Evaluating molecular clock calibrations using Bayesian analyses with soft and hard bounds

A limiting factor in many molecular dating studies is shortage of reliable calibrations. Current methods for choosing calibrations (e.g. cross-validation) treat them as either correct or incorrect, whereas calibrations probably lie on a continuum from highly accurate to very poor. Bayesian relaxed clock analysis permits inclusion of numerous candidate calibrations as priors: provided most calibrations are reliable, the model appropriate and the data informative, the accuracy of each calibration prior can be evaluated. If a calibration is accurate, then the analysis will support the prior so that the posterior estimate reflects the prior; if a calibration is poor, the posterior will be forced away from the prior. We use this approach to test two fossil dates recently proposed as standard calibrations within vertebrates. The proposed bird-crocodile calibration (approx. 247Myr ago) appears to be accurate, but the proposed bird-lizard calibration (approx. 255Myr ago) is substantially too recent.     

Bayesian estimation of species divergence times under a molecular clock using multiple fossil calibrations with soft bounds

We implement a Bayesian Markov chain Monte Carlo algorithm for estimating species divergence times that uses heterogeneous data from multiple gene loci and accommodates multiple fossil calibration nodes. A birth-death process with species sampling is used to specify a prior for divergence times, which allows easy assessment of the effects of that prior on posterior time estimates. We propose a new approach for specifying calibration points on the phylogeny, which allows the use of arbitrary and flexible statistical distributions to describe uncertainties in fossil dates. In particular, we use soft bounds, so that the probability that the true divergence time is outside the bounds is small but nonzero. A strict molecular clock is assumed in the current implementation, although this assumption may be relaxed. We apply our new algorithm to two data sets concerning divergences of several primate species, to examine the effects of the substitution model and of the prior for divergence times on Bayesian time estimation. We also conduct computer simulation to examine the differences between soft and hard bounds. We demonstrate that divergence time estimation is intrinsically hampered by uncertainties in fossil calibrations, and the error in Bayesian time estimates will not go to zero with increased amounts of sequence data. Our analyses of both real and simulated data demonstrate potentially large differences between divergence time estimates obtained using soft versus hard bounds and a general superiority of soft bounds. Our main findings are as follows. (1) When the fossils are consistent with each other and with the molecular data, and the posterior time estimates are well within the prior bounds, soft and hard bounds produce similar results. (2) When the fossils are in conflict with each other or with the molecules, soft and hard bounds behave very differently; soft bounds allow sequence data to correct poor calibrations, while poor hard bounds are impossible to overcome by any amount of data. (3) Soft bounds eliminate the need for "safe" but unrealistically high upper bounds, which may bias posterior time estimates. (4) Soft bounds allow more reliable assessment of estimation errors, while hard bounds generate misleadingly high precisions when fossils and molecules are in conflict.     

Calibrating the avian molecular clock

Molecular clocks are widely used to date phylogenetic events, yet evidence supporting the rate constancy of molecular clocks through time and across taxonomic lineages is weak. Here, we present 90 candidate avian clock calibrations obtained from fossils and biogeographical events. Cross-validation techniques were used to identify and discard 16 inconsistent calibration points. Molecular evolution occurred in an approximately clock-like manner through time for the remaining 74 calibrations of the mitochondrial gene, cytochrome b . A molecular rate of approximately 2.1% (± 0.1%, 95% confidence interval) was maintained over a 12-million-year interval and across most of 12 taxonomic orders. Minor but significant variance in rates occurred across lineages but was not explained by differences in generation time, body size or latitudinal distribution as previously suggested.     

Molecular‐clock methods for estimating evolutionary rates and timescales

The molecular clock presents a means of estimating evolutionary rates and timescales using genetic data. These estimates can lead to important insights into evolutionary processes and mechanisms, as well as providing a framework for further biological analyses. To deal with rate variation among genes and among lineages, a diverse range of molecular‐clock methods have been developed. These methods have been implemented in various software packages and differ in their statistical properties, ability to handle different models of rate variation, capacity to incorporate various forms of calibrating information and tractability for analysing large data sets. Choosing a suitable molecular‐clock model can be a challenging exercise, but a number of model‐selection techniques are available. In this review, we describe the different forms of evolutionary rate heterogeneity and explain how they can be accommodated in molecular‐clock analyses. We provide an outline of the various clock methods and models that are available, including the strict clock, local clocks, discrete clocks and relaxed clocks. Techniques for calibration and clock‐model selection are also described, along with methods for handling multilocus data sets. We conclude our review with some comments about the future of molecular clocks.     

