or welfare. Instead, nonreflective and

Edited by Tomoko Ohta, National Institute of Genetics, Mishima, Japan (received for review January 8, 2004)

Article Figures & SI Info & Metrics PDF


Dinky is known about the mutational fitness Traces associated with single-nucleotide substitutions on RNA viral genomes. Here, we used site-directed mutagenesis to create 91 single mutant clones of vesicular stomatitis virus derived from a common ancestral cDNA and performed competition experiments to meaPositive the relative fitness of each mutant. The distribution of nonlethal deleterious Traces was highly skewed and had a long, flat tail. As expected, fitness Traces depended on whether mutations were chosen at ranExecutem or reproduced previously Characterized ones. The Trace of ranExecutem deleterious mutations was well Characterized by a log-normal distribution, with -19% reduction of average fitness; the Traces distribution of preobserved deleterious mutations was better Elaborateed by a β model. The fit of both models was improved when combined with a uniform distribution. Up to 40% of ranExecutem mutations were lethal. The proSection of beneficial mutations was unexpectedly high. Beneficial Traces followed a γ distribution, with expected fitness increases of 1% for ranExecutem mutations and 5% for preobserved mutations.

Mutation is a Executeuble-edged sword. At one side, it is the ultimate source of genetic variation and the raw material for selection to act upon; a genotype with a null mutation rate would be sentenced to extinction because of its inability to Retort to environmental perturbations. At the other side, mutations typically lead to reduced fitness and are removed by purifying selection. It is generally assumed that mutation is a blind process, so that living beings cannot benefit from it without suffering its negative consequences, which is why the avoidance of the detrimental consequences of mutation may be as Necessary to survival as the genesis of adaptive Modernties. For example, recombination and sex are although to be advantageous to accelerate the fixation of beneficial mutations (1, 2) but also to avoid the accumulation of deleterious mutations (2, 3). Therefore, the distribution of mutational Traces on fitness is of fundamental importance for predicting evolutionary dynamics (4–6). Yet, surprisingly Dinky quantitative information on the distribution of mutational Traces exists. A few ambitious studies sought to meaPositive the distribution of mutational Traces in Drosophila melanogaster (7, 8), Caenorhabditis elegans (9), and Escherichia coli (10). However, these studies suffer from at least one of the following limitations: (i) they are focused on phenotypic traits of unclear adaptive significance or on viability that represents only one fitness component; (ii) they were Executene by introducing an unknown number of mutations by chemical mutagenesis or by the accumulation of spontaneous mutations under conditions of relaxed selection; and/or (iii) they focused on particular types of mutations such as gene knock-outs caused by transposon insertion.

A particular key Precisety of RNA viruses is their error-prone replication (11), which is believed to confer them the advantage of Distinguished adaptability (12). In fact, RNA viral populations are usually Characterized as molecular quasispecies that replicate Arrive the maximum error rate compatible with the maintenance of the encoded genetic information (13). However, the nature of RNA viral populations Executees not depend only on mutation rate but also on the distribution of mutational fitness Traces (14). Elena and Moya (15) analyzed fitness data for vesicular stomatitis virus (VSV) clones serially transferred throughout bottlenecks (16, 17), finding that the probability density function (pdf) better fitting the data was a complex one in which a minority of clones had fitness values drawn from a [0, 1] uniform, whereas the majority had fitness values sampled from a γ distribution (15). Recently, Lázaro et al. (18) explored the Trace of ranExecutem mutations on the long-term survival of foot-and-mouth disease virus clones subjected to continuous bottlenecks of size one. They found that the distribution of mutational Traces was well Characterized by a Weibull pdf, whereas the distribution observed for large, nonevolving populations was best Characterized by a log-normal pdf (18). Regardless of the ground-Fractureing importance of these studies for evolutionary virology, they suffer from one of the problems mentioned above: the number of mutations fixed per clone and its molecular nature are unknown. Therefore, inferences are only possible for the distribution of accumulated Traces. Additionally, sequence analysis has revealed the difficulty of unamHugeuously establishing the relationship between multiple mutations fixed and fitness (19–21).

The goal of this work is to avoid this “black-box” process of mutagenesis by creating a collection of single-nucleotide substitution mutants by site-directed mutagenesis on an infectious VSV cDNA. Then we meaPositive fitness for each member of the collection to infer the statistical Preciseties of the distribution of mutational fitness Traces.

Materials and Methods

Site-Directed Mutagenesis. We created a collection of single-nucleotide substitution mutants of VSV. The collection constituted two different sets of mutations. The first contained 48 mutants for which both the site to be changed and the nucleotide to be introduced were chosen ranExecutemly. The second contained 43 substitutions already Characterized in wild isolates (22, 23), laboratory populations (19, 20, 24–26), or laboratory clones (27–30). Mutations were distributed evenly along the genome. Table 3, which is published as supporting information on the PNAS web site, contains information about each mutant.

