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.     

Genome-wide patterns of nucleotide substitution reveal stringent functional constraints on the protein sequences of thermophiles

To test the hypothesis that the proteins of thermophilic prokaryotes are subject to unusually stringent functional constraints, we estimated the numbers of synonymous and nonsynonymous nucleotide substitutions per site between 17,957 pairs of orthologous genes from 22 pairs of closely related species of Archaea and Bacteria. The average ratio of nonsynonymous to synonymous substitutions was significantly lower in thermophiles than in nonthermophiles, and this effect was observed in both Archaea and Bacteria. There was no evidence that this difference could be explained by factors such as nucleotide content bias. Rather, the results support the hypothesis that proteins of thermophiles are subject to unusually strong purifying selection, leading to a reduced overall level of amino acid evolution per mutational event. The results show that genome-wide patterns of sequence evolution can be influenced by natural selection exerted by a species' environment and shed light on a previous observation that relatively few of the mutations arising in a thermophilic archaeon were nucleotide substitutions in contrast to indels.     

Patterns of nucleotide substitution among simultaneously duplicated gene pairs in Arabidopsis thaliana

We characterized rates and patterns of synonymous and nonsynonymous substitution in 242 duplicated gene pairs on chromosomes 2 and 4 of Arabidopsis thaliana. Based on their collinear order along the two chromosomes, the gene pairs were likely duplicated contemporaneously, and therefore comparison of genetic distances among gene pairs provides insights into the distribution of nucleotide substitution rates among plant nuclear genes. Rates of synonymous substitution varied 13.8-fold among the duplicated gene pairs, but 90% of gene pairs differed by less than 2.6-fold. Average nonsynonymous rates were approximately fivefold lower than average synonymous rates; this rate difference is lower than that of previously studied nonplant lineages. The coefficient of variation of rates among genes was 0.65 for nonsynonymous rates and 0.44 for synonymous rates, indicating that synonymous and nonsynonymous rates vary among genes to roughly the same extent. The causes underlying rate variation were explored. Our analyses tentatively suggest an effect of physical location on synonymous substitution rates but no similar effect on nonsynonymous rates. Nonsynonymous substitution rates were negatively correlated with GC content at synonymous third codon positions, and synonymous substitution rates were negatively correlated with codon bias, as observed in other systems. Finally, the 242 gene pairs permitted investigation of the processes underlying divergence between paralogs. We found no evidence of positive selection, little evidence that paralogs evolve at different rates, and no evidence of differential codon usage or third position GC content.     

A simple method for analyzing exome sequencing data shows distinct levels of nonsynonymous variation for human immune and nervous system genes

To measure the strength of natural selection that acts upon single nucleotide variants (SNVs) in a set of human genes, we calculate the ratio between nonsynonymous SNVs (nsSNVs) per nonsynonymous site and synonymous SNVs (sSNVs) per synonymous site. We transform this ratio with a respective factor f that corrects for the bias of synonymous sites towards transitions in the genetic code and different mutation rates for transitions and transversions. This method approximates the relative density of nsSNVs (rdnsv) in comparison with the neutral expectation as inferred from the density of sSNVs. Using SNVs from a diploid genome and 200 exomes, we apply our method to immune system genes (ISGs), nervous system genes (NSGs), randomly sampled genes (RSGs), and gene ontology annotated genes. The estimate of rdnsv in an individual exome is around 20% for NSGs and 30-40% for ISGs and RSGs. This smaller rdnsv of NSGs indicates overall stronger purifying selection. To quantify the relative shift of nsSNVs towards rare variants, we next fit a linear regression model to the estimates of rdnsv over different SNV allele frequency bins. The obtained regression models show a negative slope for NSGs, ISGs and RSGs, supporting an influence of purifying selection on the frequency spectrum of segregating nsSNVs. The y-intercept of the model predicts rdnsv for an allele frequency close to 0. This parameter can be interpreted as the proportion of nonsynonymous sites where mutations are tolerated to segregate with an allele frequency notably greater than 0 in the population, given the performed normalization of the observed nsSNV to sSNV ratio. A smaller y-intercept is displayed by NSGs, indicating more nonsynonymous sites under strong negative selection. This predicts more monogenically inherited or de-novo mutation diseases that affect the nervous system.     

