An examination of phylogenetic models of substitution rate variation among lineages

Molecular evolutionary rates can show significant variation among lineages, complicating the task of estimating substitution rates and divergence times using phylogenetic methods. Accordingly, relaxed molecular clock models have been developed to accommodate such rate heterogeneity, but these often make the assumption of rate autocorrelation among lineages. In this paper, I examine the validity of this assumption.     

Inconsistencies in estimating the age of HIV-1 subtypes due to heterotachy

Rate heterogeneity among lineages is a common feature of molecular evolution, and it has long impeded our ability to accurately estimate the age of evolutionary divergence events. The development of relaxed molecular clocks, which model variable substitution rates among lineages, was intended to rectify this problem. Major subtypes of pandemic HIV-1 group M are thought to exemplify closely related lineages with different substitution rates. Here, we report that inferring the time of most recent common ancestor of all these subtypes in a single phylogeny under a single (relaxed) molecular clock produces significantly different dates for many of the subtypes than does analysis of each subtype on its own. We explore various methods to ameliorate this problem. We conclude that current molecular dating methods are inadequate for dealing with this type of substitution rate variation in HIV-1. Through simulation, we show that heterotachy causes root ages to be overestimated.     

Comparing Evolutionary Patterns and Variability in the Mitochondrial Control Region and Cytochrome <Emphasis Type="Italic">b</Emphasis> in Three Species of Baleen Whales

The rapidly evolving mitochondrial control region remains an important source of information on phylogeography and demographic history for cetaceans and other vertebrates, despite great uncertainty in the rate of nucleotide substitution across both nucleotide positions and lineages. Patterns of variation in linked markers with slower rates of evolution can potentially be used to calibrate the rate of nucleotide substitution in the control region and to better understand the interplay of evolutionary and demographic forces across the mitochondrial genome above and below the species level. We have examined patterns of diversity within and between three baleen whale species (gray, humpback, and Antarctic minke whales) in order to determine how patterns of molecular evolution differ between cytochrome b and the control region. Our results show that cytochrome b is less variable than expected given the diversity in the control region for gray and humpback whales, even after functional differences are taken into account, but more variable than expected for minke whales. Differences in the frequency distributions of polymorphic sites and in best-fit models of nucleotide substitution indicate that these patterns may be the result of hypervariability in the control region in gray and humpback whales but, in minke whales, may result from a large, stable or expanding population size coupled with saturation at the control region. Using paired cytochrome b and control region data across individuals, we show that the average rate of nucleotide substitution in the control region may be on average 2.6 times higher than phylogenetically derived estimates in cetaceans. These results highlight the complexity of making inferences from control region data alone and suggest that applying simple rules of DNA sequence analyses across species may be difficult.     

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.     

Pattern and timing of diversification of Cetartiodactyla (Mammalia, Laurasiatheria), as revealed by a comprehensive analysis of mitochondrial genomes

The order Cetartiodactyla includes cetaceans (whales, dolphins and porpoises) that are found in all oceans and seas, as well as in some rivers, and artiodactyls (ruminants, pigs, peccaries, hippos, camels and llamas) that are present on all continents, except Antarctica and until recent invasions, Australia. There are currently 332 recognized cetartiodactyl species, which are classified into 132 genera and 22 families. Most phylogenetic studies have focused on deep relationships, and no comprehensive time-calibrated tree for the group has been published yet. In this study, 128 new complete mitochondrial genomes of Cetartiodactyla were sequenced and aligned with those extracted from nucleotide databases. Our alignment includes 14,902 unambiguously aligned nucleotide characters for 210 taxa, representing 183 species, 107 genera, and all cetartiodactyl families. Our mtDNA data produced a statistically robust tree, which is largely consistent with previous classifications. However, a few taxa were found to be para- or polyphyletic, including the family Balaenopteridae, as well as several genera and species. Accordingly, we propose several taxonomic changes in order to render the classification compatible with our molecular phylogeny. In some cases, the results can be interpreted as possible taxonomic misidentification or evidence for mtDNA introgression. The existence of three new cryptic species of Ruminantia should therefore be confirmed by further analyses using nuclear data. We estimate divergence times using Bayesian relaxed molecular clock models. The deepest nodes appeared very sensitive to prior assumptions leading to unreliable estimates, primarily because of the misleading effects of rate heterogeneity, saturation and divergent outgroups. In addition, we detected that Whippomorpha contains slow-evolving taxa, such as large whales and hippos, as well as fast-evolving taxa, such as river dolphins. Our results nevertheless indicate that the evolutionary history of cetartiodactyls was punctuated by four main phases of rapid radiation during the Cenozoic era: the sudden occurrence of the three extant lineages within Cetartiodactyla (Cetruminantia, Suina and Tylopoda); the basal diversification of Cetacea during the Early Oligocene; and two radiations that involve Cetacea and Pecora, one at the Oligocene/Miocene boundary and the other in the Middle Miocene. In addition, we show that the high species diversity now observed in the families Bovidae and Cervidae accumulated mainly during the Late Miocene and Plio-Pleistocene.     