A mixed relaxed clock model

Over recent years, several alternative relaxed clock models have been proposed in the context of Bayesian dating. These models fall in two distinct categories: uncorrelated and autocorrelated across branches. The choice between these two classes of relaxed clocks is still an open question. More fundamentally, the true process of rate variation may have both long-term trends and short-term fluctuations, suggesting that more sophisticated clock models unfolding over multiple time scales should ultimately be developed. Here, a mixed relaxed clock model is introduced, which can be mechanistically interpreted as a rate variation process undergoing short-term fluctuations on the top of Brownian long-term trends. Statistically, this mixed clock represents an alternative solution to the problem of choosing between autocorrelated and uncorrelated relaxed clocks, by proposing instead to combine their respective merits. Fitting this model on a dataset of 105 placental mammals, using both node-dating and tip-dating approaches, suggests that the two pure clocks, Brownian and white noise, are rejected in favour of a mixed model with approximately equal contributions for its uncorrelated and autocorrelated components. The tip-dating analysis is particularly sensitive to the choice of the relaxed clock model. In this context, the classical pure Brownian relaxed clock appears to be overly rigid, leading to biases in divergence time estimation. By contrast, the use of a mixed clock leads to more recent and more reasonable estimates for the crown ages of placental orders and superorders. Altogether, the mixed clock introduced here represents a first step towards empirically more adequate models of the patterns of rate variation across phylogenetic trees.This article is part of the themed issue ‘Dating species divergences using rocks and clocks’.     

主流分子钟定年方法的原理、误差来源和使用建议

近年来, 分子钟定年方法(molecular dating methods)得以广泛运用, 为宏观进化研究尤其是生物多样性及其格局形成历史的相关研究提供了不可或缺且十分详尽的进化时间框架。贝叶斯方法(Bayesian methods)和马尔可夫链蒙特卡罗方法 (Markov chain Monte Carlo)可容纳多维度、多类型的数据和参数设置, 因此以BEAST、PAML-MCMCTree等软件为代表的贝叶斯节点标记法(Bayesian node-dating methods)逐渐成为分子钟定年方法中最为广泛使用的类型。贝叶斯框架的优势之一在于其可以利用复杂模型考虑各种不确定性因素, 但是该类方法中各类模型和参数的设置都可能引入误差, 从而影响进化分化时间估算的可靠性。本文介绍了贝叶斯分子钟定年方法的原理和主要类型, 并以贝叶斯节点标记法为例, 重点讨论了分子钟模型、化石标记的选择与放置、采样频率及化石标记点年龄先验分布等因素对节点定年的影响; 提供了贝叶斯时间树构建软件的使用建议、节点年龄的讨论原则和不同模型下时间树的比较方法, 针对常见的引起节点年龄潜在高估和低估风险的情况作了分析并给出了合理化建议。我们认为, 合理整合多种贝叶斯方法和模型得出的结果并从中择优, 能够提高定年结果的可靠性; 研究人员应对时间树构建结果与其参数设置的关系开展讨论, 从而为其他学者提供参考; 化石记录的更新与分子钟定年方法的改进应同步不断跟进。     

A fossil-calibrated relaxed clock for Ephedra indicates an Oligocene age for the divergence of Asian and New World clades and Miocene dispersal into South America

Ephedra comprises approximately 50 species, which are roughly equally distributed between the Old and New World deserts, but not in the intervening regions （amphitropical range）. Great heterogeneity in the substitution rates of Gnetales （Ephedra, Gnetum, and Welwitschia） has made it difficult to infer the ages of the major divergence events in Ephedra, such as the timing of the Beringian disjunction in the genus and the entry into South America. Here, we use data from as many Gnetales species and genes as available from GenBank and from a recent study to investigate the timing of the major divergence events. Because of the tradeoff between the amount of missing data and taxon/gene sampling, we reduced the initial matrix of 265 accessions and 12 loci to 95 accessions and 10 loci, and further to 42 species （and 7736 aligned nucleotides） to achieve stationary distributions in the Bayesian molecular clock runs. Results from a relaxed clock with an uncorrelated rates model and fossil-based calibration reveal that New World species are monophyletic and diverged from their mostly Asian sister clade some 30 mya, fitting with many other Beringian disjunctions. The split between the single North American and the single South American clade occurred approximately 25 mya, well before the closure of the Panamanian Isthmus. Overall, the biogeographic history of Ephedra appears dominated by long-distance dispersal, but finer-scale studies are needed to test this hypothesis.     

