The Population Genetics of dN/dS

Evolutionary pressures on proteins are often quantified by the ratio of substitution rates at non-synonymous and synonymous sites. The dN/dS ratio was originally developed for application to distantly diverged sequences, the differences among which represent substitutions that have fixed along independent lineages. Nevertheless, the dN/dS measure is often applied to sequences sampled from a single population, the differences among which represent segregating polymorphisms. Here, we study the expected dN/dS ratio for samples drawn from a single population under selection, and we find that in this context, dN/dS is relatively insensitive to the selection coefficient. Moreover, the hallmark signature of positive selection over divergent lineages, dN/dS>1, is violated within a population. For population samples, the relationship between selection and dN/dS does not follow a monotonic function, and so it may be impossible to infer selection pressures from dN/dS. These results have significant implications for the interpretation of dN/dS measurements among population-genetic samples.     

The problem of counting sites in the estimation of the synonymous and nonsynonymous substitution rates: implications for the correlation between the synonymous substitution rate and codon usage bias

Most methods for estimating the rate of synonymous and nonsynonymous substitution per site define a site as a mutational opportunity: the proportion of sites that are synonymous is equal to the proportion of mutations that would be synonymous under the model of evolution being considered. Here we demonstrate that this definition of a site can give misleading results and that a physical definition of site should be used in some circumstances. We illustrate our point by reexamining the relationship between codon usage bias and the synonymous substitution rate. It has recently been shown that the rate of synonymous substitution, calculated using the Goldman-Yang method, which encapsulates the mutational-opportunity definition of a site at a high level of sophistication, is either positively correlated or uncorrelated to synonymous codon bias in Drosophila. Using other methods, which account for synonymous codon bias but define a site physically, we show that there is a negative correlation between the synonymous substitution rate and codon bias and that the lack of a negative correlation using the Goldman-Yang method is due to the way in which the number of synonymous sites is counted. We also show that there is a positive correlation between the synonymous substitution rate and third position GC content in mammals, but that the relationship is considerably weaker than that obtained using the Goldman-Yang method. We argue that the Goldman-Yang method is misleading in this context and conclude that methods that rely on a mutational-opportunity definition of a site should be used with caution.     

Uncorrected nucleotide bias in mtDNA can mimic the effects of positive Darwinian selection

The relative rates of nucleotide substitution at synonymous and nonsynonymous sites within protein-coding regions have been widely used to infer the action of natural selection from comparative sequence data. It is known, however, that mutational and repair biases can affect rates of evolution at both synonymous and nonsynonymous sites. More importantly, it is also known that synonymous sites are particularly prone to the effects of nucleotide bias. This means that nucleotide biases may affect the calculated ratio of substitution rates at synonymous and nonsynonymous sites. Using a large data set of animal mitochondrial sequences, we demonstrate that this is, in fact, the case. Highly biased nucleotide sequences are characterized by significantly elevated dN/dS ratios, but only when the nucleotide frequencies are not taken into account. When the analysis is repeated taking the nucleotide frequencies at each codon position into account, such elevated ratios disappear. These results suggest that the recently reported differences in dN/dS ratios between vertebrate and invertebrate mitochondrial sequences could be explained by variations in mitochondrial nucleotide frequencies rather than the effects of positive Darwinian selection.     

The rate of adaptive evolution in enteric bacteria

Here we estimate the rate of adaptive substitution in a set of 410 genes that are present in 6 Escherichia coli and 6 Salmonella enterica genomes. We estimate that more than 50% of amino acid substitutions in this set of genes have been fixed by positive selection between the E. coli and S. enterica lineages. We also show that the proportion of adaptive substitutions is uncorrelated with the rate of amino acid substitution or gene function but that it may be correlated with levels of synonymous codon usage bias.     

The rate of synonymous substitution in enterobacterial genes is inversely related to codon usage bias

Genes sequences from Escherichia coli, Salmonella typhimurium, and other members of the Enterobacteriaceae show a negative correlation between the degree of synonymous-codon usage bias and the rate of nucleotide substitution at synonymous sites. In particular, very highly expressed genes have very biased codon usage and accumulate synonymous substitutions very slowly. In contrast, there is little correlation between the degree of codon bias and the rate of protein evolution. It is concluded that both the rate of synonymous substitution and the degree of codon usage bias largely reflect the intensity of selection at the translational level. Because of the high variability among genes in rates of synonymous substitution, separate molecular clocks of synonymous substitution might be required for different genes.      

