Bayesian Phylogenetic Inference using Relaxed-clocks and the Multispecies Coalescent.

The multispecies coalescent (MSC) model accommodates both species divergences and within-species coalescent and provides a natural framework for phylogenetic analysis of genomic data when the gene trees vary across the genome. The MSC model implemented in the program bpp assumes a molecular clock and the Jukes-Cantor model, and is suitable for analyzing genomic data from closely related species. Here we extend our implementation to more general substitution models and relaxed clocks to allow the rate to vary among species. The MSC-with-relaxed-clock model allows the estimation of species divergence times and ancestral population sizes using genomic sequences sampled from contemporary species when the strict clock assumption is violated, and provides a simulation framework for evaluating species tree estimation methods. We conducted simulations and analyzed two real datasets to evaluate the utility of the new models. We confirm that the clock-JC model is adequate for inference of shallow trees with closely related species, but it is important to account for clock violation for distant species. Our simulation suggests that there is valuable phylogenetic information in the gene-tree branch lengths even if the molecular clock assumption is seriously violated, and the relaxed-clock models implemented in bpp are able to extract such information. Our Markov chain Monte Carlo algorithms suffer from mixing problems when used for species tree estimation under the relaxed clock and we discuss possible improvements. We conclude that the new models are currently most effective for estimating population parameters such as species divergence times when the species tree is fixed.

Relative Efficiencies of Simple and Complex Substitution Models in Estimating Divergence Times in Phylogenomics.

The conventional wisdom in molecular evolution is to apply parameter-rich models of nucleotide and amino acid substitutions for estimating divergence times. However, the actual extent of the difference between time estimates produced by highly complex models compared with those from simple models is yet to be quantified for contemporary data sets that frequently contain sequences from many species and genes. In a reanalysis of many large multispecies alignments from diverse groups of taxa, we found that the use of the simplest models can produce divergence time estimates and credibility intervals similar to those obtained from the complex models applied in the original studies. This result is surprising because the use of simple models underestimates sequence divergence for all the data sets analyzed. We found three fundamental reasons for the observed robustness of time estimates to model complexity in many practical data sets. First, the estimates of branch lengths and node-to-tip distances under the simplest model show an approximately linear relationship with those produced by using the most complex models applied on data sets with many sequences. Second, relaxed clock methods automatically adjust rates on branches that experience considerable underestimation of sequence divergences, resulting in time estimates that are similar to those from complex models. And, third, the inclusion of even a few good calibrations in an analysis can reduce the difference in time estimates from simple and complex models. The robustness of time estimates to model complexity in these empirical data analyses is encouraging, because all phylogenomics studies use statistical models that are oversimplified descriptions of actual evolutionary substitution processes.

Inflation of Molecular Clock Rates and Dates: Molecular Phylogenetics, Biogeography, and Diversification of a Global Cicada Radiation from Australasia (Hemiptera: Cicadidae: Cicadettini).

Dated phylogenetic trees are important for studying mechanisms of diversification, and molecular clocks are important tools for studies of organisms lacking good fossil records. However, studies have begun to identify problems in molecular clock dates caused by uncertainty of the modeled molecular substitution process. Here we explore Bayesian relaxed-clock molecular dating while studying the biogeography of ca. 200 species from the global cicada tribe Cicadettini. Because the available fossils are few and uninformative, we calibrate our trees in part with a cytochrome oxidase I (COI) clock prior encompassing a range of literature estimates for arthropods. We show that tribe-level analyses calibrated solely with the COI clock recover extremely old dates that conflict with published estimates for two well-studied New Zealand subclades within Cicadettini. Additional subclade analyses suggest that COI relaxed-clock rates and maximum-likelihood branch lengths become inflated relative to EF-1[Formula: see text] intron and exon rates and branch lengths as clade age increases. We present corrected estimates derived from: (i) an extrapolated EF-1[Formula: see text] exon clock derived from COI-calibrated analysis within the largest New Zealand subclade; (ii) post hoc scaling of the tribe-level chronogram using results from subclade analyses; and (iii) exploitation of a geological calibration point associated with New Caledonia. We caution that considerable uncertainty is generated due to dependence of substitution estimates on both the taxon sample and the choice of model, including gamma category number and the choice of empirical versus estimated base frequencies. Our results suggest that diversification of the tribe Cicadettini commenced in the early- to mid-Cenozoic and continued with the development of open, arid habitats in Australia and worldwide. We find that Cicadettini is a rare example of a global terrestrial animal group with an Australasian origin, with all non-Australasian genera belonging to two distal clades. Within Australia, we show that Cicadettini is more widely distributed than any other cicada tribe, diverse in temperate, arid and monsoonal habitats, and nearly absent from rainforests. We comment on the taxonomic implications of our findings for thirteen cicada genera.

