Taking Variation of Evolutionary Rates Between Sites into Account in Inferring Phylogenies

As methods of molecular phylogeny have become more explicit and more biologically realistic following the pioneering work of Thomas Jukes, they have had to relax their initial assumption that rates of evolution were equal at all sites. Distance matrix and likelihood methods of inferring phylogenies make this assumption; parsimony, when valid, is less limited by it. Nucleotide sequences, including RNA sequences, can show substantial rate variation; protein sequences show rates that vary much more widely. Assuming a prior distribution of rates such as a gamma distribution or lognormal distribution has deservedly been popular, but for likelihood methods it leads to computational difficulties. These can be resolved using hidden Markov model (HMM) methods which approximate the distribution by one with a modest number of discrete rates. Generalized Laguerre quadrature can be used to improve the selection of rates and their probabilities so as to more nearly approach the desired gamma distribution. A model based on population genetics is presented predicting how the rates of evolution might vary from locus to locus. Challenges for the future include allowing rates at a given site to vary along the tree, as in the ``covarion' model, and allowing them to have correlations that reflect three-dimensional structure, rather than position in the coding sequence. Markov chain Monte Carlo likelihood methods may be the only practical way to carry out computations for these models. Received: 8 February 2001 / Accepted: 20 May 2001     

Topological Estimation Biases with Covarion Evolution

Covarion processes allow changes in evolutionary rates at sites along the branches of a phylogenetic tree. Covarion-like evolution is increasingly recognized as an important mode of protein evolution. Several recent reports suggest that maximum likelihood estimation employing covarion models may support different optimal topologies than estimation using standard rates-across-sites (RAS) models. However, it remains to be demonstrated that ignoring covarion evolution will generally result in topological misestimation. In this study we performed analytical and theoretical studies of limiting distances under the covarion model and four-taxon tree simulations to investigate the extent to which the covarion process impacts on phylogenetic estimation. In particular, we assessed the limits of an RAS model-based maximum likelihood method to recover the phylogenies when the sequence data were simulated under the covarion processes. We find that, when ignored, covarion processes can induce systematic errors in phylogeny reconstruction. Surprisingly, when sequences are evolved under a covarion process but an RAS model is used for estimation, we find that a long branch repel bias occurs.     

Curiously Modern DNA for a ``250 Million-Year-Old' Bacterium

Studies of ancient DNA have attracted considerable attention in scientific journals and the popular press. Several of the more extreme claims for ancient DNA have been questioned on biochemical grounds (i.e., DNA surviving longer than expected) and evolutionary grounds (i.e., nucleotide substitution patterns not matching theoretical expectations for ancient DNA). A recent letter to Nature from Vreeland et al. (2000), however, tops all others with respect to age and condition of the specimen. These researchers extracted and cultured a bacterium from an inclusion body from what they claim is a 250 million-year (Myr)-old salt crystal. If substantiated, this observation could fundamentally alter views about bacterial physiology, ecology and evolution. Here we report on molecular evolutionary analyses of the 16S rDNA from this specimen. We find that 2-9-3 differs from a modern halophile, Salibacillus marismortui, by just 3 unambiguous bp in 16S rDNA, versus the ∼59 bp that would be expected if these bacteria evolved at the same rate as other bacteria. We show, using a Poisson distribution, that unless it can be shown that S. marismortui evolves 5 to 10 times more slowly than other bacteria for which 16S rDNA substitution rates have been established, Vreeland et al.'s claim would be rejected at the 0.05 level. Also, a molecular clock test and a relative rates test fail to substantiate Vreeland et al.'s claim that strain 2-9-3 is a 250-Myr-old bacterium. The report of Vreeland et al. thus falls into a long series of suspect ancient DNA studies. Received: 12 April 2001 / Accepted: 9 June 2001     

Nuclear and Nucleomorph SSU rDNA Phylogeny in the Cryptophyta and the Evolution of Cryptophyte Diversity

