Statistical models of the overdispersed molecular clock

The most commonly used statistical model to describe the rate constancy of molecular evolution (molecular clock) is a simple Poisson process in which the variance of the number of amino acid or nucleotide substitutions in a particular gene should be equal to the mean and henceforth the dispersion index, the ratio of the variance to the mean, should be equal to one. Recent sequence data, however, have shown that the substitutional process in molecular evolution is often considerably overdispersed and have called into question the generality of using a simple Poisson process. Several efforts have been made to develop more realistic models of molecular evolution. In this paper, I will show that the spatial (site-specific) variation in the rate of molecular evolution is an improbable cause of the overdispersion and then review various statistical models which take the temporal variation into account. Although these models do not immediately specify what the mechanisms of molecular evolution might be, they do make qualitatively different predictions and give some insight into their inference. One way to distinguish them is suggested. In addition, effects of selected substitutions that presumably occur after a major change in a molecule are quasi-quantitatively examined. It is most likely that the overdispersion of molecular clock is due either to a major molecular reconfiguration (fluctuating neutral space) led by a series of subliminal neutral changes or to selected substitutions fine-tuning a molecule after a major molecular change. Although the latter possibility, of course, violates the simplest neutrality assumption, it would not impair the neutral theory as a whole.     

On the virtues and pitfalls of the molecular evolutionary clock

"Informational" macromolecules--i.e., proteins and nucleic acids--have in their sequences a register of evolutionary history. Zuckerkandl and Pauling suggested in 1965 that these molecules might provide a "molecular clock" of evolution. The molecular clock would time evolutionary events and make it possible to reconstruct phylogenetic history--the branching relationships among lineages leading to modern species. Kimura's neutrality theory postulates that rates of molecular evolution are stochastically constant and, hence, that there is a molecular clock. A variety of tests have shown that molecular evolution does not behave like a stochastic clock. The variance in evolutionary rates is much too large and thus inconsistent with the neutrality theory. This, however, does not invalidate the clock, but rather leaves it without a theoretical foundation to anticipate its properties. Sequence comparisons show that molecular evolution is sufficiently regular to serve in many situations as a clock, but uncertainty concerning the properties of the clock (for example, about the circumstances that may yield large oscillations in substitution rates from time to time or from lineage to lineage) demands that it be used with caution. Few DNA or protein sequences are known from organisms that range from closely related, e.g., different mammals, to very remote, e.g., mammals and fungi. One example is cytochrome c, which has an acceptable clockwise behavior over the whole span, in spite of some irregularities. Another example is the copper-zinc superoxide dismutase (SOD), which behaves like a very erratic clock. The SOD average rate of amino acid substitution per 100 residues per 100 million years (MY) is 5.5 when fungi and animals are compared, 9.1 when comparisons are made between insects and mammals, and 27.8 when mammals are compared with each other. The question is which mode is more common over broad evolutionary spans: the regularity of cytochrome c or the capriciousness of SOD? Additional data sets will be required in order to obtain the answer and to develop expectations about the accuracy of the clock in particular instances. Until such data exist, conclusions solely based on the molecular clock are potentially fraught with error.     

Problems and paradigms: A mammalian molecular clock?

The molecular clock hypothesis remains controversial more than a quarter of a century after it was first proposed. A variety of approaches have been applied to testing the molecular clock in mammals. In many of these studies apparent refutation of the molecular clock has been based on false assumptions about the pattern of mammalian evolution. With a few exceptions there now appears to be little evidence for variation in the rate of molecular evolution among mammalian lineages, although comparison of more genes and proteins among a greater variety of mammalian orders is needed before a definitive conclusion can be reached on the issue.     

Overdispersion of the molecular clock varies between yeast, Drosophila and mammals

Although protein evolution can be approximated as a "molecular evolutionary clock," it is well known that sequence change departs from a clock-like Poisson expectation. Through studying the deviations from a molecular clock, insight can be gained into the forces shaping evolution at the level of proteins. Generally, substitution patterns that show greater variance than the Poisson expectation are said to be "overdispersed." Overdispersion of sequence change may result from temporal variation in the rate at which amino acid substitutions occur on a phylogeny. By comparing the genomes of four species of yeast, five species of Drosophila, and five species of mammals, we show that the extent of overdispersion shows a strong negative correlation with the effective population size of these organisms. Yeast proteins show very little overdispersion, while mammalian proteins show substantial overdispersion. Additionally, X-linked genes, which have reduced effective population size, have gene products that show increased overdispersion in both Drosophila and mammals. Our research suggests that mutational robustness is more pervasive in organisms with large population sizes and that robustness acts to stabilize the molecular evolutionary clock of sequence change.     

