Inferring speciation times under an episodic molecular clock

We extend our recently developed Markov chain Monte Carlo algorithm for Bayesian estimation of species divergence times to allow variable evolutionary rates among lineages. The method can use heterogeneous data from multiple gene loci and accommodate multiple fossil calibrations. Uncertainties in fossil calibrations are described using flexible statistical distributions. The prior for divergence times for nodes lacking fossil calibrations is specified by use of a birth-death process with species sampling. The prior for lineage-specific substitution rates is specified using either a model with autocorrelated rates among adjacent lineages (based on a geometric Brownian motion model of rate drift) or a model with independent rates among lineages specified by a log-normal probability distribution. We develop an infinite-sites theory, which predicts that when the amount of sequence data approaches infinity, the width of the posterior credibility interval and the posterior mean of divergence times form a perfect linear relationship, with the slope indicating uncertainties in time estimates that cannot be reduced by sequence data alone. Simulations are used to study the influence of among-lineage rate variation and the number of loci sampled on the uncertainty of divergence time estimates. The analysis suggests that posterior time estimates typically involve considerable uncertainties even with an infinite amount of sequence data, and that the reliability and precision of fossil calibrations are critically important to divergence time estimation. We apply our new algorithms to two empirical data sets and compare the results with those obtained in previous Bayesian and likelihood analyses. The results demonstrate the utility of our new algorithms.     

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.     

Evaluating fossil calibrations for dating phylogenies in light of rates of molecular evolution: a comparison of three approaches

Evolutionary and biogeographic studies increasingly rely on calibrated molecular clocks to date key events. Although there has been significant recent progress in development of the techniques used for molecular dating, many issues remain. In particular, controversies abound over the appropriate use and placement of fossils for calibrating molecular clocks. Several methods have been proposed for evaluating candidate fossils; however, few studies have compared the results obtained by different approaches. Moreover, no previous study has incorporated the effects of nucleotide saturation from different data types in the evaluation of candidate fossils. In order to address these issues, we compared three approaches for evaluating fossil calibrations: the single-fossil cross-validation method of Near, Meylan, and Shaffer (2005. Assessing concordance of fossil calibration points in molecular clock studies: an example using turtles. Am. Nat. 165:137-146), the empirical fossil coverage method of Marshall (2008. A simple method for bracketing absolute divergence times on molecular phylogenies using multiple fossil calibration points. Am. Nat. 171:726-742), and the Bayesian multicalibration method of Sanders and Lee (2007. Evaluating molecular clock calibrations using Bayesian analyses with soft and hard bounds. Biol. Lett. 3:275-279) and explicitly incorporate the effects of data type (nuclear vs. mitochondrial DNA) for identifying the most reliable or congruent fossil calibrations. We used advanced (Caenophidian) snakes as a case study; however, our results are applicable to any taxonomic group with multiple candidate fossils, provided appropriate taxon sampling and sufficient molecular sequence data are available. We found that data type strongly influenced which fossil calibrations were identified as outliers, regardless of which method was used. Despite the use of complex partitioned models of sequence evolution and multiple calibrations throughout the tree, saturation severely compressed basal branch lengths obtained from mitochondrial DNA compared with nuclear DNA. The effects of mitochondrial saturation were not ameliorated by analyzing a combined nuclear and mitochondrial data set. Although removing the third codon positions from the mitochondrial coding regions did not ameliorate saturation effects in the single-fossil cross-validations, it did in the Bayesian multicalibration analyses. Saturation significantly influenced the fossils that were selected as most reliable for all three methods evaluated. Our findings highlight the need to critically evaluate the fossils selected by data with different rates of nucleotide substitution and how data with different evolutionary rates affect the results of each method for evaluating fossils. Our empirical evaluation demonstrates that the advantages of using multiple independent fossil calibrations significantly outweigh any disadvantages.     

