Performance of a divergence time estimation method under a probabilistic model of rate evolution

Rates of molecular evolution vary over time and, hence, among lineages. In contrast, widely used methods for estimating divergence times from molecular sequence data assume constancy of rates. Therefore, methods for estimation of divergence times that incorporate rate variation are attractive. Improvements on a previously proposed Bayesian technique for divergence time estimation are described. New parameterization more effectively captures the phylogenetic structure of rate evolution on a tree. Fossil information and other evidence can now be included in Bayesian analyses in the form of constraints on divergence times. Simulation results demonstrate that the accuracy of divergence time estimation is substantially enhanced when constraints are included.     

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.     

The Power of Relative Rates Tests Depends on the Data

One of the most useful features of molecular phylogenetic analyses is the potential for estimating dates of divergence of evolutionary lineages from the DNA of extant species. But lineage-specific variation in rate of molecular evolution complicates molecular dating, because a calibration rate estimated from one lineage may not be an accurate representation of the rate in other lineages. Many molecular dating studies use a ``clock test' to identify and exclude sequences that vary in rate between lineages. However, these clock tests should not be relied upon without a critical examination of their effectiveness at removing rate variable sequences from any given data set, particularly with regard to the sequence length and number of variable sites. As an illustration of this problem we present a power test of a frequently employed triplet relative rates test. We conclude that (1) relative rates tests are unlikely to detect moderate levels of lineage-specific rate variation (where one lineage has a rate of molecular evolution 1.5 to 4.0 times the other) for most commonly used sequences in molecular dating analyses, and (2) this lack of power is likely to result in substantial error in the estimation of dates of divergence. As an example, we show that the well-studied rate difference between murid rodents and great apes will not be detected for many of the sequences used to date the divergence between these two lineages and that this failure to detect rate variation is likely to result in consistent overestimation the date of the rodent–primate split. Received: 9 June 1999 / Accepted: 22 October 1999     

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.     

Rates of molecular evolution and the fraction of nucleotide positions free to vary

Summary Selective constraints on DNA sequence change were incorporated into a model of DNA divergence by restricting substitutions to a subset of nucleotide positions. A simple model showed that both mutation rate and the fraction of nucleotide positions free to vary are strong determinants of DNA divergence over time.When divergence between two species approaches the fraction of positions free to vary, standard methods that correct for multiple mutations yield severe underestimates of the number of substitutions per site. A modified method appropriate for use with DNA sequence, restriction site, or thermal renaturation data is derived taking this fraction into account. The model also showed that the ratio of divergence in two gene classes (e.g., nuclear and mitochondrial) may vary widely over time even if the ratio of mutation rates remains constant.DNA sequence divergence data are used increasingly to detect differences in rates of molecular evolution. Often, variation in divergence rate is assumed to represent variation in mutation rate. The present model suggests that differing divergence rates among comparisons (either among gene classes or taxa) should be interpreted cautiously. Differences in the fraction of nucleotide positions free to vary can serve as an important alternative hypothesis to explain differences in DNA divergence rates.     

Time scale of eutherian evolution estimated without assuming a constant rate of molecular evolution

Controversies over the molecular clock hypothesis were reviewed. Since it is evident that the molecular clock does not hold in an exact sense, accounting for evolution of the rate of molecular evolution is a prerequisite when estimating divergence times with molecular sequences. Recently proposed statistical methods that account for this rate variation are overviewed and one of these procedures is applied to the mitochondrial protein sequences and to the nuclear gene sequences from many mammalian species in order to estimate the time scale of eutherian evolution. This Bayesian method not only takes account of the variation of molecular evolutionary rate among lineages and among genes, but it also incorporates fossil evidence via constraints on node times. With denser taxonomic sampling and a more realistic model of molecular evolution, this Bayesian approach is expected to increase the accuracy of divergence time estimates.     

