Molecular evolution of cadherin-related neuronal receptor/protocadherin(alpha) (CNR/Pcdh(alpha)) gene cluster in Mus musculus subspecies

The mouse cadherin-related neuronal receptor/protocadherin (CNR/Pcdh) gene clusters are located on chromosome 18. We sequenced single-nucleotide polymorphisms (SNPs) of the CNR/Pcdh(alpha)-coding region among 12 wild-derived and four laboratory strains; these included the four major subspecies groups of Mus musculus: domesticus, musculus, castaneus, and bactrianus. We detected 883 coding SNPs (cSNPs) in the CNR/Pcdh(alpha) variable exons and three in the constant exons. Among all the cSNPs, 586 synonymous (silent) and 297 nonsynonymous (amino acid exchanged) substitutions were found; therefore, the K(a)/K(s) ratio (nonsynonymous substitutions per synonymous substitution) was 0.51. The synonymous cSNPs were relatively concentrated in the first and fifth extracellular cadherin domain-encoding regions (ECs) of CNR/Pcdh(alpha). These regions have high nucleotide homology among the CNR/Pcdh(alpha) paralogs, suggesting that gene conversion events in synonymous and homologous regions of the CNR/Pcdh(alpha) cluster are related to the generation of cSNPs. A phylogenetic analysis revealed gene conversion events in the EC1 and EC5 regions. Assuming that the common sequences between rat and mouse are ancestral, the GC content of the third codon position has increased in the EC1 and EC5 regions, although biased substitutions from GC to AT were detected in all the codon positions. In addition, nonsynonymous substitutions were extremely high (11 of 13, K(a)/K(s) ratio 5.5) in the laboratory mouse strains. The artificial environment of laboratory mice may allow positive selection for nonsynonymous amino acid variations in CNR/Pcdh(alpha) during inbreeding. In this study, we analyzed the direction of cSNP generation, and concluded that subspecies-specific nucleotide substitutions and region-restricted gene conversion events may have contributed to the generation of genetic variations in the CNR/Pcdh genes within and between species.     

Recombinogenic activity of chimeric recA genes (Pseudomonas aeruginosa/Escherichia coli): a search for RecA protein regions responsible for this activity

The nature of selection on capsid genes of foot-and-mouth disease virus (FMDV) was characterized by examining the ratio of nonsynonymous to synonymous substitutions in 11 data sets of sequences obtained from six different serotypes of FMDV. Using a method of analysis that assigns each codon position to one of a number of estimated values of nonsynonymous to synonymous ratio, significant evidence of positive selection was identified in 5 data sets, operating at 1-7% of codon positions. Evidence of positive selection was identified in complete capsid sequences of serotypes A and C and in VP1 sequences of serotypes SAT 1 and 2. Sequences of serotype SAT-2 recovered from a persistently infected African buffalo also revealed evidence for positive selection. Locations of codons under positive selection coincide closely with those of antigenic sites previously identified with the use of monoclonal antibody escape mutants. The vast majority of codons are under mild to strong purifying selection. However, these results suggest that arising antigenic variants benefit from a selective advantage in their interaction with the immune system, either during the course of an infection or in transmission to individuals with previous exposure to antigen. Analysis of amino acid usage at sites under positive selection indicates that this selective advantage can be conferred by amino acid substitutions that share physicochemically similar properties.     

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.     

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.     

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.     

A method for detecting positive selection at single amino acid sites

A method was developed for detecting the selective force at single amino acid sites given a multiple alignment of protein-coding sequences. The phylogenetic tree was reconstructed using the number of synonymous substitutions. Then, the neutrality was tested for each codon site using the numbers of synonymous and nonsynonymous changes throughout the phylogenetic tree. Computer simulation showed that this method accurately estimated the numbers of synonymous and nonsynonymous substitutions per site, as long as the substitution number on each branch was relatively small. The false-positive rate for detecting the selective force was generally low. On the other hand, the true-positive rate for detecting the selective force depended on the parameter values. Within the range of parameter values used in the simulation, the true-positive rate increased as the strength of the selective force and the total branch length (namely the total number of synonymous substitutions per site) in the phylogenetic tree increased. In particular, with the relative rate of nonsynonymous substitutions to synonymous substitutions being 5.0, most of the positively selected codon sites were correctly detected when the total branch length in the phylogenetic tree was > or = 2.5. When this method was applied to the human leukocyte antigen (HLA) gene, which included antigen recognition sites (ARSs), positive selection was detected mainly on ARSs. This finding confirmed the effectiveness of the present method with actual data. Moreover, two amino acid sites were newly identified as positively selected in non-ARSs. The three-dimensional structure of the HLA molecule indicated that these sites might be involved in antigen recognition. Positively selected amino acid sites were also identified in the envelope protein of human immunodeficiency virus and the influenza virus hemagglutinin protein. This method may be helpful for predicting functions of amino acid sites in proteins, especially in the present situation, in which sequence data are accumulating at an enormous speed.     