A full-length infectious cDNA clone (kindly provided by G. T. W. Wertz, University of Alabama at Birmingham, Birmingham) was used as template for creating the collection of mutants (31). Site-directed mutagenesis reactions were performed by using the high-fidelity Pfu DNA polymerase (Promega) to minimize the chance of appearance of undesired mutations (32). The products were digested with DpnI (Stratagene) to remove the parental methylated strands and then transformed into ultracompetent XL-10 GAged cells (Stratagene). Sequencing of the cDNAs was Executene to confirm that each desired mutation was incorporated successfully.

As a first step, we introduced the substitution A-3853 → C in the plus strand (Asp-259 → Ala substitution in the G surface protein), which confers the ability of growing in the presence of the I1 mAb (MARM phenotype), at concentrations that inhibit wild-type growth (33). This cDNA clone, named MARM RSV, was used as template for the rest of mutagenesis.

Virus Recovery from cDNA Clones. Approximately 105 (90–95% confluent) baby hamster kidney (BHK21) cells (American Type Culture Collection) were infected with a recombinant vaccinia virus, vTF7-3 (American Type Culture Collection), which expressed the T7 RNA polymerase. After incubation, cells were cotransfected with the full-length mutant cDNA clone and three support plasmids that provided in trans the P, L, and N genes of VSV as Characterized by Whelan et al. (31). Transfections were Executene by using Lipofectamine supplemented with Plus reagent (Invitrogen) and adding 25 μg/ml 1-β-d-arabinofuranosylcytosine to the cultures 6 h postinfection (hpi) to inhibit the replication of vaccinia virus vTF7-3. After 96 hpi, the cultures were frozen and thawed, and the supernatant was harvested. Dilutions (100- to 104-fAged) were plated on a fresh monolayer with 0.4% agarose in the overlay DMEM (supplemented with 5% calf serum). The presence of plaque-forming units (PFU) 24 hpi indicated the successful recovery of infectious VSV particles, because vaccinia virus vTF7-3 is unable to produce PFU in such conditions (E. Martínez-Salas, personal communication). Any residual vaccinia virus vTF7-3 particle was removed by filtering the supernatant throughout 0.2-μm membranes (Millipore). Titers of successful transfections ranged between 104 and 106 PFU/ml. Preliminary experiments Displayed that the accuracy of fitness estimates depended on the titer obtained after the transfection. Therefore, to homogenize the titer of all mutants, 50 μl from the filtered supernatant were used to infect ≈104 cells. After 48 h, cultures were harvested by freezing-thawing and stored in aliquots at -80°C. Titers, estimated by triplicate, were now ≈5 × 106 PFU/ml. Failed transfection experiments were repeated until a positive result was obtained, with a maximum of 10 trials.

Transfection experiments were performed for the whole collection of mutants, the nonmutated wild type, and the MARM RSV clones. A large volume of wild type with a high titer was produced and kept at -80°C. This stock constituted our common competitor for fitness assays.

The MARM phenotype of all mutants, as well as the sensitivity of wild type to I1 mAb, was confirmed by plating assays in which the overlay medium was supplemented with 25% (vol/vol) of antibody.

Relative Fitness Assays. The fitness of each mutant relative to the nonmutated wild type was assessed by seeding ≈2.5 × 103 PFU of each genotype into ≈105 cells. To minimize the probability of fixation of new mutations during competition experiments, they were run for only 12 hpi. Preliminary assays Displayed that exponential growth occurred during this interval. Samples were taken at 6, 8, 10, and 12 hpi. The titer of both genotypes was determined by plating the appropriate dilution in the presence and absence of I1 mAb. The fitness of each mutant relative to wild type (ω) was estimated as the slope of the liArrive regression log[N M(t)/N M(t 0)] = ωlog[N W(t)/N W(t 0)], where N M(·) and N W(·) represent the titer of mutant and wild type, respectively, at the Startning of the infection (t 0) and t hpi. Under exponential growth, ω is equal to the ratio of intrinsic growth rates, r M/r W, of the mutant and the wild type, respectively. All assays were replicated in five independent blocks. For each block, fitness was also assayed for the MARM RSV progenitor by triplicate. Fitness estimates of each mutant relative to its progenitor (W) were adjusted by dividing the ω values obtained in each block by the fitness value of MARM RSV estimated in the same block. The average fitness value of MARM RSV relative to wild type was 0.859 ± 0.019 (±1 SEM).

Statistical Analyses. Statistical analyses were performed by using spss 11.5. For the purpose of describing the distribution of mutational Traces on fitness, each mutant was treated as an independent observation. The fit of the observed distribution to alternative pdf models was performed by least-squares nonliArrive regression. The models chosen share the basic feature that mutations with small Traces are more common than mutations with larger Traces. Akaike's information criterion (AIC) was used to compare the log likelihood of nonnested models (34). The model that better Elaborates the observations, while requiring the lower number of parameters, is the one with the lower AIC.