Simulating and detecting autocorrelation of molecular evolutionary rates among lineages

Evolutionary timescales can be estimated from genetic data using phylogenetic methods based on the molecular clock. To account for molecular rate variation among lineages, a number of relaxed‐clock models have been developed. Some of these models assume that rates vary among lineages in an autocorrelated manner, so that closely related species share similar rates. In contrast, uncorrelated relaxed clocks allow all of the branch‐specific rates to be drawn from a single distribution, without assuming any correlation between rates along neighbouring branches. There is uncertainty about which of these two classes of relaxed‐clock models are more appropriate for biological data. We present an R package, NELSI, that allows the evolution of DNA sequences to be simulated according to a range of clock models. Using data generated by this package, we assessed the ability of two Bayesian phylogenetic methods to distinguish among different relaxed‐clock models and to quantify rate variation among lineages. The results of our analyses show that rate autocorrelation is typically difficult to detect, even when there is complete taxon sampling. This provides a potential explanation for past failures to detect rate autocorrelation in a range of data sets.     

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.     

Molecular clocks and evolutionary relationships: Possible distortions due to horizontal gene flow

Summary This paper discusses recent evidence suggesting that genetic information from one species occasionally transfers to another remotely related species. Besides addressing the issue of whether or not the molecular data are consistent with a wide-spread influence of horizontal gene transfer, the paper shows that horizontal gene flow would not necessarily preclude a linear molecular clock or change the rate of molecular evolution (assuming the neutral allele theory). A pervasive influence of horizontal gene transfer is more than just consistent with the data of molecular evolution, it also provides a unique explanation for a number of possibly conflicting phylogenies and contradictory clocks. This phenomenon might explain why some protein clocks are linear while the superoxide dismutase clock is not, how the molecular data on the phylogeny of apes and Australian song birds are not necessarily in conflict with those based on morphology, and, finally, why the mycoplasmas have an accelerated molecular clock.     

Exploring the correlations between sequence evolution rate and phenotypic divergence across the Mammalian tree provides insights into adaptive evolution

Sequence evolution behaves in a relatively consistent manner, leading to one of the fundamental paradigms in biology, the existence of a ??molecular clock??. The molecular clock can be distilled to the concept of accumulation of substitutions, through time yielding a stable rate from which we can estimate lineage divergence. Over the last 50?years, evolutionary biologists have obtained an in-depth understanding of this clock??s nuances. It has been fine-tuned by taking into account the vast heterogeneity in rates across lineages and genes, leading to ??relaxed?? molecular clock methods for timetree reconstruction. Sequence rate varies with life history traits including body size, generation time and metabolic rate, and we review recent studies on this topic. However, few studies have explicitly examined correlates between molecular evolution and morphological evolution. The patterns observed across diverse lineages suggest that rates of molecular and morphological evolution are largely decoupled. We discuss how identifying the molecular mechanisms behind rapid functional radiations are central to understanding evolution. The vast functional divergence within mammalian lineages that have relatively ??slow?? sequence evolution refutes the hypotheses that pulses in diversification yielding major phenotypic change are the result of steady accumulation of substitutions. Patterns rather suggest phenotypic divergence is likely caused by regulatory alterations mediated through mechanisms such as insertions/deletions in functional regions. These can rapidly arise and sweep to fixation faster than predicted from a lineage??s sequence neutral substitution rate, enabling species to leapfrog between phenotypic ??islands??. We suggest research directions that could illuminate mechanisms behind the functional diversity we see today.     