A fossil‐calibrated relaxed clock for Ephedra indicates an Oligocene age for the divergence of Asian and New World clades and Miocene dispersal into South America

Abstract Ephedra comprises approximately 50 species, which are roughly equally distributed between the Old and New World deserts, but not in the intervening regions (amphitropical range). Great heterogeneity in the substitution rates of Gnetales (Ephedra, Gnetum, and Welwitschia) has made it difficult to infer the ages of the major divergence events in Ephedra, such as the timing of the Beringian disjunction in the genus and the entry into South America. Here, we use data from as many Gnetales species and genes as available from GenBank and from a recent study to investigate the timing of the major divergence events. Because of the tradeoff between the amount of missing data and taxon/gene sampling, we reduced the initial matrix of 265 accessions and 12 loci to 95 accessions and 10 loci, and further to 42 species (and 7736 aligned nucleotides) to achieve stationary distributions in the Bayesian molecular clock runs. Results from a relaxed clock with an uncorrelated rates model and fossil‐based calibration reveal that New World species are monophyletic and diverged from their mostly Asian sister clade some 30 mya, fitting with many other Beringian disjunctions. The split between the single North American and the single South American clade occurred approximately 25 mya, well before the closure of the Panamanian Isthmus. Overall, the biogeographic history of Ephedra appears dominated by long‐distance dispersal, but finer‐scale studies are needed to test this hypothesis.     

Exploring uncertainty in the calibration of the molecular clock

Calibration is a critical step in every molecular clock analysis but it has been the least considered. Bayesian approaches to divergence time estimation make it possible to incorporate the uncertainty in the degree to which fossil evidence approximates the true time of divergence. We explored the impact of different approaches in expressing this relationship, using arthropod phylogeny as an example for which we established novel calibrations. We demonstrate that the parameters distinguishing calibration densities have a major impact upon the prior and posterior of the divergence times, and it is critically important that users evaluate the joint prior distribution of divergence times used by their dating programmes. We illustrate a procedure for deriving calibration densities in Bayesian divergence dating through the use of soft maximum constraints.     

TESTING THE MUSEUM VERSUS CRADLE TROPICAL BIOLOGICAL DIVERSITY HYPOTHESIS: PHYLOGENY,DIVERSIFICATION, AND ANCESTRAL BIOGEOGRAPHIC RANGE EVOLUTION OF THE ANTS

Ants are one of the most ecologically and numerically dominant group of terrestrial organisms with most species diversity currently found in tropical climates. Several explanations for the disparity of biological diversity in the tropics compared to temperate regions have been proposed including that the tropics may act as a “museum” where older lineages persist through evolutionary time or as a “cradle” where new species continue to be generated. We infer the molecular phylogenetic relationships of 295 ant specimens including members of all 21 extant subfamilies to explore the evolutionary diversification and biogeography of the ants. By constraining the topology and age of the root node while using 45 fossils as minimum constraints, we converge on an age of 139–158 Mya for the modern ants. Further diversification analyses identified 10 periods with a significant change in the tempo of diversification of the ants, although these shifts did not appear to correspond to ancestral biogeographic range shifts. Likelihood‐based historical biogeographic reconstructions suggest that the Neotropics were important in early ant diversification (e.g., Cretaceous). This finding coupled with the extremely high‐current species diversity suggests that the Neotropics have acted as both a museum and cradle for ant diversity.     

