Molecular dating for phylogenies containing a mix of populations and species by using Bayesian and RelTime approaches

Simultaneous molecular dating of population and species divergences is essential in many biological investigations, including phylogeography, phylodynamics and species delimitation studies. In these investigations, multiple sequence alignments consist of both intra‐ and interspecies samples (mixed samples). As a result, the phylogenetic trees contain interspecies, interpopulation and within‐population divergences. Bayesian relaxed clock methods are often employed in these analyses, but they assume the same tree prior for both inter‐ and intraspecies branching processes and require specification of a clock model for branch rates (independent vs. autocorrelated rates models). We evaluated the impact of a single tree prior on Bayesian divergence time estimates by analysing computer‐simulated data sets. We also examined the effect of the assumption of independence of evolutionary rate variation among branches when the branch rates are autocorrelated. Bayesian approach with coalescent tree priors generally produced excellent molecular dates and highest posterior densities with high coverage probabilities. We also evaluated the performance of a non‐Bayesian method, RelTime, which does not require the specification of a tree prior or a clock model. RelTime's performance was similar to that of the Bayesian approach, suggesting that it is also suitable to analyse data sets containing both populations and species variation when its computational efficiency is needed.     

Bias and conflict in phylogenetic inference of myco-heterotrophic plants: a case study in Thismiaceae

Due to morphological reduction and absence of amplifiable plastid genes, the identification of photosynthetic relatives of heterotrophic plants is problematic. Although nuclear and mitochondrial gene sequences may offer a welcome alternative source of phylogenetic markers, the presence of rate heterogeneity in these genes may introduce bias/systematic error in phylogenetic analyses. We examine the phylogenetic position of Thismiaceae based on nuclear 18S rDNA and mitochondrial atpA DNA sequence data, as well as using parsimony, likelihood and Bayesian inference methods. Significant differences in evolutionary rates of these genes between closely related taxa lead to conflicting results: while parsimony analyses of 18S rDNA and combined data strongly support the monophyly of Thismiaceae, Bayesian inference, with and without a relaxed molecular clock, as well as the Swofford–Olsen–Waddell–Hillis (SOWH) test confidently reject this hypothesis. We show that rate heterogeneity in our data leads to long-branch attraction artifacts in parsimony analysis. However, using model-based inference methods the question of whether Thismiaceae are monophyletic remains elusive. On the one hand maximum likelihood nonparametric bootstrapping and parametric hypothesis tests fail to support a paraphyletic Thismiaceae, on the other hand Bayesian inference methods (both without and with a relaxed clock) significantly reject a monophyletic Thismiaceae. These results show that an adequate sampling, the use of rate homogeneous data, and the application of different inference methods are important factors for developing phylogenetic hypotheses of myco-heterotrophic plants. © The Willi Hennig Society 2009.     

Use of spectral analysis to test hypotheses on the origin of pinnipeds

The evolutionary origin of the pinnipeds (seals, sea lions, and walruses) is still uncertain. Most authors support a hypothesis of a monophyletic origin of the pinnipeds from a caniform carnivore. A minority view suggests a diphyletic origin with true seals being related to the mustelids (otters and ferrets). The phylogenetic relationships of the walrus to other pinniped and carnivore families are also still particularly problematic. Here we examined the relative support for mono- and diphyletic hypotheses using DNA sequence data from the mitochondrial small subunit (12S) rRNA and cytochrome b genes. We first analyzed a small group of taxa representing the three pinniped families (Phocidae, Otariidae, and Odobenidae) and caniform carnivore families thought to be related to them. We inferred phylogenetic reconstructions from DNA sequence data using standard parsimony and neighbor-joining algorithms for phylogenetic inference as well as a new method called spectral analysis (Hendy and Penny) in which phylogenetic information is displayed independently of any selected tree. We identified and compensated for potential sources of error known to lead to selection of incorrect phylogenetic trees. These include sampling error, unequal evolutionary rates on lineages, unequal nucleotide composition among lineages, unequal rates of change at different sites, and inappropriate tree selection criteria. To correct for these errors, we performed additional transformations of the observed substitution patterns in the sequence data, applied more stringent structural constraints to the analyses, and included several additional taxa to help resolve long, unbranched lineages in the tree. We find that there is strong support for a monophyletic origin of the pinnipeds from within the caniform carnivores, close to the bear/raccoon/panda radiation. Evidence for a diphyletic origin was very weak and can be partially attributed to unequal nucleotide compositions among the taxa analyzed. Subsequently, there is slightly more evidence for grouping the walrus with the eared seals versus the true seals. A more conservative interpretation, however, is that the walrus is an early, but not the first, independent divergence from the common pinniped ancestor.      

