Synonymous and Nonsynonymous Substitutions in Mammalian Genes: Intragenic Correlations

Previous investigations indicated that synonymous and nonsynonymous substitution rates are correlated in mammalian genes. In the present work, this correlation has been studied at the intragenic level using a dataset of 48 orthologous genes from species belonging to at least four different mammalian orders. The results obtained show that the intragenic variability in synonymous rates is correlated with that of nonsynonymous rates. Moreover, the variation in GC level (and especially of C level) of silent positions along each gene is correlated with the variation in synonymous rate. These results reinforce the previous conclusions that synonymous and nonsynonymous rates as well as GC levels of silent positions are to some extent under common selective constraints. Received: 10 July 1997 / Accepted: 13 August 1997     

Gene Expression, Amino Acid Conservation, and Hydrophobicity Are the Main Factors Shaping Codon Preferences in Mycobacterium tuberculosis and Mycobacterium leprae

Mycobacterium tuberculosis and Mycobacterium leprae are the ethiological agents of tuberculosis and leprosy, respectively. After performing extensive comparisons between genes from these two GC-rich bacterial species, we were able to construct a set of 275 homologous genes. Since these two bacterial species also have a very low growth rate, translational selection could not be so determinant in their codon preferences as it is in other fast-growing bacteria. Indeed, principal-components analysis of codon usage from this set of homologous genes revealed that the codon choices in M. tuberculosis and M. leprae are correlated not only with compositional constraints and translational selection, but also with the degree of amino acid conservation and the hydrophobicity of the encoded proteins. Finally, significant correlations were found between GC₃ and synonymous distances as well as between synonymous and nonsynonymous distances. Received: 30 October 1998 / Accepted: 16 August 1999     

Sensitivity of Patterns of Molecular Evolution to Alterations in Methodology: A Critique of Hughes and Yeager

Employing a set of 43 othologous mouse and rat genes, Hughes and Yeager (J. Mol. Evol. 45:125–130, 1997) reported (1) no correlation between synonymous and nonsynonymous rates of nucleotide substitution, (2) a positive correlation between intronic GC contents (GC _i) and intronic substitution rates (K _i), (3) that the average K _i value was very similar to the average K _s value, and (4) that the compositional correlation between the rat and the mouse genes is stronger at the third codon position (GC₃) than at the first and second codon positions (GC₁₂). We have examined the robustness of these results to alterations in substitution rate estimation protocol, alignment protocol, and statistical procedure. We find that a significant correlation between K _a and K _s is observed either if a rank correlation statistic is used instead of regression analysis, if one outlier is excluded from the analysis, or if a regression weighted by gene size is employed. The correlation between K _i and GC _i we find to be sensitive to changes in alignment protocol and disappears on the use of weighted means. The finding that K _s and K _i are approximately the same is dependent on the method for estimating K _s values. Finally, the variance around the regression line of rat GC₃ versus mouse GC₃ we find to be significantly higher than that in GC₁₂. The source of the discrepancy between this and Hughes and Yeager's result is unclear. The variance around the line for GC₄ is higher still, as might be expected. Using a methodology that may be considered preferable to that of Hughes and Yeager, we find that all four of their results are contradicted. More importantly this analysis reinforces the need for caution in assembling and analyzing data sets, as the degree of sensitivity to what many might consider minor methodological alterations is unexpected. Received: 2 February 1998 / Accepted: 23 March 1998     

Molecular Evolution of Cytochrome c Oxidase Subunit IV: Evidence for Positive Selection in Simian Primates

Cytochrome c oxidase (COX) is a multi-subunit enzyme complex that catalyzes the final step of electron transfer through the respiratory chain on the mitochondrial inner membrane. Up to 13 subunits encoded by both the mitochondrial (subunits I, II, and III) and nuclear genomes occur in eukaryotic organisms ranging from yeast to human. Previously, we observed a high number of amino acid replacements in the human COX IV subunit compared to mouse, rat, and cow orthologues. Here we examined COX IV evolution in the two groups of anthropoid primates, the catarrhines (hominoids, cercopithecoids) and platyrrhines (ceboids), as well as one prosimian primate (lorisiform), by sequencing PCR-amplified portions of functional COX4 genes from genomic DNAs. Phylogenetic analysis of the COX4 sequence data revealed that accelerated nonsynonymous substitution rates were evident in the early evolution of both catarrhines and, to a lesser extent, platyrrhines. These accelerated rates were followed later by decelerated rates, suggesting that positive selection for adaptive amino acid replacement became purifying selection, preserving replacements that had occurred. The evidence for positive selection was especially pronounced along the catarrhine lineage to hominoids in which the nonsynonymous rate was first faster than the synonymous rate, then later much slower. The rates of three types of ``neutral DNA' nucleotide substitutions (synonymous substitutions, pseudogene nucleotide substitutions, and intron nucleotide substitutions) are similar and are consistent with previous observations of a slower rate of such substitutions in the nuclear genomes of hominoids than in the nuclear genomes of other primate and mammalian lineages. Received: 22 May 1996 / Accepted: 24 November 1996     