Tectonic blocks and molecular clocks

Evolutionary timescales have mainly used fossils for calibrating molecular clocks, though fossils only really provide minimum clade age constraints. In their place, phylogenetic trees can be calibrated by precisely dated geological events that have shaped biogeography. However, tectonic episodes are protracted, their role in vicariance is rarely justified, the biogeography of living clades and their antecedents may differ, and the impact of such events is contingent on ecology. Biogeographic calibrations are no panacea for the shortcomings of fossil calibrations, but their associated uncertainties can be accommodated. We provide examples of how biogeographic calibrations based on geological data can be established for the fragmentation of the Pangaean supercontinent: (i) for the uplift of the Isthmus of Panama, (ii) the separation of New Zealand from Gondwana, and (iii) for the opening of the Atlantic Ocean. Biogeographic and fossil calibrations are complementary, not competing, approaches to constraining molecular clock analyses, providing alternative constraints on the age of clades that are vital to avoiding circularity in investigating the role of biogeographic mechanisms in shaping modern biodiversity.This article is part of the themed issue ‘Dating species divergences using rocks and clocks’.     

Tree imbalance causes a bias in phylogenetic estimation of evolutionary timescales using heterochronous sequences

Phylogenetic estimation of evolutionary timescales has become routine in biology, forming the basis of a wide range of evolutionary and ecological studies. However, there are various sources of bias that can affect these estimates. We investigated whether tree imbalance, a property that is commonly observed in phylogenetic trees, can lead to reduced accuracy or precision of phylogenetic timescale estimates. We analysed simulated data sets with calibrations at internal nodes and at the tips, taking into consideration different calibration schemes and levels of tree imbalance. We also investigated the effect of tree imbalance on two empirical data sets: mitogenomes from primates and serial samples of the African swine fever virus. In analyses calibrated using dated, heterochronous tips, we found that tree imbalance had a detrimental impact on precision and produced a bias in which the overall timescale was underestimated. A pronounced effect was observed in analyses with shallow calibrations. The greatest decreases in accuracy usually occurred in the age estimates for medium and deep nodes of the tree. In contrast, analyses calibrated at internal nodes did not display a reduction in estimation accuracy or precision due to tree imbalance. Our results suggest that molecular‐clock analyses can be improved by increasing taxon sampling, with the specific aims of including deeper calibrations, breaking up long branches and reducing tree imbalance.     

Bayesian phylogenetic estimation of fossil ages

Recent advances have allowed for both morphological fossil evidence and molecular sequences to be integrated into a single combined inference of divergence dates under the rule of Bayesian probability. In particular, the fossilized birth–death tree prior and the Lewis-Mk model of discrete morphological evolution allow for the estimation of both divergence times and phylogenetic relationships between fossil and extant taxa. We exploit this statistical framework to investigate the internal consistency of these models by producing phylogenetic estimates of the age of each fossil in turn, within two rich and well-characterized datasets of fossil and extant species (penguins and canids). We find that the estimation accuracy of fossil ages is generally high with credible intervals seldom excluding the true age and median relative error in the two datasets of 5.7% and 13.2%, respectively. The median relative standard error (RSD) was 9.2% and 7.2%, respectively, suggesting good precision, although with some outliers. In fact, in the two datasets we analyse, the phylogenetic estimate of fossil age is on average less than 2 Myr from the mid-point age of the geological strata from which it was excavated. The high level of internal consistency found in our analyses suggests that the Bayesian statistical model employed is an adequate fit for both the geological and morphological data, and provides evidence from real data that the framework used can accurately model the evolution of discrete morphological traits coded from fossil and extant taxa. We anticipate that this approach will have diverse applications beyond divergence time dating, including dating fossils that are temporally unconstrained, testing of the ‘morphological clock'', and for uncovering potential model misspecification and/or data errors when controversial phylogenetic hypotheses are obtained based on combined divergence dating analyses.This article is part of the themed issue ‘Dating species divergences using rocks and clocks’.     

A mitogenomic timescale for birds detects variable phylogenetic rates of molecular evolution and refutes the standard molecular clock

