Estimates Of Species Divergence Times Research Articles

Estimation of species divergence times in presence of cross-species gene flow.

Cross-species introgression can have significant impacts on phylogenomic reconstruction of species divergence events. Here, we used simulations to show how the presence of even a small amount of introgression can bias divergence time estimates when gene flow is ignored in the analysis. Using advances in analytical methods under the multispecies coalescent (MSC) model, we demonstrate that by accounting for incomplete lineage sorting and introgression using large phylogenomic data sets this problem can be avoided. The multispecies-coalescent-with-introgression (MSci) model is capable of accurately estimating both divergence times and ancestral effective population sizes, even when only a single diploid individual per species is sampled. We characterize some general expectations for biases in divergence time estimation under three different scenarios: 1) introgression between sister species, 2) introgression between non-sister species, and 3) introgression from an unsampled (i.e., ghost) outgroup lineage. We also conducted simulations under the isolation-with-migration (IM) model and found that the MSci model assuming episodic gene flow was able to accurately estimate species divergence times despite high levels of continuous gene flow. We estimated divergence times under the MSC and MSci models from two published empirical datasets with previous evidence of introgression, one of 372 target-enrichment loci from baobabs (Adansonia), and another of 1000 transcriptome loci from 14 species of the tomato relative, Jaltomata. The empirical analyses not only confirm our findings from simulations, demonstrating that the MSci model can reliably estimate divergence times but also show that divergence time estimation under the MSC can be robust to the presence of small amounts of introgression in empirical datasets with extensive taxon sampling. [divergence time; gene flow; hybridization; introgression; MSci model; multispecies coalescent].

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.

Multispecies coalescent and its applications to infer species phylogenies and cross-species gene flow.

Multispecies coalescent (MSC) is the extension of the single-population coalescent model to multiple species. It integrates the phylogenetic process of species divergences and the population genetic process of coalescent, and provides a powerful framework for a number of inference problems using genomic sequence data from multiple species, including estimation of species divergence times and population sizes, estimation of species trees accommodating discordant gene trees, inference of cross-species gene flow and species delimitation. In this review, we introduce the major features of the MSC model, discuss full-likelihood and heuristic methods of species tree estimation and summarize recent methodological advances in inference of cross-species gene flow. We discuss the statistical and computational challenges in the field and research directions where breakthroughs may be likely in the next few years.

Selective Sampling of Species and Fossils Influences Age Estimates Under the Fossilized Birth-Death Model.

The fossilized birth–death (FBD) model allows the estimation of species divergence times from molecular and fossil information in a coherent framework of diversification and fossil sampling. Some assumptions of the FBD model, however, are difficult to meet in phylogenetic analyses of highly diverse groups. Here, I use simulations to assess the impact of extreme model violations, including diversified sampling of species and the exclusive use of the oldest fossils per clade, on divergence times estimated with the FBD model. My results demonstrate that selective sampling of fossils can produce dramatically overestimated divergence times when the FBD model is used for inference, due to an interplay of underestimates for the model parameters net diversification rate, turnover, and fossil-sampling proportion. In contrast, divergence times estimated with CladeAge, a method that uses information about the oldest fossils per clade together with estimates of sampling and diversification rates, are accurate under these conditions. Practitioners of Bayesian divergence-time estimation should therefore ensure that the dataset conforms to the expectations of the FBD model, or estimates of sampling and diversification rates should be obtained a priori so that CladeAge can be used for the inference.

Phylogenomic Resolution of the Cetacean Tree of Life Using Target Sequence Capture.