Comparisons of dN/dS are time dependent for closely related bacterial genomes

The ratio of non-synonymous (dN) to synonymous (dS) changes between taxa is frequently computed to assay the strength and direction of selection. Here we note that for comparisons between closely related strains and/or species a second parameter needs to be considered, namely the time since divergence of the two sequences under scrutiny. We demonstrate that a simple time lag model provides a general, parsimonious explanation of the extensive variation in the dN/dS ratio seen when comparing closely related bacterial genomes. We explore this model through simulation and comparative genomics, and suggest a role for hitch-hiking in the accumulation of non-synonymous mutations. We also note taxon-specific differences in the change of dN/dS over time, which may indicate variation in selection, or in population genetics parameters such as population size or the rate of recombination. The effect of comparing intra-species polymorphism and inter-species substitution, and the problems associated with these concepts for asexual prokaryotes, are also discussed. We conclude that, because of the critical effect of time since divergence, inter-taxa comparisons are only possible by comparing trajectories of dN/dS over time and it is not valid to compare taxa on the basis of single time points.     

Evolution of duplicate genes in a tetraploid animal, Xenopus laevis

To understand the evolution of duplicate genes, we compared rates of nucleotide substitution between 17 pairs of nonallelic duplicated genes in the tetraploid frog Xenopus laevis with rates between the orthologous loci of human and rodent. For all duplicated X. laevis genes, the number of synonymous substitutions per site (dS) was greater than the number of nonsynonymous substitutions per site (dN), indicating that these genes are subject to purifying selection. There was also a significant positive correlation (r = 0.915) between dN for the X. laevis genes and dN for the mammalian genes, suggesting that, at the amino acid level, the X. laevis genes and the mammalian genes are under similar constraints. Results of relative-rate tests showed nearly equal rates of nonsynonymous substitution in each copy of the X. laevis genes; apparently there are similar constraints on both copies. No correlation was found between dS for the X. laevis genes and dS for the mammalian genes. There was a significant positive correlation both between members of pairs of duplicated X. laevis genes (r = 0.951) and between human and rodent orthologues (r = 0.854) with respect to third- position G+C content but no such relationship between the X. laevis genes and either of their mammalian orthologues. The results indicate that both copies of a duplicate gene can be subject to purifying selection and thus support the hypothesis of selection against all genotypes containing a null allele at either of two duplicate loci.      

The effect of tandem substitutions on the correlation between synonymous and nonsynonymous rates in rodents.

Nonsynonymous substitutions in DNA cause amino acid substitutions while synonymous substitutions in DNA leave amino acids unchanged. The cause of the correlation between the substitution rates at nonsynonymous (K(A)) and synonymous (K(S)) sites in mammals is a contentious issue, and one that impacts on many aspects of molecular evolution. Here we use a large set of orthologous mammalian genes to investigate the causes of the K(A)-K(S) correlation in rodents. The strength of the K(A)-K(S) correlation exceeds the neutral theory expectation when substitution rates are estimated using algorithmic methods, but not when substitution rates are estimated by maximum likelihood. Irrespective of this methodological uncertainty the strength of the K(A)-K(S) correlation appears mostly due to tandem substitutions, an excess of which is generated by substitutional nonindependence. Doublet mutations cannot explain the excess of tandem synonymous-nonsynonymous substitutions, and substitution patterns indicate that selection on silent sites is the likely cause. We find no evidence for selection on codon usage. The nature of the relationship between synonymous divergence and base composition is unclear because we find a significant correlation if we use maximum-likelihood methods but not if we use algorithmic methods. Finally, we find that K(S) is reduced at the start of genes, which suggests that selection for RNA structure may affect silent sites in mammalian protein-coding genes.     