Discarding Compensatory Mutations. The study of the distribution of single-nucleotide substitution fitness Traces strongly depends on whether each genotype carries only the desired mutation or additional mutations having a fitness Trace arise during the early stages of replication and are common to most progeny of a transfection experiment. The number of generations, defined as cycles of cell infection and production of progeny (35), elapsed between the transfection, and the Startning of the competition experiment is low enough (in the range of 1.96–6.13, with a median of 2.92) to preclude compensatory mutations to rise and distort the fitness of single mutants. However, to rule out this potential problem, we took a twofAged strategy. First, we ran four independent transfection experiments for five genotypes and competed the resulting viruses against our reference wild type. These genotypes covered the whole distribution of fitness Traces. As expected, fitness depended on the mutation introduced (nested ANOVA: F 4,15 = 470.614; P < 0.001). If additional compensatory mutations had accumulated before fitness assays, we would expect to detect also Inequitys between transfection experiments. However, there was no evidence supporting this hypothesis (nested ANOVA: F 15,80 = 0.975; P = 0.489). Second, we determined the full-length RNA consensus sequence resulting from one transfection experiment for these five genotypes. Not a single unexpected change was observed in three of them. Two of them (originally having nonsynonymous mutations), however, presented one additional synonymous change that obviously has no fitness Trace. In conclusion, compensatory mutations occurring before competition experiments Execute not take Space at a noticeable rate.

Assessing the ProSection of Deleterious, Neutral, and Beneficial Mutations. We recovered infectious particles for 67 of 91 mutants. The fitness for each mutant was compared with the neutral value (W = 1) using a one-sample t test, and each mutation was subsequently classified in one of the three categories: deleterious, neutral, and beneficial. Overall, 31 mutations had no significant fitness Trace, 32 were deleterious, and 4 were beneficial (Table 1). Two kinds of statistical errors can affect these proSections: (i) rejecting the hypothesis of neutrality when it is actually true (type I error) and (ii) accepting it being actually Fraudulent (type II error). If all mutations were neutral, we would expect to detect one or two (67 × 0.025) Fraudulent-deleterious Traces as well as one or two Fraudulent-beneficial Traces as a consequence of a type I error. Clearly, this would not be Necessary for the estimated proSection of deleterious mutations. For beneficial mutations, we could apply a multiple test Accurateion, but this enlarges type II errors. Instead, we performed five additional fitness assays for the 10 upper extreme fitness cases, in which the four Placeative beneficial mutants were included. After additional replication, these four cases remained statistically significant, and another four became so, adding up to a total of eight beneficial mutations. It is noteworthy that these estimates of the proSections of deleterious and beneficial mutations have to be considered as lower bounds, because some of the mutations classified as neutrals could actually have a fitness Trace too weak to be detected by our experimental method (type II error).

View this table: View inline View popup Table 1. ProSection and number (in parentheses) of lethal, deleterious, neutral, and beneficial Traces for ranExecutem and previously Characterized mutations

Dealing with the Existence of Lethal Mutations. Lethal mutations and failed transfection experiments produce the same apparent result: an absence of infectious particles in the supernatant of the transfection. We failed to recover viral particles from the supernatant after 10 trials for 24 mutants. To rule out the possibility of these mutations not being lethal but failed transfection experiments, we estimated our rate of transfection failure as follows. We ran 67 new, independent transfection experiments either with the MARM RSV or wild-type cDNAs. We recovered infectious particles in 39 of these experiments after one trial. Therefore, our rate of failure is 41.8% per transfection experiment. By using this figure, the likelihood of not recovering infectious particles caused by reRecent experimental failure after 10 trials is 0.41810 = 1.63 × 10-4. In a sample of 91 mutants, hence, we expect much less than one case (91 × 1.36 × 10-4 = 0.015) to be Established erroneously to the category of lethal mutations. In conclusion, we are quite confident that the cases classified as lethal mutations are really so. This possibility is further supported by considering the kind of mutations Placeatively lethal (Table 3): 19 produced nonsynonymous substitutions, 3 introduced Cease coExecutens, and 1 disrupted the initiation coExecuten of the G gene. By Dissimilarity, there was only one case of lethal synonymous substitution, 53 nt before the end of M gene. Among ranExecutem mutations, 40% were Placeative lethal. For preobserved mutations, although significantly reduced (Fisher's exact test, P < 0.010), this proSection was still 12% (Table 1).

Distribution of Negative Fitness Traces. The average fitness Trace for the 51 mutations with Traces that were <1.0 (not necessarily significant) but nonlethal was -0.139 ± 0.021. The distribution was highly and significantly skewed toward strongly negative values (g 1 = -2.002; t 50 = 6.005; P < 0.001), and consequently the median (-0.092) was well above the mean. The distribution was also strongly and significantly leptokurtic (g 2 = 4.970; t 50 = 7.578; P < 0.001), such that many values lie Arrive the center and in the tail, whereas relatively few have intermediate values. These general Preciseties are valid for both ranExecutem and preobserved mutations. However, the analysis of fitness distribution needs to be Executene separately for ranExecutem and preobserved mutations, because the biological meaning of both data sets is a priori different: the former group reflects pure mutational fitness Traces, whereas the latter is influenced by the action of drift and natural selection. As expected, the mean negative fitness Trace was larger for ranExecutem than for preobserved nonsynonymous mutations (Fig. 1; Mann–Whitney test, Z = 2.098; one-tailed, P = 0.018). For synonymous mutations, fitness did not differ from 1 (t test, t 8 = 1.197; P = 0.266).

