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.     

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

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

Bayesian estimation of species divergence times under a molecular clock using multiple fossil calibrations with soft bounds

We implement a Bayesian Markov chain Monte Carlo algorithm for estimating species divergence times that uses heterogeneous data from multiple gene loci and accommodates multiple fossil calibration nodes. A birth-death process with species sampling is used to specify a prior for divergence times, which allows easy assessment of the effects of that prior on posterior time estimates. We propose a new approach for specifying calibration points on the phylogeny, which allows the use of arbitrary and flexible statistical distributions to describe uncertainties in fossil dates. In particular, we use soft bounds, so that the probability that the true divergence time is outside the bounds is small but nonzero. A strict molecular clock is assumed in the current implementation, although this assumption may be relaxed. We apply our new algorithm to two data sets concerning divergences of several primate species, to examine the effects of the substitution model and of the prior for divergence times on Bayesian time estimation. We also conduct computer simulation to examine the differences between soft and hard bounds. We demonstrate that divergence time estimation is intrinsically hampered by uncertainties in fossil calibrations, and the error in Bayesian time estimates will not go to zero with increased amounts of sequence data. Our analyses of both real and simulated data demonstrate potentially large differences between divergence time estimates obtained using soft versus hard bounds and a general superiority of soft bounds. Our main findings are as follows. (1) When the fossils are consistent with each other and with the molecular data, and the posterior time estimates are well within the prior bounds, soft and hard bounds produce similar results. (2) When the fossils are in conflict with each other or with the molecules, soft and hard bounds behave very differently; soft bounds allow sequence data to correct poor calibrations, while poor hard bounds are impossible to overcome by any amount of data. (3) Soft bounds eliminate the need for "safe" but unrealistically high upper bounds, which may bias posterior time estimates. (4) Soft bounds allow more reliable assessment of estimation errors, while hard bounds generate misleadingly high precisions when fossils and molecules are in conflict.     

Model-based multi-locus estimation of decapod phylogeny and divergence times

Phylogenetic relationships among all of the major decapod infraorders have never been estimated using molecular data, while morphological studies produce conflicting results. In the present study, the phylogenetic relationships among the decapod basal suborder Dendrobranchiata and all of the currently recognized decapod infraorders within the suborder Pleocyemata (Caridea, Stenopodidea, Achelata, Astacidea, Thalassinidea, Anomala, and Brachyura) were inferred using 16S mtDNA, 18S and 28S rRNA, and the histone H3 gene. Phylogenies were reconstructed using the model-based methods of maximum likelihood and Bayesian methods coupled with Markov Chain Monte Carlo inference. The phylogenies revealed that the seven infraorders are monophyletic, with high clade support values (bp>70; pP>0.95) under both methods. The two suborders also were recovered as monophyletic, but with weaker support (bp=70; pP=0.74). Although the nodal support values for infraordinal relationships were low (bp<50; pP<0.77) the Anomala and Brachyura were basal to the rest of the 'Reptantia' in both reconstructions and using Bayesian tree topology tests alternate morphology-based hypotheses were rejected (P<0.01). Newly developed multi-locus Bayesian and likelihood heuristic rate-smoothing methods to estimate divergence times were compared using eight fossil and geological calibrations. Estimated times revealed that the Decapoda originated earlier than 437MYA and that the radiation within the group occurred rapidly, with all of the major lineages present by 325MYA. Node time estimation under both approaches is severely affected by the number and phylogenetic distribution of the fossil calibrations chosen. For analyses incorporating fossils as fixed ages, more consistent results were obtained by using both shallow and deep or clade-related calibration points. Divergence time estimation using fossils as lower and upper limits performed well with as few as one upper limit and a single deep fossil lower limit calibration.     

