A method for estimating the numbers of synonymous and nonsynonymous substitutions per site

A method for estimating the numbers of synonymous (Ks) and nonsynonymous (Ka) substitutions per site is proposed. The method is based on the Li's (J Mol. Evol. 36:96–99, 1993) and Pamilo and Bianchi's (Mol. Biol. Evol. 10:271–281, 1993) method, but a putative source of bias is solved. It is proposed that the number of synonymous substitutions that are actually transitions or transversions should be computed by separating the twofold degenerate sites into two types of sites, 2S-fold and 2V-fold, where only transitional and transversional substitutions are synonymous, respectively. Kimura's (J. Mol. Evol. 16:111–120, 1980) two-parameter correcting method for multiple substitutions at a site is then applied using the overall observed synonymous transversion frequency to estimate both the numbers of synonymous transversional (Bs) and transitional (As) substitutions per site. This approach, therefore, also minimizes stochastic errors. Computer simulations indicate that the method presented gives more accurate Ks and Ka estimates than the aforementioned methods. Furthermore, the obtention of confidence intervals for divergence estimates by computer simulation is proposed.     

Estimating synonymous and nonsynonymous substitution rates

Partitioning the total substitution rate into synnonymous and nonsynonymous components is a key aspect of many analyses in molecular evolution. Numerous methods exist for estimating these rates. However, until recently none of the estimation procedures were based on a sound statistical footing. In this paper, the evolutionary model of Muse and Gaut (1994) is used as the basis for two sets of parameters quantifying silent and replacement substitution rates. The parameters are shown to be equal when the four nucleotides are equally frequent and unequal otherwise. Maximum-likelihood estimation of these parameters is described, and the performance of these estimates is compared to that of existing estimation procedures. It is shown that the estimates of Nei and Gojobori (1986) are not unbiased for either set of parameters, although they provide very good estimates for one set as long as sequence divergence is not too high. However, some disturbing properties are found for the Nei and Gojobori estimates. In particular, it is shown that the expected value of the Nei and Gojobori estimate of silent substitution rate is a function of both the silent and replacement substitution rates. The maximum-likelihood estimates have no such problems.      

Estimating synonymous and nonsynonymous substitution rates under realistic evolutionary models

Approximate methods for estimating the numbers of synonymous and nonsynonymous substitutions between two DNA sequences involve three steps: counting of synonymous and nonsynonymous sites in the two sequences, counting of synonymous and nonsynonymous differences between the two sequences, and correcting for multiple substitutions at the same site. We examine complexities involved in those steps and propose a new approximate method that takes into account two major features of DNA sequence evolution: transition/transversion rate bias and base/codon frequency bias. We compare the new method with maximum likelihood, as well as several other approximate methods, by examining infinitely long sequences, performing computer simulations, and analyzing a real data set. The results suggest that when there are transition/transversion rate biases and base/codon frequency biases, previously described approximate methods for estimating the nonsynonymous/synonymous rate ratio may involve serious biases, and the bias can be both positive and negative. The new method is, in general, superior to earlier approximate methods and may be useful for analyzing large data sets, although maximum likelihood appears to always be the method of choice.     

Evaluation of six methods for estimating synonymous and nonsynonymous substitution rates

Methods for estimating synonymous and nonsynonymous substitution rates among protein-coding sequences adopt different mutation （substitution） models with subtle yet significant differences, which lead to different estimates of evolutionary information. Little attention has been devoted to the comparison of methods for obtaining reliable estimates since the amount of sequence variations within targeted datasets is always unpredictable. To our knowledge, there is little information available in literature about evaluation of these different methods. In this study, we compared six widely used methods and provided with evaluation results using simulated sequences. The results indicate that incorporating sequence features （such as transition/transversion bias and nucleotide/codon frequency bias） into methods could yield better performance. We recommend that conclusions related to or derived from Ka and Ks analyses should not be readily drawn only according to results from one method.     