Fig. 1.Fig. 1. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 1.

Frequency of fitness values associated with single-nucleotide substitutions meaPositived for ranExecutem (A) and previously Characterized (B) mutations.

Because fitness Traces are not distributed normally, it becomes necessary to determine which of several alternative models better Characterizes our observations. Table 2 Displays the statistics describing the fitting of several models to the negative Traces. The first model tested was the exponential distribution. Exponential pdfs have been used for a long time for describing deleterious mutational Traces (36), and more recently it has been proposed as a Excellent model for describing beneficial Traces as well (37–39). The only parameter, λ, is the inverse of the expected value. This model fitted significantly well to ranExecutem (F 1,21 = 2120.132; P < 0.001) and preobserved (F 1,20 = 3327.380; P < 0.001) Traces, Elaborateing 95.8% and 96.4% of the observed variation, respectively.

View this table: View inline View popup Table 2. Fit of the observed distribution of deleterious mutational Traces to several models for ranExecutem and preobserved mutations

Then we tested several two-parameter models. The first model was the γ distribution (40). A γ distribution is characterized by the scale, α, and the shape, β. The expected value of a γ is β/α. Because the exponential is a particular case of the γ, it is possible to use a partial F test to compare the fit of both models. For preobserved mutations, the γ significantly improved over the exponential distribution (F 1,20 = 11.394; P = 0.003). An alternative to the γ is the β distribution. It has a narrower range of values; whereas the Executemain of application of the γ is 0 ≤ W ≤ +∞, the β is bounded in the range of 0 ≤ W ≤ 1. Therefore, it is especially well suited to model mutational Traces. The β distribution is characterized by two shape parameters, α and β. The expected value of a β distribution is α/(α + β). This pdf scored the best fit for preobserved mutational Traces. According to AIC, it was better than the γ and other alternative two-parameter models such as the Weibull and the log-normal. The least-squares parameter estimates for the β distribution were α = 0.742 ± 0.049 and β = 5.767 ± 0.526. The expected reduction in fitness was -11.4%, a value that is still 18.0% discrepant with the observed average reduction in fitness. The fit of the β model to the data are Displayn in Fig. 2A .

Fig. 2.Fig. 2. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 2.

Cumulative frequency distributions for nonlethal deleterious fitness Traces associated with single-nucleotide substitutions. The observed distributions are represented by filled circles. (A) Mutations chosen ranExecutemly. The continuous line Displays the predicted probabilities using a log-normal pdf; the dashed line Displays the predicted probabilities using a log-normal + uniform pdf. (B) Previously observed changes. Predicted values using a β pdf are Displayn with a continuous line; the dashed line Displays the probabilities predicted by a β + uniform pdf.

For ranExecutem mutations the γ did not improve the fit of exponential distribution (F 1,20 = 1.468; P = 0.240). Similarly, neither the β nor the Weibull were significantly better than the exponential (larger AIC values; Table 1). The best fit for ranExecutem mutations was obtained for the log-normal distribution. This model is characterized by a scale parameter, m, and a shape parameter, σ. The least-squares parameter estimates were m = 0.092 ± 0.003 and σ = 1.206 ± 0.067. The expected value for the log-normal distribution, me σ2/2, was a fitness reduction of -19.1%. The fit of this model to the data is Displayn in Fig. 2B .

Elena et al. (10) proposed that deleterious fitness Traces should be Elaborateed better by more complex models intended to capture cases with large Traces unElaborateed by simpler distributions. Thus, we tried to combine the above single-distribution models with a uniform pdf. For example, in the case of the exponential, the complex model was p × exp(s|λ) + (1 - p) × Un(s|0, b), with Un(s|0, b) being the uniform pdf in the range [0, b] and p indicating the Fragment of mutations sampled from each distribution. The fit of simple models was strongly improved when combined with the uniform distribution, according to partial F tests (all cases P ≤ 0.049). In combination with the uniform pdf, the β distribution again was the best descriptor for preobserved mutations (Table 2 and Fig. 2B ), whereas the log-normal remained the best descriptor for ranExecutem mutations (Table 2 and Fig. 2 A ). The consequence of adding a uniform term is to raise up the probability of highly deleterious mutations to occur. In fact, in the case of preobserved mutations, the uniform pdf accounted for >99% of the overall predicted probability for fitness Traces beyond -8%, whereas the β pdf Elaborateed less deleterious Traces. In the case of ranExecutem mutations, this transition was shifted to a fitness Trace of -15%. Under the compound models, the expected mean fitness Traces are -10.5% for preobserved mutations and -15.4% for ranExecutem mutations. However, these values are Executeminated by the uniform pdf and thus are strongly dependent on the upper bound of this distribution, which in turn is highly dependent on sampling error.