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     

Variable Substitution Rates of the 18 Domain Sequences in Artemia Hemoglobin

The Artemia hemoglobin is a dimer comprising two nine-domain covalent polymers in quaternary association. Each polymer is encoded by a gene representing nine successive globin domains which have different sequences and are presumed to have been copied originally from a single-domain gene. Two different polymers exist as the result of a complete duplication of the nine-domain gene, allowing the formation of either homodimers or the heterodimer. The total population size of 18 domains comprising nine corresponding pairs, coupled with the probability that they reflect several hundred million years of evolution in the same lineage, provides a unique model in which the process of gene multiplication can be analyzed. The outcome has important implications for the reliability of local molecular clocks. The two polymers differ from each other at 11.7% of amino acid sites; however when corresponding individual domains are compared between polymers, amino acid substitution fluctuates by a factor of 2.7-fold from lowest to highest. This variation is not obvious at the DNA level: Domain pair identity values fluctuate by 1.3-fold. Identity values are, however, uncorrected for multiple substitutions, and both silent and nonsilent changes are pooled. Therefore, to determine the variability in relative substitution rates at the DNA level, we have used the method of Li (1993, J Mol Evol 36:96–99) to determine estimates of nonsynonymous (K _A ) and synonymous (K _S ) substitutions per site for the nine pairs of domains. As expected, the overall level of silent substitutions (K _S of 56.9%) far exceeded nonsilent substitutions (K _A of 6.7%); however, for corresponding domain pairs, K _A fluctuates by 2.3-fold and K _S by 1.7-fold. The large discrepancies reflected in the expressed protein have accrued within a single lineage and the implication is that divergence dates of different genera based on amino acid sequences, even with well-studied proteins of reasonable size, can be wrong by a factor well in excess of 2. Received: 4 June 1997 / Accepted: 17 December 1997     

Coding sequence divergence between two closely related plant species: Arabidopsis thaliana and Brassica rapa ssp. pekinensis

To characterize the coding-sequence divergence of closely related genomes, we compared DNA sequence divergence between sequences from a Brassica rapa ssp. pekinensis EST library isolated from flower buds and genomic sequences from Arabidopsis thaliana. The specific objectives were (i) to determine the distribution of and relationship between K _a and K _s, (ii) to identify genes with the lowest and highest K _a:K _s values, and (iii) to evaluate how codon usage has diverged between two closely related species. We found that the distribution of K _a:K _s was unimodal, and that substitution rates were more variable at nonsynonymous than synonymous sites, and detected no evidence that K _a and K _s were positively correlated. Several genes had K _a:K _s values equal to or near zero, as expected for genes that have evolved under strong selective constraint. In contrast, there were no genes with K _a:K _s >1 and thus we found no strong evidence that any of the 218 sequences we analyzed have evolved in response to positive selection. We detected a stronger codon bias but a lower frequency of GC at synonymous sites in A. thaliana than B. rapa. Moreover, there has been a shift in the profile of most commonly used synonymous codons since these two species diverged from one another. This shift in codon usage may have been caused by stronger selection acting on codon usage or by a shift in the direction of mutational bias in the B. rapa phylogenetic lineage.     