The plastid-bearing members of the Cryptophyta contain two functional eukaryotic genomes of different phylogenetic origin, residing in the nucleus and in the nucleomorph, respectively. These widespread and diverse protists thus offer a unique opportunity to study the coevolution of two different eukaryotic genomes within one group of organisms. In this study, the SSU rRNA genes of both genomes were PCR-amplified with specific primers and phylogenetic analyses were performed on different data sets using different evolutionary models. The results show that the composition of the principal clades obtained from the phylogenetic analyses of both genes was largely congruent, but striking differences in evolutionary rates were observed. These affected the topologies of the nuclear and nucleomorph phylogenies differently, resulting in long-branch attraction artifacts when simple evolutionary models were applied. Deletion of long-branch taxa stabilized the internal branching order in both phylogenies and resulted in a completely resolved topology in the nucleomorph phylogeny. A comparison of the tree topologies derived from SSU rDNA sequences with characters previously used in cryptophyte systematics revealed that the biliprotein type was congruent, but the type of inner periplast component incongruent, with the molecular trees. The latter is indicative of a hidden cellular dimorphism (cells with two periplast types present in a single clonal strain) of presumably widespread occurrence throughout cryptophyte diversity, which, in consequence, has far-reaching implications for cryptophyte systematics as it is practiced today.     

A mixed branch length model of heterotachy improves phylogenetic accuracy

Evolutionary relationships are typically inferred from molecular sequence data using a statistical model of the evolutionary process. When the model accurately reflects the underlying process, probabilistic phylogenetic methods recover the correct relationships with high accuracy. There is ample evidence, however, that models commonly used today do not adequately reflect real-world evolutionary dynamics. Virtually all contemporary models assume that relatively fast-evolving sites are fast across the entire tree, whereas slower sites always evolve at relatively slower rates. Many molecular sequences, however, exhibit site-specific changes in evolutionary rates, called "heterotachy." Here we examine the accuracy of 2 phylogenetic methods for incorporating heterotachy, the mixed branch length model--which incorporates site-specific rate changes by summing likelihoods over multiple sets of branch lengths on the same tree--and the covarion model, which uses a hidden Markov process to allow sites to switch between variable and invariable as they evolve. Under a variety of simple heterogeneous simulation conditions, the mixed model was dramatically more accurate than homotachous models, which were subject to topological biases as well as biases in branch length estimates. When data were simulated with strong versions of the types of heterotachy observed in real molecular sequences, the mixed branch length model was more accurate than homotachous techniques. Analyses of empirical data sets confirmed that the mixed branch length model can improve phylogenetic accuracy under conditions that cause homotachous models to fail. In contrast, the covarion model did not improve phylogenetic accuracy compared with homotachous models and was sometimes substantially less accurate. We conclude that a mixed branch length approach, although not the solution to all phylogenetic errors, is a valuable strategy for improving the accuracy of inferred trees.     

Substitution Model of Sequence Evolution for the Human Immunodeficiency Virus Type 1 Subtype B gp120 Gene over the C2-V5 Region

Phylogenetic analyses frequently rely on models of sequence evolution that detail nucleotide substitution rates, nucleotide frequencies, and site-to-site rate heterogeneity. These models can influence hypothesis testing and can affect the accuracy of phylogenetic inferences. Maximum likelihood methods of simultaneously constructing phylogenetic tree topologies and estimating model parameters are computationally intensive, and are not feasible for sample sizes of 25 or greater using personal computers. Techniques that initially construct a tree topology and then use this non-maximized topology to estimate ML substitution rates, however, can quickly arrive at a model of sequence evolution. The accuracy of this two-step estimation technique was tested using simulated data sets with known model parameters. The results showed that for a star-like topology, as is often seen in human immunodeficiency virus type 1 (HIV-1) subtype B sequences, a random starting topology could produce nucleotide substitution rates that were not statistically different than the true rates. Samples were isolated from 100 HIV-1 subtype B infected individuals from the United States and a 620 nt region of the env gene was sequenced for each sample. The sequence data were used to obtain a substitution model of sequence evolution specific for HIV-1 subtype B env by estimating nucleotide substitution rates and the site-to-site heterogeneity in 100 individuals from the United States. The method of estimating the model should provide users of large data sets with a way to quickly compute a model of sequence evolution, while the nucleotide substitution model we identified should prove useful in the phylogenetic analysis of HIV-1 subtype B env sequences. Received: 4 October 2000 / Accepted: 1 March 2001     