The age and diversification of the angiosperms re-revisited

? Premise of the study: It has been 8 years since the last comprehensive analysis of divergence times across the angiosperms. Given recent methodological improvements in estimating divergence times, refined understanding of relationships among major angiosperm lineages, and the immense interest in using large angiosperm phylogenies to investigate questions in ecology and comparative biology, new estimates of the ages of the major clades are badly needed. Improved estimations of divergence times will concomitantly improve our understanding of both the evolutionary history of the angiosperms and the patterns and processes that have led to this highly diverse clade. ? Methods: We simultaneously estimated the age of the angiosperms and the divergence times of key angiosperm lineages, using 36 calibration points for 567 taxa and a "relaxed clock" methodology that does not assume any correlation between rates, thus allowing for lineage-specific rate heterogeneity. ? Key results: Based on the analysis for which we set fossils to fit lognormal priors, we obtained an estimated age of the angiosperms of 167-199 Ma and the following age estimates for major angiosperm clades: Mesangiospermae (139-156 Ma); Gunneridae (109-139 Ma); Rosidae (108-121 Ma); Asteridae (101-119 Ma). ? Conclusions: With the exception of the age of the angiosperms themselves, these age estimates are generally younger than other recent molecular estimates and very close to dates inferred from the fossil record. We also provide dates for all major angiosperm clades (including 45 orders and 335 families [208 stem group age only, 127 both stem and crown group ages], sensu APG III). Our analyses provide a new comprehensive source of reference dates for major angiosperm clades that we hope will be of broad utility.     

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.     

Data partitioning and correction for ascertainment bias reduce the uncertainty of placental mammal divergence times inferred from the morphological clock

Bayesian estimates of divergence times based on the molecular clock yield uncertainty of parameter estimates measured by the width of posterior distributions of node ages. For the relaxed molecular clock, previous works have reported that some of the uncertainty inherent to the variation of rates among lineages may be reduced by partitioning data. Here we test this effect for the purely morphological clock, using placental mammals as a case study. We applied the uncorrelated lognormal relaxed clock to morphological data of 40 extant mammalian taxa and 4,533 characters, taken from the largest published matrix of discrete phenotypic characters. The morphologically derived timescale was compared to divergence times inferred from molecular and combined data. We show that partitioning data into anatomical units significantly reduced the uncertainty of divergence time estimates for morphological data. For the first time, we demonstrate that ascertainment bias has an impact on the precision of morphological clock estimates. While analyses including molecular data suggested most divergences between placental orders occurred near the K‐Pg boundary, the partitioned morphological clock recovered older interordinal splits and some younger intraordinal ones, including significantly later dates for the radiation of bats and rodents, which accord to the short‐fuse hypothesis.     

Diversity versus disparity and the radiation of modern cetaceans

Modern whales are frequently described as an adaptive radiation spurred by either the evolution of various key innovations (such as baleen or echolocation) or ecological opportunity following the demise of archaic whales. Recent analyses of diversification rate shifts on molecular phylogenies raise doubts about this interpretation since they find no evidence of increased speciation rates during the early evolution of modern taxa. However, one of the central predictions of ecological adaptive radiation is rapid phenotypic diversification, and the tempo of phenotypic evolution has yet to be quantified in cetaceans. Using a time-calibrated molecular phylogeny of extant cetaceans and a morphological dataset on size, we find evidence that cetacean lineages partitioned size niches early in the evolutionary history of neocetes and that changes in cetacean size are consistent with shifts in dietary strategy. We conclude that the signature of adaptive radiations may be retained within morphological traits even after equilibrium diversity has been reached and high extinction or fluctuations in net diversification have erased any signature of an early burst of diversification in the structure of the phylogeny.     

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.     

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’.     