Variation in synonymous substitution rates among mammalian genes and the correlation between synonymous and nonsynonymous divergences

Using mammalian gene sequences, the variances in the numbers of synonymous and nonsynonymous substitutions among genes were estimated together with the correlation coefficient between the two. The expected correlation coefficient can be obtained under the neutral theory using these estimated values of the variances. The expected coefficient is found to often be one-half to two-thirds of the observed value. Possible causes for the disagreement were discussed, such as correlated selective constraints on the two types of substitutions and excess doublet mutations. The variance of mutation rate and that of selective constraint were also estimated. The results show that the coefficient of variation of the former is 0.2–0.3, whereas that of the latter is 0.7–0.9. Correspondence to: T. Ohta     

Synonymous and nonsynonymous substitutions in mammalian genes and the nearly neutral theory

The nearly neutral theory of molecular evolution predicts larger generation-time effects for synonymous than for nonsynonymous substitutions. This prediction is tested using the sequences of 49 single-copy genes by calculating the average and variance of synonymous and nonsynonymous substitutions in mammalian star phylogenies (rodentia, artiodactyla, and primates). The average pattern of the 49 genes supports the prediction of the nearly neutral theory, with some notable exceptions.The nearly neutral theory also predicts that the variance of the evolutionary rate is larger than the value predicted by the completely neutral theory. This prediction is tested by examining the dispersion index (ratio of the variance to the mean), which is positively correlated with the average substitution number. After weighting by the lineage effects, this correlation almost disappears for nonsynonymous substitutions, but not quite so for synonymous substitutions. After weighting, the dispersion indices of both synonymous and nonsynonymous substitutions still exceed values expected under the simple Poisson process. The results indicate that both the systematic bias in evolutionary rate among the lineages and the episodic type of rate variation are contributing to the large variance. The former is more significant to synonymous substitutions than to nonsynonymous substitutions. Isochore evolution may be similar to synonymous substitutions. The rate and pattern found here are consistent with the nearly neutral theory, such that the relative contributions of drift and selection differ between the two types of substitutions. The results are also consistent with Gillespie's episodic selection theory.     

Estimating absolute rates of synonymous and nonsynonymous nucleotide substitution in order to characterize natural selection and date species divergences

The rate of molecular evolution can vary among lineages. Sources of this variation have differential effects on synonymous and nonsynonymous substitution rates. Changes in effective population size or patterns of natural selection will mainly alter nonsynonymous substitution rates. Changes in generation length or mutation rates are likely to have an impact on both synonymous and nonsynonymous substitution rates. By comparing changes in synonymous and nonsynonymous rates, the relative contributions of the driving forces of evolution can be better characterized. Here, we introduce a procedure for estimating the chronological rates of synonymous and nonsynonymous substitutions on the branches of an evolutionary tree. Because the widely used ratio of nonsynonymous and synonymous rates is not designed to detect simultaneous increases or simultaneous decreases in synonymous and nonsynonymous rates, the estimation of these rates rather than their ratio can improve characterization of the evolutionary process. With our Bayesian approach, we analyze cytochrome oxidase subunit I evolution in primates and infer that nonsynonymous rates have a greater tendency to change over time than do synonymous rates. Our analysis of these data also suggests that rates have been positively correlated.     

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.     

Site-to-site variation of synonymous substitution rates

We develop a new model for studying the molecular evolution of protein-coding DNA sequences. In contrast to existing models, we incorporate the potential for site-to-site heterogeneity of both synonymous and nonsynonymous substitution rates. We demonstrate that within-gene heterogeneity of synonymous substitution rates appears to be common. Using the new family of models, we investigate the utility of a variety of new statistical inference procedures, and we pay particular attention to issues surrounding the detection of sites undergoing positive selection. We discuss how failure to model synonymous rate variation in the model can lead to misidentification of sites as positively selected.     

Comparison of three methods for estimating rates of synonymous and nonsynonymous nucleotide substitutions

Three frequently used methods for estimating the synonymous and nonsynonymous substitution rates (Ks and Ka) were evaluated and compared for their accuracies; these methods are denoted by LWL85, LPB93, and GY94, respectively. For this purpose, we used a codon-evolution model to obtain the expected Ka and Ks values for the above three methods and compared the values with those obtained by the three methods. We also proposed some modifications of LWL85 and LPB93 to increase their accuracies. Our computer simulations under the codon-evolution model showed that for sequences < or =300 codons, the performance of GY94 may not be reliable. For longer sequences, GY94 is more accurate for estimating the Ka/Ks ratio than the modified LPB93 and LWL85 in the majority of the cases studied. This is particularly so when k > or = 3, which is the transition/transversion (mutation) rate ratio. However, when k is approximately 2 and when the sequence divergence is relatively large, the modified LWL85 performed better than GY94 and the modified LPB93. The inferiority of LPB93 to LWL85 is surprising because LPB93 was intended to improve LWL85. Also, it has been thought that the codon-based method of GY94 is better than the heuristic method of LWL85, but our simulation results showed that in many cases, the opposite was true, even though our simulation was based on the codon-evolution model.     