Exploring uncertainty in the calibration of the molecular clock

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

To what extent do new fossil discoveries change our understanding of clade evolution? A cautionary tale from burying beetles (Coleoptera: Nicrophorus)

Divergence time estimates derived from phylogenies are crucial to infer historical biogeography and diversification dynamics. Yet, the impact of fossil record incompleteness on macroevolutionary reconstructions remains equivocal. Here, we investigate to what extent gaps in the fossil record can impinge downstream evolutionary inferences in the beetle family Silphidae. Recent discoveries have pushed back the fossil record of this group from the Eocene into the Jurassic. We estimated the divergence times of the family using both its currently understood fossil record and the fossil record known prior to these recent discoveries. All fossil calibrations were informed with different parametric distributions to investigate the weight of priors on posterior age estimates. Based on time‐calibrated trees, we assessed the impact of fossil calibrations on the inference of ancestral ranges and diversification rate dynamics in the genus Nicrophorus. Depending upon the selected sets of fossil constraints, the age discrepancies had a major impact on the macroevolutionary inferences: the biogeographic extrapolations relative to paleogeography are markedly contrasting, and the calculated rates at which species form or go extinct (and when they varied) are strikingly different. We show that soft prior distributions do not necessarily alleviate such shortcomings therefore preventing the inference of reliable macroevolutionary patterns in groups presenting a taphonomic bias in their fossil record.     

Dating primate divergences through an integrated analysis of palaeontological and molecular data

Estimation of divergence times is usually done using either the fossil record or sequence data from modern species. We provide an integrated analysis of palaeontological and molecular data to give estimates of primate divergence times that utilize both sources of information. The number of preserved primate species discovered in the fossil record, along with their geological age distribution, is combined with the number of extant primate species to provide initial estimates of the primate and anthropoid divergence times. This is done by using a stochastic forwards-modeling approach where speciation and fossil preservation and discovery are simulated forward in time. We use the posterior distribution from the fossil analysis as a prior distribution on node ages in a molecular analysis. Sequence data from two genomic regions (CFTR on human chromosome 7 and the CYP7A1 region on chromosome 8) from 15 primate species are used with the birth-death model implemented in mcmctree in PAML to infer the posterior distribution of the ages of 14 nodes in the primate tree. We find that these age estimates are older than previously reported dates for all but one of these nodes. To perform the inference, a new approximate Bayesian computation (ABC) algorithm is introduced, where the structure of the model can be exploited in an ABC-within-Gibbs algorithm to provide a more efficient analysis.     

Are pollen fossils useful for calibrating relaxed molecular clock dating of phylogenies? A comparative study using Myrtaceae

The identification and application of reliable fossil calibrations represents a key component of many molecular studies of evolutionary timescales. In studies of plants, most paleontological calibrations are associated with macrofossils. However, the pollen record can also inform age calibrations if fossils matching extant pollen groups are found. Recent work has shown that pollen of the myrtle family, Myrtaceae, can be classified into a number of morphological groups that are synapomorphic with molecular groups. By assembling a data matrix of pollen morphological characters from extant and fossil Myrtaceae, we were able to measure the fit of 26 pollen fossils to a molecular phylogenetic tree using parsimony optimisation of characters. We identified eight Myrtaceidites fossils as appropriate for calibration based on the most parsimonious placements of these fossils on the tree. These fossils were used to inform age constraints in a Bayesian phylogenetic analysis of a sequence alignment comprising two sequences from the chloroplast genome (matK and ndhF) and one nuclear locus (ITS), sampled from 106 taxa representing 80 genera. Three additional analyses were calibrated by placing pollen fossils using geographic and morphological information (eight calibrations), macrofossils (five calibrations), and macrofossils and pollen fossils in combination (12 calibrations). The addition of new fossil pollen calibrations led to older crown ages than have previously been found for tribes such as Eucalypteae and Myrteae. Estimates of rate variation among lineages were affected by the choice of calibrations, suggesting that the use of multiple calibrations can improve estimates of rate heterogeneity among lineages. This study illustrates the potential of including pollen-based calibrations in molecular studies of divergence times.     

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.     