Evolution of hominoid mitochondrial DNA with special reference to the silent substitution rate over the genome

Summary Focusing on the synonymous substitution rate, we carried out detailed sequence analyses of hominoid mitochondrial (mt) DNAs of ca. 5-kb length. Owing to the outnumbered transitions and strong biases in the base compositions, synonymous substitutions in mtDNA reach rapidly a rather low saturation level. The extent of the compositional biases differs from gene to gene. Such changes in base compositions, even if small, can bring about considerable variation in observed synonymous differences and may result in the region-dependent estimate of the synonymous substitution rate. We demonstrate that such a region dependency is due to a failure to take proper account of heterogeneous compositional biases from gene to gene but that the actual synonymous substitution rate is rather uniform. The synonymous substitution rate thus estimated is 2.37 ± 0.11 × 10^–8 per site per year and comparable to the overall rate for the noncoding region. On the other hand, the rate of nonsynonymous substitutions differs considerably from gene to gene, as expected under the neutral theory of molecular evolution. The lowest rate is 0.8 × 10^–9 per site per year forCOI and the highest rate is 4.5 × 10^–9 forATPase 8, the degree of functional constraints (measured by the ratio of the nonsynonymous to the synonymous substitution rate) being 0.03 and 0.19, respectively. Transfer RNA (tRNA) genes also show variability in the base contents and thus in the nucleotide differences. The average rate for 11 tRNAs contained in the 5-kb region is 3.9 × 10^–9 per site per year. The nucleotide substitutions in the genome suggest that the transition rate is about 17 times faster than the transversion rate.     

Variation in the pattern of synonymous and nonsynonymous difference between two fungal genomes

The proportion of synonymous nucleotide differences per synonymous site (p(S)) and the proportion of nonsynonymous differences per nonsynonymous site (p(N)) were computed at 1,993,217 individual codons in 4,133 protein-coding genes between the two yeast species Saccharomyces cerevisiae and Saccharomyces paradoxus. When the modified Nei-Gojobori method was used, significantly more codons with p(N) > p(S) were observed than expected, based on random pairing of observed p(S) and p(N) values. However, this finding was most likely explained by the presence of a strong negative correlation between the number of synonymous differences and the number of nonsynonymous differences at codons with at least one difference. As a result of this correlation, codons with p(N) > p(S) were characterized not only by unusually high p(N) but also by unusually low p(S). On the other hand, the number of codons with p(N)>p(S) (where p(S) is the mean p(S) for all codons) was very similar to the random expectation, and the observed number of 30-codon windows with p(N) > p(S) was significantly lower than the random expectation. These results imply that the occurrence of a certain number of codons or codon windows with p(N) > p(S) is expected given the nature of nucleotide substitution and need not imply the action of positive Darwinian selection.     

Unbiased estimation of the rates of synonymous and nonsynonymous substitution

Summary The current convention in estimating the number of substitutions per synonymous site (K _S ) and per nonsynonymous site (K _A ) between two protein-coding genes is to count each twofold degenerate site as one-third synonymous and two-thirds nonsynonymous because one of the three possible changes at such a site is synonymous and the other two are nonsynonymous. This counting rule can considerably overestimate theK _S value because transitional mutations tend to occur more often than transversional mutations and because most transitional mutations at twofold degenerate sites are synonymous. A new method that gives unbiased estimates is proposed. An application of the new and the old method to 14 pairs of mouse and rat genes shows that the new method gives aK _S value very close to the number of substitutions per fourfold degenerate site whereas the old method gives a value 30% higher. Both methods give aK _A value close to the number of substitutions per nondegenerate site.     

Departure from neutrality at the mitochondrial NADH dehydrogenase subunit 2 gene in humans,but not in chimpanzees.