A hierarchical Bayesian model for calibrating estimates of species divergence times

In Bayesian divergence time estimation methods, incorporating calibrating information from the fossil record is commonly done by assigning prior densities to ancestral nodes in the tree. Calibration prior densities are typically parametric distributions offset by minimum age estimates provided by the fossil record. Specification of the parameters of calibration densities requires the user to quantify his or her prior knowledge of the age of the ancestral node relative to the age of its calibrating fossil. The values of these parameters can, potentially, result in biased estimates of node ages if they lead to overly informative prior distributions. Accordingly, determining parameter values that lead to adequate prior densities is not straightforward. In this study, I present a hierarchical Bayesian model for calibrating divergence time analyses with multiple fossil age constraints. This approach applies a Dirichlet process prior as a hyperprior on the parameters of calibration prior densities. Specifically, this model assumes that the rate parameters of exponential prior distributions on calibrated nodes are distributed according to a Dirichlet process, whereby the rate parameters are clustered into distinct parameter categories. Both simulated and biological data are analyzed to evaluate the performance of the Dirichlet process hyperprior. Compared with fixed exponential prior densities, the hierarchical Bayesian approach results in more accurate and precise estimates of internal node ages. When this hyperprior is applied using Markov chain Monte Carlo methods, the ages of calibrated nodes are sampled from mixtures of exponential distributions and uncertainty in the values of calibration density parameters is taken into account.     

Phylogenetic relationships and estimation of divergence times among Sisoridae catfishes

Nineteen taxa representing 10 genera of Sisoridae were subjected to phylogenetic analyses of sequence data for the nuclear genes Plagl2 and ADNP and the mitochondrial gene cytochrome b. The three data sets were analyzed separately and combined into a single data set to reconstruct phylogenetic relationships among Chinese sisorids. Both Chinese Sisoridae as a whole and the glyptosternoid taxa formed monophyletic groups. The genus Pseudecheneis is likely to be the earliest diverging extant genus among the Chinese Sisoridae. The four Pareuchiloglanis species included in the study formed a monophyletic group. Glaridoglanis was indicated to be earliest diverging glyptosternoid, followed by Glyptosternon maculatum and Exostoma labiatum. Our data supported the conclusion that Oreoglanis and Pseudexostoma both formed a monophyletic group. On the basis of the fossil record and the results of a molecular dating analysis, we estimated that the Sisoridae diverged in the late Miocene about 12.2 Mya. The glyptosternoid clade was indicated to have diverged, also in the late Miocene, about 10.7 Mya, and the more specialized glyptosternoid genera, such as Pareuchiloglanis, originated in the Pleistocene (within 1.9 Mya). The speciation of glyptosternoid fishes is hypothesized to be closely related with the uplift of the Qinghai-Tibet Plateau.     

贝叶斯支端定年法推断分异时间和演化速率

贝叶斯支端定年法是近些年开发的推断类群分异时间和演化速率的方法。它克服了传统分步计算的缺陷,但涉及的统计学知识也更多。本文从贝叶斯统计计算的角度分层剖析了支端定年法的原理和计算过程,按照分异时间的先验分布、演化速率的先验分布、特征状态变化的模型和马氏链蒙特卡罗算法几个部分,叙述并讨论了定年计算中的主要模型和算法。旨在一定程度上为古生物学家分析实际数据提供参考。     

Phylogeny of hoplocercine lizards (Squamata: Iguania) with estimates of relative divergence times

Hoplocercine lizards form a clade of 11 currently recognized species traditionally placed in three genera (Enyalioides, Hoplocercus, and Morunasaurus) that occur in the lowlands on both sides of the Andes between Panama and the Brazilian Cerrado. We analyze 11 mitochondrial and two nuclear loci using probabilistic methods and different partitioning strategies to (1) infer the phylogenetic relationships among species of Hoplocercinae, (2) examine amounts of inter- and intraspecific sequence divergence, (3) address monophyly of four species, (4) test previous phylogenetic hypotheses, and (5) estimate divergence times. Our preferred hypothesis places H. spinosus as the sister taxon to all other species of hoplocercines, with M. annularis nested within Enyalioides. Species with multiple samples are monophyletic except for Enyalioides oshaughnessyi, which is paraphyletic relative to an undescribed species of Enyalioides. All previously published phylogenetic hypotheses for hoplocercines are rejected. Monophyly of Enyalioides cannot be rejected and, consequently, the position of Morunasaurus remains unclear. The most recent common ancestor of Hoplocercinae probably occurred east of the Andes; western taxa included in our analyses originated from at least two separate colonizations whether pre- or post-dating vicariance resulting from uplift of the Andes.     

