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     

Assessing concordance of fossil calibration points in molecular clock studies: an example using turtles

Although still controversial, estimation of divergence times using molecular data has emerged as a powerful tool to examine the tempo and mode of evolutionary change. Two primary obstacles in improving the accuracy of molecular dating are heterogeneity in DNA substitution rates and accuracy of the fossil record as calibration points. Recent methodological advances have provided powerful methods that estimate relative divergence times in the face of heterogeneity of nucleotide substitution rates among lineages. However, relatively little attention has focused on the accuracy of fossil calibration points that allow one to translate relative divergence times into absolute time. We present a new cross-validation method that identifies inconsistent fossils when multiple fossil calibrations are available for a clade and apply our method to a molecular phylogeny of living turtles with fossil calibration times for 17 of the 22 internal nodes in the tree. Our cross-validation procedure identified seven inconsistent fossils. Using the consistent fossils as calibration points, we found that despite their overall antiquity as a lineage, the most species-rich clades of turtles diversified well within the Cenozoic. Many of the truly ancient lineages of turtles are currently represented by a few, often endangered species that deserve high priority as conservation targets.     

Can fast early rates reconcile molecular dates with the Cambrian explosion?

Molecular dates consistently place the divergence of major metazoan lineages in the Precambrian, leading to the suggestion that the 'Cambrian explosion' is an artefact of preservation which left earlier forms unrecorded in the fossil record. While criticisms of molecular analyses for failing to deal with variation in the rate of molecular evolution adequately have been countered by analyses which allow both site-to-site and lineage-specific rate variation, no analysis to date has allowed the rates to vary temporally. If the rates of molecular evolution were much higher early in the metazoan radiation, molecular dates could consistently overestimate the divergence times of lineages. Here, we use a new method which uses multiple calibration dates and an empirically determined range of possible substitution rates to place bounds on the basal date of divergence of lineages in order to ask whether faster rates of molecular evolution early in the metazoan radiation could possibly account for the discrepancy between molecular and palaeontological date estimates. We find that allowing basal (interphylum) lineages the fastest observed substitution rate brings the minimum possible divergence date (586 million years ago) to the Vendian period, just before the first multicellular animal fossils, but excludes divergence of the major metazoan lineages in a Cambrian explosion.     

Bayesian relaxed clock estimation of divergence times in foraminifera

Accurate and precise estimation of divergence times during the Neo-Proterozoic is necessary to understand the speciation dynamic of early Eukaryotes. However such deep divergences are difficult to date, as the molecular clock is seriously violated. Recent improvements in Bayesian molecular dating techniques allow the relaxation of the molecular clock hypothesis as well as incorporation of multiple and flexible fossil calibrations. Divergence times can then be estimated even when the evolutionary rate varies among lineages and even when the fossil calibrations involve substantial uncertainties. In this paper, we used a Bayesian method to estimate divergence times in Foraminifera, a group of unicellular eukaryotes, known for their excellent fossil record but also for the high evolutionary rates of their genomes. Based on multigene data we reconstructed the phylogeny of Foraminifera and dated their origin and the major radiation events. Our estimates suggest that Foraminifera emerged during the Cryogenian (650-920 Ma, Neo-Proterozoic), with a mean time around 770 Ma, about 220 Myr before the first appearance of reliable foraminiferal fossils in sediments (545 Ma). Most dates are in agreement with the fossil record, but in general our results suggest earlier origins of foraminiferal orders. We found that the posterior time estimates were robust to specifications of the prior. Our results highlight inter-species variations of evolutionary rates in Foraminifera. Their effect was partially overcome by using the partitioned Bayesian analysis to accommodate rate heterogeneity among data partitions and using the relaxed molecular clock to account for changing evolutionary rates. However, more coding genes appear necessary to obtain more precise estimates of divergence times and to resolve the conflicts between fossil and molecular date estimates.     

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.     