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.     

Evolution of Rh Blood Group Genes Have Experienced Gene Conversions and Positive Selection

There are two tightly linked loci (D and CE) for the human Rh blood group. Their gene products are membrane proteins having 12 transmembrane domains and form a complex with Rh50 glycoprotein on erythrocytes. We constructed phylogenetic networks of human and nonhuman primate Rh genes, and the network patterns suggested the occurrences of gene conversions. We therefore used a modified site-by-site reconstruction method by using two assumed gene trees and detected 9 or 11 converted regions. After eliminating the effect of gene conversions, we estimated numbers of nonsynonymous and synonymous substitutions for each branch of both trees. Whichever gene tree we selected the branch connecting hominoids and Old World monkeys showed significantly higher nonsynonymous than synonymous substitutions, an indication of positive selection. Many other branches also showed higher nonsynonymous than synonymous substitutions; this suggests that the Rh genes have experienced some kind of positive selection. Received: 16 March 1999 / Accepted: 17 June 1999     

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.     

Synonymous and nonsynonymous polymorphisms versus divergences in bacterial genomes

Comparison of the ratio of nonsynonymous to synonymous polymorphisms within species with the ratio of nonsynonymous to synonymous substitutions between species has been widely used as a supposed indicator of positive Darwinian selection, with the ratio of these 2 ratios being designated as a neutrality index (NI). Comparison of genome-wide polymorphism within 12 species of bacteria with divergence from an outgroup species showed substantial differences in NI among taxa. A low level of nonsynonymous polymorphism at a locus was the best predictor of NI < 1, rather than a high level of nonsynonymous substitution between species. Moreover, genes with NI < 1 showed a strong tendency toward the occurrence of rare nonsynonymous polymorphisms, as expected under the action of ongoing purifying selection. Thus, our results are more consistent with the hypothesis that a high relative rate of between-species nonsynonymous substitution reflects mainly the action of purifying selection within species to eliminate slightly deleterious mutations rather than positive selection between species. This conclusion is consistent with previous results highlighting an important role of slightly deleterious variants in bacterial evolution and suggests caution in the use of the McDonald-Kreitman test and related statistics as tests of positive selection.     

Calibration of multiple poliovirus molecular clocks covering an extended evolutionary range

We have calibrated five different molecular clocks for circulating poliovirus based upon the rates of fixation of total substitutions (K(t)), synonymous substitutions (K(s)), synonymous transitions (A(s)), synonymous transversions (B(s)), and nonsynonymous substitutions (K(a)) into the P1/capsid region (2,643 nucleotides). Rates were determined over a 10-year period by analysis of sequences of 31 wild poliovirus type 1 isolates representing a well-defined phylogeny derived from a common imported ancestor. Similar rates were obtained by linear regression, the maximum likelihood/single-rate dated-tip method, and Bayesian inference. The very rapid K(t) [(1.03 +/- 0.10) x 10(-2) substitutions/site/year] and K(s) [(1.00 +/- 0.08) x 10(-2)] clocks were driven primarily by the A(s) clock [(0.96 +/- 0.09) x 10(-2)], the B(s) clock was approximately 10-fold slower [(0.10 +/- 0.03) x 10(-2)], and the more stochastic K(a) clock was approximately 30-fold slower [(0.03 +/- 0.01) x 10(-2)]. Nonsynonymous substitutions at all P1/capsid sites, including the neutralizing antigenic sites, appeared to be constrained by purifying selection. Simulation of the evolution of third-codon positions suggested that saturation of synonymous transitions would be evident at 10 years and complete at approximately 65 years of independent transmission. Saturation of synonymous transversions was predicted to be minimal at 20 years and incomplete at 100 years. The rapid evolution of the K(t), K(s), and A(s) clocks can be used to estimate the dates of divergence of closely related viruses, whereas the slower B(s) and K(a) clocks may be used to explore deeper evolutionary relationships within and across poliovirus genotypes.     