Molecular clock in neutral protein evolution

Background

A frequent observation in molecular evolution is that amino-acid substitution rates show an index of dispersion (that is, ratio of variance to mean) substantially larger than one. This observation has been termed the overdispersed molecular clock. On the basis of in silico protein-evolution experiments, Bastolla and coworkers recently proposed an explanation for this observation: Proteins drift in neutral space, and can temporarily get trapped in regions of substantially reduced neutrality. In these regions, substitution rates are suppressed, which results in an overall substitution process that is not Poissonian. However, the simulation method of Bastolla et al. is representative only for cases in which the product of mutation rate μ and population size N_e is small. How the substitution process behaves when μN_e is large is not known.

Results

Here, I study the behavior of the molecular clock in in silico protein evolution as a function of mutation rate and population size. I find that the index of dispersion decays with increasing μN_e, and approaches 1 for large μN_e . This observation can be explained with the selective pressure for mutational robustness, which is effective when μN_e is large. This pressure keeps the population out of low-neutrality traps, and thus steadies the ticking of the molecular clock.

Conclusions

The molecular clock in neutral protein evolution can fall into two distinct regimes, a strongly overdispersed one for small μN_e, and a mostly Poissonian one for large μN_e. The former is relevant for the majority of organisms in the plant and animal kingdom, and the latter may be relevant for RNA viruses.

     

Effects of models of rate evolution on estimation of divergence dates with special reference to the metazoan 18S ribosomal RNA phylogeny

The molecular clock, i.e., constancy of the rate of evolution over time, is commonly assumed in estimating divergence dates. However, this assumption is often violated and has drastic effects on date estimation. Recently, a number of attempts have been made to relax the clock assumption. One approach is to use maximum likelihood, which assigns rates to branches and allows the estimation of both rates and times. An alternative is the Bayes approach, which models the change of the rate over time. A number of models of rate change have been proposed. We have extended and evaluated models of rate evolution, i.e., the lognormal and its recent variant, along with the gamma, the exponential, and the Ornstein-Uhlenbeck processes. These models were first applied to a small hominoid data set, where an empirical Bayes approach was used to estimate the hyperparameters that measure the amount of rate variation. Estimation of divergence times was sensitive to these hyperparameters, especially when the assumed model is close to the clock assumption. The rate and date estimates varied little from model to model, although the posterior Bayes factor indicated the Ornstein-Uhlenbeck process outperformed the other models. To demonstrate the importance of allowing for rate change across lineages, this general approach was used to analyze a larger data set consisting of the 18S ribosomal RNA gene of 39 metazoan species. We obtained date estimates consistent with paleontological records, the deepest split within the group being about 560 million years ago. Estimates of the rates were in accordance with the Cambrian explosion hypothesis and suggested some more recent lineage-specific bursts of evolution.     

Molecular clocks in reptiles: life history influences rate of molecular evolution

Life history has been implicated as a determinant of variation in rate of molecular evolution amongst vertebrate species because of a negative correlation between body size and substitution rate for many molecular data sets. Both the generality and the cause of the negative body size trend have been debated, and the validity of key studies has been questioned (particularly concerning the failure to account for phylogenetic bias). In this study, a comparative method has been used to test for an association between a range of life-history variables-such as body size, age at maturity, and clutch size-and DNA substitution rate for three genes (NADH4, cytochrome b, and c-mos). A negative relationship between body size and rate of molecular evolution was found for phylogenetically independent pairs of reptile species spanning turtles, lizards, snakes, crocodile, and tuatara. Although this study was limited by the number of comparisons for which both sequence and life-history data were available, the results suggest that a negative body size trend in rate of molecular evolution may be a general feature of reptile molecular evolution, consistent with similar studies of mammals and birds. This observation has important implications for uncovering the mechanisms of molecular evolution and warns against assuming that related lineages will share the same substitution rate (a local molecular clock) in order to date evolutionary divergences from DNA sequences.     