Assessing the quality of molecular divergence time estimates by fossil calibrations and fossil-based model selection

Estimates of species divergence times using DNA sequence data are playing an increasingly important role in studies of evolution, ecology and biogeography. Most work has centred on obtaining appropriate kinds of data and developing optimal estimation procedures, whereas somewhat less attention has focused on the calibration of divergences using fossils. Case studies with multiple fossil calibration points provide important opportunities to examine the divergence time estimation problem in new ways. We discuss two cross-validation procedures that address different aspects of inference in divergence time estimation. 'Fossil cross-validation' is a procedure used to identify the impact of different individual calibrations on overall estimation. This can identify fossils that have an exceptionally large error effect and may warrant further scrutiny. 'Fossil-based model cross-validation' is an entirely different procedure that uses fossils to identify the optimal model of molecular evolution in the context of rate smoothing or other inference methods. Both procedures were applied to two recent studies: an analysis of monocot angiosperms with eight fossil calibrations and an analysis of placental mammals with nine fossil calibrations. In each case, fossil calibrations could be ranked from most to least influential, and in one of the two studies, the fossils provided decisive evidence about the optimal molecular evolutionary model.     

Correlated evolutionary divergence of egg size and a mitochondrial protein across the Isthmus of Panama

An explicit assumption of studies that employ a mitochondrial DNA (mtDNA) molecular clock is that mtDNA evolves independently of morphology. Here we report a very strong correlation between egg size divergence and cytochrome c oxidase-1 (CO1) amino acid sequence divergence among sister species of bivalve molluscs separated by the Central American Isthmus (i.e., "geminate" species). Analyses of the molecular data reveal that CO1 sequences likely did not diverge as a function of time or evolve in response to positive natural selection. Given that an excess of CO1 amino acid polymorphism exists within species (as expected if most mutations are only slightly deleterious), a third hypothesis is that reductions in effective population size could simultaneously increase the fixation rate of nearly neutral mtDNA polymorphisms and in some way also facilitate egg size evolution. The remarkable strength of the relationship between egg size and CO1 amino acid sequence demonstrates that, even in the absence of an obvious functional relationship or clock-like evolution, the amounts of molecular and morphological change can be tightly correlated, and therefore may reflect common processes. Accordingly, the assumption that the evolutionary divergence of molecules and morphology are independent must always be carefully examined.     

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.     

Making a robust biomolecular time scale for phylogenetic studies

The further evolution of informational molecular sequences should depend on the number of viable alternatives possible for the sequences as set by selection, the unrepaired mutation rate, and time. Most biomolecular clocks are based on Kimura's nearly neutral mutation random-drift hypothesis. This clock assumes that informational sequences are in equilibrium, i.e., the nucleotides mutate at a uniform rate and the number of nucleotides unconstrained by selection remains constant. Correcting for deviations from these assumptions should produce a more accurate clock. Informational molecules probably formed from polynucleotides having some other function such as nitrogen or nucleotide storage, thus being initially functionally unselected. At any time the rate of development of functionality in a protein may be expected to be proportional to the number of viable alternatives of sequence in its potentially interacting regions. Assuming the rate of unrepaired mutations is constant, these clocks should exponentially slow as they evolve, each with a different rate toward individual equilibria. Also if the degree of selection changes, its clock rate should change. For a more precise clock two approaches are suggested to estimate these time dependent changes in evolutionary rate. An improved clock could improve estimation of phylogeny and put a time scale on that phylogeny.     

Molecular evolution: Codes,clocks, genes and genomes

The discoveries, advancements and continuing controversies in the field of molecular evolution are reviewed. Topics summarized are (1) the evolution of the genetic code, (2) gene evolution including the demonstration of homology, estimation of sequence divergence, phylogenetic trees, the molecular clock and the origin of genes and gene families by various genetic mechanisms, and (3) eukaryotic genome evolution, including the highly repeated satellite sequences, the interspersed and potentially mobile repeated sequences and the unique sequence fraction of the genome.     

Dating the time of viral subtype divergence

Precise dating of viral subtype divergence enables researchers to correlate divergence with geographic and demographic occurrences. When historical data are absent (that is, the overwhelming majority), viral sequence sampling on a time scale commensurate with the rate of substitution permits the inference of the times of subtype divergence. Currently, researchers use two strategies to approach this task, both requiring strong conditions on the molecular clock assumption of substitution rate. As the underlying structure of the substitution rate process at the time of subtype divergence is not understood and likely highly variable, we present a simple method that estimates rates of substitution, and from there, times of divergence, without use of an assumed molecular clock. We accomplish this by blending estimates of the substitution rate for triplets of dated sequences where each sequence draws from a distinct viral subtype, providing a zeroth-order approximation for the rate between subtypes. As an example, we calculate the time of divergence for three genes among influenza subtypes A-H3N2 and B using subtype C as an outgroup. We show a time of divergence approximately 100 years ago, substantially more recent than previous estimates which range from 250 to 3800 years ago.     