The evolution of cetaceans, from their early transition to an aquatic lifestyle to their subsequent diversification, has been the subject of numerous studies. However, although the higher-level relationships among cetacean families have been largely settled, several aspects of the systematics within these groups remain unresolved. Problematic clades include the oceanic dolphins (37 spp.), which have experienced a recent rapid radiation, and the beaked whales (22 spp.), which have not been investigated in detail using nuclear loci. The combined application of high-throughput sequencing with techniques that target specific genomic sequences provide a powerful means of rapidly generating large volumes of orthologous sequence data for use in phylogenomic studies. To elucidate the phylogenetic relationships within the Cetacea, we combined sequence capture with Illumina sequencing to generate data for n}{}sim 3200 protein-coding genes for 68 cetacean species and their close relatives including the pygmy hippopotamus. By combining data from n}{}>38,000 exons with existing sequences from 11 cetaceans and seven outgroup taxa, we produced the first comprehensive comparative genomic data set for cetaceans, spanning 6,527,596 aligned base pairs (bp) and 89 taxa. Phylogenetic trees reconstructed with maximum likelihood and Bayesian inference of concatenated loci, as well as with coalescence analyses of individual gene trees, produced mostly concordant and well-supported trees. Our results completely resolve the relationships among beaked whales as well as the contentious relationships among oceanic dolphins, especially the problematic subfamily Delphinidae. We carried out Bayesian estimation of species divergence times using MCMCTree and compared our complete data set to a subset of clocklike genes. Analyses using the complete data set consistently showed less variance in divergence times than the reduced data set. In addition, integration of new fossils (e.g., Mystacodon selenensis) indicates that the diversification of Crown Cetacea began before the Late Eocene and the divergence of Crown Delphinidae as early as the Middle Miocene. [Cetaceans; phylogenomics; Delphinidae; Ziphiidae; dolphins; whales.]

Ignoring stratigraphic age uncertainty leads to erroneous estimates of species divergence times under the fossilized birth-death process.

Fossil information is essential for estimating species divergence times, and can be integrated into Bayesian phylogenetic inference using the fossilized birth–death (FBD) process. An important aspect of palaeontological data is the uncertainty surrounding specimen ages, which can be handled in different ways during inference. The most common approach is to fix fossil ages to a point estimate within the known age interval. Alternatively, age uncertainty can be incorporated by using priors, and fossil ages are then directly sampled as part of the inference. This study presents a comparison of alternative approaches for handling fossil age uncertainty in analysis using the FBD process. Based on simulations, we find that fixing fossil ages to the midpoint or a random point drawn from within the stratigraphic age range leads to biases in divergence time estimates, while sampling fossil ages leads to estimates that are similar to inferences that employ the correct ages of fossils. Second, we show a comparison using an empirical dataset of extant and fossil cetaceans, which confirms that different methods of handling fossil age uncertainty lead to large differences in estimated node ages. Stratigraphic age uncertainty should thus not be ignored in divergence time estimation and instead should be incorporated explicitly.

Bayesian Estimation of Species Divergence Times Using Correlated Quantitative Characters.

Discrete morphological data have been widely used to study species evolution, but the use of quantitative (or continuous) morphological characters is less common. Here, we implement a Bayesian method to estimate species divergence times using quantitative characters. Quantitative character evolution is modeled using Brownian diffusion with character correlation and character variation within populations. Through simulations, we demonstrate that ignoring the population variation (or population "noise") and the correlation among characters leads to biased estimates of divergence times and rate, especially if the correlation and population noise are high. We apply our new method to the analysis of quantitative characters (cranium landmarks) and molecular data from carnivoran mammals. Our results show that time estimates are affected by whether the correlations and population noise are accounted for or ignored in the analysis. The estimates are also affected by the type of data analyzed, with analyses of morphological characters only, molecular data only, or a combination of both; showing noticeable differences among the time estimates. Rate variation of morphological characters among the carnivoran species appears to be very high, with Bayesian model selection indicating that the independent-rates model fits the morphological data better than the autocorrelated-rates model. We suggest that using morphological continuous characters, together with molecular data, can bring a new perspective to the study of species evolution. Our new model is implemented in the MCMCtree computer program for Bayesian inference of divergence times.

Notes on the birth-death prior with fossil calibrations for Bayesian estimation of species divergence times.