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 practical guide to molecular dating

Molecular dating has now become a common tool for many biologists and considerable methodological improvements have been made over the last few years. However, the practice of estimating divergence times using molecular data is highly variable among researchers and it is not straightforward for a newcomer to the field to know how to start. Here I provide a brief overview of the current state-of-the-art of molecular dating practice. I review some of the important choices that must be made when conducting a divergence time analysis, including how to select and use calibrations and which relaxed clock model and program to use, with a focus on some practical aspects. I then provide some guidelines for the interpretation of results and briefly review some alternatives to molecular dating for obtaining divergence times. Last, I present some promising developments for the future of the field, related to the improvement of the calibration process.     

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.     

Timing primate evolution: Lessons from the discordance between molecular and paleontological estimates

The molecular clock has become an increasingly important tool in evolutionary biology and biological anthropology. Nevertheless, a source of contention with respect to this method is the frequent discordance with fossil‐based estimates of divergence times. The primate radiation is a case in point: Numerous studies have dated the major primate nodes (reviewed in Steiper and Young, 1 , 2 ) and there are many instances where molecular and fossil‐based estimates of divergence times differ (Fig. 1). Some investigators have recently focused on phenomena such as stratigraphic dating, the stochastic nature of molecular time estimates, and other sources as potential biases in molecular clock estimates. 3 , 4 In this paper we do not focus on accuracy or statistical error; rather, we argue that discordance is a predictable phenomenon that provides valuable information about the tempo and mode of primate molecular and morphological evolution. Using this perspective, we reexamine the principal theoretical and methodological factors that lead to discordance between molecular and fossil estimates of the origins of taxa and discuss how a better understanding of these factors can help to improve our understanding of primate evolution.     

CALIBRATING DIVERGENCE TIMES ON SPECIES TREES VERSUS GENE TREES: IMPLICATIONS FOR SPECIATION HISTORY OF APHELOCOMA JAYS

Estimates of the timing of divergence are central to testing the underlying causes of speciation. Relaxed molecular clocks and fossil calibration have improved these estimates; however, these advances are implemented in the context of gene trees, which can overestimate divergence times. Here we couple recent innovations for dating speciation events with the analytical power of species trees, where multilocus data are considered in a coalescent context. Divergence times are estimated in the bird genus Aphelocoma to test whether speciation in these jays coincided with mountain uplift or glacial cycles. Gene trees and species trees show general agreement that diversification began in the Miocene amid mountain uplift. However, dates from the multilocus species tree are more recent, occurring predominately in the Pleistocene, consistent with theory that divergence times can be significantly overestimated with gene‐tree based approaches that do not correct for genetic divergence that predates speciation. In addition to coalescent stochasticity, Haldane's rule could account for some differences in timing estimates between mitochondrial DNA and nuclear genes. By incorporating a fossil calibration applied to the species tree, in addition to the process of gene lineage coalescence, the present approach provides a more biologically realistic framework for dating speciation events, and hence for testing the links between diversification and specific biogeographic and geologic events.     

Approximate likelihood calculation on a phylogeny for Bayesian estimation of divergence times

The molecular clock provides a powerful way to estimate species divergence times. If information on some species divergence times is available from the fossil or geological record, it can be used to calibrate a phylogeny and estimate divergence times for all nodes in the tree. The Bayesian method provides a natural framework to incorporate different sources of information concerning divergence times, such as information in the fossil and molecular data. Current models of sequence evolution are intractable in a Bayesian setting, and Markov chain Monte Carlo (MCMC) is used to generate the posterior distribution of divergence times and evolutionary rates. This method is computationally expensive, as it involves the repeated calculation of the likelihood function. Here, we explore the use of Taylor expansion to approximate the likelihood during MCMC iteration. The approximation is much faster than conventional likelihood calculation. However, the approximation is expected to be poor when the proposed parameters are far from the likelihood peak. We explore the use of parameter transforms (square root, logarithm, and arcsine) to improve the approximation to the likelihood curve. We found that the new methods, particularly the arcsine-based transform, provided very good approximations under relaxed clock models and also under the global clock model when the global clock is not seriously violated. The approximation is poorer for analysis under the global clock when the global clock is seriously wrong and should thus not be used. The results suggest that the approximate method may be useful for Bayesian dating analysis using large data sets.     