To test whether patterns of mitochondrial DNA (mtDNA) variation are consistent with a neutral model of molecular evolution, nucleotide sequences were determined for the 1041 bp of the NADH dehydrogenase subunit 2 (ND2) gene in 20 geographically diverse humans and 20 common chimpanzees. Contingency tests of neutrality were performed using four mutational categories for the ND2 molecule: synonymous and nonsynonymous mutations in the transmembrane regions, and synonymous and nonsynonymous mutations in the surface regions. The following three topological mutational categories were also used: intraspecific tips, intraspecific interiors, and interspecific fixed differences. The analyses reveal a significantly greater number of nonsynonymous polymorphisms within human transmembrane regions than expected based on interspecific comparisons, and they are inconsistent with a neutral equilibrium model. This pattern of excess nonsynonymous polymorphism is not seen within chimpanzees. Statistical tests of neutrality, such as TAJIMA''s D test, and the D and F tests proposed by FU and LI, indicate an excess of low frequency polymorphisms in the human data, but not in the chimpanzee data. This is consistent with recent directional selection, a population bottleneck or background selection of slightly deleterious mutations in human mtDNA samples. The analyses further support the idea that mitochondrial genome evolution is governed by selective forces that have the potential to affect its use as a "neutral" marker in evolutionary and population genetic studies.     

Simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions

Two simple methods for estimating the numbers of synonymous and nonsynonymous nucleotide substitutions are presented. Although they give no weights to different types of codon substitutions, these methods give essentially the same results as those obtained by Miyata and Yasunaga's and by Li et al.'s methods. Computer simulation indicates that estimates of synonymous substitutions obtained by the two methods are quite accurate unless the number of nucleotide substitutions per site is very large. It is shown that all available methods tend to give an underestimate of the number of nonsynonymous substitutions when the number is large.      

On the varied pattern of evolution of 2 fungal genomes: a critique of Hughes and Friedman

A number of statistical tests have been proposed to detect positive Darwinian selection affecting a few amino acid sites in a protein, exemplified by an excess of nonsynonymous nucleotide substitutions. These tests are often more powerful than pairwise sequence comparison, which averages synonymous (d(S)) and nonsynonymous (d(N)) rates over the whole gene. In a recent study, however, Hughes AL and Friedman R (2005. Variation in the pattern of synonymous and nonsynonymous difference between two fungal genomes. Mol Bio Evol. 22: 1320-1324) argue that d(S) and d(N) are expected to fluctuate along the sequence by chance and that an excess of nonsynonymous differences in individual codons is no evidence for positive selection. The authors compared codons in protein-coding genes from the genomes of 2 yeast species, Saccharomyces cerevisiae and Saccharomyces paradoxus. They calculated the proportions of synonymous and nonsynonymous differences per site (p(S) and p(N)) in every codon and discovered that p(N) is often greater than p(S) and that among some codons p(S) and p(N) are negatively correlated. The authors argued that these results invalidate previous tests of codons under positive selection. Here I discuss several errors of statistics in the analysis of Hughes and Friedman, including confusion of statistics with parameters, arbitrary data filtering, and derivation of hypotheses from data. I also apply likelihood ratio tests of positive selection to the yeast data and illustrate empirically that Hughes and Friedman's criticisms on such tests are not valid.     

Rates of Conservative and Radical Nonsynonymous Nucleotide Substitutions in Mammalian Nuclear Genes