Cytochrome b nucleotide sequences and the identification of five primary lineages of extant cetaceans

Relationships among and within baleen and toothed whales were examined using the complete sequence of the mitochondrial cytochrome b gene. Based on parsimony analyses of conservative nucleotide substitutions, five primary evolutionary lineages of extant cetaceans were identified, one represented by baleen whales (Mysticeti) and four represented by odontocetes (toothed whales). Based on the most comprehensive representation of taxa, both cetaceans and artiodactyls, the most parsimonious relationship among the five lineages is (Mysticeti, Odontoceti (Platanistoidea (Physeteroidea (Ziphioidea (Delphinida))))). This relationship, however, is labile and sensitive to ingroup representation and the choice of outgroup. The short nodes among the five cetacean lineages suggest that the divergence among these lineages occurred over a narrow time period, a finding consistent with the limited fossil evidence that indicates a major cetacean radiation 30-34 Mya. The level of divergence among the five cetacean lineages, and that seen between cetaceans and artiodactyls, suggests that cetaceans and artiodactyls had a common ancestor approximately 60 Mya.      

Maximum-likelihood models for combined analyses of multiple sequence data

Models of nucleotide substitution were constructed for combined analyses of heterogeneous sequence data (such as those of multiple genes) from the same set of species. The models account for different aspects of the heterogeneity in the evolutionary process of different genes, such as differences in nucleotide frequencies, in substitution rate bias (for example, the transition/transversion rate bias), and in the extent of rate variation across sites. Model parameters were estimated by maximum likelihood and the likelihood ratio test was used to test hypotheses concerning sequence evolution, such as rate constancy among lineages (the assumption of a molecular clock) and proportionality of branch lengths for different genes. The example data from a segment of the mitochondrial genome of six hominoid species (human, common and pygmy chimpanzees, gorilla, orangutan, and siamang) were analyzed. Nucleotides at the three codon positions in the protein-coding regions and from the tRNA-coding regions were considered heterogeneous data sets. Statistical tests showed that the amount of evolution in the sequence data reflected in the estimated branch lengths can be explained by the codon-position effect and lineage effect of substitution rates. The assumption of a molecular clock could not be rejected when the data were analyzed separately or when the rate variation among sites was ignored. However, significant differences in substitution rate among lineages were found when the data sets were combined and when the rate variation among sites was accounted for in the models. Under the assumption that the orangutan and African apes diverged 13 million years ago, the combined analysis of the sequence data estimated the times for the human-chimpanzee separation and for the separation of the gorilla as 4.3 and 6.8 million years ago, respectively.     

Slow molecular clocks in Old World monkeys,apes, and humans

Two longstanding issues on the molecular clock hypothesis are studied in this article. First, is there a global molecular clock in mammals? Although many authors have observed unequal rates of nucleotide substitution among mammalian lineages, some authors have proposed a global clock for all eutherians, i.e., a single global rate of 2.2 x 10(-9) substitutions per nucleotide site per year. We reexamine this issue using noncoding, nonrepetitive DNA from Old World monkeys (OWMs), chimpanzee, and human. First, using the minimal date of 6 MYA for the human-chimpanzee divergence and more than 2.5 million base pairs of genomic sequences from human and chimpanzee, we estimate a maximal rate of 0.99 x 10(-9) for noncoding, nonrepetitive genomic regions for these two species. This estimate is less than half of the proposed global rate and much smaller than the commonly used rate (3.5 x 10(-9)) for eutherians. Further, using a minimal date of 23 MYA for the human-OWM divergence, we estimate a maximal rate of 1.5 x 10(-9) for both introns and fourfold degenerate sites in humans and OWMs. In addition, with the New World monkey (NWM) lineage as an outgroup, we estimate that the rate of substitution in introns is 30% higher in the OWM lineage than in the human lineage. Clearly, there is no global molecular clock in eutherians. Second, although many studies have indicated considerable variation in the mutation rate among regions of the mammalian genome, a recent study proposed a uniform rate. Using new and existing intron sequence data from higher primates, we find significant rate variation among genomic regions and a positive correlation between the rate of substitution and the GC content, refuting the claim of a uniform rate.     