Accommodating heterogenous rates of evolution in molecular divergence dating methods: an example using intercontinental dispersal of Plestiodon (Eumeces) lizards

Identifying and dating historical biological events is a fundamental goal of evolutionary biology, and recent analytical advances permit the modeling of factors known to affect both the accuracy and the precision of molecular date estimates. As the use of multilocus data sets becomes increasingly routine, it becomes more important to evaluate the potentially confounding effects of rate heterogeneity both within (e.g., codon positions) and among loci when estimating divergence times. Here, using Plestiodon lizards as a test case, we examine the effects of accommodating rate heterogeneity among data partitions on divergence time estimation. Plestiodon inhabits both East Asia and North America, yet both the geographic origin of the genus and timing of dispersal between the continents have been debated. For each of the eight independently evolving loci and a combined data set, we conduct single model and partitioned analyses. We found that extreme saturation has obscured the underlying rate of evolution in the mitochondrial DNA (mtDNA), resulting in severe underestimation of the rate in this locus. As a result, the age of the crown Plestiodon clade was overestimated by 15-17 Myr by the unpartitioned analysis of the combined loci data. However, the application of partition-specific models to the combined data resulted in ages that were fully congruent with those inferred by the individual nuclear loci. Although partitioning improved divergence date estimates of the mtDNA-only analysis, the ages were nonetheless overestimated, thus indicating an inadequacy of our current models to capture the complex nature of mtDNA evolution in over large time scales. Finally, the statistically incongruent age distributions inferred by the partitioned and unpartitioned analyses of the combined data support mutually exclusive hypotheses of the timing of intercontinental dispersal of Plestiodon from Asia to North America. Analyses that best capture the rate of evolution in the combined data set infer that this exchange occurred via Beringia ～18.0-30 Ma.     

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.     

Integration of Bayesian molecular clock methods and fossil-based soft bounds reveals early Cenozoic origin of African lacertid lizards

Background  

Although current molecular clock methods offer greater flexibility in modelling evolutionary events, calibration of the clock with dates from the fossil record is still problematic for many groups. Here we implement several new approaches in molecular dating to estimate the evolutionary ages of Lacertidae, an Old World family of lizards with a poor fossil record and uncertain phylogeny. Four different models of rate variation are tested in a new program for Bayesian phylogenetic analysis called TreeTime, based on a combination of mitochondrial and nuclear gene sequences. We incorporate paleontological uncertainty into divergence estimates by expressing multiple calibration dates as a range of probabilistic distributions. We also test the reliability of our proposed calibrations by exploring effects of individual priors on posterior estimates.     

Playing chicken (Gallus gallus): methodological inconsistencies of molecular divergence date estimates due to secondary calibration points

For any given taxonomic divergence event, one may find in the literature a wide range of time estimates. Many factors contribute to the variation in molecular date estimates for the same evolutionary event. High on the list is the choice of calibration points for converting genetic distances into evolutionary rates and, subsequently, into dates of divergence. In this study, we investigate one critical source of error in estimating divergence times, i.e. the use of secondary calibration points, which are divergence time estimates that have been derived from one molecular dataset on the basis of a primary external calibration point, and which are used again independently of the original external calibration point on a second dataset. Unless particular care is exercised, this practice leads to internal inconsistencies, and the inferred dates of divergence are by necessity unreliable. We present a consistency test for assessing the reliability of divergence time estimates based on secondary calibration points. As a case study, we examine recent estimates of divergence times among phyla and kingdoms based on multiple nuclear protein-coding genes, and show that they fail the consistency test.     