Current understanding of the diversification of birds is hindered by their incomplete fossil record and uncertainty in phylogenetic relationships and phylogenetic rates of molecular evolution. Here we performed the first comprehensive analysis of mitogenomic data of 48 vertebrates, including 35 birds, to derive a Bayesian timescale for avian evolution and to estimate rates of DNA evolution. Our approach used multiple fossil time constraints scattered throughout the phylogenetic tree and accounts for uncertainties in time constraints, branch lengths, and heterogeneity of rates of DNA evolution. We estimated that the major vertebrate lineages originated in the Permian; the 95% credible intervals of our estimated ages of the origin of archosaurs (258 MYA), the amniote-amphibian split (356 MYA), and the archosaur-lizard divergence (278 MYA) bracket estimates from the fossil record. The origin of modern orders of birds was estimated to have occurred throughout the Cretaceous beginning about 139 MYA, arguing against a cataclysmic extinction of lineages at the Cretaceous/Tertiary boundary. We identified fossils that are useful as time constraints within vertebrates. Our timescale reveals that rates of molecular evolution vary across genes and among taxa through time, thereby refuting the widely used mitogenomic or cytochrome b molecular clock in birds. Moreover, the 5-Myr divergence time assumed between 2 genera of geese (Branta and Anser) to originally calibrate the standard mitochondrial clock rate of 0.01 substitutions per site per lineage per Myr (s/s/l/Myr) in birds was shown to be underestimated by about 9.5 Myr. Phylogenetic rates in birds vary between 0.0009 and 0.012 s/s/l/Myr, indicating that many phylogenetic splits among avian taxa also have been underestimated and need to be revised. We found no support for the hypothesis that the molecular clock in birds "ticks" according to a constant rate of substitution per unit of mass-specific metabolic energy rather than per unit of time, as recently suggested. Our analysis advances knowledge of rates of DNA evolution across birds and other vertebrates and will, therefore, aid comparative biology studies that seek to infer the origin and timing of major adaptive shifts in vertebrates.     

Why do species vary in their rate of molecular evolution?

Despite hopes that the processes of molecular evolution would be simple, clock-like and essentially universal, variation in the rate of molecular evolution is manifest at all levels of biological organization. Furthermore, it has become clear that rate variation has a systematic component: rate of molecular evolution can vary consistently with species body size, population dynamics, lifestyle and location. This suggests that the rate of molecular evolution should be considered part of life-history variation between species, which must be taken into account when interpreting DNA sequence differences between lineages. Uncovering the causes and correlates of rate variation may allow the development of new biologically motivated models of molecular evolution that may improve bioinformatic and phylogenetic analyses.     

Sudden expansion of a single brown bear maternal lineage across northern continental Eurasia after the last ice age: a general demographic model for mammals?

The brown bear has proved a useful model for studying Late Quaternary mammalian phylogeography. However, information is lacking from northern continental Eurasia, which constitutes a large part of the species' current distribution. We analysed mitochondrial DNA sequences (totalling 1943 bp) from 205 bears from northeast Europe and Russia in order to characterize the maternal phylogeography of bears in this region. We also estimated the formation times of the sampled brown bear lineages and those of its extinct relative, the cave bear.
Four closely related haplogroups belonging to a single mitochondrial subclade were identified in northern continental Eurasia. Several haplotypes were found throughout the whole study area, while one haplogroup was restricted to Kamchatka. The haplotype network, estimated divergence times and various statistical tests indicated that bears in northern continental Eurasia recently underwent a sudden expansion, preceded by a severe bottleneck. This brown bear population was therefore most likely founded by a small number of bears that were restricted to a single refuge area during the last glacial maximum. This pattern has been described previously for other mammal species and as such may represent one general model for the phylogeography of Eurasian mammals. Bayesian divergence time estimates are presented for different brown and cave bear clades. Moreover, our results demonstrate the extent of substitution rate variation occurring throughout the phylogenetic tree, highlighting the need for appropriate calibration when estimating divergence times.     

Fossil calibrations and molecular divergence time estimates in centrarchid fishes (Teleostei: Centrarchidae)