Total-Evidence Dating under the Fossilized Birth-Death Process.

Bayesian total-evidence dating involves the simultaneous analysis of morphological data from the fossil record and morphological and sequence data from recent organisms, and it accommodates the uncertainty in the placement of fossils while dating the phylogenetic tree. Due to the flexibility of the Bayesian approach, total-evidence dating can also incorporate additional sources of information. Here, we take advantage of this and expand the analysis to include information about fossilization and sampling processes. Our work is based on the recently described fossilized birth-death (FBD) process, which has been used to model speciation, extinction, and fossilization rates that can vary over time in a piecewise manner. So far, sampling of extant and fossil taxa has been assumed to be either complete or uniformly at random, an assumption which is only valid for a minority of data sets. We therefore extend the FBD process to accommodate diversified sampling of extant taxa, which is standard practice in studies of higher-level taxa. We verify the implementation using simulations and apply it to the early radiation of Hymenoptera (wasps, ants, and bees). Previous total-evidence dating analyses of this data set were based on a simple uniform tree prior and dated the initial radiation of extant Hymenoptera to the late Carboniferous (309 Ma). The analyses using the FBD prior under diversified sampling, however, date the radiation to the Triassic and Permian (252 Ma), slightly older than the age of the oldest hymenopteran fossils. By exploring a variety of FBD model assumptions, we show that it is mainly the accommodation of diversified sampling that causes the push toward more recent divergence times. Accounting for diversified sampling thus has the potential to close the long-discussed gap between rocks and clocks. We conclude that the explicit modeling of fossilization and sampling processes can improve divergence time estimates, but only if all important model aspects, including sampling biases, are adequately addressed.

The fossilized birth-death process for coherent calibration of divergence-time estimates.

Time-calibrated species phylogenies are critical for addressing a wide range of questions in evolutionary biology, such as those that elucidate historical biogeography or uncover patterns of coevolution and diversification. Because molecular sequence data are not informative on absolute time, external data--most commonly, fossil age estimates--are required to calibrate estimates of species divergence dates. For Bayesian divergence time methods, the common practice for calibration using fossil information involves placing arbitrarily chosen parametric distributions on internal nodes, often disregarding most of the information in the fossil record. We introduce the "fossilized birth-death" (FBD) process--a model for calibrating divergence time estimates in a Bayesian framework, explicitly acknowledging that extant species and fossils are part of the same macroevolutionary process. Under this model, absolute node age estimates are calibrated by a single diversification model and arbitrary calibration densities are not necessary. Moreover, the FBD model allows for inclusion of all available fossils. We performed analyses of simulated data and show that node age estimation under the FBD model results in robust and accurate estimates of species divergence times with realistic measures of statistical uncertainty, overcoming major limitations of standard divergence time estimation methods. We used this model to estimate the speciation times for a dataset composed of all living bears, indicating that the genus Ursus diversified in the Late Miocene to Middle Pliocene.

Characterization of the uncertainty of divergence time estimation under relaxed molecular clock models using multiple loci.