Calibrated tree priors for relaxed phylogenetics and divergence time estimation

The use of fossil evidence to calibrate divergence time estimation has a long history. More recently, Bayesian Markov chain Monte Carlo has become the dominant method of divergence time estimation, and fossil evidence has been reinterpreted as the specification of prior distributions on the divergence times of calibration nodes. These so-called "soft calibrations" have become widely used but the statistical properties of calibrated tree priors in a Bayesian setting hashave not been carefully investigated. Here, we clarify that calibration densities, such as those defined in BEAST 1.5, do not represent the marginal prior distribution of the calibration node. We illustrate this with a number of analytical results on small trees. We also describe an alternative construction for a calibrated Yule prior on trees that allows direct specification of the marginal prior distribution of the calibrated divergence time, with or without the restriction of monophyly. This method requires the computation of the Yule prior conditional on the height of the divergence being calibrated. Unfortunately, a practical solution for multiple calibrations remains elusive. Our results suggest that direct estimation of the prior induced by specifying multiple calibration densities should be a prerequisite of any divergence time dating analysis.     

Dated Phylogenies of the Sister Genera Macaranga and Mallotus (Euphorbiaceae): Congruence in Historical Biogeographic Patterns?

Molecular phylogenies and estimates of divergence times within the sister genera Macaranga and Mallotus were estimated using Bayesian relaxed clock analyses of two generic data sets, one per genus. Both data sets were based on different molecular markers and largely different samples. Per genus three calibration points were utilised. The basal calibration point (crown node of all taxa used) was taken from literature and used for both taxa. The other three calibrations were based on fossils of which two were used per genus. We compared patterns of dispersal and diversification in Macaranga and Mallotus using ancestral area reconstruction in RASP (S-DIVA option) and contrasted our results with biogeographical and geological records to assess accuracy of inferred age estimates. A check of the fossil calibration point showed that the Japanese fossil, used for dating the divergence of Mallotus, probably had to be attached to a lower node, the stem node of all pioneer species, but even then the divergence time was still younger than the estimated age of the fossil. The African (only used in the Macaranga data set) and New Zealand fossils (used for both genera) seemed reliably placed. Our results are in line with existing geological data and the presence of stepping stones that provided dispersal pathways from Borneo to New Guinea-Australia, from Borneo to mainland Asia and additionally at least once to Africa and Madagascar via land and back to India via Indian Ocean island chains. The two genera show congruence in dispersal patterns, which corroborate divergence time estimates, although the overall mode and tempo of dispersal and diversification differ significantly as shown by distribution patterns of extant species.     

Multiple Miocene Melastomataceae dispersal between Madagascar, Africa and India

Melastomataceae sensu stricto (excluding Memecylaceae) comprise some 3000 species in the neotropics, 1000 in Asia, 240 in Africa, and 230 in Madagascar. Previous family-wide morphological and DNA analyses have shown that the Madagascan species belong to at least three unrelated lineages, which were hypothesized to have arrived by trans-oceanic dispersal. An alternative hypothesis posits that the ancestors of Madagascan, as well as Indian, Melastomataceae arrived from Africa in the Late Cretaceous. This study tests these hypotheses in a Bayesian framework, using three combined sequence datasets analysed under a relaxed clock and simultaneously calibrated with fossils, some not previously used. The new fossil calibration comes from a re-dated possibly Middle or Upper Eocene Brazilian fossil of Melastomeae. Tectonic events were also tentatively used as constraints because of concerns that some of the family's fossils are difficult to assign to nodes in the phylogeny. Regardless of how the data were calibrated, the estimated divergence times of Madagascan and Indian lineages were too young for Cretaceous explanations to hold. This was true even of the oldest ages within the 95% credibility interval around each estimate. Madagascar's Melastomeae appear to have arrived from Africa during the Miocene. Medinilla, with some 70 species in Madagascar and two in Africa, too, arrived during the Miocene, but from Asia. Gravesia, with 100 species in Madagascar and four in east and west Africa, also appears to date to the Miocene, but its monophyly has not been tested. The study afforded an opportunity to compare divergence time estimates obtained earlier with strict clocks and single calibrations, with estimates based on relaxed clocks and different multiple calibrations and taxon sampling.     