To understand the process and mechanism of protein evolution, it is important to know what types of amino acid substitutions are more likely to be under selection and what types are mostly neutral. An amino acid substitution can be classified as either conservative or radical, depending on whether it involves a change in a certain physicochemical property of the amino acid. Assuming Kimura's two-parameter model of nucleotide substitution, I present a method for computing the numbers of conservative and radical nonsynonymous (amino acid altering) nucleotide substitutions per site and estimate these rates for 47 nuclear genes from mammals. The results are as follows. (1) The average radical/conservative rate ratio is 0.81 for charge changes, 0.85 for polarity changes, and 0.49 when both polarity and volume changes are considered. (2) The radical/conservative rate ratio is positively correlated with the nonsynonymous/synonymous rate ratio for charge changes or when both polarity and volume changes are considered. (3) Both the conservative/synonymous rate ratio and the radical/synonymous rate ratio are lower in the rodent lineage than in the primate or artiodactyl lineage, suggesting more intense purifying selection in the rodent lineage, for both conservative and radical nonsynonymous substitutions. (4) Neglecting transition/transversion bias would cause an underestimation of both radical and conservative rates and the ratio thereof. (5) Transversions induce more dramatic genetic alternations than transitions in that transversions produce more amino acid altering changes and among which, more radical changes. Received: 6 April 1999 / Accepted: 16 August 1999     

A survey of genome‐wide single nucleotide polymorphisms through genome resequencing in the Périgord black truffle (Tuber melanosporum Vittad.)

The Périgord black truffle (Tuber melanosporum Vittad.), considered a gastronomic delicacy worldwide, is an ectomycorrhizal filamentous fungus that is ecologically important in Mediterranean French, Italian and Spanish woodlands. In this study, we developed a novel resource of single nucleotide polymorphisms (SNPs) for T. melanosporum using Illumina high‐throughput resequencing. The genome from six T. melanosporum geographical accessions was sequenced to a depth of approximately 20×. These geographical accessions were selected from different populations within the northern and southern regions of the geographical species distribution. Approximately 80% of the reads for each of the six resequenced geographical accessions mapped against the reference T. melanosporum genome assembly, estimating the core genome size of this organism to be approximately 110 Mbp. A total of 442 326 SNPs corresponding to 3540 SNPs/Mbps were identified as being included in all seven genomes. The SNPs occurred more frequently in repeated sequences (85%), although 4501 SNPs were also identified in the coding regions of 2587 genes. Using the ratio of nonsynonymous mutations per nonsynonymous site (pN) to synonymous mutations per synonymous site (pS) and Tajima's D index scanning the whole genome, we were able to identify genomic regions and genes potentially subjected to positive or purifying selection. The SNPs identified represent a valuable resource for future population genetics and genomics studies.     

Reduction of synonymous substitutions in the core protein gene of hepatitis C virus

Molecular evolutionary analyses were carried out to elucidate the phylogenetic relationships, the evolutionary rate, and the divergence times of hepatitis C viruses. Using the nucleotide sequences of the viruses isolated from various locations in the world, we constructed phylogenetic trees. The trees showed that strains isolated from a single location were not necessarily clustered as a group. This suggests that the viruses may be transferred with blood on a worldwide scale. We estimated the evolutionary rates at synonymous and nonsynonymous sites for all genes in the viral genome. We then found that the rate (1.35 × 10^–3 per site per year) at synonymous sites for the C gene was much smaller than those for the other genes (e.g., 6.29 × 10^–3 per site per year for the E gene). This indicates that a special type of functional constraint on synonymous substitutions may exist in the C gene. Because we found an open reading frame (ORF) with the C gene region, the possibility exists that synonymous substitutions for the C gene are constrained by the overlapping ORF whose reading frame is different from that of the C gene. Applying the evolutionary rates to the trees, we also suggest that major groups of hepatitis C viruses diverged from their common ancestor several hundred years ago. Correspondence to: T. Gojobori     

Inference of site frequency spectra from high-throughput sequence data: quantification of selection on nonsynonymous and synonymous sites in humans