A Survey of the Molecular Evolutionary Dynamics of Twenty-Five Multigene Families from Four Grass Taxa

We surveyed the molecular evolutionary characteristics of 25 plant gene families, with the goal of better understanding general processes in plant gene family evolution. The survey was based on 247 GenBank sequences representing four grass species (maize, rice, wheat, and barley). For each gene family, orthology and paralogy relationships were uncertain. Recognizing this uncertainty, we characterized the molecular evolution of each gene family in four ways. First, we calculated the ratio of nonsynonymous to synonymous substitutions (d _N/d _S) both on branches of gene phylogenies and across codons. Our results indicated that the d _N/d _S ratio was statistically heterogeneous across branches in 17 of 25 (68%) gene families. The vast majority of d _N/d _S estimates were <<1.0, suggestive of selective constraint on amino acid replacements, and no estimates were >1.0, either across phylogenetic lineages or across codons. Second, we tested separately for nonsynonymous and synonymous molecular clocks. Sixty-eight percent of gene families rejected a nonsynonymous molecular clock, and 52% of gene families rejected a synonymous molecular clock. Thus, most gene families in this study deviated from clock-like evolution at either synonymous or nonsynonymous sites. Third, we calculated the effective number of codons and the proportion of G+C synonymous sites for each sequence in each gene family. One or both quantities vary significantly within 18 of 25 gene families. Finally, we tested for gene conversion, and only six gene families provided evidence of gene conversion events. Altogether, evolution for these 25 gene families is marked by selective constraint that varies among gene family members, a lack of molecular clock at both synonymous and nonsynonymous sites, and substantial variation in codon usage. Received: 25 May 2000 / Accepted: 16 October 2000     

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     

Synonymous Nucleotide Divergence and Saturation: Effects of Site-Specific Variations in Codon Bias and Mutation Rates

The synonymous divergence between Escherichia coli and Salmonella typhimurium is explained in a model where there is a large variation between mutation rates at different nucleotide sites in the genome. The model is based on the experimental observation that spontaneous mutation rates can vary over several orders of magnitude at different sites in a gene. Such site-specific variation must be taken into account when studying synonymous divergence and will result in an apparent saturation below the level expected from an assumption of uniform rates. Recently, it has been suggested that codon preference in enterobacteria has a very large site-specific variation and that the synonymous divergence between different species, e.g., E. coli and Salmonella, is saturated. In the present communication it is shown that when site-specific variation in mutation rates is introduced, there is no need to invoke assumptions of saturation and a large variability in codon preference. The same rate variation will also bring average mutation rates as estimated from synonymous sequence divergence into numerical agreement with experimental values. Received: 10 July 1998 / Accepted: 20 August 1998     

Rapid Evolution of the Ribonuclease A Superfamily: Adaptive Expansion of Independent Gene Clusters in Rats and Mice

The two eosinophil ribonucleases, eosinophil-derived neurotoxin (EDN/RNase 2) and eosinophil cationic protein (ECP/RNase 3), are among the most rapidly evolving coding sequences known among primates. The eight mouse genes identified as orthologs of EDN and ECP form a highly divergent, species-limited cluster. We present here the rat ribonuclease cluster, a group of eight distinct ribonuclease A superfamily genes that are more closely related to one another than they are to their murine counterparts. The existence of independent gene clusters suggests that numerous duplications and diversification events have occurred at these loci recently, sometime after the divergence of these two rodent species (∼10–15 million years ago). Nonsynonymous substitutions per site (d _N) calculated for the 64 mouse/rat gene pairs indicate that these ribonucleases are incorporating nonsilent mutations at accelerated rates, and comparisons of nonsynonymous to synonymous substitution (d _N / d _S) suggest that diversity in the mouse ribonuclease cluster is promoted by positive (Darwinian) selection. Although the pressures promoting similar but clearly independent styles of rapid diversification among these primate and rodent genes remain uncertain, our recent findings regarding the function of human EDN suggest a role for these ribonucleases in antiviral host defense. Received: 8 April 1999 / Accepted: 22 June 1999     

Diversifying Selection Governs Sequence Polymorphism in the Major Adhesin Proteins FimA, PapA, and SfaA of Escherichia coli

Fimbriae or pili are essential adherence factors usually found in pathogenic bacteria to aid colonization of host cells. Three major structural pilin genes, fimA, sfaA, and papA, from Escherichia coli natural isolates were examined and nucleotide sequence data revealed elevated levels of both synonymous and nonsynonymous site variation at these loci. Examination of synonymous site variation shows a fivefold increase in fimA sites, relative to the housekeeping gene mdh; and similarly the sfaA and papA genes have increased synonymous sites variation relative to fimA. Nonsynonymous site variation is also elevated at all three loci but, in particular, at the papA locus (k _N= 0.44). The k _N/k _S ratio for the three genes are among the highest yet reported for E. coli genes. Regional variation in nucleotide polymorphism within each of the genes reveal hypervariable segments where nonsynonymous substitutions exceed synonymous substitutions. We propose that at the fimA, papA, and sfaA genes, diversifying selection has brought about the increase levels of polymorphism. Received: 7 August 1997 / Accepted: 8 March 1998     