Likelihood ratio tests for detecting positive selection and application to primate lysozyme evolution

An excess of nonsynonymous substitutions over synonymous ones is an important indicator of positive selection at the molecular level. A lineage that underwent Darwinian selection may have a nonsynonymous/synonymous rate ratio (dN/dS) that is different from those of other lineages or greater than one. In this paper, several codon-based likelihood models that allow for variable dN/dS ratios among lineages were developed. They were then used to construct likelihood ratio tests to examine whether the dN/dS ratio is variable among evolutionary lineages, whether the ratio for a few lineages of interest is different from the background ratio for other lineages in the phylogeny, and whether the dN/dS ratio for the lineages of interest is greater than one. The tests were applied to the lysozyme genes of 24 primate species. The dN/dS ratios were found to differ significantly among lineages, indicating that the evolution of primate lysozymes is episodic, which is incompatible with the neutral theory. Maximum- likelihood estimates of parameters suggested that about nine nonsynonymous and zero synonymous nucleotide substitutions occurred in the lineage leading to hominoids, and the dN/dS ratio for that lineage is significantly greater than one. The corresponding estimates for the lineage ancestral to colobine monkeys were nine and one, and the dN/dS ratio for the lineage is not significantly greater than one, although it is significantly higher than the background ratio. The likelihood analysis thus confirmed most, but not all, conclusions Messier and Stewart reached using reconstructed ancestral sequences to estimate synonymous and nonsynonymous rates for different lineages.      

Protein Evolutionary Rates Correlate with Expression Independently of Synonymous Substitutions in Helicobacter pylori

In free-living microorganisms, such as Escherichia coli and Saccharomyces cerevisiae, both synonymous and nonsynonymous substitution frequencies correlate with expression levels. Here, we have tested the hypothesis that the correlation between amino acid substitution rates and expression is a by-product of selection for codon bias and translational efficiency in highly expressed genes. To this end, we have examined the correlation between protein evolutionary rates and expression in the human gastric pathogen Helicobacter pylori, where the absence of selection on synonymous sites enables the two types of substitutions to be uncoupled. The results revealed a statistically significant negative correlation between expression levels and nonsynonymous substitutions in both H. pylori and E. coli. We also found that neighboring genes located on the same, but not on opposite strands, evolve at significantly more similar rates than random gene pairs, as expected by co-expression of genes located in the same operon. However, the two species differ in that synonymous substitutions show a strand-specific pattern in E. coli, whereas the weak similarity in synonymous substitutions for neighbors in H. pylori is independent of gene orientation. These results suggest a direct influence of expression levels on nonsynonymous substitution frequencies independent of codon bias and selective constraints on synonymous sites. Electronic Supplementary Material Electronic Supplementary material is available for this article at and accessible for authorised users. [Reviewing Editor: Dr. Nicolas Galtier]     

A phylogenetic model for investigating correlated evolution of substitution rates and continuous phenotypic characters

The comparative approach is routinely used to test for possible correlations between phenotypic or life-history traits. To correct for phylogenetic inertia, the method of independent contrasts assumes that continuous characters evolve along the phylogeny according to a multivariate Brownian process. Brownian diffusion processes have also been used to describe time variations of the parameters of the substitution process, such as the rate of substitution or the ratio of synonymous to nonsynonymous substitutions. Here, we develop a probabilistic framework for testing the coupling between continuous characters and parameters of the molecular substitution process. Rates of substitution and continuous characters are jointly modeled as a multivariate Brownian diffusion process of unknown covariance matrix. The covariance matrix, the divergence times and the phylogenetic variations of substitution rates and continuous characters are all jointly estimated in a Bayesian Monte Carlo framework, imposing on the covariance matrix a prior conjugate to the Brownian process so as to achieve a greater computational efficiency. The coupling between rates and phenotypes is assessed by measuring the posterior probability of positive or negative covariances, whereas divergence dates and phenotypic variations are marginally reconstructed in the context of the joint analysis. As an illustration, we apply the model to a set of 410 mammalian cytochrome b sequences. We observe a negative correlation between the rate of substitution and mass and longevity, which was previously observed. We also find a positive correlation between ω = dN/dS and mass and longevity, which we interpret as an indirect effect of variations of effective population size, thus in partial agreement with the nearly neutral theory. The method can easily be extended to any parameter of the substitution process and to any continuous phenotypic or environmental character.     

Synonymous substitutions are clustered in enterobacterial genes

The spatial distribution of synonymous substitutions in enterobacterial genes is investigated. It is shown that synonymous substitutions are significantly clustered in such a way that a synonymous substitution in one codon elevates the rate of synonymous substitution in an adjacent codon by about 10%. The level of clustering does not appear to be related to the level of gene expression, and it is restricted to a range of two or three codons. There are at least three possible explanations: (1) sequence-directed mutagenesis, (2) recombination, and (3) selection.     