Sequencing errors and random sampling of nucleotide types among sequencing reads at heterozygous sites present challenges for accurate, unbiased inference of single-nucleotide polymorphism genotypes from high-throughput sequence data. Here, we develop a maximum-likelihood approach to estimate the frequency distribution of the number of alleles in a sample of individuals (the site frequency spectrum), using high-throughput sequence data. Our method assumes binomial sampling of nucleotide types in heterozygotes and random sequencing error. By simulations, we show that close to unbiased estimates of the site frequency spectrum can be obtained if the error rate per base read does not exceed the population nucleotide diversity. We also show that these estimates are reasonably robust if errors are nonrandom. We then apply the method to infer site frequency spectra for zerofold degenerate, fourfold degenerate, and intronic sites of protein-coding genes using the low coverage human sequence data produced by the 1000 Genomes Project phase-one pilot. By fitting a model to the inferred site frequency spectra that estimates parameters of the distribution of fitness effects of new mutations, we find evidence for significant natural selection operating on fourfold sites. We also find that a model with variable effects of mutations at synonymous sites fits the data significantly better than a model with equal mutational effects. Under the variable effects model, we infer that 11% of synonymous mutations are subject to strong purifying selection.     

Molecular evolution of the major capsid protein VP1 of enterovirus 70.

Nucleotide sequences of the genome RNA encoding capsid protein VP1 (918 nucleotides) of 18 enterovirus 70 (EV70) isolates collected from various parts of the world in 1971 to 1981 were determined, and nucleotide substitutions among them were studied. The genetic distances between isolates were calculated by the pairwise comparison of nucleotide difference. Regression analysis of the genetic distances against time of isolation of the strains showed that the synonymous substitution rate was very high at 21.53 x 10(-3) substitution per nucleotide per year, while the nonsynonymous rate was extremely low at 0.32 x 10(-3) substitution per nucleotide per year. The rate estimated by the average value of synonymous and nonsynonymous substitutions (W.-H. Li, C.-C. Wu, and C.-C. Luo, Mol. Biol. Evol. 2:150-174, 1985) was 5.00 x 10(-3) substitution per nucleotide per year. Taking the average value of synonymous and nonsynonymous substitutions as genetic distances between isolates, the phylogenetic tree was inferred by the unweighted pairwise grouping method of arithmetic average and by the neighbor-joining method. The tree indicated that the virus had evolved from one focal place, and the time of emergence was estimated to be August 1967 +/- 15 months, 2 years before first recognition of the pandemic of acute hemorrhagic conjunctivitis. By superimposing every nucleotide substitution on the branches of the phylogenetic tree, we analyzed nucleotide substitution patterns of EV70 genome RNA. In synonymous substitutions, the proportion of transitions, i.e., C<==>U and G<==>A, was found to be extremely frequent in comparison with that reported on other viruses or pseudogenes. In addition, parallel substitutions (independent substitutions at the same nucleotide position on different branches, i.e., different isolates, of the tree) were frequently found in both synonymous and nonsynonymous substitutions. These frequent parallel substitutions and the low nonsynonymous substitution rate despite the very high synonymous substitution rate described above imply a strong restriction on nonsynonymous substitution sites of VP1, probably due to the requirement for maintaining the rigid icosahedral conformation of the virus.     

Selection on rapidly evolving proteins in the Arabidopsis genome

Genes that have undergone positive or diversifying selection are likely to be associated with adaptive divergence between species. One indicator of adaptive selection at the molecular level is an excess of amino acid replacement fixed differences per replacement site relative to the number of synonymous fixed differences per synonymous site (omega = K(a)/K(s)). We used an evolutionary expressed sequence tag (EST) approach to estimate the distribution of omega among 304 orthologous loci between Arabidopsis thaliana and A. lyrata to identify genes potentially involved in the adaptive divergence between these two Brassicaceae species. We find that 14 of 304 genes (approximately 5%) have an estimated omega > 1 and are candidates for genes with increased selection intensities. Molecular population genetic analyses of 6 of these rapidly evolving protein loci indicate that, despite their high levels of between-species nonsynonymous divergence, these genes do not have elevated levels of intraspecific replacement polymorphisms compared to previously studied genes. A hierarchical Bayesian analysis of protein-coding region evolution within and between species also indicates that the selection intensities of these genes are elevated compared to previously studied A. thaliana nuclear loci.     