New methods for estimating the numbers of synonymous and nonsynonymous substitutions

New methods for estimating the numbers of synonymous and nonsynonymous substitutions per site were developed. The methods are unweighted pathway methods based on Kimura's two-parameter model. Computer simulations were conducted to evaluate the accuracies of the new methods, Nei and Gojobori's (NG) method, Miyata and Yasunaga's (MY) method, Li, Wu, and Luo's (LWL) method, and Pamilo, Bianchi, and Li's (PBL) method. The following results were obtained: (1) The NG, MY, and LWL methods give overestimates of the number of synonymous substitutions and underestimates of the number of nonsynonymous substitutions. The major cause for the biased estimation is that these three methods underestimate the number of synonymous sites and overestimate the number of nonsynonymous sites. (2) The PBL method gives better estimates of the numbers of synonymous and nonsynonymous substitutions than those obtained by the NG, MY, and LWL methods. (3) The new methods also give better estimates of the numbers of synonymous and nonsynonymous substitutions than those obtained by the NG, MY, and LWL methods. In addition, estimates of the numbers of synonymous and nonsynonymous sites obtained by the new methods are reasonably accurate. (4) In some cases, the new methods and the PBL method give biased estimates of substitution numbers. However, from the number of nucleotide substitutions at the third position of codons, we can examine whether estimates obtained by the new methods are good or not, whereas we cannot make an examination of estimates obtained by the PBL method. (5) When there are strong transition/transversion and nucleotide-frequency biases like mitochondrial genes, all of the above methods give biased estimates of substitution numbers. In such cases, Kondo et al.'s method is recommended to be used for estimating the number of synonymous substitutions, although their method cannot estimate the number of nonsynonymous substitutions and is time-consuming. These results, particularly result (1), call for reexaminations of some genes. This is because evolutionary pictures of genes have often been discussed on the basis of results obtained by the NG, MY, and LWL methods, which are favorable for the neutral theory of molecular evolution.     

A likelihood approach for comparing synonymous and nonsynonymous nucleotide substitution rates, with application to the chloroplast genome

A model of DNA sequence evolution applicable to coding regions is presented. This represents the first evolutionary model that accounts for dependencies among nucleotides within a codon. The model uses the codon, as opposed to the nucleotide, as the unit of evolution, and is parameterized in terms of synonymous and nonsynonymous nucleotide substitution rates. One of the model's advantages over those used in methods for estimating synonymous and nonsynonymous substitution rates is that it completely corrects for multiple hits at a codon, rather than taking a parsimony approach and considering only pathways of minimum change between homologous codons. Likelihood-ratio versions of the relative-rate test are constructed and applied to data from the complete chloroplast DNA sequences of Oryza sativa, Nicotiana tabacum, and Marchantia polymorpha. Results of these tests confirm previous findings that substitution rates in the chloroplast genome are subject to both lineage-specific and locus-specific effects. Additionally, the new tests suggest tha the rate heterogeneity is due primarily to differences in nonsynonymous substitution rates. Simulations help confirm previous suggestions that silent sites are saturated, leaving no evidence of heterogeneity in synonymous substitution rates.      