On the Pattern of Polymorphisms at Major Histocompatibility Complex Loci

The pattern of polymorphisms at major histocompatibility complex loci was studied by computer simulations and by DNA sequence analysis. Two types of selection, overdominance plus short-term selection and maternal–fetal incompatibility, were simulated for a gene family with intra- and interlocus gene conversion. Both types of selection were found to be consistent with the observed patterns of polymorphisms. It was also found that the more interlocus conversion occurs, the higher the divergence becomes at both nonsynonymous and synonymous sites. The ratio of nonsynonymous-to-synonymous divergence among alleles decreases as the interlocus conversion rate increases. These results agree with the interpretation that the rate of interlocus conversion is lower in human genes than in genes of other nonprimate mammals. This is because, in the latter, synonymous divergence at the ARS (antigen recognition site) is often higher than that at the non-ARS, whereas in the former, this is not so. Also, the ratio of nonsynonymous to synonymous substitutions at the ARS tends to be higher in human genes than in other mammalian genes. The main difference between overdominance plus short-term selection and maternal–fetal interaction is that the number of alleles and heterozygosity per locus are higher in the latter than in the former under the presumed selection intensities. However, the average divergence among alleles tends to be lower in the latter than in the former under similar conditions. Received: 30 September 1997 / Accepted: 15 December 1997     

Extraordinary Conservation of Cysteines Among Homologous Chironomus Silk Proteins sp185 and sp220

Aquatic larvae of the midge, Chironomus tentans, synthesize a 185-kDa silk protein (sp185) with the cysteine-containing motif Cys-X-Cys-X-Cys (where X is any residue) every 20–28 residues. We report here the cloning and full-length sequence of cDNAs encoding homologous silk proteins from Chironomus pallidivittatus (sp185) and Chironomus thummi (sp220). Deduced amino acid sequences reveal proteins of nearly identical mass composed of 72 blocks of 20–28 residues, 61% of which can be described by the motif X_5–8-Cys-X₅-(Trp/Phe/Tyr)-X₄-Cys-X-Cys-X-Cys. Spatial arrangement of these residues is preserved more than surrounding sequences. cDNA clones enabled us to map the genes on polytene chromosomes and identify for the first time the homolog of the Camptochironomus Balbiani ring 3 locus in Chironomus thummi. The apparent molecular weight difference between these proteins (185 vs 220 kDa) is not attributable to primary structure and may be due to differential N-linked glycosylation. DNA distances and codon substitutions indicate that the C. tentans and C. pallidivittatus genes are more related to each other than either is to C. thummi; however, substitution rates for the 5′- and 3′-halves of these genes are different. Blockwise sequence comparisons suggest intragenic variation in that some regions evolved slower or faster than the mean and may have been subjected to different selective pressures. Received: 30 August 1996 / Accepted: 6 November 1996     

Molecular evolution of nitrate reductase genes

To understand the evolutionary mechanisms and relationships of nitrate reductases (NRs), the nucleotide sequences encoding 19 nitrate reductase (NR) genes from 16 species of fungi, algae, and higher plants were analyzed. The NR genes examined show substantial sequence similarity, particularly within functional domains, and large variations in GC content at the third codon position and intron number. The intron positions were different between the fungi and plants, but conserved within these groups. The overall and nonsynonymous substitution rates among fungi, algae, and higher plants were estimated to be 4.33 × 10⁻¹⁰ and 3.29 × 10⁻¹⁰ substitutions per site per year. The three functional domains of NR genes evolved at about one-third of the rate of the N-terminal and the two hinge regions connecting the functional domains. Relative rate tests suggested that the nonsynonymous substitution rates were constant among different lineages, while the overall nucleotide substitution rates varied between some lineages. The phylogenetic trees based on NR genes correspond well with the phylogeny of the organisms determined from systematics and other molecular studies. Based on the nonsynonymous substitution rate, the divergence time of monocots and dicots was estimated to be about 340 Myr when the fungi–plant or algae–higher plant divergence times were used as reference points and 191 Myr when the rice–barley divergence time was used as a reference point. These two estimates are consistent with other estimates of divergence times based on these reference points. The lack of consistency between these two values appears to be due to the uncertainty of the reference times. Received: 10 April 1995 / Accepted: 10 September 1995     

Multiple Substitutions Affect the Phylogenetic Utility of Cytochrome b and 12S rDNA Data: Examining a Rapid Radiation in Leporid (Lagomorpha) Evolution