Integrating fossil preservation biases in the selection of calibrations for molecular divergence time estimation

The selection of fossil data to use as calibration age priors in molecular divergence time estimates inherently links neontological methods with paleontological theory. However, few neontological studies have taken into account the possibility of a taphonomic bias in the fossil record when developing approaches to fossil calibration selection. The Sppil-Rongis effect may bias the first appearance of a lineage toward the recent causing most objective calibration selection approaches to erroneously exclude appropriate calibrations or to incorporate multiple calibrations that are too young to accurately represent the divergence times of target lineages. Using turtles as a case study, we develop a Bayesian extension to the fossil selection approach developed by Marshall (2008. A simple method for bracketing absolute divergence times on molecular phylogenies using multiple fossil calibrations points. Am. Nat. 171:726-742) that takes into account this taphonomic bias. Our method has the advantage of identifying calibrations that may bias age estimates to be too recent while incorporating uncertainty in phylogenetic parameter estimates such as tree topology and branch lengths. Additionally, this method is easily adapted to assess the consistency of potential calibrations to any one calibration in the candidate pool.     

Phylogenomic datasets provide both precision and accuracy in estimating the timescale of placental mammal phylogeny

The fossil record suggests a rapid radiation of placental mammals following the Cretaceous-Paleogene (K-Pg) mass extinction 65 million years ago (Ma); nevertheless, molecular time estimates, while highly variable, are generally much older. Early molecular studies suffer from inadequate dating methods, reliance on the molecular clock, and simplistic and over-confident interpretations of the fossil record. More recent studies have used Bayesian dating methods that circumvent those issues, but the use of limited data has led to large estimation uncertainties, precluding a decisive conclusion on the timing of mammalian diversifications. Here we use a powerful Bayesian method to analyse 36 nuclear genomes and 274 mitochondrial genomes (20.6 million base pairs), combined with robust but flexible fossil calibrations. Our posterior time estimates suggest that marsupials diverged from eutherians 168-178 Ma, and crown Marsupialia diverged 64-84 Ma. Placentalia diverged 88-90 Ma, and present-day placental orders (except Primates and Xenarthra) originated in a ～20 Myr window (45-65 Ma) after the K-Pg extinction. Therefore we reject a pre K-Pg model of placental ordinal diversification. We suggest other infamous instances of mismatch between molecular and palaeontological divergence time estimates will be resolved with this same approach.     

Bayesian analysis of combined chloroplast loci, using multiple calibrations, supports the recent arrival of Melastomataceae in Africa and Madagascar

A new biogeographic scenario for Melastomataceae (Morley and Dick, American Journal of Botany 90(11) pp. 1638-1645, 2003) accepts an ndhF-based phylogeny for the family by Renner et al. (American Journal of Botany 88(7): 1290-1300, 2001), but rejects those authors' divergence time estimates. Morley and Dick concluded that Gondwanan vicariance, rather than the more recent long dispersal proposed by Renner et al. explains the presence of the family in Africa and Madagascar. To assess the strength of this conclusion, a Bayesian analysis was conducted on three times the amount of sequence data used before (ndhF, rbcL, rpl16; 3100 base pairs [bp], excluding all gaps). The Bayesian approach to divergence time estimation does not rely on a strict molecular clock and employs multiple simultaneous minimal or maximal bounds on node ages. Reliance on northern mid-latitude fossils of Melastomataceae for calibrations was avoided or reduced by using alternative fossil and tectonic calibrations, including all those suggested by Morley and Dick. Results reaffirm the relatively recent spread of melastome lineages among the southern continents and refute the breakup of Gondwana as a plausible explanation for the presence of Dissochaeteae/Sonerileae in Madagascar and Africa and the presence of Melastomeae in Africa and Southeast Asia. Melastomeae appear to have reached Africa around 17-15 million years (my) ago, while Dissochaeteae and Sonerileae apparently reached Madagascar at 17-15 and 20-18 my ago. I also explored the effects of constraining Melastomeae to minimally 76 my old (to have reached Africa by island hopping as postulated by Morley and Dick). This resulted in an estimate for their arrival in Africa of 35 my ago and for Dissochaeteae and Sonerileae in Madagascar of 28 and 33 my ago, still implying long-distance dispersal. The Bayesian 95% credibility ranges around these dates, however, are large. Regardless of the increasing sophistication of molecular estimates of divergence time, Gondwanan scenarios will remain untestable as long as biases in the fossil record can justifiably be invoked to explain away the absence of fossils.     