DISENTANGLING THE EFFECTS OF KEY INNOVATIONS ON THE DIVERSIFICATION OF BROMELIOIDEAE (BROMELIACEAE)

The evolution of key innovations, novel traits that promote diversification, is often seen as major driver for the unequal distribution of species richness within the tree of life. In this study, we aim to determine the factors underlying the extraordinary radiation of the subfamily Bromelioideae, one of the most diverse clades among the neotropical plant family Bromeliaceae. Based on an extended molecular phylogenetic data set, we examine the effect of two putative key innovations, that is, the Crassulacean acid metabolism (CAM) and the water‐impounding tank, on speciation and extinction rates. To this aim, we develop a novel Bayesian implementation of the phylogenetic comparative method, binary state speciation and extinction, which enables hypotheses testing by Bayes factors and accommodates the uncertainty on model selection by Bayesian model averaging. Both CAM and tank habit were found to correlate with increased net diversification, thus fulfilling the criteria for key innovations. Our analyses further revealed that CAM photosynthesis is correlated with a twofold increase in speciation rate, whereas the evolution of the tank had primarily an effect on extinction rates that were found five times lower in tank‐forming lineages compared to tank‐less clades. These differences are discussed in the light of biogeography, ecology, and past climate change.     

Bayesian selection of continuous-time Markov chain evolutionary models

We develop a reversible jump Markov chain Monte Carlo approach to estimating the posterior distribution of phylogenies based on aligned DNA/RNA sequences under several hierarchical evolutionary models. Using a proper, yet nontruncated and uninformative prior, we demonstrate the advantages of the Bayesian approach to hypothesis testing and estimation in phylogenetics by comparing different models for the infinitesimal rates of change among nucleotides, for the number of rate classes, and for the relationships among branch lengths. We compare the relative probabilities of these models and the appropriateness of a molecular clock using Bayes factors. Our most general model, first proposed by Tamura and Nei, parameterizes the infinitesimal change probabilities among nucleotides (A, G, C, T/U) into six parameters, consisting of three parameters for the nucleotide stationary distribution, two rate parameters for nucleotide transitions, and another parameter for nucleotide transversions. Nested models include the Hasegawa, Kishino, and Yano model with equal transition rates and the Kimura model with a uniform stationary distribution and equal transition rates. To illustrate our methods, we examine simulated data, 16S rRNA sequences from 15 contemporary eubacteria, halobacteria, eocytes, and eukaryotes, 9 primates, and the entire HIV genome of 11 isolates. We find that the Kimura model is too restrictive, that the Hasegawa, Kishino, and Yano model can be rejected for some data sets, that there is evidence for more than one rate class and a molecular clock among similar taxa, and that a molecular clock can be rejected for more distantly related taxa.     

A compound poisson process for relaxing the molecular clock

The molecular clock hypothesis remains an important conceptual and analytical tool in evolutionary biology despite the repeated observation that the clock hypothesis does not perfectly explain observed DNA sequence variation. We introduce a parametric model that relaxes the molecular clock by allowing rates to vary across lineages according to a compound Poisson process. Events of substitution rate change are placed onto a phylogenetic tree according to a Poisson process. When an event of substitution rate change occurs, the current rate of substitution is modified by a gamma-distributed random variable. Parameters of the model can be estimated using Bayesian inference. We use Markov chain Monte Carlo integration to evaluate the posterior probability distribution because the posterior probability involves high dimensional integrals and summations. Specifically, we use the Metropolis-Hastings-Green algorithm with 11 different move types to evaluate the posterior distribution. We demonstrate the method by analyzing a complete mtDNA sequence data set from 23 mammals. The model presented here has several potential advantages over other models that have been proposed to relax the clock because it is parametric and does not assume that rates change only at speciation events. This model should prove useful for estimating divergence times when substitution rates vary across lineages.     