Calibrating the chelicerate clock: a paleontological reply to Jeyaprakash and Hoy

Divergence times inferred for major lineages of Chelicerata (scorpions, spiders, mites, pycnogonids and xiphosurans) in a recent paper on mitochondrial phylogeny by Jeyaprakash and Hoy are compared to the known stratigraphical occurrences of these groups. Erroneous statements concerning fossil date estimates in the original study are corrected. We emphasize that the fossil record of chelicerates is more complete than is sometimes assumed, and that paleontology plays a key role in dating cladogenesis by setting minimum divergence times, which can and do falsify molecular clock estimates where the inferred divergence is substantially younger than the known fossil record. The oldest representatives of each chelicerate order are documented here, together with similar data for the major mite lineages down to family level. Through these, we hope to provide a robust framework and reference points for future molecular systematic studies of this nature.     

Influence of gene flow on divergence dating – implications for the speciation history of Takydromus grass lizards

Dating the time of divergence and understanding speciation processes are central to the study of the evolutionary history of organisms but are notoriously difficult. The difficulty is largely rooted in variations in the ancestral population size or in the genealogy variation across loci. To depict the speciation processes and divergence histories of three monophyletic Takydromus species endemic to Taiwan, we sequenced 20 nuclear loci and combined with one mitochondrial locus published in GenBank. They were analysed by a multispecies coalescent approach within a Bayesian framework. Divergence dating based on the gene tree approach showed high variation among loci, and the divergence was estimated at an earlier date than when derived by the species‐tree approach. To test whether variations in the ancestral population size accounted for the majority of this variation, we conducted computer inferences using isolation‐with‐migration (IM) and approximate Bayesian computation (ABC) frameworks. The results revealed that gene flow during the early stage of speciation was strongly favoured over the isolation model, and the initiation of the speciation process was far earlier than the dates estimated by gene‐ and species‐based divergence dating. Due to their limited dispersal ability, it is suggested that geographical isolation may have played a major role in the divergence of these Takydromus species. Nevertheless, this study reveals a more complex situation and demonstrates that gene flow during the speciation process cannot be overlooked and may have a great impact on divergence dating. By using multilocus data and incorporating Bayesian coalescence approaches, we provide a more biologically realistic framework for delineating the divergence history of Takydromus.     

Testing the impact of calibration on molecular divergence times using a fossil-rich group: the case of Nothofagus (Fagales)

Although temporal calibration is widely recognized as critical for obtaining accurate divergence-time estimates using molecular dating methods, few studies have evaluated the variation resulting from different calibration strategies. Depending on the information available, researchers have often used primary calibrations from the fossil record or secondary calibrations from previous molecular dating studies. In analyses of flowering plants, primary calibration data can be obtained from macro- and mesofossils (e.g., leaves, flowers, and fruits) or microfossils (e.g., pollen). Fossil data can vary substantially in accuracy and precision, presenting a difficult choice when selecting appropriate calibrations. Here, we test the impact of eight plausible calibration scenarios for Nothofagus (Nothofagaceae, Fagales), a plant genus with a particularly rich and well-studied fossil record. To do so, we reviewed the phylogenetic placement and geochronology of 38 fossil taxa of Nothofagus and other Fagales, and we identified minimum age constraints for up to 18 nodes of the phylogeny of Fagales. Molecular dating analyses were conducted for each scenario using maximum likelihood (RAxML + r8s) and Bayesian (BEAST) approaches on sequence data from six regions of the chloroplast and nuclear genomes. Using either ingroup or outgroup constraints, or both, led to similar age estimates, except near strongly influential calibration nodes. Using "early but risky" fossil constraints in addition to "safe but late" constraints, or using assumptions of vicariance instead of fossil constraints, led to older age estimates. In contrast, using secondary calibration points yielded drastically younger age estimates. This empirical study highlights the critical influence of calibration on molecular dating analyses. Even in a best-case situation, with many thoroughly vetted fossils available, substantial uncertainties can remain in the estimates of divergence times. For example, our estimates for the crown group age of Nothofagus varied from 13 to 113 Ma across our full range of calibration scenarios. We suggest that increased background research should be made at all stages of the calibration process to reduce errors wherever possible, from verifying the geochronological data on the fossils to critical reassessment of their phylogenetic position.     

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.