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.     

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

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

The fossil record and estimating divergence times between lineages: Maximum divergene times and the importance of reliable phylogenies

Summary Bounded estimates on divergence times between lineaes are crucial to the calculation of absolute rates of molecular evolution. Upper (minimum) bounds on divergence times are easily estimated based on earliest fossil finds. Lower (maximum) bounds are more difficult to estimate; the age of putative ancestors may be used, though in practice it is virtually impossible to distinguish ancestors from primitive sister groups, which do not, of logical necessit, consitute lower bounds on divergence times. Two relatively new approaches to estimating lower bounds directly assess the incompleteness of the fossil record. The first uses taphonomic control groups to distinguish real absences from nonpreservation, while the second, and probably more powerful, uses the quality of the fossil recored to estimate confidence intervals on the bases of stratigraphic ranges. For some groups, especially vertebrates, the inclusion or exclusion of problematic fossils can dramaticaly affect estimated lower bounds on divergence times, often swamping the uncertainties due to the incompleteness of the fossil record and/or corelation and dating errors. When datable paleogeographic events reflect ancient divisions of faunas, a lower bound on the divergence time of speices within a fauna can be established based on the geologic, rather than fossil, record. The fossil records of hominids, eutherianmammals, echinoids, and geese are used as examples.This article was presented at the C.S.E.O.L. Conferrence on DNA-DNA Hybridization and Evolution, Lake Arrowhead, California, May 11–14, 1989     

A Simple Method for Estimating Informative Node Age Priors for the Fossil Calibration of Molecular Divergence Time Analyses

Molecular divergence time analyses often rely on the age of fossil lineages to calibrate node age estimates. Most divergence time analyses are now performed in a Bayesian framework, where fossil calibrations are incorporated as parametric prior probabilities on node ages. It is widely accepted that an ideal parameterization of such node age prior probabilities should be based on a comprehensive analysis of the fossil record of the clade of interest, but there is currently no generally applicable approach for calculating such informative priors. We provide here a simple and easily implemented method that employs fossil data to estimate the likely amount of missing history prior to the oldest fossil occurrence of a clade, which can be used to fit an informative parametric prior probability distribution on a node age. Specifically, our method uses the extant diversity and the stratigraphic distribution of fossil lineages confidently assigned to a clade to fit a branching model of lineage diversification. Conditioning this on a simple model of fossil preservation, we estimate the likely amount of missing history prior to the oldest fossil occurrence of a clade. The likelihood surface of missing history can then be translated into a parametric prior probability distribution on the age of the clade of interest. We show that the method performs well with simulated fossil distribution data, but that the likelihood surface of missing history can at times be too complex for the distribution-fitting algorithm employed by our software tool. An empirical example of the application of our method is performed to estimate echinoid node ages. A simulation-based sensitivity analysis using the echinoid data set shows that node age prior distributions estimated under poor preservation rates are significantly less informative than those estimated under high preservation rates.     

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.     

Molecular clocks do not support the Cambrian explosion

The fossil record has long supported the view that most animal phyla originated during a brief period approximately 520 MYA known as the Cambrian explosion. However, molecular data analyses over the past 3 decades have found deeper divergences among animals (approximately 800 to 1,200 MYA), with and without the assumption of a global molecular clock. Recently, two studies have instead reported time estimates apparently consistent with the fossil record. Here, we demonstrate that methodological problems in these studies cast doubt on the accuracy and interpretations of the results obtained. In the study by Peterson et al., young time estimates were obtained because fossil calibrations were used as maximum limits rather than as minimum limits, and not because invertebrate calibrations were used. In the study by Aris-Brosou and Yang, young time estimates were obtained because of problems with rate models and other methods specific to the study, and not because Bayesian methods were used. This also led to many anomalous findings in their study, including a primate-rodent divergence at 320 MYA. With these results aside, molecular clocks continue to support a long period of animal evolution before the Cambrian explosion of fossils.