A molecular-clock date for the origin of the animal phyla

Although the reliability of the molecular clock for determining divergence times that are not visible in the fossil record has been questioned, the amino-acid sequence differences in the α and β haemoglobins of a variety of living vertebrates do not support this view. While the molecular clock is clearly probabilistic rather than metronomic, it can be shown that the α and β haemoglobins have been evolving at a statistically equal rate since they first appeared some 450–500 million years ago. If this rate has always been constant for all globins, then the percentage sequence differences between several invertebrate and some vertebrate globins can be used to indicate that the initial radiation of the animal phyla occurred at least 900–1000 million years ago. ?Molecular evolution, Metazoa, haemoglobin.     

Erratic rates of molecular evolution and incongruence of fossil and molecular divergence time estimates in Ostracoda (Crustacea)

Dating evolutionary origins of taxa is essential for understanding rates and timing of evolutionary events, often inciting intense debate when molecular estimates differ from first fossil appearances. For numerous reasons, ostracods present a challenging case study of rates of evolution and congruence of fossil and molecular divergence time estimates. On the one hand, ostracods have one of the densest fossil records of any metazoan group. However, taxonomy of fossil ostracods is controversial, owing at least in part to homoplasy of carapaces, the most commonly fossilized part. In addition, rates of evolution are variable in ostracods. Here, we report evidence of extreme variation in the rate of molecular evolution in different ostracod groups. This rate is significantly elevated in Halocyprid ostracods, a widespread planktonic group, consistent with previous observations that planktonic groups show elevated rates of molecular evolution. At the same time, the rate of molecular evolution is slow in the lineage leading to Manawa staceyi, a relict species that we estimate diverged approximately 500 million years ago from its closest known living relative. We also report multiple cases of significant incongruence between fossil and molecular estimates of divergence times in Ostracoda. Although relaxed clock methods improve the congruence of fossil and molecular divergence estimates over strict clock models, incongruence is present regardless of method. We hypothesize that this observed incongruence is driven largely by problems with taxonomy of fossil Ostracoda. Our results illustrate the difficulty in consistently estimating lineage divergence times, even in the presence of a voluminous fossil record.     

The origin and diversification of eukaryotes: problems with molecular phylogenetics and molecular clock estimation

Determining the relationships among and divergence times for the major eukaryotic lineages remains one of the most important and controversial outstanding problems in evolutionary biology. The sequencing and phylogenetic analyses of ribosomal RNA (rRNA) genes led to the first nearly comprehensive phylogenies of eukaryotes in the late 1980s, and supported a view where cellular complexity was acquired during the divergence of extant unicellular eukaryote lineages. More recently, however, refinements in analytical methods coupled with the availability of many additional genes for phylogenetic analysis showed that much of the deep structure of early rRNA trees was artefactual. Recent phylogenetic analyses of a multiple genes and the discovery of important molecular and ultrastructural phylogenetic characters have resolved eukaryotic diversity into six major hypothetical groups. Yet relationships among these groups remain poorly understood because of saturation of sequence changes on the billion-year time-scale, possible rapid radiations of major lineages, phylogenetic artefacts and endosymbiotic or lateral gene transfer among eukaryotes. Estimating the divergence dates between the major eukaryote lineages using molecular analyses is even more difficult than phylogenetic estimation. Error in such analyses comes from a myriad of sources including: (i) calibration fossil dates, (ii) the assumed phylogenetic tree, (iii) the nucleotide or amino acid substitution model, (iv) substitution number (branch length) estimates, (v) the model of how rates of evolution change over the tree, (vi) error inherent in the time estimates for a given model and (vii) how multiple gene data are treated. By reanalysing datasets from recently published molecular clock studies, we show that when errors from these various sources are properly accounted for, the confidence intervals on inferred dates can be very large. Furthermore, estimated dates of divergence vary hugely depending on the methods used and their assumptions. Accurate dating of divergence times among the major eukaryote lineages will require a robust tree of eukaryotes, a much richer Proterozoic fossil record of microbial eukaryotes assignable to extant groups for calibration, more sophisticated relaxed molecular clock methods and many more genes sampled from the full diversity of microbial eukaryotes.     