Substitution rates in hepatitis delta virus

Substitution rates were estimated for the coding and noncoding regions of the hepatitis delta virus (HDV). The estimated rates of synonymous substitution in HDV were lower than the rates of substitution at nonsynonymous sites and in the noncoding region. HDV has lower synonymous substitution rates than the hepatitis C virus, though both are RNA viruses. The relatively low rate of synonymous substitution in HDV may be due to a strong preference of G and C nucleotides at third codon positions. Variation in substitution rate among HDV lineages may be correlated with the clinical development of the HDV-induced hepatitis. The phylogenetic tree inferred for 24 HDV strains reveals similarities between lineages isolated from the same geographic region. Correspondence to: W.-H. Li     

Synonymous and nonsynonymous rate variation in nuclear genes of mammals

A maximum likelihood approach was used to estimate the synonymous and nonsynonymous substitution rates in 48 nuclear genes from primates, artiodactyls, and rodents. A codon-substitution model was assumed, which accounts for the genetic code structure, transition/transversion bias, and base frequency biases at codon positions. Likelihood ratio tests were applied to test the constancy of nonsynonymous to synonymous rate ratios among branches (evolutionary lineages). It is found that at 22 of the 48 nuclear loci examined, the nonsynonymous/synonymous rate ratio varies significantly across branches of the tree. The result provides strong evidence against a strictly neutral model of molecular evolution. Our likelihood estimates of synonymous and nonsynonymous rates differ considerably from previous results obtained from approximate pairwise sequence comparisons. The differences between the methods are explored by detailed analyses of data from several genes. Transition/transversion rate bias and codon frequency biases are found to have significant effects on the estimation of synonymous and nonsynonymous rates, and approximate methods do not adequately account for those factors. The likelihood approach is preferable, even for pairwise sequence comparison, because more-realistic models about the mutation and substitution processes can be incorporated in the analysis. Received: 17 May 1997 / Accepted: 28 September 1997     

Pattern of nucleotide substitution and divergence of prophenoloxidase in decapods

Despite the unprecedented development in identification and characterization of prophenoloxidase (proPO) in commercially important decapods, little is known about the evolutionary relationship, rate of amino acid replacement and differential selection pressures operating on proPO of different species of decapods. Here we report the evolutionary relationship among these nine decapod species based on proPO gene and types of selective pressures operating on proPO codon sites. Our analyses revealed that all the nine decapod species shared a common ancestor. The mean percentage sequence divergence at proPO gene was 34.4+/-0.6%. Pairwise estimates of nonsynonymous to synonymous ratio (omega) for Homarus americanus-H. gammarus is greater than one, therefore indicating adaptive evolution (functional diversification) of proPO in these two species. In contrast, strong purifying selection (omega<1) was observed in all other species pairs. However, phylogenetically closely related decapods revealed relatively higher omega value (omega=0.15+/-0.3) than the distantly related species pairs (omega=0.0075+/-0.005). These discrepancies could be due to higher fixation probability of beneficial mutation in closely related species. Maximum likelihood-based codon substitution analyses revealed a strong purifying selection operating on most of the codon sites, therefore suggesting proPO is functionally constrained (purifying selection). Codon substitution analyses have also revealed the evidence of strong purifying selection in haemocyanin subunits of decapods.     

The molecular clock ticks regularly in muroid rodents and hamsters

Summary Extensive DNA sequence data are used to compare the rates of nucleotide substitution in the mouse, rat, and hamster lineages. A relative rate test using hamster sequences as references shows that the rates of synonymous and nonsynonymous substitution in the mouse and rat lineages are nearly equal and a test using human sequences as references shows that the rates in the mouse, rat, and hamster lineages are also nearly equal. Under the assumptions that the guinea pig lineage and the myomorph (mouse, rat, and hamster) lineage diverged 70–100 million years (Myr) ago and that the rate of nucleotide substitution has been constant in all these lineages since their divergence, the date of the mouse-rat split is estimated to be between 20 and 29 Myr ago, which is considerably older than the date ( 12 Myr) suggested by available rodent fossils and considerably younger than the date ( 35 Myr) suggested by Wilson and colleagues. The murid-hamster split is estimated to be 1.6 times older than the mouse-rat split.     