Positive selection on the Plasmodium falciparum sporozoite threonine-asparagine-rich protein: analysis of isolates mainly from low endemic areas

The sporozoite threonine-asparagine-rich protein (STARP) of Plasmodium falciparum is an attractive target for a pre-erythrocytic stage malaria vaccine because both naturally acquired and experimentally induced anti-STARP antibodies can block sporozoite invasion of hepatocytes. To explore the extent of sequence variation, we surveyed nucleotide polymorphism across the entire gene, encompassing 2 exons and an intron, of 124 P. falciparum-infected blood samples from Thailand and 10 from 4 other endemic areas. In total 24 haplotypes were identified despite low-level nucleotide diversity at this locus. The mean number of nonsynonymous substitutions per nonsynonymous site (d(N)) significantly exceeded that of synonymous substitutions per synonymous site (d(S)), suggesting that the STARP gene has evolved under positive selection, probably from host immune pressure. The preponderance of conservative amino acid exchanges and a strongly biased T-nucleotide toward the third position of codons in repeat arrays have reflected simultaneous constraints on this molecule, probably from its respective unknown function and nucleotide composition. Sequence conservation in the STARP locus among clinical isolates from different disease endemic areas would not compromise vaccine incorporation.     

Genetic heterogeneity of hypervariable region 1 of the hepatitis C virus (HCV) genome and sensitivity of HCV to alpha interferon therapy

Hepatitis C virus (HCV) populations persist in vivo as a mixture of heterogeneous viruses called quasispecies. The relationship between the genetic heterogeneity of these variants and their responses to antiviral treatment remains to be elucidated. We have studied 26 virus strains to determine the influence of hypervariable region 1 (HVR-1) of the HCV genome on the effectiveness of alpha interferon (IFN-alpha) therapy. Following PCR amplification, we cloned and sequenced HVR-1. Pretreatment serum samples from 13 individuals with chronic hepatitis C whose virus was subsequently eradicated by treatment were compared with samples from 13 nonresponders matched according to the major factors known to influence the response, i.e., sex, genotype, and pretreatment serum HCV RNA concentration. The degree of virus variation was assessed by analyzing 20 clones per sample and by calculating nucleotide sequence entropy (complexity) and genetic distances (diversity). Types of mutational changes were also determined by calculating nonsynonymous substitutions per nonsynonymous site (K(a)) and synonymous substitutions per synonymous site (K(s)). The paired-comparison analysis of the nucleotide sequence entropy and genetic distance showed no statistical differences between responders and nonresponders. By contrast, nonsynonymous substitutions were more frequent than synonymous substitutions (P 相似文献   

Contrasting patterns of synonymous and nonsynonymous sequence evolution in asexual and sexual freshwater snail lineages

In asexual lineages, both synonymous and nonsynonymous sequence polymorphism may be reduced due to severe founder effects when asexual lineages originate. However, mildly deleterious (nonsynonymous) mutations may accumulate after asexual lineages are formed, because the efficiency of purifying selection is reduced even in the nonrecombining mitochondrial genome. Here we examine patterns of synonymous and nonsynonymous mitochondrial sequence polymorphism in asexual and sexual lineages of the freshwater snail Campeloma. Using clade-specific estimates, we found that synonymous sequence polymorphism was significantly reduced by 75% in asexuals relative to sexuals, whereas nonsynonymous sequence polymorphism did not differ significantly between sexuals and asexuals. Two asexual clades had high negative values for Tajima's D statistic. Coalescent simulations confirmed that various bottleneck scenarios can account for this result. We also used branch-specific estimates of the ratio of amino acid to silent substitutions, K(a)/K(s). Our study revealed that K(a)/K(s) ratios are six times higher in terminal branches of independent asexual lineages compared to sexuals. Coalescent-based reconstruction of gene networks for all sexual and asexual clades indicated that nonsynonymous mutations occurred at a higher frequency in recently derived asexual haplotypes. These findings suggest that patterns of synonymous and nonsynonymous nucleotide polymorphism in asexual snail lineages may be shaped by both severe founder effect and relaxed purifying selection.     

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.