Widespread positive selection in synonymous sites of mammalian genes

Evolution of protein sequences is largely governed by purifying selection, with a small fraction of proteins evolving under positive selection. The evolution at synonymous positions in protein-coding genes is not nearly as well understood, with the extent and types of selection remaining, largely, unclear. A statistical test to identify purifying and positive selection at synonymous sites in protein-coding genes was developed. The method compares the rate of evolution at synonymous sites (Ks) to that in intron sequences of the same gene after sampling the aligned intron sequences to mimic the statistical properties of coding sequences. We detected purifying selection at synonymous sites in approximately 28% of the 1,562 analyzed orthologous genes from mouse and rat, and positive selection in approximately 12% of the genes. Thus, the fraction of genes with readily detectable positive selection at synonymous sites is much greater than the fraction of genes with comparable positive selection at nonsynonymous sites, i.e., at the level of the protein sequence. Unlike other genes, the genes with positive selection at synonymous sites showed no correlation between Ks and the rate of evolution in nonsynonymous sites (Ka), indicating that evolution of synonymous sites under positive selection is decoupled from protein evolution. The genes with purifying selection at synonymous sites showed significant anticorrelation between Ks and expression level and breadth, indicating that highly expressed genes evolve slowly. The genes with positive selection at synonymous sites showed the opposite trend, i.e., highly expressed genes had, on average, higher Ks. For the genes with positive selection at synonymous sites, a significantly lower mRNA stability is predicted compared to the genes with negative selection. Thus, mRNA destabilization could be an important factor driving positive selection in nonsynonymous sites, probably, through regulation of expression at the level of mRNA degradation and, possibly, also translation rate. So, unexpectedly, we found that positive selection at synonymous sites of mammalian genes is substantially more common than positive selection at the level of protein sequences. Positive selection at synonymous sites might act through mRNA destabilization affecting mRNA levels and translation.     

Molecular population genetics of the gene encoding the human fertilization protein zonadhesin reveals rapid adaptive evolution

A hallmark of positive selection (adaptive evolution) in protein-coding regions is a d(N)/d(S) ratio >1, where d(N) is the number of nonsynonymous substitutions/nonsynonymous sites and d(S) is the number of synonymous substitutions/synonymous sites. Zonadhesin is a male reproductive protein localized on the sperm head, comprising many domains known to be involved in cell-cell interaction or cell adhesion. Previous studies have shown that VWD domains (homologous to the D domains of the von Willebrand factor) are involved directly in binding to the female zona pellucida (ZP) in a species-specific manner. In this study, we sequenced 47 coding exons in 12 primate species and, by using maximum-likelihood methods to determine sites under positive selection, we show that VWD2, membrane/A5 antigen mu receptor, and mucin-like domains in zonadhesin are rapidly evolving and, thus, may be involved in binding to the ZP in a species-specific manner in primates. In addition, polymorphism data from 48 human individuals revealed significant polymorphism-to-divergence heterogeneity and a significant departure from equilibrium-neutral expectations in the frequency spectrum, suggesting balancing selection and positive selection occurring in zonadhesin (ZAN) within human populations. Finally, we observe adaptive evolution in haplotypes segregating for a frameshift mutation that was previously thought to indicate that ZAN was a potential pseudogene.     

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     

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.     

False-positive results obtained from the branch-site test of positive selection

Natural selection operating at the amino acid sequence level can be detected by comparing the rates of synonymous (r(S)) and nonsynonymous (r(N)) nucleotide substitutions, where r(N)/r(S) (omega) > 1 and omega < 1 suggest positive and negative selection, respectively. The branch-site test has been developed for detecting positive selection operating at a group of amino acid sites for a pre-specified (foreground) branch of a phylogenetic tree by taking into account the heterogeneity of omega among sites and branches. Here the performance of the branch-site test was examined by computer simulation, with special reference to the false-positive rate when the divergence of the sequences analyzed was small. The false-positive rate was found to inflate when the assumptions made on the omega values for the foreground and other (background) branches in the branch-site test were violated. In addition, under a similar condition, false-positive results were often obtained even when Bonferroni correction was conducted and the false-discovery rate was controlled in a large-scale analysis. False-positive results were also obtained even when the number of nonsynonymous substitutions for the foreground branch was smaller than the minimum value required for detecting positive selection. The existence of a codon site with a possibility of occurrence of multiple nonsynonymous substitutions for the foreground branch often caused the branch-site test to falsely identify positive selection. In the re-analysis of orthologous trios of protein-coding genes from humans, chimpanzees, and macaques, most of the genes previously identified to be positively selected for the human or chimpanzee branch by the branch-site test contained such a codon site, suggesting a possibility that a significant fraction of these genes are false-positives.     

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.     

Rates of nucleotide substitution and mammalian nuclear gene evolution. Approximate and maximum-likelihood methods lead to different conclusions

Rates and patterns of synonymous and nonsynonymous substitutions have important implications for the origin and maintenance of mammalian isochores and the effectiveness of selection at synonymous sites. Previous studies of mammalian nuclear genes largely employed approximate methods to estimate rates of nonsynonymous and synonymous substitutions. Because these methods did not account for major features of DNA sequence evolution such as transition/transversion rate bias and unequal codon usage, they might not have produced reliable results. To evaluate the impact of the estimation method, we analyzed a sample of 82 nuclear genes from the mammalian orders Artiodactyla, Primates, and Rodentia using both approximate and maximum-likelihood methods. Maximum-likelihood analysis indicated that synonymous substitution rates were positively correlated with GC content at the third codon positions, but independent of nonsynonymous substitution rates. Approximate methods, however, indicated that synonymous substitution rates were independent of GC content at the third codon positions, but were positively correlated with nonsynonymous rates. Failure to properly account for transition/transversion rate bias and unequal codon usage appears to have caused substantial biases in approximate estimates of substitution rates.