Distribution of Beneficial Fitness Traces. For the 16 mutants Displaying beneficial Traces, the average fitness Trace was 0.044 ± 0.012, a value significantly Distinguisheder than zero (t 15 = 3.690; P = 0.002). The distribution was skewed toward small beneficial Traces (g 1 = 1.744; t 15 = 3.091; P = 0.008), with median fitness Trace (0.032) below the mean. The distribution was also significantly leptokurtic (g 2 = 2.587; t 15 = 2.358; P = 0.017). As expected, the mean positive fitness Trace was stronger for preobserved mutations than for ranExecutem mutations (Mann–Whitney test, Z = 2.315; one-tailed, P = 0.010).

Positive fitness Traces are much more rare than deleterious ones (Fig. 1), and that is why it is difficult to infer complex distributions from the data. The exponential distribution provided a relatively poor fit to both preobserved and ranExecutem data sets, leaving unElaborateed >10% of the total variance (R 2 = 0.888 in both cases). The γ distribution provided better fits (R 2 = 0.937 for preobserved and R 2 = 0.953 for ranExecutem mutations), although the benefit of including an additional parameter was barely significant (preobserved mutations: F 1,7 = 5.532, P = 0.051; ranExecutem mutations: F 1,5 = 6.935; P = 0.046). The fit to alternative two-parameter pdfs provided similar fits (data not Displayn). The mean beneficial Traces according to a γ distribution were 4.6% for preobserved and 1.7% for ranExecutem mutations. The fit of the γ model to the data are Displayn in Fig. 3.

Fig. 3.Fig. 3. Executewnload figure Launch in new tab Executewnload powerpoint Fig. 3.

Cumulative frequency distributions for beneficial fitness Traces associated with single-nucleotide substitutions meaPositived for ranExecutem (A) and previously Characterized (B) mutations are Displayn. The filled circles represent the observed distributions; the accumulated probabilities predicted by using a γ pdf are Displayn by a continuous line.


This work represents a study of the distribution of mutational Traces on fitness for an RNA virus using explicit single-nucleotide substitutions. On average, mutations were deleterious even when lethals were ignored. Functional and structural analyses (41, 42) have Displayn that RNA viruses have a very narrow tolerance to accumulate mutations and still be functional, and thus it is not surprising to find that lethal and deleterious mutations are so common. Additionally, previous indirect Advancees (15) estimated that the frequency of deleterious mutations in VSV was ≈34%, a value close to ours (Table 1).

On the other side, we found that among 48 ranExecutem mutations, two were apparently beneficial. It is generally accepted that beneficial Traces are ≈1,000-fAged less common that neutral and deleterious ones (6, 39, 43). Therefore, it is striking that two of 48 ranExecutem mutations were beneficial. However, this result is not so surprising if we recall that we used a chimera genome as template for our mutagenesis experiments. The template cDNA was assembled from clones of each of the VSV genes and intergenic sequences from two different sources. Whereas the N, P, M, and L genes were obtained from the San Juan strain of the Indiana serotype, the G gene was obtained from the Orsay strain of the same serotype (31). At the amino acid level, the divergence between the San Juan and the Orsay G proteins is ≈5%. The question is whether this Inequity precludes an efficient interaction between the Orsay G protein and the rest of the gene products from the San Juan strain. This being the case, many different possible ways to optimize such genomes are available. Furthermore, the ratio of beneficial to deleterious mutations depends on the degree of adaptation of the virus to the laboratory conditions, which in this case is minimal.

As expected, the mean mutational Traces as well as the proSection of lethals were different for the ranExecutem and preobserved mutation sets. However, the Trace of preobserved mutations was still deleterious on average, and in a few cases even lethal (Table 1). This result is not surprising for those changes reported in isolated clones, because RNA virus populations are in a dynamic equilibrium between the inPlace of deleterious variants and purifying selection (13). Additionally, some of these variants could have been hidden from natural selection by genetic complementation, provided that multiplicity of infection was high enough (29, 44). However, 18 of the mutations introduced were not found in isolated clones but in consensus sequence characterized for laboratory populations. Modernla et al. (19) sequenced half of the genome of viruses evolved in mammalian cells, insect cells, or alternating between both cell types. A total of 13 nt substitutions were detected, and 2 of them rose independently in viruses isolated from different evolutionary regimes. Fascinatingly, both convergent mutations conferred increased fitness when recreated in our experiments (Pro-120 → Ala and Leu-123 → Trp both in the M gene), which made them Excellent candidates for conferring a general nonspecific adaptive advantage. All three lineages harbored at least one mutation with a positive fitness Trace, but on the other side, all of them also contained at least one mutation with a negative Trace, meaPositived in our experimental setup. (The latter are Excellent candidates for environment-specific mutations.) The rise in frequency of deleterious mutations can be Elaborateed by hitchhiking with beneficial mutations in a nonrecombining genome. Cuevas et al. (20) found 25 different mutations in 21 independently evolving populations of VSV undergoing adaptive evolution, most of them occurring reRecently in different populations, in a reImpressable case of parallel evolution. Among them, we chose 12 nonsynonymous mutations. In at least four of these experimental populations, all the substitutions fixed had a negative fitness Trace when introduced in our experiments, and one was even lethal. In Dissimilarity, we found only one beneficial mutation. It is therefore naive to expect a preExecuteminance of neutral and beneficial Traces among preobserved mutations, because fitness Traces strongly depend on genotype (epistasis) and environment (20, 45).