Partial sequences of two mitochondrial genes, the 12S ribosomal gene (739 bp) and the cytochrome b gene (672 bp), were analyzed in hopes of reconstructing the evolutionary relationships of 11 leporid species, representative of seven genera. However, partial cytochrome b sequences were of little phylogenetic value in this study. A suite of pairwise comparisons between taxa revealed that at the intergeneric level, the cytochrome b gene is saturated at synonymous coding positions due to multiple substitution events. Furthermore, variation at the nonsynonymous positions is limited, rendering the cytochrome b gene of little phylogenetic value for assessing the relationships between leporid genera. If the cytochrome b data are analyzed without accounting for these two classes of nucleotides (i.e., synonymous and nonsynonymous sites), one may incorrectly conclude that signal exists in the cytochrome b data. The mitochondrial 12S rRNA gene, on the other hand, has not experienced excessive saturation at either stem or loop positions. Phylogenies reconstructed from the 12S rDNA data support hypotheses based on fossil evidence that African rock rabbits (Pronolagus) are outside of the main leporid stock and that leporids experienced a rapid radiation. However, the molecular data suggest that this radiation event occurred in the mid-Miocene several millions of years earlier than the Pleistocene dates suggested by paleontological evidence. Received: 23 April 1998 / Accepted: 14 May 1998     

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     

The Codon-Degeneracy Model of Molecular Evolution

Mitochondrial genetic codons can be categorized by four patterns of nucleotide-site degeneracy based on varying combinations of twofold- or nondegenerate sites at first codon positions and twofold- or fourfold-degenerate sites at third codon positions. Herein, a model of molecular evolution is introduced that uses these patterns to calculate expected substitution frequencies for each codon position and substitution type relative to overall number of synonymous or nonsynonymous substitutions. Regions of the pocket gopher cytochrome oxidase subunit I (COI) and cytochrome b (cyt-b) genes are analyzed using this model. Chi-square distributions are used to produce relative goodness-of-fit (GF) scores for measuring the difference between substitution frequencies predicted by the codon-degeneracy model (CDM), and frequencies inferred using a well-supported phylogenetic tree of closely related species. The GF scores for expected and observed synonymous (GF_syn= 0.429, p= 0.807) and nonsynonymous (GF_ns= 2.309, p= 0.679) substitution frequencies resulted in a failure to reject the CDM as a null hypothesis for the molecular evolution of COI and cyt-b in pocket gophers. Alternative tree topologies and calculations of transition bias for these data result in higher GF scores. Received: 25 March 1999 / Accepted: 17 September 1999     

Intragenic Variation of Synonymous Substitution Rates Is Caused by Nonrandom Mutations at Methylated CpG

It has been observed that synonymous substitution rates vary among genes in various organisms, although the cause of the variation is unresolved. At the intragenic level, however, the variation of synonymous substitutions is somewhat controversial. By developing a rigorous statistical test and applying the test to 418 homologous gene pairs between mouse and rat, we found that more than 90% of gene pairs showed a statistical significance in intragenic variation of synonymous substitution rates. Moreover, by examining all conceivable possibilities for the cause of the variation, we successfully found that intragenic variation of synonymous substitutions in mammalian genes is caused mainly by a nonrandom mutation due to the methylation of CpG dinucleotides rather than by functional constraints. Received: 12 January 2001 / Accepted: 28 February 2001     

Molecular Evolution Modeled as a Fractal Renewal Point Process in Agreement with the Dispersion of Substitutions in Mammalian Genes

A fractal renewal point process (FRPP) is used to model molecular evolution in agreement with the relationship between the variance and the mean numbers of nonsynonymous and synonymous substitutions in mammals. Like other episodic models such as the doubly stochastic Poisson process, this model accounts for the large variances observed in amino acid substitution rates, but unlike certain other episodic models, it also accounts for the increase in the index of dispersion with the mean number of substitutions in Ohta's (1995) data. We find that this correlation is significant for nonsynonymous substitutions at the 1% level and for synonymous substitutions at the 10% level, even after removing lineage effects and when using Bulmer's (1989) unbiased estimator of the index of dispersion. This model is simpler than most other overdispersed models of evolution in the sense that it is fully specified by a single interevent probability distribution. Interpretations in terms of chaotic dynamics and in terms of chance and selection are discussed. Received: 12 January 1998 / Accepted: 19 May 1998