The evolution of mitochondrial genomes in subterranean caviomorph rodents: adaptation against a background of purifying selection

South American tuco-tucos (Ctenomys) and the related coruro (Spalacopus) are two rodent lineages that have independently colonised the subterranean niche. The energetically demanding lifestyles of these species, coupled with the hypoxic atmospheres characteristic of subterranean environments, may have altered the selective regimes on genes encoding proteins related to cellular respiration. Here, we examined the molecular evolution of 13 protein-coding genes in the mitochondrial genome of seven caviomorph rodents, including these two subterranean genera and their above-ground relatives. Using maximum-likelihood and Bayesian approaches, we estimated rates of synonymous (dS) and nonsynonymous (dN) substitutions. We found a significantly higher ω ratio (dN/dS) in subterranean groups as compared to their non-subterranean counterparts in 11 of 13 genes, although no ω ratio was larger than 1. Additionally, we applied a method based on quantitative physicochemical properties to test for positive selection. Amino acid changes implicated in radical structural or functional shifts in the protein property were found to be ubiquitous across the phylogeny, but concentrated in the subterranean lineages. Convergent changes were also found between the subterranean genera used in this study and other mammals adapted to hypoxia. The results of this study suggest a link between niche shifts and weak directional (or episodic) selection at the molecular level against a background of purifying selection.     

Substitution rates in Drosophila nuclear genes: implications for translational selection

The relationships between synonymous and nonsynonymous substitution rates and between synonymous rate and codon usage bias are important to our understanding of the roles of mutation and selection in the evolution of Drosophila genes. Previous studies used approximate estimation methods that ignore codon bias. In this study we reexamine those relationships using maximum-likelihood methods to estimate substitution rates, which accommodate the transition/transversion rate bias and codon usage bias. We compiled a sample of homologous DNA sequences at 83 nuclear loci from Drosophila melanogaster and at least one other species of Drosophila. Our analysis was consistent with previous studies in finding that synonymous rates were positively correlated with nonsynonymous rates. Our analysis differed from previous studies, however, in that synonymous rates were unrelated to codon bias. We therefore conducted a simulation study to investigate the differences between approaches. The results suggested that failure to properly account for multiple substitutions at the same site and for biased codon usage by approximate methods can lead to an artifactual correlation between synonymous rate and codon bias. Implications of the results for translational selection are discussed.     

Evolutionary models accounting for layers of selection in protein-coding genes and their impact on the inference of positive selection

The selective forces acting on a protein-coding gene are commonly inferred using evolutionary codon models by contrasting the rate of nonsynonymous substitutions to the rate of synonymous substitutions. These models usually assume that the synonymous substitution rate, Ks, is homogenous across all sites, which is justified if synonymous sites are free from selection. However, a growing body of evidence indicates that the DNA and RNA levels of protein-coding genes are subject to varying degrees of selective constraints due to various biological functions encoded at these levels. In this paper, we develop evolutionary models that account for these layers of selection by allowing for both among-site variability of substitution rates at the DNA/RNA level (which leads to Ks variability among protein-coding sites) and among-site variability of substitution rates at the protein level (Ka variability). These models are constructed so that positive selection is either allowed or not. This enables statistical testing of positive selection when variability at the DNA/RNA substitution rate is accounted for. Using this methodology, we show that variability of the baseline DNA/RNA substitution rate is a widespread phenomenon in coding sequence data of mammalian genomes, most likely reflecting varying degrees of selection at the DNA and RNA levels. Additionally, we use simulations to examine the impact that accounting for the variability of the baseline DNA/RNA substitution rate has on the inference of positive selection. Our results show that ignoring this variability results in a high rate of erroneous positive-selection inference. Our newly developed model, which accounts for this variability, does not suffer from this problem and hence provides a likelihood framework for the inference of positive selection on a background of variability in the baseline DNA/RNA substitution rate.     

Nucleic acid composition,codon usage,and the rate of synonymous substitution in protein-coding genes

Summary Based on the rates of synonymous substitution in 42 protein-codin gene pairs from rat and human, a correlation is shown to exist between the frequency of the nucleotides in all positions of the codon and the synonymous substitution rate. The correlation coefficients were positive for A and T and negative for C and G. This means that AT-rich genes accumulate more synonymous substitutions than GC-rich genes. Biased patterns of mutation could not account for this phenomenon. Thus, the variation in synonymous substitution rates and the resulting unequal codon usage must be the consequence of selection against A and T in synonymous positions. Most of the varition in rates of synonymous substitution can be explained by the nucleotide composition in synonymous positions. Codon-anticodon interactions, dinucleotide frequencies, and contextual factors influence neither the rates of synonymous substitution nor codon usage. Interestingly, the nucleotide in the second position of codons (always a nonsynonymous position) was found to affect the rate of synonymous substitution. This finding links the rate of nonsynonymous substitution with the synonymous rate. Consequently, highly conservative proteins are expected to be encoded by genes that evolve slowly in terms of synonymous substitutions, and are consequently highly biased in their codon usage.     