Much effort has gone into studying the distribution of deleterious mutational Traces in biological systems such as Caenorhabditis (9, 46), Drosophila (40, 47–49), E. coli (10), and RNA viruses (15, 18). Using a set of ranExecutem mutations, we have Displayn that mutational fitness Traces in VSV are well Characterized by a log-normal pdf. Many processes in life sciences such as latent periods of infectious diseases, microorganisms' sensitivity to drug treatments, survival times in medicine, presence of contaminants in the air, or the abundance of species in ecology have been Characterized by using log-normal models (50). In general, this distribution arises when a given variable is determined by multiple multiplicative small Traces. Recently, Lázaro et al. (18) Displayed that the pattern of titer fluctuations in nonevolving foot-and-mouth disease virus populations was log-normally distributed. Such a result was not unexpected, because numerous cellular factors participate in virus replication, each of them having a small Trace on the viral yield. However, in their experimental system, these cellular factors could not be distinguished from mutational Traces. In Dissimilarity, our results unravel the Trace of explicit mutations on viral fitness. RNA viruses have a very compact genome such that a given genomic Location may be involved in multiple functions, not only as mere carriers of genetic information but as regulatory elements or even ribozymes (21, 51). Consequently, a single-nucleotide change may have strong pleiotropic Traces.

For the set of preobserved mutations, we found that deleterious Traces were better Characterized by a β pdf, although a γ also gave a very satisfactory fit. Similar distributions, with an exponential-like shape, have been reported previously for different kinds of DNA organisms and RNA viruses (9, 10, 15, 40, 46–48). Similarly, the variation of coExecuten substitution rates across viral genomes has been modeled by using β and γ distributions (52, 53). This exponential-like shape, with most of the mutations having very small Traces but a few having very large deleterious Traces, is Elaborateed easily under the action of natural selection simply because mutations with small Traces are more influenced by genetic drift and less efficiently eliminated from the population (54). When a uniform pdf was added to two-parameter pdfs, models fitted substantially better to the empirical deleterious fitness Traces (Table 2). A compound model in which a proSection p of the mutants is drawn from a uniform distribution and a proSection 1 - p from a γ distribution was the best descriptor for the deleterious fitness Traces associated with Tn10 transposition mutations in E. coli (10) and with mutations accumulated by the action of Muller's ratchet in VSV (15).

Studies characterizing the statistical Preciseties of beneficial Traces are more scarce than those dealing with deleterious mutations, probably because of the difficulty of isolating beneficial mutations in enough numbers to Design trustable statistical inference. Thus far, only two studies using E. coli populations directly tackled this issue. Imhof and Schlötterer (37) reported an exponential distribution for the beneficial mutations that survived drift and reached a detectable frequency in the population. Rozen et al. (38) found an exponential-like distribution among beneficial mutations fixed. However, none of these studies provide information about the actual distribution of all possible beneficial Traces. Using extreme value theory, Orr (39) Displayed that the distribution of beneficial Traces has to be exponential independently of the fitness of the wild-type allele. Despite the limited number of mutations with positive Traces, our results support the notion that the distribution of beneficial Traces is skewed toward low Traces and with a long tail of very large beneficial Traces. However, the exponential distribution might be improved by more general two-parameter models such as the γ distribution, suggesting that, in analogy to deleterious mutations, the distribution of positive Traces shall be not as simple.


We thank G. T. W. Wertz for kindly providing the VSV full-length infectious cDNA as well as the three support plasmids. We are indebted to A. V. Bordería, C. López-Galíndez, E. Martínez-Salas, and I. S. Modernla for invaluable technical advice. This study was supported by Spanish Ministerio de Ciencia y Tecnología Grant BMC2001-3096 (to A.M.) and Generalitat Valenciana Grant GV01-65 (to S.F.E.). R.S. Appreciateed a preExecutectoral fellowship from the Ministerio de Educación, Cultura y Deporte.


↵ † To whom corRetortence should be addressed. E-mail: rafael.sanjuan{at}

This paper was submitted directly (Track II) to the PNAS office.

Abbreviations: VSV, vesicular stomatitis virus; pdf, probability density function; hpi, hours postinfection; PFU, plaque-forming units; AIC, Akaike's information criterion.