Genetic sequence data provide information about the distances between species or branch lengths in a phylogeny, but not about the absolute divergence times or the evolutionary rates directly. Bayesian methods for dating species divergences estimate times and rates by assigning priors on them. In particular, the prior on times (node ages on the phylogeny) incorporates information in the fossil record to calibrate the molecular tree. Because times and rates are confounded, our posterior time estimates will not approach point values even if an infinite amount of sequence data are used in the analysis. In a previous study we developed a finite-sites theory to characterize the uncertainty in Bayesian divergence time estimation in analysis of large but finite sequence data sets under a strict molecular clock. As most modern clock dating analyses use more than one locus and are conducted under relaxed clock models, here we extend the theory to the case of relaxed clock analysis of data from multiple loci (site partitions). Uncertainty in posterior time estimates is partitioned into three sources: Sampling errors in the estimates of branch lengths in the tree for each locus due to limited sequence length, variation of substitution rates among lineages and among loci, and uncertainty in fossil calibrations. Using a simple but analogous estimation problem involving the multivariate normal distribution, we predict that as the number of loci ([Formula: see text]) goes to infinity, the variance in posterior time estimates decreases and approaches the infinite-data limit at the rate of 1/[Formula: see text], and the limit is independent of the number of sites in the sequence alignment. We then confirmed the predictions by using computer simulation on phylogenies of two or three species, and by analyzing a real genomic data set for six primate species. Our results suggest that with the fossil calibrations fixed, analyzing multiple loci or site partitions is the most effective way for improving the precision of posterior time estimation. However, even if a huge amount of sequence data is analyzed, considerable uncertainty will persist in time estimates.

Do missing data influence the accuracy of divergence-time estimation with BEAST?

Time-calibrated phylogenies have become essential to evolutionary biology. A recurrent and unresolved question for dating analyses is whether genes with missing data cells should be included or excluded. This issue is particularly unclear for the most widely used dating method, the uncorrelated lognormal approach implemented in BEAST. Here, we test the robustness of this method to missing data. We compare divergence-time estimates from a nearly complete dataset (20 nuclear genes for 32 species of squamate reptiles) to those from subsampled matrices, including those with 5 or 2 complete loci only and those with 5 or 8 incomplete loci added. In general, missing data had little impact on estimated dates (mean error of ∼5Myr per node or less, given an overall age of ∼220Myr in squamates), even when 80% of sampled genes had 75% missing data. Mean errors were somewhat higher when all genes were 75% incomplete (∼17Myr). However, errors increased dramatically when only 2 of 9 fossil calibration points were included (∼40Myr), regardless of missing data. Overall, missing data (and even numbers of genes sampled) may have only minor impacts on the accuracy of divergence dating with BEAST, relative to the dramatic effects of fossil calibrations.

On the Way to Speciation: Shedding Light on the Karstic Phylogeography of the Microendemic Cave Beetle Aphaenops cerberus in the Pyrenees.

The highly modified morphology and ecological features of cave-dwelling organisms are a strong obstacle to dispersion. Hence, they represent ideal models for the study of historical biogeography at both large and fine timescales. Here, we study the phylogeography of Aphaenops cerberus, an endemic hypogean ground beetle with a fragmented distribution in the French Northern Pyrenees. We extracted 75 exemplars of 17 populations of A. cerberus and sequenced one mitochondrial and one nuclear marker to assess the geographic structuration as well as the recent biogeographic history of this species. We used Bayesian Inference and Maximum Likelihood to reconstruct the relationships among most of the extant populations of this species across its distributional range. We inferred divergence time estimates using carabid substitution rates and reconstructed haplotype networks to investigate the recent biogeographic history of this lineage. We recover a strong geographic structuration of the populations across the mountain range. The strong impact of geology on the structure of the populations is evidenced although geological continuity does not systematically lead to continual gene flow. The origin of the species is dated from the Early Pleistocene and the dispersal predates the main Last Glacial Maximum. Our results indicate broad similitudes between islands and karsts, which make cave organisms an excellent model for the study of evolution mechanisms.

Multiple transgressions of Wallace's Line explain diversity of flightless Trigonopterus weevils on Bali.