Constructing a multi-dimensional prior on the times of divergence (the node ages) of species in a phylogeny is not a trivial task, in particular, if the prior density is the result of combining different sources of information such as a speciation process with fossil calibration densities. Yang & Rannala (2006 Mol. Biol. Evol 23, 212-226. (doi:10.1093/molbev/msj024)) laid out the general approach to combine the birth-death process with arbitrary fossil-based densities to construct a prior on divergence times. They achieved this by calculating the density of node ages without calibrations conditioned on the ages of the calibrated nodes. Here, I show that the conditional density obtained by Yang & Rannala is misspecified. The misspecified density can sometimes be quite strange-looking and can lead to unintentionally informative priors on node ages without fossil calibrations. I derive the correct density and provide a few illustrative examples. Calculation of the density involves a sum over a large set of labelled histories, and so obtaining the density in a computer program seems hard at the moment. A general algorithm that may provide a way forward is given.This article is part of the themed issue 'Dating species divergences using rocks and clocks'.

The impact of ancestral population size and incomplete lineage sorting on Bayesian estimation of species divergence times

Abstract Although the effects of the coalescent process on sequence divergence and genealogies are well understood, the virtual majority of studies that use molecular sequences to estimate times of divergence among species have failed to account for the coalescent process. Here we study the impact of ancestral population size and incomplete lineage sorting on Bayesian estimates of species divergence times under the molecular clock when the inference model ignores the coalescent process. Using a combination of mathematical analysis, computer simulations and analysis of real data, we find that the errors on estimates of times and the molecular rate can be substantial when ancestral populations are large and when there is substantial incomplete lineage sorting. For example, in a simple three-species case, we find that if the most precise fossil calibration is placed on the root of the phylogeny, the age of the internal node is overestimated, while if the most precise calibration is placed on the internal node, then the age of the root is underestimated. In both cases, the molecular rate is overestimated. Using simulations on a phylogeny of nine species, we show that substantial errors in time and rate estimates can be obtained even when dating ancient divergence events. We analyse the hominoid phylogeny and show that estimates of the neutral mutation rate obtained while ignoring the coalescent are too high. Using a coalescent-based technique to obtain geological times of divergence, we obtain estimates of the mutation rate that are within experimental estimates and we also obtain substantially older divergence times within the phylogeny.

The BPP program for species tree estimation and species delimitation

Abstract This paper provides an overview and a tutorial of the BPP program, which is a Bayesian MCMC program for analyzing multi-locus genomic sequence data under the multispecies coalescent model. An example dataset of five nuclear loci from the East Asian brown frogs is used to illustrate four different analyses, including estimation of species divergence times and population size parameters under the multispecies coalescent model on a fixed species phylogeny (A00), species tree estimation when the assignment and species delimitation are fixed (A01), species delimitation using a fixed guide tree (A10), and joint species delimitation and species-tree estimation or unguided species delimitation (A11). For the joint analysis (A11), two new priors are introduced, which assign uniform probabilities for the different numbers of delimited species, which may be useful when assignment, species delimitation, and species phylogeny are all inferred in one joint analysis. The paper ends with a discussion of the assumptions, the strengths and weaknesses of the BPP analysis.

Closed form modeling of evolutionary rates by exponential Brownian functionals.

Accurate estimation of species divergence times from the analysis of genetic sequences relies on probabilistic models of evolution of the rate of molecular evolution. Importantly, while these models describe the sample paths of the substitution rates along a phylogenetic tree, only the (random) average rate can be estimated on each edge. For mathematical convenience, the stochastic nature of these averages is generally ignored. In this article we derive the probabilistic distribution of the average substitution rate assuming a geometric Brownian motion for the sample paths, and we investigate the corresponding error bounds via numerical simulations. In particular we confirm the validity of the gamma approximation proposed in Guindon (Syst Biol 62(1):22-34, 2013) for "small" values of the autocorrelation parameter.

Relationship between phylogeny and immunity suggests older Caribbean coral lineages are more resistant to disease.