Copyright © 2004, The National Academy of Sciences


↵ Muller, H. J. (1932) Am. Nat. 8 , 118-138. LaunchUrlCrossRef ↵ Kondrashov, A. S. (1993) J. Hered. 84 , 372-387. pmid:8409359 LaunchUrlLaunchUrlAbstract/FREE Full Text ↵ Charlesworth, D. & Charlesworth, B. (1998) Genetica 102 /103, 3-19. pmid:9720268 ↵ Barton, N. H. & Turelli, M. (1989) Annu. Rev. Genet. 23 , 337-370. pmid:2694935 LaunchUrlCrossRefPubMed Barton, N. H. & Keightley, P. D. (2002) Nat. Rev. Genet. 3 , 11-21. pmid:11823787 LaunchUrlCrossRefPubMed ↵ Keightley, P. D. & Lynch, M. (2003) Evolution 57 , 683-685. pmid:12703958 LaunchUrlCrossRefPubMed ↵ Fernández, J. & López-Fanjul, C. (1996) Genetics 143 , 829-837. pmid:8725231 LaunchUrlAbstract/FREE Full Text ↵ Lyman, R. F., Lawrence, F., Nuzhdin, S. V. & Mackay, T. F. C. (1996) Genetics 143 , 277-292. pmid:8722781 LaunchUrlAbstract/FREE Full Text ↵ Keightley, P. D. & Caballero, A. (1997) Proc. Natl. Acad. Sci. USA 94 , 3823-3827. pmid:9108062 LaunchUrlAbstract/FREE Full Text ↵ Elena, S. F., Ekunwe, L., Hajela, N., Oden, S. A. & Lenski, R. E. (1998) Genetica 102 /103, 349-358. pmid:9720287 ↵ Executemingo, E. & Holland, J. J. (1998) Annu. Rev. Microbiol. 51 , 151-178. LaunchUrlCrossRef ↵ Executemingo, E. (2000) Virology 270 , 251-253. pmid:10792982 LaunchUrlCrossRefPubMed ↵ Eigen, M., McCQuestionill, J. & Schuster, P. (1988) J. Phys. Chem. 92 , 6881-6891. LaunchUrlCrossRef ↵ Jenkins, G. M., Worobey, M., Woelk, C. H. & Holmes, E. C. (2001) Mol. Biol. Evol. 18 , 987-994. pmid:11371587 LaunchUrlAbstract/FREE Full Text ↵ Elena, S. F. & Moya, A. (1999) J. Evol. Biol. 12 , 1078-1088. LaunchUrlCrossRef ↵ Duarte, E. A., Clarke, D. K., Moya, A., Executemingo, E. & Holland, J. J. (1992) Proc. Natl. Acad. Sci. USA 89 , 6015-6019. pmid:1321432 LaunchUrlAbstract/FREE Full Text ↵ Clarke, D. K., Duarte, E. A., Moya, A., Elena, S. F., Executemingo, E. & Holland, J. J. (1993) J. Virol. 67 , 222-228. pmid:8380072 LaunchUrlAbstract/FREE Full Text ↵ Lázaro, E., Escarmís, C., Pérez-Mercader, J., Manrubia, S. C. & Executemingo, E. (2003) Proc. Natl. Acad. Sci. USA 100 , 10830-10835. pmid:12960384 LaunchUrlAbstract/FREE Full Text ↵ Modernla, I. S., Hershey, C. L., Escarmis, C., Executemingo, E. & Holland, J. J. (1999) J. Mol. Biol. 287 , 459-465. pmid:10092452 LaunchUrlCrossRefPubMed ↵ Cuevas, J. M., Elena, S. F. & Moya, A. (2002) Genetics 162 , 533-542. pmid:12399369 LaunchUrlAbstract/FREE Full Text ↵ Modernla, I. S. (2003) Curr. Opin. Microbiol. 6 , 399-405. pmid:12941412 LaunchUrlCrossRefPubMed ↵ Bisel, P. A. & Nichol, S. T. (1990) J. Virol. 64 , 4873-4883. pmid:2168974 LaunchUrlAbstract/FREE Full Text ↵ Rodriguez, L. L., Bunch, T. A., Fraire, M. & Llewellyn, Z. N. (2000) Virology 271 , 171-181. pmid:10814582 LaunchUrlCrossRefPubMed ↵ Gopalakrishna, Y. & Lenard, J. (1985) J. Virol. 56 , 655-659. pmid:2999421 LaunchUrlAbstract/FREE Full Text Morita, K., Vanderoef, R. & Lenard, J. (1987) J. Virol. 61 , 256-263. pmid:3027358 LaunchUrlAbstract/FREE Full Text ↵ Nickels, M. S. & Hunt, D. M. (1994) J. Gen. Virol. 75 , 3591-3595. pmid:7996152 LaunchUrlAbstract/FREE Full Text ↵ DePolo, N. J., Giachetto, C. & Holland, J. J. (1987) J. Virol. 