Synonymous substitution rates in Drosophila: Mitochondrial versus nuclear genes

Synonymous substitution rates in mitochondrial and nuclear genes of Drosophila were compared. To make accurate comparisons, we considered the following: (1) relative synonymous rates, which do not require divergence time estimates, should be used; (2) methods estimating divergence should take into account base composition; (3) only very closely related species should be used to avoid effects of saturation; (4) the heterogeneity of rates should be examined. We modified the methods estimating synonymous substitution numbers to account for base composition bias. By using these methods, we found that mitochondrial genes have 1.7–3.4 times higher synonymous substitution rates than the fastest nuclear genes or 4.5–9.0 times higher rates than the average nuclear genes. The average rate of synonymous transversions was 2.7 (estimated from the melanogaster species subgroup) or 2.9 (estimated from the obscura group) times higher in mitochondrial genes than in nuclear genes. Synonymous transversions in mitochondrial genes occurred at an approximately equivalent rate to those in the fastest nuclear genes. This last result is not consistent with the hypothesis that the difference in turnover rates between mitochondrial and nuclear genomes is the major factor determining higher synonymous substitution rates in mtDNA. We conclude that the difference in synonymous substitution rates is due to a combination of two factors: a higher transitional mutation rate in mtDNA and constraints on nuclear genes due to selection for codon usage. Received: 27 November 1996 / Accepted: 8 May 1997     

A new method for estimating synonymous and nonsynonymous rates of nucleotide substitution considering the relative likelihood of nucleotide and codon changes

A new method is proposed for estimating the number of synonymous and nonsynonymous nucleotide substitutions between homologous genes. In this method, a nucleotide site is classified as nondegenerate, twofold degenerate, or fourfold degenerate, depending on how often nucleotide substitutions will result in amino acid replacement; nucleotide changes are classified as either transitional or transversional, and changes between codons are assumed to occur with different probabilities, which are determined by their relative frequencies among more than 3,000 changes in mammalian genes. The method is applied to a large number of mammalian genes. The rate of nonsynonymous substitution is extremely variable among genes; it ranges from 0.004 X 10(-9) (histone H4) to 2.80 X 10(-9) (interferon gamma), with a mean of 0.88 X 10(-9) substitutions per nonsynonymous site per year. The rate of synonymous substitution is also variable among genes; the highest rate is three to four times higher than the lowest one, with a mean of 4.7 X 10(-9) substitutions per synonymous site per year. The rate of nucleotide substitution is lowest at nondegenerate sites (the average being 0.94 X 10(-9), intermediate at twofold degenerate sites (2.26 X 10(-9)). and highest at fourfold degenerate sites (4.2 X 10(-9)). The implication of our results for the mechanisms of DNA evolution and that of the relative likelihood of codon interchanges in parsimonious phylogenetic reconstruction are discussed.     

Relative rates of synonymous substitutions in the mitochondrial, chloroplast and nuclear genomes of seed plants

Previous studies have estimated that, in angiosperms, the synonymous substitution rate of chloroplast genes is three times higher than that of mitochondrial genes and that of nuclear genes is twelve times higher than that of mitochondrial genes. Here we used 12 genes in 27 seed plant species to investigate whether these relative rates of substitutions are common to diverse seed plant groups. We find that the overall relative rate of synonymous substitutions of mitochondrial, chloroplast and nuclear genes of all seed plants is 1:3:10, that these ratios are 1:2:4 in gymnosperms but 1:3:16 in angiosperms and that they go up to 1:3:20 in basal angiosperms. Our results show that the mitochondrial, chloroplast and nuclear genomes of seed plant groups have different synonymous substitutions rates, that these rates are different in different seed plant groups and that gymnosperms have smaller ratios than angiosperms.     

Unbiased estimation of symmetrical directional mutation pressure from protein-coding DNA

The most generally applicable procedure for obtaining estimates of the symmetrical, or strand-nonspecific, directional mutation pressure (μ_D) on protein-coding DNA sequences is to determine the G+C content at synonymous codon sites (P _syn), and to divide P _syn by twice the arithmetic mean of the G+C content at synonymous codon sites of a large number of randomly generated, synonymously coding DNA sequences (P _syn). Unfortunately, the original procedure yields biased estimates of P _syn and μ_D and is computationally expensive. We here present a fast procedure for estimating unbiased μ_D values. The procedure employs direct calculation of P _syn (≈P _syn) and two normalization procedures, one for P _syn≤P _syn and another for P _syn≥P _syn. The normalization removes a bias sometimes caused by codons specifying arginine, asparagine, isoleucine, and leucine. Consequently, comparison of protein-coding genes that are translated using different genetic codes is facilitated. Received: 5 May 1995 / Accepted: 30 November 1995