Diseases affect coral species fitness and contribute significantly to the deterioration of coral reefs. The increase in frequency and severity of disease outbreaks has made evaluating and determining coral resistance a priority. Phylogenetic patterns in immunity and disease can provide important insight to how corals may respond to current and future environmental and/or biologically induced diseases. The purpose of this study was to determine if immunity, number of diseases and disease prevalence show a phylogenetic signal among Caribbean corals. We characterized the constitutive levels of six distinct innate immune traits in 14 Caribbean coral species and tested for the presence of a phylogenetic signal on each trait. Results indicate that constitutive levels of some individual immune related processes (i.e. melanin concentration, peroxidase and inhibition of bacterial growth), as well as their combination show a phylogenetic signal. Additionally, both the number of diseases affecting each species and disease prevalence (as measures of disease burden) show a significant phylogenetic signal. The phylogenetic signal of immune related processes, combined with estimates of species divergence times, indicates that among the studied species, those belonging to older lineages tend to resist/fight infections better than more recently diverged coral lineages. This result, combined with the increasing stressful conditions on corals in the Caribbean, suggest that future reefs in the region will likely be dominated by older lineages while modern species may face local population declines and/or geographic extinction.

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.

Divergence and biogeography of the recently evolved Macaronesian red Festuca (Gramineae) species inferred from coalescence‐based analyses

Studying the biogeography and the phylogeography of the endemic Macaronesian red Festuca species (Loliinae, Poaceae) is of prime interest in understanding the speciation and colonization patterns of recently evolved groups in oceanic archipelagos. Coalescence-based analyses of plastid trnLF sequences were employed to estimate evolutionary parameters and to test different species-history scenarios that model the pattern of species divergence. Bayesian IM estimates of species divergence times suggested that ancestral lineages of diploid Macaronesian and Iberian red fescues could have diverged between 1.2 and 1.57 Ma. When empirical data were compared to coalescence-based simulated distributions of discordance and p-distance statistics, two species-history models were chosen in which the first branching lineage derived in Canarian Festuca agustinii. Its sister lineage could have involved a recent polytomy leading to the Madeiran Festuca jubata, the Azorean Festuca francoi + Festuca petraea and the continental Festuca rivularis lineages (Canarian model) or the sequential branching of lineages leading to F. jubata and finally to the sister clades of F.rivularis and F.francoi + F.petraea (Sequential model). Nested clade phylogeographic analysis (NCPA) and a first adapted host-parasite co-evolutionary ParaFit method were used to detect the phylogeographic signal. NCPA inferred long-distance colonizations for the entire diploid red Festuca complex, but allopatric-fragmentation and isolation-by-distance (IBD) patterns were inferred within archipelagos. In addition, the ParaFit method suggested a generalized pattern of a stepping-stone model at all hierarchical levels. Maximum-likelihood-based dispersal-extinction-cladogenesis (DEC) models were superimposed on the Sequential model species tree. The three-independent-colonization (3IC) model was the best supported biogeographic scenario, concurring with previous analysis based on multilocus AFLP data.

The role of peripheral endemism in species diversification: Evidence from the coral reef fish genus Anampses (Family: Labridae)

We examined how peripherally isolated endemic species may have contributed to the biodiversity of the Indo-Australian Archipelago biodiversity hotspot by reconstructing the evolutionary history of the wrasse genus Anampses. We identified three alternate models of diversification: the vicariance-based ‘successive division’ model, and the dispersal-based ‘successive colonisation’ and ‘peripheral budding’ models. The genus was well suited for this study given its relatively high proportion (42%) of endemic species, its reasonably low diversity (12 species), which permitted complete taxon sampling, and its widespread tropical Indo-Pacific distribution. Monophyly of the genus was strongly supported by three phylogenetic analyses: maximum parsimony, maximum likelihood, and Bayesian inference based on mitochondrial CO1 and 12S rRNA and nuclear S7 sequences. Estimates of species divergence times from fossil-calibrated Bayesian inference suggest that Anampses arose in the mid-Eocene and subsequently diversified throughout the Miocene. Evolutionary relationships within the genus, combined with limited spatial and temporal concordance among endemics, offer support for all three alternate models of diversification. Our findings emphasise the importance of peripherally isolated locations in creating and maintaining endemic species and their contribution to the biodiversity of the Indo-Australian Archipelago.