A dirichlet process prior for estimating lineage-specific substitution rates

We introduce a new model for relaxing the assumption of a strict molecular clock for use as a prior in Bayesian methods for divergence time estimation. Lineage-specific rates of substitution are modeled using a Dirichlet process prior (DPP), a type of stochastic process that assumes lineages of a phylogenetic tree are distributed into distinct rate classes. Under the Dirichlet process, the number of rate classes, assignment of branches to rate classes, and the rate value associated with each class are treated as random variables. The performance of this model was evaluated by conducting analyses on data sets simulated under a range of different models. We compared the Dirichlet process model with two alternative models for rate variation: the strict molecular clock and the independent rates model. Our results show that divergence time estimation under the DPP provides robust estimates of node ages and branch rates without significantly reducing power. Further analyses were conducted on a biological data set, and we provide examples of ways to summarize Markov chain Monte Carlo samples under this model.     

Relaxed clocks and inferences of heterogeneous patterns of nucleotide substitution and divergence time estimates across whales and dolphins (Mammalia: Cetacea)

Various nucleotide substitution models have been developed to accommodate among lineage rate heterogeneity, thereby relaxing the assumptions of the strict molecular clock. Recently developed "uncorrelated relaxed clock" and "random local clock" (RLC) models allow decoupling of nucleotide substitution rates between descendant lineages and are thus predicted to perform better in the presence of lineage-specific rate heterogeneity. However, it is uncertain how these models perform in the presence of punctuated shifts in substitution rate, especially between closely related clades. Using cetaceans (whales and dolphins) as a case study, we test the performance of these two substitution models in estimating both molecular rates and divergence times in the presence of substantial lineage-specific rate heterogeneity. Our RLC analyses of whole mitochondrial genome alignments find evidence for up to ten clade-specific nucleotide substitution rate shifts in cetaceans. We provide evidence that in the uncorrelated relaxed clock framework, a punctuated shift in the rate of molecular evolution within a subclade results in posterior rate estimates that are either misled or intermediate between the disparate rate classes present in baleen and toothed whales. Using simulations, we demonstrate abrupt changes in rate isolated to one or a few lineages in the phylogeny can mislead rate and age estimation, even when the node of interest is calibrated. We further demonstrate how increasing prior age uncertainty can bias rate and age estimates, even while the 95% highest posterior density around age estimates decreases; in other words, increased precision for an inaccurate estimate. We interpret the use of external calibrations in divergence time studies in light of these results, suggesting that rate shifts at deep time scales may mislead inferences of absolute molecular rates and ages.     

The evolution of the mitochondrial D-loop region and the origin of modern man.

The origin of modern man is a highly debated issue that has recently been tackled by using mitochondrial DNA sequences. The limited genetic variability of human mtDNA has been explained in terms of a recent common genetic ancestry, thus implying that all modern-population mtDNAs originated from a single woman who lived in Africa less than 0.2 Mya. This divergence time is based on both the estimation of the rate of mtDNA change and its calibration date. Because different estimates of the rate of mtDNA evolution can completely change the scenario of the origin of modern man, we have reanalyzed the available mitochondrial sequence data by using an improved version of the statistical model, the "Markov clock," devised in our laboratory. Our analysis supports the African origin of modern man, but we found that the ancestral female from which all extant human mtDNAs originated lived in a time span of 0.3-0.8 Mya. Pushing back the date of the deepest root of the human implies that the earliest divergence would have been in the Homo erectus population.     

The effect of gene conversion on the divergence between duplicated genes

Nonindependent evolution of duplicated genes is called concerted evolution. In this article, we study the evolutionary process of duplicated regions that involves concerted evolution. The model incorporates mutation and gene conversion: the former increases d, the divergence between two duplicated regions, while the latter decreases d. It is demonstrated that the process consists of three phases. Phase I is the time until d reaches its equilibrium value, d(0). In phase II d fluctuates around d(0), and d increases again in phase III. Our simulation results demonstrate that the length of concerted evolution (i.e., phase II) is highly variable, while the lengths of the other two phases are relatively constant. It is also demonstrated that the length of phase II approximately follows an exponential distribution with mean tau, which is a function of many parameters including gene conversion rate and the length of gene conversion tract. On the basis of these findings, we obtain the probability distribution of the level of divergence between a pair of duplicated regions as a function of time, mutation rate, and tau. Finally, we discuss potential problems in genomic data analysis of duplicated genes when it is based on the molecular clock but concerted evolution is common.     

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.