Selective processes and adaptive evolution of the cytochrome b gene in salamanders of the genus Salamandrella

Sequence analysis of the cytochrome b gene fragment in the salamanders of the genus Salamandrella, Siberian salamander and Schrenk salamander was performed with the purpose to elucidate the effect of natural selection on the evolution of mitochondrial DNA (mtDNA) in these species. It was demonstrated that despite of notable influence of negative selection (expressed as very low dN/dS values), speciation and intraspecific divergence in salamanders was accompanied by the appearance of radical amino acid substitutions, caused by the influence of positive (directional) selection. To examine the evolutionary pattern of synonymous mtDNA sites, distribution of conservative and non-conservative substitutions was analyzed. The rates of conservative and non-conservative substitutions were nearly equal, pointing to neutrality of mutation process at synonymous mtDNA sites of salamanders. Analysis of conservative and non-conservative synonymous substitution distributions in different parts of phylogenetic trees showed that the differences between the synonymous groups compared were statistically significant only in one phylogenetic group of Siberian salamander (haplogroup C) (P = 0.02). In the group of single substitutions, located at terminal phylogenetic branches of Siberian salamanders from group C, increased rate of conservative substitutions was observed. Based on these findings, it was suggested that selective processes could have an influence on the formation of the synonymous substitution profile in the Siberian salamander mtDNA fragment examined.     

Molecular considerations in the evolution of bacterial genes

Summary Synonymous and nonsynonymous substitution rates at the loci encoding glyceraldehyde-3-phosphate dehydrogenase (gap) and outer membrane protein 3A (ompA) were examined in 12 species of enteric bacteria. By examining homologous sequences in species of varying degrees of relatedness and of known phylogenetic relationships, we analyzed the patterns of synonymous and nonsynonymous substitutions within and among these genes. Although both loci accumulate synonymous substitutions at reduced rates due to codon usage bias, portions of thegap andompA reading frames show significant deviation in synonymous substitution rates not attributable to local codon bias. A paucity of synonymous substitutions in portions of theompA gene may reflect selection for a novel mRNA secondary structure. In addition, these studies allow comparisons of homologous protein-coding sequences (gap) in plants, animals, and bacteria, revealing differences in evolutionary constraints on this glycolytic enzyme in these lineages.     

Molecular evolution of nuclear genes in Cupressacea, a group of conifer trees

We surveyed the molecular evolutionary characteristics of 11 nuclear genes from 10 conifer trees belonging to the Taxodioideae, the Cupressoideae, and the Sequoioideae. Comparisons of substitution rates among the lineages indicated that the synonymous substitution rates of the Cupressoideae lineage were higher than those of the Taxodioideae. This result parallels the pattern previously found in plastid genes. Likelihood-ratio tests showed that the nonsynonymous-synonymous rate ratio did not change significantly among lineages. In addition, after adjustments for lineage effects, the dispersion indices of synonymous and nonsynonymous substitutions were considerably reduced, and the latter was close to 1. These results indicated that the acceleration of evolutionary rates in the Cupressoideae lineage occurred in both the nuclear and plastid genomes, and that generally, this lineage effect affected synonymous and nonsynonymous substitutions similarly. We also investigated the relationship of synonymous substitution rates with the nonsynonymous substitution rate, base composition, and codon bias in each lineage. Synonymous substitution rates were positively correlated with nonsynonymous substitution rates and GC content at third codon positions, but synonymous substitution rates were not correlated with codon bias. Finally, we tested the possibility of positive selection at the protein level, using maximum likelihood models, assuming heterogeneous nonsynonymous-synonymous rate ratios among codon (amino acid) sites. Although we did not detect strong evidence of positively selected codon sites, the analysis suggested that significant variation in nonsynonymous-synonymous rate ratio exists among the sites. The most likely sites for action of positive selection were found in the ferredoxin gene, which is an important component of the apparatus for photosynthesis.