Partition number,rate priors and unreliable divergence times in Bayesian phylogenetic dating

More loci/partitions should improve Bayesian estimation of divergence times on phylogenies but it has recently been shown that this can lead to surprisingly poor estimation due to the way it affects the prior on mean substitution rate. Here we consider the likely impact of partition number on divergence time analyses carried out using the program BEAST. Mitochondrial genome data from toad‐headed lizards (genus Phrynocephalus) from the Qinghai–Tibetan Plateau were used to examine this effect. Under increased partitioning of the sequences, BEAST posterior divergence times became unreasonably narrow and downwardly biased due to misspecification of the mean substitution rate prior. This effect was detectable when relatively few partitions were used (i.e. between four and eight), but became very acute for 27–86 partitions. Fortunately, a correction that adjusts the standard deviation of the mean of locus rates led to results that were equivalent to those obtained using the latest version of the program MCMCtree, which implements a new gamma‐Dirichlet prior to overcome this problem. A review of the literature shows that a substantial number of BEAST dating studies are likely to have been affected by this misspecification of the rate prior.     

Molecular estimation of eulipotyphlan divergence times and the evolution of "Insectivora"

"Insectivores" are one of the key groups in understanding mammalian origins. For years, systematics of "Lipotyphla" taxa remained extremely unstable and challenged. Today, with the application of molecular techniques, "Lipotyphla" appears to be a paraphyletic assemblage that encompasses hedgehogs, shrews, and moles (i.e., Eulipotyphla-a member of Laurasiatheria), and golden moles and tenrecs (i.e., Afrosoricida-a member of Afrotheria). Based on nuclear genes and on this well-established phylogenetic framework, we estimated Bayesian relaxed molecular clock divergence times among major lineages of "Lipotyphla." Crown placental mammals are shown to diversify 102+/-6 million years ago (Mya; mean+/-one standard-deviation), followed by Boreoeutheria (94+/-6 Mya), Laurasiatheria (85+/-5 Mya), and Eulipotyphla (73+/-5), with moles separating from hedgehogs+shrews just at the K/T boundary (65+/-5 Mya). During the Early and Middle Eocene, all extant eulipotyphlan subfamilies originated: Uropsilinae (52+/-5 Mya), and Desmaninae, Talpinae, Erinaceinae, Hylomyinae, Soricinae, and Crocidurinae (38-42+/-5 Mya). Afrosoricida separated from Macroscelidae 69+/-5 Mya, golden moles from tenrecs 63+/-5 Mya, and the diversification within tenrecs occurred 43+/-5 Mya. Divergence times are shown to be in reasonably good agreement with the fossil record of eulipotyphlans, but not with the one of afrosoricid "insectivores." Eulipotyphlans diversification might have been sculpted by variations in paleoclimates of the cenozoic era.     

Statistics of divergence times.

Given the number of nucleotide substitutions between two species (K) and the substitution rate nu, the expectation of the corresponding divergence time is usually calculated as K/(2 nu). This is strictly true only if nu is regarded as a constant because the ratio of two random variables, such as K/(2 nu), has distributional properties different from those of the distribution of K. Therefore, both the mean and any confidence interval for divergence times are unknown in this situation. We model the distribution of K and nu using the Gamma distribution and calculate the mean and 95% confidence interval for the corresponding divergence time. These calculations are compared with results obtained by bootstrapping sequence data from the model plant Arabidopsis thaliana and its relatives. We show that for nonoverlapping pairs of phylogenetic distances, our method approaches the bootstrap results very closely. In contrast, regarding the mutation rate as a constant leads to strong underestimation of the confidence interval. An implementation of our method of computing divergence times is accessible through a web interface at http://www.soft.ice.mpg.de/cite.     