Combining fossil and molecular data to date the diversification of New World Primates

Recent methodological advances in molecular dating associated with the growing availability of sequence data have prompted the study of the evolution of New World Anthropoidea in recent years. Motivated by questions regarding historical biogeography or the mode of evolution, these works aimed to obtain a clearer scenario of Platyrrhini origins and diversification. Although some consensus was found, disputed issues, especially those relating to the evolutionary affinities of fossil taxa, remain. The use of fossil taxa for divergence time analysis is traditionally restricted to the provision of calibration priors. However, new analytical approaches have been developed that incorporate fossils as terminals and, thus, directly assign ages to the fossil tips. In this study, we conducted a combined analysis of molecular and morphological data, including fossils, to derive the timescale of New World anthropoids. Differently from previous studies that conducted total‐evidence analysis of molecules and morphology, our approach investigated the morphological clock alone. Our results corroborate the hypothesis that living platyrrhines diversified in the last 20 Ma and that Miocene Patagonian fossils compose an independent evolutionary radiation that diversified in the late Oligocene. When compared to the node ages inferred from the molecular timescale, the inclusion of fossils augmented the precision of the estimates for nodes constrained by the fossil tips. We show that morphological data can be analysed using the same methodological framework applied in relaxed molecular clock studies.     

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.     

Mitochondrial rate variation among lineages of passerine birds

The order Passeriformes comprises the majority of extant avian species. Analyses of molecular data have provided important insights into the evolution of this diverse order. However, molecular estimates of the evolutionary and demographic timescales of passerine species have been hindered by a lack of reliable calibrations. This has led to a reliance on the application of standard substitution rates to mitochondrial DNA data, particularly rates estimated from analyses of the gene encoding cytochrome b (CYTB). To investigate patterns of rate variation across passerine lineages, we used a Bayesian phylogenetic approach to analyse the protein‐coding genes of 183 mitochondrial genomes. We found that the most commonly used mitochondrial marker, CYTB, has low variation in rates across passerine lineages. This lends support to its widespread use as a molecular clock in birds. However, we also found that the patterns of among‐lineage rate variation in CYTB are only weakly related to the evolutionary rate of the mitochondrial genome as a whole. Our analyses confirmed the presence of mutational saturation at third codon positions across the protein‐coding genes of the mitochondrial genome, reinforcing the view that these sites should be excluded in studies of deep passerine relationships. The results of our analyses have provided information that will be useful for molecular‐clock studies of passerine evolution.     

Understanding Neutral Genomic Molecular Clocks

The molecular clock hypothesis is a central concept in molecular evolution and has inspired much research into why evolutionary rates vary between and within genomes. In the age of modern comparative genomics, understanding the neutral genomic molecular clock occupies a critical place. It has been demonstrated that molecular clocks run differently between closely related species, and generation time is an important determinant of lineage specific molecular clocks. Moreover, it has been repeatedly shown that regional molecular clocks vary even within a genome, which should be taken into account when measuring evolutionary constraint of specific genomic regions. With the availability of a large amount of genomic sequence data, new insights into the patterns and causes of variation in molecular clocks are emerging. In particular, factors such as nucleotide composition, molecular origins of mutations, weak selection and recombination rates are important determinants of neutral genomic molecular clocks.     

Assessing the sensitivity of divergence time estimates to locus sampling,calibration points,and model priors in a RAD-seq phylogeny of Carex section Schoenoxiphium

Restriction site-associated DNA sequencing (RAD-seq) and related methods have become relatively common approaches to resolve species-level phylogeny. It is not clear, however, whether RAD-seq data matrices are well suited to relaxed clock inference of divergence times, given the size of the matrices and the abundance of missing data. We investigated the sensitivity of Bayesian relaxed clock estimates of divergence times to alternative analytical decisions on an empirical RAD-seq phylogenetic matrix. We explored the relative contribution of secondary calibration strategies, amount of missing data, and the data partition analyzed to overall variance in divergence times inferred using BEAST MCMC analyses of Carex section Schoenoxiphium (Cyperaceae)—a recent radiation for which we have nearly complete species sampling of RAD-seq data. The crown node for Schoenoxiphium was estimated to be 15.22 (9.56–21.18) Ma using a single calibration point and low missing data, 11.93 (8.07–16.03) Ma using multiple calibration points and low missing data, and 8.34 (5.41–11.22) using multiple calibrations but high missing data. We found that using matrices with more than half of the individuals with missing data inferred younger mean ages for all nodes. Moreover, we have found that our molecular clock estimates are sensitive to the positions of the calibration(s) in our phylogenetic tree (using matrices with low missing data), especially when only a single calibration was applied to estimate divergence times. These results argue for sensitivity analyses and caution in interpreting divergence time estimates from RAD-seq data.     