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     

Testing for covarion-like evolution in protein sequences

The covarion hypothesis of molecular evolution proposes that selective pressures on an amino acid or nucleotide site change through time, thus causing changes of evolutionary rate along the edges of a phylogenetic tree. Several kinds of Markov models for the covarion process have been proposed. One model, proposed by Huelsenbeck (2002), has 2 substitution rate classes: the substitution process at a site can switch between a single variable rate, drawn from a discrete gamma distribution, and a zero invariable rate. A second model, suggested by Galtier (2001), assumes rate switches among an arbitrary number of rate classes but switching to and from the invariable rate class is not allowed. The latter model allows for some sites that do not participate in the rate-switching process. Here we propose a general covarion model that combines features of both models, allowing evolutionary rates not only to switch between variable and invariable classes but also to switch among different rates when they are in a variable state. We have implemented all 3 covarion models in a maximum likelihood framework for amino acid sequences and tested them on 23 protein data sets. We found significant likelihood increases for all data sets for the 3 models, compared with a model that does not allow site-specific rate switches along the tree. Furthermore, we found that the general model fit the data better than the simpler covarion models in the majority of the cases, highlighting the complexity in modeling the covarion process. The general covarion model can be used for comparing tree topologies, molecular dating studies, and the investigation of protein adaptation.     

The cytochrome b gene as a phylogenetic marker: the limits of resolution for analyzing relationships among cichlid fishes

The mitochondrial cytochrome b (cyt-b) gene is widely used in systematic studies to resolve divergences at many taxonomic levels. The present study focuses mainly on the utility of cyt-b as a molecular marker for inferring phylogenetic relationship at various levels within the fish family Cichlidae. A total of 78 taxa were used in the present analysis, representing all the major groups in the family Cichlidae (72 taxa) and other families from the suborders Labroidei and Percoidei. Gene trees obtained from cyt-b are compared to a published total evidence tree derived from previous studies. Minimum evolution trees based on cyt-b data resulted in topologies congruent with all previous analyses. Parsimony analyses downweighting transitions relative to transversions (ts1:tv4) or excluding transitions at third codon positions resulted in more robust bootstrap support for recognized clades than unweighted parsimony. Relative rate tests detected significantly long branches for some taxa (LB taxa) which were composed mainly by dwarf Neotropical cichlids. An improvement of the phylogenetic signal, as shown by the four-cluster likelihood mapping analysis, and higher bootstrap values were obtained by excluding LB taxa. Despite some limitations of cyt-b as a phylogenetic marker, this gene either alone or in combination with other data sets yields a tree that is in agreement with the well-established phylogeny of cichlid fish. Received: 11 October 2000 / Accepted: 26 February 2001     

The Ghost of Selection Past: Rates of Evolution and Functional Divergence of Anciently Duplicated Genes

The duplication of genes and even complete genomes may be a prerequisite for major evolutionary transitions and the origin of evolutionary novelties. However, the evolutionary mechanisms of gene evolution and the origin of novel gene functions after gene duplication have been a subject of many debates. Recently, we compiled 26 groups of orthologous genes, which included one gene from human, mouse, and chicken, one or two genes from the tetraploid Xenopus and two genes from zebrafish. Comparative analysis and mapping data showed that these pairs of zebrafish genes were probably produced during a fish-specific genome duplication that occurred between 300 and 450 Mya, before the teleost radiation (Taylor et al. 2001). As discussed here, many of these retained duplicated genes code for DNA binding proteins. Different models have been developed to explain the retention of duplicated genes and in particular the subfunctionalization model of Force et al. (1999) could explain why so many developmental control genes have been retained. Other models are harder to reconcile with this particular set of duplicated genes. Most genes seem to have been subjected to strong purifying selection, keeping properties such as charge and polarity the same in both duplicates, although some evidence was found for positive Darwinian selection, in particular for Hox genes. However, since only the cumulative pattern of nucleotide substitutions can be studied, clear indications of positive Darwinian selection or neutrality may be hard to find for such anciently duplicated genes. Nevertheless, an increase in evolutionary rate in about half of the duplicated genes seems to suggest that either positive Darwinian selection has occurred or that functional constraints have been relaxed at one point in time during functional divergence. Received: 4 January 2001 / Accepted: 29 March 2001     