Historical contingency and behavioural divergence in territorial Anolis lizards

The extent that evolution - including adaptation - is historically contingent (dependent on past events) has often been hotly debated, but is still poorly understood. In particular, there are little data on the degree that behaviour, an aspect of the phenotype that is strongly linked to contemporary environments (social or physical), retains the imprint of evolutionary history. In this study, I examined whether differences in the design of the territorial displays among species of Caribbean Anolis lizards reflect island-specific selection regimes, or historically contingent predispositions associated with different clade histories. Adult males advertise territory ownership using a series of headbobs and dewlap extensions, bouts of which vary in duration among species. When display durations were mapped onto the Anolis phylogeny, prominent differences between species belonging to the Western and Eastern Caribbean radiations were apparent. Statistical analyses confirmed that species differences in the duration of headbob displays, and to some extent the duration of dewlap extensions, were historically contingent. The unique evolutionary histories of each clade have seemingly had a profound effect on the subsequent direction of display evolution among descendent taxa. These results combined with those from previous studies on these lizards show that past history can have an important impact on the type of behaviour exhibited by species today, to the point that adaptive evolution can proceed quite differently in lineages originating from different evolutionary starting points.     

Historical influence of predation pressure on escape by Podarcis lizards in the Balearic Islands

Island tameness (reduced escape behaviour on islands where prey have experienced prolonged relaxation of predation pressure) is known in several taxa, although the relationships between recent predation pressure and escape on islands are poorly known. We investigated escape by numerous populations exposed to differing predation pressure of two sister species of Podarcis lizards in the Balearic Islands. Our main findings are that flight initiation distance was greater in Podarcis pityusensis than Podarcis lilfordi and increased as predation pressure increased in P. pityusensis. Island tameness led to extinction of P. lilfordi on Menorca and Mallorca following anthropogenic introduction of predators; this species is extant only on nearby islets. The lack of relationship between recent predation pressure and flight initiation distance in P. lilfordi indicates that the historically acquired deficit in the ability to adjust escape behaviour to predation pressure still exists. Podarcis pityusensis, which was exposed to greater natural predation pressure before human introduction of predators, survives on Ibiza and Formentera, as well as on islets. Retention of the ability to respond to predation pressure is consistent with our finding that flight initiation distance increases as predation pressure increases among current populations. © 2012 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, ?? , ??–??.     

Unidentifiable divergence times in rates-across-sites models

The rates-across-sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is the product of a character-specific scale factor and a rate matrix that is particular to that edge. Thus, evolution follows basically the same process for all characters, except that it occurs faster for some characters than others. To allow estimation of tree topologies and edge lengths for such models, it is commonly assumed that the scale factors are not arbitrary unknown constants, but rather unobserved, independent, identically distributed draws from a member of some parametric family of distributions. A popular choice is the gamma family. We consider an example of a clock-like tree with three taxa, one unknown edge length, a known root state, and a parametric family of scale factor distributions that contains the gamma family. This model has the property that, for a generic choice of unknown edge length and scale factor distribution, there is another edge length and scale factor distribution which generates data with exactly the same distribution, so that even with infinitely many data it will be typically impossible to make correct inferences about the unknown edge length.     