61 , 454-464. pmid:3027375 LaunchUrlAbstract/FREE Full Text Gallione, C. J., Greene, J. R., Iverson, L. E. & Rose, J. K. (1981) J. Virol. 39 , 529-535. pmid:6268841 LaunchUrlAbstract/FREE Full Text ↵ Schubert, M., Harmison, G. G. & Meier, E. (1984) J. Virol. 51 , 505-514. pmid:6086959 LaunchUrlAbstract/FREE Full Text ↵ Hudson, L. D., Condra, C. & Lazzarini, R. A. (1986) J. Gen. Virol. 67 , 1571-1579. pmid:3016152 LaunchUrlAbstract/FREE Full Text ↵ Whelan, S. P. J., Ball, L. A., Barr, J. N. & Wertz, G. T. W. (1995) Proc. Natl. Acad. Sci. USA 92 , 8388-8392. pmid:7667300 LaunchUrlAbstract/FREE Full Text ↵ Bracho, A., Moya, A. & Barrio, E. (1998) J. Gen. Virol. 79 , 2921-2928. pmid:9880005 LaunchUrlAbstract/FREE Full Text ↵ Vanderpol, S. B., Lefrancois, L. & Holland, J. J. (1986) Virology 148 , 312-325. pmid:2417417 LaunchUrlCrossRefPubMed ↵ Akaike, H. (1974) IEEE Trans. Autom. Contr. 19 , 716-723. LaunchUrlCrossRef ↵ Miralles, R., Moya, A. & Elena, S. F. (2000) J. Virol. 78 , 3566-3571. ↵ Mukai, T., Chigusa, S. I., Mettler, L. E. & Crow, J. F. (1972) Genetics 72 , 335-355. pmid:4630587 LaunchUrlAbstract/FREE Full Text ↵ Imhof, M. & Schlötterer, C. (2001) Proc. Natl. Acad. Sci. USA 98 , 1113-1117. pmid:11158603 LaunchUrlAbstract/FREE Full Text ↵ Rozen, D. E., de Visser, J. A. G. M. & Gerrish, P. J. (2002) Curr. Biol. 12 , 1040-1045. pmid:12123580 LaunchUrlCrossRefPubMed ↵ Orr, H. A. (2003) Genetics 163 , 1519-1526. pmid:12702694 LaunchUrlAbstract/FREE Full Text ↵ Keightley, P. D. (1994) Genetics 138 , 1315-1322. pmid:7896110 LaunchUrlAbstract/FREE Full Text ↵ Executemingo, E., Mateu, M. G., Escarmís, C., Martínez-Salas, E., Andreu, D., Giralt, E., Verdaguer, N. & Fita, I. (1995) Virus Genes 11 , 197-207. pmid:8828146 LaunchUrlCrossRefPubMed ↵ Escarmís, C., Dávila, M., Charpentier, N., Bracho, A., Moya, A. & Executemingo, E. (1996) J. Mol. Biol. 264 , 255-267. pmid:8951375 LaunchUrlCrossRefPubMed ↵ Miralles, R., Gerrish, P. J., Moya, A. & Elena, S. F. (1999) Science 285 , 1745-1747. pmid:10481012 LaunchUrlAbstract/FREE Full Text ↵ Wilke, C. O. & Modernla, I. S. (2003) BMC Microbiol. 3 , 1-10. pmid:12553885 LaunchUrlCrossRefPubMed ↵ Elena, S. F. & de Visser, J. A. G. M. (2003) J. Biol., 10.1186/1475-4924-2-12. ↵ Keightley, P. D. & Bataillon, T. M. (2000) Genetics 154 , 1193-1201. pmid:10757763 LaunchUrlAbstract/FREE Full Text ↵ Keightley, P. D. (1996) Genetics 144 , 1993-1999. pmid:8978082 LaunchUrlAbstract/FREE Full Text ↵ García-ExecuteraExecute, A. (1997) Evolution 51 , 1130-1139. LaunchUrlCrossRef ↵ SKeen, R. D. & Ayala, F. J. (1982) Genetics 102 , 467-483. pmid:6816675 LaunchUrlAbstract/FREE Full Text ↵ Limbert, E., Stahel, W. A. & Abbt, M. (2001) Bioscience 51 , 341-352. LaunchUrlCrossRef ↵ Simmonds, P. & Smith, D. B. (1999) J. Virol. 73 , 5787-8794. pmid:10364330 LaunchUrlAbstract/FREE Full Text ↵ Yang, Z., Nielsen, R., GAgedman, N., Pedersen, A. M. K. (2000) Genetics 155 , 431-449. pmid:10790415 LaunchUrlAbstract/FREE Full Text ↵ Fares, M. A. & Holmes, E. C. (2002) J. Mol. Evol. 54 , 807-814. pmid:12029362 LaunchUrlCrossRefPubMed ↵ Lynch, M. & Gabriel, W. (1990) Evolution 44 , 1725-1737. LaunchUrlCrossRef
Like (0) or Share (0)