Isolation of Mhc Class II DMA and DMB cDNA Sequences in a Marsupial: The Gray Short-Tailed Opossum (Monodelphis domestica)

We report the cDNA sequences for the DMA and DMB family of Mhc genes of the gray short-tailed opossum. Until now DM sequences were available only in eutherian mammals. The marsupial sequences indicate that both members of the family are old and probably diverged from other classical class II families about the time of the radiation of jawed vertebrates some 450 million years ago. We examine the evolutionary rates of equivalent sets of classical and nonclassical genes to check for rate heterogeneity. We find the α-1 domain of the DR genes to be untypically conservative in its evolutionary mode. The DM genes appear to evolve at rates typical of other class II genes, indicating that their placement at the root of class II gene evolutionary trees may be justified. Received: 2 March 1998 / Accepted: 2 June 1998     

Molecular Timing of Primate Divergences as Estimated by Two Nonprimate Calibration Points

The complete mitochondrial DNA (mtDNA) molecule of the hamadryas baboon, Papio hamadryas, was sequenced and included in a molecular analysis of 24 complete mammalian mtDNAs. The particular aim of the study was to time the divergence between Cercopithecoidea and Hominoidea. That divergence, set at 30 million years before present (MYBP) was a fundamental reference for the original proposal of recent hominoid divergences, according to which the split among gorilla, chimpanzee, and Homo took place 5 MYBP. In the present study the validity of the postulated 30 MYBP dating of the Cercopithecoidea/Hominoidea divergence was examined by applying two independent nonprimate molecular references, the divergence between artiodactyls and cetaceans set at 60 MYBP and that between Equidae and Rhinocerotidae set at 50 MYBP. After calibration for differences in evolutionary rates, application of the two references suggested that the Cercopithecoidea/Hominoidea divergence took place >50 MYBP. Consistent with the marked shift in the dating of the Cercopithecoidea/Hominoidea split, all hominoid divergences receive a much earlier dating. Thus the estimated date of the divergence between Pan (chimpanzee) and Homo is 10–13 MYBP and that between Gorilla and the Pan/Homo linage ≈17 MYBP. The same datings were obtained in an analysis of clocklike evolving genes. The findings show that recalculation is necessary of all molecular datings based directly or indirectly on a Cercopithecoidea/Hominoidea split 30 MYBP. Received: 1 April 1998 / Accepted: 1 July 1998     

An Estimate of Divergence Time of Parazoa and Eumetazoa and That of Cephalochordata and Vertebrata by Aldolase and Triose Phosphate Isomerase Clocks

Previously we suggested that four proteins including aldolase and triose phosphate isomerase (TPI) evolved with approximately constant rates over long periods covering the whole animal phyla. The constant rates of aldolase and TPI evolution were reexamined based on three different models for estimating evolutionary distances. It was shown that the evolutionary rates remain essentially unchanged in comparisons not only between different classes of vertebrates but also between vertebrates and arthropods and even between animals and plants, irrespective of the models used. Thus these enzymes might be useful molecular clocks for inferring divergence times of animal phyla. To know the divergence time of Parazoa and Eumetazoa and that of Cephalochordata and Vertebrata, the aldolase cDNAs from Ephydatia fluviatilis, a freshwater sponge, and the TPI cDNAs from Ephydatia fluviatilis and Branchiostoma belcheri, an amphioxus, have been cloned and sequenced. Comparisons of the deduced amino acid sequences of aldolase and TPI from the freshwater sponge with known sequences revealed that the Parazoa–Eumetazoa split occurred about 940 million years ago (Ma) as determined by the average of two proteins and three models. Similarly, the aldolase and TPI clocks suggest that vertebrates and amphioxus last shared a common ancestor around 700 Ma and they possibly diverged shortly after the divergence of deuterostomes and protostomes.     