Evolutionary divergence of ribosomal internal transcribed spacer 2 in lizards

Internal transcribed spacers 1 and 2 (ITS1 and ITS2) are known to play an important role in rRNA maturation, yet the mechanism of their action is still not completely understood. Comparison of the ITS1 and ITS2 nucleotide sequences for various organisms reveals conserved regions, which are potentially involved in rRNA biogenesis, and yields new information about the evolutionary divergence of the corresponding region of the genome. The rDNA fragments containing ITS2 were amplified, cloned, and sequenced for three lizard species: Darevskia armeniaca, Lacerta strigata (Lacertidae), and Agama caucasia (Agamidae). The lizard ITS2 sequences were compared with their counterparts from other organisms and proved to contain not only universally conserved elements characteristic of the consensus secondary structure of vertebrate ITS2, but also lizard-specific regions. Comparison of the ITS2 size and the distribution of homologous regions for the two lizard families made it possible to assume that evolution of the modern species involved duplication of ITS2 in the genome of their common ancestor.     

Branch length estimation and divergence dating: estimates of error in Bayesian and maximum likelihood frameworks

Background  

Estimates of divergence dates between species improve our understanding of processes ranging from nucleotide substitution to speciation. Such estimates are frequently based on molecular genetic differences between species; therefore, they rely on accurate estimates of the number of such differences (i.e. substitutions per site, measured as branch length on phylogenies). We used simulations to determine the effects of dataset size, branch length heterogeneity, branch depth, and analytical framework on branch length estimation across a range of branch lengths. We then reanalyzed an empirical dataset for plethodontid salamanders to determine how inaccurate branch length estimation can affect estimates of divergence dates.     

Estimating divergence times in large phylogenetic trees

A new method, PATHd8, for estimating ultrametric trees from trees with edge (branch) lengths proportional to the number of substitutions is proposed. The method allows for an arbitrary number of reference nodes for time calibration, each defined either as absolute age, minimum age, or maximum age, and the tree need not be fully resolved. The method is based on estimating node ages by mean path lengths from the node to the leaves but correcting for deviations from a molecular clock suggested by reference nodes. As opposed to most existing methods allowing substitution rate variation, the new method smoothes substitution rates locally, rather than simultaneously over the whole tree, thus allowing for analysis of very large trees. The performance of PATHd8 is compared with other frequently used methods for estimating divergence times. In analyses of three separate data sets, PATHd8 gives similar divergence times to other methods, the largest difference being between crown group ages, where unconstrained nodes get younger ages when analyzed with PATHd8. Overall, chronograms obtained from other methods appear smoother, whereas PATHd8 preserves more of the heterogeneity seen in the original edge lengths. Divergence times are most evenly spread over the chronograms obtained from the Bayesian implementation and the clock-based Langley-Fitch method, and these two methods produce very similar ages for most nodes. Evaluations of PATHd8 using simulated data suggest that PATHd8 is slightly less precise compared with penalized likelihood, but it gives more sensible answers for extreme data sets. A clear advantage with PATHd8 is that it is more or less instantaneous even with trees having several thousand leaves, whereas other programs often run into problems when analyzing trees with hundreds of leaves. PATHd8 is implemented in freely available software.     

Estimating divergence times from DNA sequences

The patterns of genetic variation within and among individuals and populations can be used to make inferences about the evolutionary forces that generated those patterns. Numerous population genetic approaches have been developed in order to infer evolutionary history. Here, we present the “Two-Two (TT)” and the “Two-Two-outgroup (TTo)” methods; two closely related approaches for estimating divergence time based in coalescent theory. They rely on sequence data from two haploid genomes (or a single diploid individual) from each of two populations. Under a simple population-divergence model, we derive the probabilities of the possible sample configurations. These probabilities form a set of equations that can be solved to obtain estimates of the model parameters, including population split times, directly from the sequence data. This transparent and computationally efficient approach to infer population divergence time makes it possible to estimate time scaled in generations (assuming a mutation rate), and not as a compound parameter of genetic drift. Using simulations under a range of demographic scenarios, we show that the method is relatively robust to migration and that the TTo method can alleviate biases that can appear from drastic ancestral population size changes. We illustrate the utility of the approaches with some examples, including estimating split times for pairs of human populations as well as providing further evidence for the complex relationship among Neandertals and Denisovans and their ancestors.