A Bayesian evaluation of human mitochondrial substitution rates

Accurate estimates of mitochondrial substitution rates are central to molecular studies of human evolution, but meaningful comparisons of published studies are problematic because of the wide range of methodologies and data sets employed. These differences are nowhere more pronounced than among rates estimated from phylogenies, genealogies, and pedigrees. By using a data set comprising mitochondrial genomes from 177 humans, we estimate substitution rates for various data partitions by using Bayesian phylogenetic analysis with a relaxed molecular clock. We compare the effect of multiple internal calibrations with the customary human-chimpanzee split. The analyses reveal wide variation among estimated substitution rates and divergence times made with different partitions and calibrations, with evidence of substitutional saturation, natural selection, and significant rate heterogeneity among lineages and among sites. Collectively, the results support dates for migration out of Africa and the common mitochondrial ancestor of humans that are considerably more recent than most previous estimates. Our results also demonstrate that human mitochondrial genomes exhibit a number of molecular evolutionary complexities that necessitate the use of sophisticated analytical models for genetic analyses.     

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.     

Bayesian random local clocks,or one rate to rule them all

Background  

Relaxed molecular clock models allow divergence time dating and "relaxed phylogenetic" inference, in which a time tree is estimated in the face of unequal rates across lineages. We present a new method for relaxing the assumption of a strict molecular clock using Markov chain Monte Carlo to implement Bayesian modeling averaging over random local molecular clocks. The new method approaches the problem of rate variation among lineages by proposing a series of local molecular clocks, each extending over a subregion of the full phylogeny. Each branch in a phylogeny (subtending a clade) is a possible location for a change of rate from one local clock to a new one. Thus, including both the global molecular clock and the unconstrained model results, there are a total of 2^2n-2 possible rate models available for averaging with 1, 2, ..., 2n - 2 different rate categories.     

Ancient dates or accelerated rates? Morphological clocks and the antiquity of placental mammals

Analyses of a comprehensive morphological character matrix of mammals using ‘relaxed’ clock models (which simultaneously estimate topology, divergence dates and evolutionary rates), either alone or in combination with an 8.5 kb nuclear sequence dataset, retrieve implausibly ancient, Late Jurassic–Early Cretaceous estimates for the initial diversification of Placentalia (crown-group Eutheria). These dates are much older than all recent molecular and palaeontological estimates. They are recovered using two very different clock models, and regardless of whether the tree topology is freely estimated or constrained using scaffolds to match the current consensus placental phylogeny. This raises the possibility that divergence dates have been overestimated in previous analyses that have applied such clock models to morphological and total evidence datasets. Enforcing additional age constraints on selected internal divergences results in only a slight reduction of the age of Placentalia. Constraining Placentalia to less than 93.8 Ma, congruent with recent molecular estimates, does not require major changes in morphological or molecular evolutionary rates. Even constraining Placentalia to less than 66 Ma to match the ‘explosive’ palaeontological model results in only a 10- to 20-fold increase in maximum evolutionary rate for morphology, and fivefold for molecules. The large discrepancies between clock- and fossil-based estimates for divergence dates might therefore be attributable to relatively small changes in evolutionary rates through time, although other explanations (such as overly simplistic models of morphological evolution) need to be investigated. Conversely, dates inferred using relaxed clock models (especially with discrete morphological data and MrBayes) should be treated cautiously, as relatively minor deviations in rate patterns can generate large effects on estimated divergence dates.     

Local molecular clocks in three nuclear genes: divergence times for rodents and other mammals and incompatibility among fossil calibrations

Reconstructing the chronology of mammalian evolution is a debated issue between molecule- and fossil-based inferences. A methodological limitation of molecules is the evolutionary rate variation among lineages, precluding the application of the global molecular clock. We considered 2422 first and second codon positions of the combined ADRA2B, IRBP, and vWF nuclear genes for a well-documented set of placentals including an extensive sampling of rodents. Using seven independent calibration points and a maximum-likelihood framework, we evaluated whether molecular and paleontological estimates of mammalian divergence dates may be reconciled by the local molecular clocks approach, allowing local constancy of substitution rates with variations at larger phylogenetic scales. To handle the difficulty of choosing among all possible rate assignments for various lineages, local molecular clocks were based on the results of branch-length and two-cluster tests. Extensive lineage-specific variation of evolutionary rates was detected, even among rodents. Cross-calibrations indicated some incompatibilities between divergence dates based on different paleontological references. To decrease the impact of a single calibration point, estimates derived from independent calibrations displaying only slight reciprocal incompatibility were averaged. The divergence dates inferred for the split between mice and rats (approximately 13-19 Myr) was younger than previously published molecular estimates. The most recent common ancestors of rodents, primates and rodents, boreoeutherians, and placentals were estimated to be, respectively, approximately 60, 70, 75, and 78 Myr old. Global clocks, local clocks, and quartet dating analyses suggested a Late Cretaceous origin of the crown placental clades followed by a Tertiary radiation of some placental orders like rodents.