A Probabilistic Treatment of Phylogeny and Sequence Alignment

Carrying out simultaneous tree-building and alignment of sequence data is a difficult computational task, and the methods currently available are either limited to a few sequences or restricted to highly simplified models of alignment and phylogeny. A method is given here for overcoming these limitations by Bayesian sampling of trees and alignments simultaneously. The method uses a standard substitution matrix model for residues together with a hidden Markov model structure that allows affine gap penalties. It escapes the heavy computational burdens of other models by using an approximation called the ``*' rule, which replaces missing data by a sum over all possible values of variables. The behavior of the model is demonstrated on test sets of globins. Received: 25 May 1998 / Accepted: 8 December 1998     

Performance of 18S rRNA in Littorinid Phylogeny (Gastropoda: Caenogastropoda)

In the past, 18S rRNA sequences have proved to be very useful for tracing ancient divergences but were rarely used for resolving more recent ones. Moreover, it was suggested that the molecule does not contain useful information to resolve divergences which took place during less than 40 Myr. The present paper takes littorinid phylogeny as a case study to reevaluate the utility of the molecule for resolving recent divergences. Two data sets for nine species of the snail family Littorinidae were analyzed, both separately and combined. One data set comprised 7 new complete 18S rRNA sequences aligned with 2 published littorinid sequences; the other comprised 12 morphological, 1 biochemical, and 2 18S rRNA secondary structure characters. On the basis of its ability to confirm generally accepted relationships and the congruence of results derived from the different data sets, it is concluded that 18S rRNA sequences do contain information to resolve ``rapid' cladogenetic events, provided that they occurred in the not too distant past. 18S rRNA sequences yielded support for (1) the branching order (L. littorea, (L. obtusata, (L. saxatilis, L. compressa))) and (2) the basal position of L. striata in the Littorina clade. Received: 6 February 1998 / Accepted: 20 March 1998     

Ancient Origin of Human Complement Factor H

We studied the evolutionary history of two homologous proteins of the human complement system, factor H (FH) and the α chain of the C4b binding protein (C4bpα), and included in this study the related proteins from the barred sand bass (P. nebulifer) and the nematode C. elegans. Phylogenetic trees inferred from individual short consensus repeats (SCRs) and divergence among repeats from different genes suggest that human FH has a much closer evolutionary relationship to putative complement components from P. nebulifer and C. elegans than does the C4bpα. This indicates that a member of the alternative pathway of the complement system (FH) has an ancient origin, while a homologous member of the classical pathway (C4bpα) appeared later in evolutionary history as a result of gene duplication. The ancient evolutionary position of FH is in agreement with the suggestion that the alternative pathway of the complement system is older than the classical pathway. Phylogenetic analysis also shows that the sand bass cofactor protein SBP1 and cofactor related protein SBCRP-1 have diverged very recently. Received: 1 December 1997 / Accepted: 3 June 1998     

Accelerated Evolution of Cytochrome b in Simian Primates: Adaptive Evolution in Concert with Other Mitochondrial Proteins?

We have sequenced the cytochrome b gene of Horsfield's tarsier, Tarsius bancanus, to complete a data set of sequences for this gene from representatives of each primate infraorder. These primate cytochrome b sequences were combined with those from representatives of three other mammalian orders (cat, whale, and rat) in an analysis of relative evolutionary rates. The nonsynonymous nucleotide substitution rate of the cytochrome b gene has increased approximately twofold along lineages leading to simian primates compared to that of the tarsier and other primate and nonprimate mammalian species. However, the rate of transversional substitutions at fourfold degenerate sites has remained uniform among all lineages. This increase in the evolutionary rate of cytochrome b is similar in character and magnitude to that described previously for the cytochrome c oxidase subunit II gene. We propose that the evolutionary rate increase observed for cytochrome b and cytochrome c oxidase subunit II may underlie an episode of coadaptive evolution of these two proteins in the mitochondria of simian primates. Received: 15 December 1997 / Accepted: 24 February 1998     

Phylogeny of Ultra-Rapidly Evolving Dinoflagellate Chloroplast Genes: A Possible Common Origin for Sporozoan and Dinoflagellate Plastids