The fauna of Bali, situated immediately west of Wallace's Line, is supposedly of recent Javanese origin and characterized by low levels of endemicity. In flightless Trigonopterus weevils, however, we find 100% endemism for the eight species here reported for Bali. Phylogeographic analyses show extensive in situ differentiation, including a local radiation of five species. A comprehensive molecular phylogeny and ancestral area reconstruction of Indo-Malayan-Melanesian species reveals a complex colonization pattern, where the three Balinese lineages all arrived from the East, i.e. all of them transgressed Wallace's Line. Although East Java possesses a rich fauna of Trigonopterus, no exchange can be observed with Bali. We assert that the biogeographic picture of Bali has been dominated by the influx of mobile organisms from Java, but different relationships may be discovered when flightless invertebrates are studied. Our results highlight the importance of in-depth analyses of spatial patterns of biodiversity.

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.

Using multiple relaxed-clock models to estimate evolutionary timescales from DNA sequence data.

Molecular data sets comprising DNA sequences from multiple genes are now commonplace in phylogenetic studies. These data sets should be analysed using methods that can account for heterogeneity in the molecular evolutionary process among genes. A common problem is determining how many evolutionary models should be applied to subsets of the data. Different genes can exhibit differing patterns of rate variation among lineages, making it appropriate to assign a separate molecular-clock model to each subset of the data (i.e., a 'partitioned' clock model). The impact of clock-partitioning on estimates of evolutionary rates and timescales is largely unknown. In this study, we use a recently developed method, ClockstaR, to evaluate the effect of using different clock-partitioning schemes. We conduct Bayesian phylogenetic analyses of simulated and empirical multigene data sets. Our analyses show strong statistical support for the clock-partitioning scheme chosen by ClockstaR. In addition, we find that the optimal clock-partitioning scheme produces more reliable estimates of node ages than other schemes.

Phylogeny and molecular dating of the cerato-platanin-encoding genes.

The cerato-platanin family consists of proteins that can induce immune responses, cause necrosis, change chemotaxis and locomotion and may be related to the growth and development of various fungi. In this work, we analyzed the phylogenetic relationships among genes encoding members of the cerato-platanin family and computed the divergence times of the genes and corresponding fungi. The results showed that cerato-platanin-encoding genes could be classified into 10 groups but did not cluster according to fungal classes or their functions. The genes transferred horizontally and showed duplication. Molecular dating and adaptive evolution analyses indicated that the cerato-platanin gene originated with the appearance of saprophytes and that the gene was under positive selection. This finding suggests that cerato-platanin-encoding genes evolved with the development of fungal parasitic characteristics.

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

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

Rates and Rocks: Strengths and Weaknesses of Molecular Dating Methods.

I present here an in-depth, although non-exhaustive, review of two topics in molecular dating. Clock models, which describe the evolution of the rate of evolution, are considered first. Some of the shortcomings of popular approaches-uncorrelated clock models in particular-are presented and discussed. Autocorrelated models are shown to be more reasonable from a biological perspective. Some of the most recent autocorrelated models also rely on a coherent treatment of instantaneous and average substitution rates while previous models are based on implicit approximations. Second, I provide a brief overview of the processes involved in collecting and preparing fossil data. I then review the main techniques that use this data for calibrating the molecular clock. I argue that, in its current form, the fossilized birth-death process relies on assumptions about the mechanisms underlying fossilization and the data collection process that may negatively impact the date estimates. Node-dating approaches make better use of the data available, even though they rest on paleontologists' intervention to prepare raw fossil data. Altogether, this study provides indications that may help practitioners in selecting appropriate methods for molecular dating. It will also hopefully participate in defining the contour of future methodological developments in the field.

Bayesian tip dating reveals heterogeneous morphological clocks in Mesozoic birds.

Recently, comprehensive morphological datasets including nearly all the well-recognized Mesozoic birds became available, making it feasible for statistically rigorous methods to unveil finer evolutionary patterns during early avian evolution. Here, we exploited the advantage of Bayesian tip dating under relaxed morphological clocks to estimate both the divergence times and evolutionary rates while accounting for their uncertainties. We further subdivided the characters into six body regions (i.e. skull, axial skeleton, pectoral girdle and sternum, forelimb, pelvic girdle and hindlimb) to assess evolutionary rate heterogeneity both along the lineages and across partitions. We observed extremely high rates of morphological character changes during early avian evolution, and the clock rates are quite heterogeneous among the six regions. The branch subtending Pygostylia shows an extremely high rate in the axial skeleton, while the branches subtending Ornithothoraces and Enantiornithes show notably high rates in the pectoral girdle and sternum and moderately high rates in the forelimb. The extensive modifications in these body regions largely correspond to refinement of the flight capability. This study reveals the power and flexibility of Bayesian tip dating implemented in MrBayes to investigate evolutionary dynamics in deep time.