Molecular clock methods allow biologists to estimate divergence times, which in turn play an important role in comparative studies of many evolutionary processes. It is well known that molecular age estimates can be biased by heterogeneity in rates of molecular evolution, but less attention has been paid to the issue of potentially erroneous fossil calibrations. In this study we estimate the timing of diversification in Centrarchidae, an endemic major lineage of the diverse North American freshwater fish fauna, through a new approach to fossil calibration and molecular evolutionary model selection. Given a completely resolved multi-gene molecular phylogeny and a set of multiple fossil-inferred age estimates, we tested for potentially erroneous fossil calibrations using a recently developed fossil cross-validation. We also used fossil information to guide the selection of the optimal molecular evolutionary model with a new fossil jackknife method in a fossil-based model cross-validation. The centrarchid phylogeny resulted from a mixed-model Bayesian strategy that included 14 separate data partitions sampled from three mtDNA and four nuclear genes. Ten of the 31 interspecific nodes in the centrarchid phylogeny were assigned a minimal age estimate from the centrarchid fossil record. Our analyses identified four fossil dates that were inconsistent with the other fossils, and we removed them from the molecular dating analysis. Using fossil-based model cross-validation to determine the optimal smoothing value in penalized likelihood analysis, and six mutually consistent fossil calibrations, the age of the most recent common ancestor of Centrarchidae was 33.59 million years ago (mya). Penalized likelihood analyses of individual data partitions all converged on a very similar age estimate for this node, indicating that rate heterogeneity among data partitions is not confounding our analyses. These results place the origin of the centrarchid radiation at a time of major faunal turnover as the fossil record indicates that the most diverse lineages of the North American freshwater fish fauna originated at the Eocene-Oligocene boundary, approximately 34 mya. This time coincided with major global climate change from warm to cool temperatures and a signature of elevated lineage extinction and origination in the fossil record across the tree of life. Our analyses demonstrate the utility of fossil cross-validation to critically assess individual fossil calibration points, providing the ability to discriminate between consistent and inconsistent fossil age estimates that are used for calibrating molecular phylogenies.     

A general comparison of relaxed molecular clock models

Several models have been proposed to relax the molecular clock in order to estimate divergence times. However, it is unclear which model has the best fit to real data and should therefore be used to perform molecular dating. In particular, we do not know whether rate autocorrelation should be considered or which prior on divergence times should be used. In this work, we propose a general bench mark of alternative relaxed clock models. We have reimplemented most of the already existing models, including the popular lognormal model, as well as various prior choices for divergence times (birth-death, Dirichlet, uniform), in a common Bayesian statistical framework. We also propose a new autocorrelated model, called the "CIR" process, with well-defined stationary properties. We assess the relative fitness of these models and priors, when applied to 3 different protein data sets from eukaryotes, vertebrates, and mammals, by computing Bayes factors using a numerical method called thermodynamic integration. We find that the 2 autocorrelated models, CIR and lognormal, have a similar fit and clearly outperform uncorrelated models on all 3 data sets. In contrast, the optimal choice for the divergence time prior is more dependent on the data investigated. Altogether, our results provide useful guidelines for model choice in the field of molecular dating while opening the way to more extensive model comparisons.     

Calibration uncertainty in molecular dating analyses: there is no substitute for the prior evaluation of time priors

Calibration is the rate-determining step in every molecular clock analysis and, hence, considerable effort has been expended in the development of approaches to distinguish good from bad calibrations. These can be categorized into a priori evaluation of the intrinsic fossil evidence, and a posteriori evaluation of congruence through cross-validation. We contrasted these competing approaches and explored the impact of different interpretations of the fossil evidence upon Bayesian divergence time estimation. The results demonstrate that a posteriori approaches can lead to the selection of erroneous calibrations. Bayesian posterior estimates are also shown to be extremely sensitive to the probabilistic interpretation of temporal constraints. Furthermore, the effective time priors implemented within an analysis differ for individual calibrations when employed alone and in differing combination with others. This compromises the implicit assumption of all calibration consistency methods, that the impact of an individual calibration is the same when used alone or in unison with others. Thus, the most effective means of establishing the quality of fossil-based calibrations is through a priori evaluation of the intrinsic palaeontological, stratigraphic, geochronological and phylogenetic data. However, effort expended in establishing calibrations will not be rewarded unless they are implemented faithfully in divergence time analyses.     

Transitions,transversions, and the molecular evolutionary clock

Summary Nucleotide substitutions in the form of transitions (purine-purine or pyrimidine-pyrimidine interchanges) and transversions (purine-pyrimidine interchanges) occur during evolution and may be complied by aligning the sequences of homologous genes. Referring to the genetic code tables, silent transitions take place in third positions of codons in family boxes and two-codon sets. Silent transversions in third positions occur only in family boxes, except for AC transversions between AGR and CGR arginine codons (R=A or G). Comparisons of several protein genes have been made, and various subclasses of transitional and transversional nucleotide substitutions have been compiled. Considerable variations occur among the relative proportions of transitions and transversions. Such variations could possibly be caused by mutator genes, favoring either transitions or, conversely, transversions, during DNA replication. At earlier stages of evolutionary divergence, transitions are usually more frequent, but there are exceptions. No indication was found that transversions usually originate from multiple substitutions in transitions.