Complete chloroplast 23S rRNA and psbA genes from five peridinin-containing dinoflagellates (Heterocapsa pygmaea, Heterocapsa niei, Heterocapsa rotun-data, Amphidinium carterae, and Protoceratium reticulatum) were amplified by PCR and sequenced; partial sequences were obtained from Thoracosphaera heimii and Scrippsiella trochoidea. Comparison with chloroplast 23S rRNA and psbA genes of other organisms shows that dinoflagellate chloroplast genes are the most divergent and rapidly evolving of all. Quartet puzzling, maximum likelihood, maximum parsimony, neighbor joining, and LogDet trees were constructed. Intersite rate variation and invariant sites were allowed for with quartet puzzling and neighbor joining. All psbA and 23S rRNA trees showed peridinin-containing dinoflagellate chloroplasts as monophyletic. In psbA trees they are related to those of chromists and red algae. In 23S rRNA trees, dinoflagellates are always the sisters of Sporozoa (apicomplexans); maximum likelihood analysis of Heterocapsa triquetra 16S rRNA also groups the dinoflagellate and sporozoan sequences, but the other methods were inconsistent. Thus, dinoflagellate chloroplasts may actually be related to sporozoan plastids, but the possibility of reproducible long-branch artifacts cannot be strongly ruled out. The results for all three genes fit the idea that dinoflagellate chloroplasts originated from red algae by a secondary endosymbiosis, possibly the same one as for chromists and Sporozoa. The marked disagreement between 16S rRNA trees using different phylogenetic algorithms indicates that this is a rather poor molecule for elucidating overall chloroplast phylogeny. We discuss possible reasons why both plastid and mitochondrial genomes of alveolates (Dinozoa, Sporozoa and Ciliophora) have ultra-rapid substitution rates and a proneness to unique genomic rearrangements. Received: 27 December 1999 / Accepted: 24 March 2000     

Why are translationally sub-optimal synonymous codons used in Escherichia coli?

Natural selection favors certain synonymous codons which aid translation in Escherichia coli, yet codons not favored by translational selection persist. We use the frequency distributions of synonymous polymorphisms to test three hypotheses for the existence of translationally sub-optimal codons: (1) selection is a relatively weak force, so there is a balance between mutation, selection, and drift; (2) at some sites there is no selection on codon usage, so some synonymous sites are unaffected by translational selection; and (3) translationally sub-optimal codons are favored by alternative selection pressures at certain synonymous sites. We find that when all the data is considered, model 1 is supported and both models 2 and 3 are rejected as sole explanations for the existence of translationally sub-optimal codons. However, we find evidence in favor of both models 2 and 3 when the data is partitioned between groups of amino acids and between regions of the genes. Thus, all three mechanisms appear to contribute to the existence of translationally sub-optimal codons in E. coli. Received: 18 July 2000 / Accepted: 17 April 2001     

Nucleotide Substitution Rate of Mammalian Mitochondrial Genomes

We present here for the first time a comprehensive study based on the analysis of closely related organisms to provide an accurate determination of the nucleotide substitution rate in mammalian mitochondrial genomes. This study examines the evolutionary pattern of the different functional mtDNA regions as accurately as possible on the grounds of available data, revealing some important ``genomic laws.' The main conclusions can be summarized as follows. (1) High intragenomic variability in the evolutionary dynamic of mtDNA was found. The substitution rate is strongly dependent on the region considered, and slow- and fast-evolving regions can be identified. Nonsynonymous sites, the D-loop central domain, and tRNA and rRNA genes evolve much more slowly than synonymous sites and the two peripheral D-loop region domains. The synonymous rate is fairly uniform over the genome, whereas the rate of nonsynonymous sites depends on functional constraints and therefore differs considerably between genes. (2) The commonly accepted statement that mtDNA evolves more rapidly than nuclear DNA is valid only for some regions, thus it should be referred to specific mitochondrial components. In particular, nonsynonymous sites show comparable rates in mitochondrial and nuclear genes; synonymous sites and small rRNA evolve about 20 times more rapidly and tRNAs about 100 times more rapidly in mitochondria than in their nuclear counterpart. (3) A species-specific evolution is particularly evident in the D-loop region. As the divergence times of the organism pairs under consideration are known with sufficient accuracy, absolute nucleotide substitution rates are also provided. Received: 11 May 1998 / Accepted: 2 September 1998