Six Impossible Things before Breakfast: Assumptions, Models, and Belief in Molecular Dating.

Confidence in molecular dating analyses has grown with the increasing sophistication of the methods. Some problematic cases where molecular dates disagreed with paleontological estimates appear to have been resolved with a growing agreement between molecules and fossils. But we cannot relax just yet. The growing analytical sophistication of many molecular dating methods relies on an increasingly large number of assumptions about evolutionary history and processes. Many of these assumptions are based on statistical tractability rather than being informed by improved understanding of molecular evolution, yet changing the assumptions can influence molecular dates. How can we tell if the answers we get are driven more by the assumptions we make than by the molecular data being analyzed?

RelTime Rates Collapse to a Strict Clock When Estimating the Timeline of Animal Diversification.

Establishing an accurate timescale for the history of life is crucial to understand evolutionary processes. For this purpose, relaxed molecular clock models implemented in a Bayesian MCMC framework are generally used. However, these methods are time consuming. RelTime, a non-Bayesian method implementing a fast, ad hoc, algorithm for relative dating, was developed to overcome the computational inefficiencies of Bayesian software. RelTime was recently used to investigate the timing of origin of animals, yielding results consistent with early strict clock studies from the 1980s and 1990s, estimating metazoans to have a Mesoproterozoic origin-over a billion years ago. RelTime results are unexpected and disagree with the largest majority of modern, relaxed, Bayesian molecular clock analyses, which suggest animals originated in the Tonian-Cryogenian (less that 850 million years ago). Here, we demonstrate that RelTime-inferred divergence times for the origin of animals are spurious, a consequence of the inability of RelTime to relax the clock along the internal branches of the animal phylogeny. RelTime-inferred divergence times are comparable to strict-clock estimates because they are essentially inferred under a strict clock. Our results warn us of the danger of using ad hoc algorithms making implicit assumptions about rate changes along a tree. Our study roundly rejects a Mesoproterozoic origin of animals; metazoans emerged in the Tonian-Cryogenian, and diversified in the Ediacaran, in the immediate prelude to the routine fossilization of animals in the Cambrian associated with the emergence of readily preserved skeletons.

Age estimation for the genus Cymbidium (Orchidaceae: Epidendroideae) with implementation of fossil data calibration using molecular markers (ITS2 & matK) and phylogeographic inference from ancestral area reconstruction.

Intercontinental dislocations between tropical regions harboring two-thirds of the flowering plants have always drawn attention from taxonomists and biogeographers. One such family belonging to angiosperms is Orchidaceae with an herbaceous habit and high species diversity in the tropics. Here, we investigate the evolutionary and biogeographical history of the genus Cymbidium, which represents a monophyletic subfamily (Epidendroideae) of the orchids and comprises 50 odd species that are distinctly distributed in tropical to temperate regions. Much is not known about correlations among the level of CAM activity (one of the photosynthetic pathways often regarded as an adaptation to water stress in land plants), habitat, life forms, and phylogenetic relationships of orchids from an evolutionary perspective. A relatively well-resolved and highly supported phylogeny for Cymbidium orchids is reconstructed based on sequence analysis of ITS2 and matK regions from the chloroplast DNA available in public repositories viz. GenBank at NCBI. This study examines a genus level analysis by integrating different molecular matrices to existing fossil data on orchids in a molecular Bayesian relaxed clock employed in BEAST and assessed divergence times for the genus Cymbidium with a focus on evolutionary history of photosynthetic characters. Our study has enabled age estimations (45Ma) as well as ancestral area reconstruction for the genus Cymbidium using BEAST by addition of previously analyzed two internal calibration points.

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.