Overdispersion of the molecular clock: temporal variation of gene-specific substitution rates in Drosophila

Simple models of molecular evolution assume that sequences evolve by a Poisson process in which nucleotide or amino acid substitutions occur as rare independent events. In these models, the expected ratio of the variance to the mean of substitution counts equals 1, and substitution processes with a ratio greater than 1 are called overdispersed. Comparing the genomes of 10 closely related species of Drosophila, we extend earlier evidence for overdispersion in amino acid replacements as well as in four-fold synonymous substitutions. The observed deviation from the Poisson expectation can be described as a linear function of the rate at which substitutions occur on a phylogeny, which implies that deviations from the Poisson expectation arise from gene-specific temporal variation in substitution rates. Amino acid sequences show greater temporal variation in substitution rates than do four-fold synonymous sequences. Our findings provide a general phenomenological framework for understanding overdispersion in the molecular clock. Also, the presence of substantial variation in gene-specific substitution rates has broad implications for work in phylogeny reconstruction and evolutionary rate estimation.     

A Molecular Genetic Timescale for the Diversification of Autotrophic Stramenopiles (Ochrophyta): Substantive Underestimation of Putative Fossil Ages

Background

Stramenopiles constitute a large and diverse eukaryotic clade that is currently poorly characterized from both phylogenetic and temporal perspectives at deeper taxonomic levels. To better understand this group, and in particular the photosynthetic stramenopiles (Ochrophyta), we analyzed sequence data from 135 taxa representing most major lineages. Our analytical approach utilized several recently developed methods that more realistically model the temporal evolutionary process.

Methodology/Principal Findings

Phylogenetic reconstruction employed a Bayesian joint rate- and pattern-heterogeneity model to reconstruct the evolutionary history of these taxa. Inferred phylogenetic resolution was generally high at all taxonomic levels, sister-class relationships in particular receiving good statistical support. A signal for heterotachy was detected in clustered portions of the tree, although this does not seem to have had a major influence on topological inference. Divergence time estimates, assuming a lognormally-distributed relaxed molecular clock while accommodating topological uncertainty, were broadly congruent over alternative temporal prior distributions. These data suggest that Ochrophyta originated near the Proterozoic-Phanerozoic boundary, diverging from their sister-taxon Oomycota. The evolution of the major ochrophyte lineages appears to have proceeded gradually thereafter, with most lineages coming into existence by ∼200 million years ago.

Conclusions/Significance

The evolutionary timescale of the autotrophic stramenopiles reconstructed here is generally older than previously inferred from molecular clocks. However, this more ancient timescale nevertheless casts serious doubt on the taxonomic validity of putative xanthophyte/phaeophyte fossils from the Proterozoic, which predate by as much as a half billion years or more the age suggested by our molecular genetic data. If these fossils truly represent crown stramenopile lineages, then this would imply that molecular rate evolution in this group proceeds in a fashion that is fundamentally incompatible with the relaxed molecular clock model employed here. A more likely scenario is that there is considerable convergent morphological evolution within Heterokonta, and that these fossils have been taxonomically misdiagnosed.     

Relaxed phylogenetics and dating with confidence

In phylogenetics, the unrooted model of phylogeny and the strict molecular clock model are two extremes of a continuum. Despite their dominance in phylogenetic inference, it is evident that both are biologically unrealistic and that the real evolutionary process lies between these two extremes. Fortunately, intermediate models employing relaxed molecular clocks have been described. These models open the gate to a new field of “relaxed phylogenetics.” Here we introduce a new approach to performing relaxed phylogenetic analysis. We describe how it can be used to estimate phylogenies and divergence times in the face of uncertainty in evolutionary rates and calibration times. Our approach also provides a means for measuring the clocklikeness of datasets and comparing this measure between different genes and phylogenies. We find no significant rate autocorrelation among branches in three large datasets, suggesting that autocorrelated models are not necessarily suitable for these data. In addition, we place these datasets on the continuum of clocklikeness between a strict molecular clock and the alternative unrooted extreme. Finally, we present analyses of 102 bacterial, 106 yeast, 61 plant, 99 metazoan, and 500 primate alignments. From these we conclude that our method is phylogenetically more accurate and precise than the traditional unrooted model while adding the ability to infer a timescale to evolution.