The Impact of the Representation of Fossil Calibrations on Bayesian Estimation of Species Divergence Times

Bayesian inference provides a powerful framework for integrating different sources of information (in particular, molecules and fossils) to derive estimates of species divergence times. Indeed, it is currently the only framework that can adequately account for uncertainties in fossil calibrations. We use 2 Bayesian Markov chain Monte Carlo programs, MULTIDIVTIME and MCMCTREE, to analyze 3 empirical datasets to estimate divergence times in amphibians, actinopterygians, and felids. We evaluate the impact of various factors, including the priors on rates and times, fossil calibrations, substitution model, the violation of the molecular clock and the rate-drift model, and the exact and approximate likelihood calculation. Assuming the molecular clock caused seriously biased time estimates when the clock is violated, but 2 different rate-drift models produced similar estimates. The prior on times, which incorporates fossil-calibration information, had the greatest impact on posterior time estimation. In particular, the strategies used by the 2 programs to incorporate minimum- and maximum-age bounds led to very different time priors and were responsible for large differences in posterior time estimates in a previous study. The results highlight the critical importance of fossil calibrations to molecular dating and the need for probabilistic modeling of fossil depositions, preservations, and sampling to provide statistical summaries of information in the fossil record concerning species divergence times.

Estimation of Hominoid Ancestral Population Sizes under Bayesian Coalescent Models Incorporating Mutation Rate Variation and Sequencing Errors

Estimation of population parameters for the common ancestors of humans and the great apes is important in understanding our evolutionary history. In particular, inference of population size for the human-chimpanzee common ancestor may shed light on the process by which the 2 species separated and on whether the human population experienced a severe size reduction in its early evolutionary history. In this study, the Bayesian method of ancestral inference of Rannala and Yang (2003. Bayes estimation of species divergence times and ancestral population sizes using DNA sequences from multiple loci. Genetics. 164:1645-1656) was extended to accommodate variable mutation rates among loci and random species-specific sequencing errors. The model was applied to analyze a genome-wide data set of approximately 15,000 neutral loci (7.4 Mb) aligned for human, chimpanzee, gorilla, orangutan, and macaque. We obtained robust and precise estimates for effective population sizes along the hominoid lineage extending back approximately 30 Myr to the cercopithecoid divergence. The results showed that ancestral populations were 5-10 times larger than modern humans along the entire hominoid lineage. The estimates were robust to the priors used and to model assumptions about recombination. The unusually low X chromosome divergence between human and chimpanzee could not be explained by variation in the male mutation bias or by current models of hybridization and introgression. Instead, our parameter estimates were consistent with a simple instantaneous process for human-chimpanzee speciation but showed a major reduction in X chromosome effective population size peculiar to the human-chimpanzee common ancestor, possibly due to selective sweeps on the X prior to separation of the 2 species.

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.

PAML 4: Phylogenetic Analysis by Maximum Likelihood

PAML, currently in version 4, is a package of programs for phylogenetic analyses of DNA and protein sequences using maximum likelihood (ML). The programs may be used to compare and test phylogenetic trees, but their main strengths lie in the rich repertoire of evolutionary models implemented, which can be used to estimate parameters in models of sequence evolution and to test interesting biological hypotheses. Uses of the programs include estimation of synonymous and nonsynonymous rates (d(N) and d(S)) between two protein-coding DNA sequences, inference of positive Darwinian selection through phylogenetic comparison of protein-coding genes, reconstruction of ancestral genes and proteins for molecular restoration studies of extinct life forms, combined analysis of heterogeneous data sets from multiple gene loci, and estimation of species divergence times incorporating uncertainties in fossil calibrations. This note discusses some of the major applications of the package, which includes example data sets to demonstrate their use. The package is written in ANSI C, and runs under Windows, Mac OSX, and UNIX systems. It is available at -- (http://abacus.gene.ucl.ac.uk/software/paml.html).

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.