Modeling nucleotide evolution at the mesoscale: the phylogeny of the neotropical pitvipers of the Porthidium group (viperidae: crotalinae)

We analyzed the phylogeny of the Neotropical pitvipers within the Porthidium group (including intra-specific through inter-generic relationships) using 1.4 kb of DNA sequences from two mitochondrial protein-coding genes (ND4 and cyt-b). We investigated how Bayesian Markov chain Monte-Carlo (MCMC) phylogenetic hypotheses based on this 'mesoscale' dataset were affected by analysis under various complex models of nucleotide evolution that partition models across the dataset. We develop an approach, employing three statistics (Akaike weights, Bayes factors, and relative Bayes factors), for examining the performance of complex models in order to identify the best-fit model for data analysis. Our results suggest that: (1) model choice may have important practical effects on phylogenetic conclusions even for mesoscale datasets, (2) the use of a complex partitioned model did not produce widespread increases or decreases in nodal posterior probability support, and (3) most differences in resolution resulting from model choice were concentrated at deeper nodes. Our phylogenetic estimates of relationships among members of the Porthidium group (genera: Atropoides, Cerrophidion, and Porthidium) resolve the monophyly of the three genera. Bayesian MCMC results suggest that Cerrophidion and Porthidium form a clade that is the sister taxon to Atropoides. In addition to resolving the intra-specific relationships among a majority of Porthidium group taxa, our results highlight phylogeographic patterns across Middle and South America and suggest that each of the three genera may harbor undescribed species diversity.     

Strange bayes indeed: uniform topological priors imply non-uniform clade priors

While Bayesian analysis has become common in phylogenetics, the effects of topological prior probabilities on tree inference have not been investigated. In Bayesian analyses, the prior probability of topologies is almost always considered equal for all possible trees, and clade support is calculated from the majority rule consensus of the approximated posterior distribution of topologies. These uniform priors on tree topologies imply non-uniform prior probabilities of clades, which are dependent on the number of taxa in a clade as well as the number of taxa in the analysis. As such, uniform topological priors do not model ignorance with respect to clades. Here, we demonstrate that Bayesian clade support, bootstrap support, and jackknife support from 17 empirical studies are significantly and positively correlated with non-uniform clade priors resulting from uniform topological priors. Further, we demonstrate that this effect disappears for bootstrap and jackknife when data sets are free from character conflict, but remains pronounced for Bayesian clade supports, regardless of tree shape. Finally, we propose the use of a Bayes factor to account for the fact that uniform topological priors do not model ignorance with respect to clade probability.     

A dirichlet process prior for estimating lineage-specific substitution rates

We introduce a new model for relaxing the assumption of a strict molecular clock for use as a prior in Bayesian methods for divergence time estimation. Lineage-specific rates of substitution are modeled using a Dirichlet process prior (DPP), a type of stochastic process that assumes lineages of a phylogenetic tree are distributed into distinct rate classes. Under the Dirichlet process, the number of rate classes, assignment of branches to rate classes, and the rate value associated with each class are treated as random variables. The performance of this model was evaluated by conducting analyses on data sets simulated under a range of different models. We compared the Dirichlet process model with two alternative models for rate variation: the strict molecular clock and the independent rates model. Our results show that divergence time estimation under the DPP provides robust estimates of node ages and branch rates without significantly reducing power. Further analyses were conducted on a biological data set, and we provide examples of ways to summarize Markov chain Monte Carlo samples under this model.     

Bayesian random local clocks,or one rate to rule them all

Background  

Relaxed molecular clock models allow divergence time dating and "relaxed phylogenetic" inference, in which a time tree is estimated in the face of unequal rates across lineages. We present a new method for relaxing the assumption of a strict molecular clock using Markov chain Monte Carlo to implement Bayesian modeling averaging over random local molecular clocks. The new method approaches the problem of rate variation among lineages by proposing a series of local molecular clocks, each extending over a subregion of the full phylogeny. Each branch in a phylogeny (subtending a clade) is a possible location for a change of rate from one local clock to a new one. Thus, including both the global molecular clock and the unconstrained model results, there are a total of 2^2n-2 possible rate models available for averaging with 1, 2, ..., 2n - 2 different rate categories.     

Modelling heterotachy in phylogenetic inference by reversible-jump Markov chain Monte Carlo

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon--known as heterotachy--can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site over more than one set of branch lengths on the same tree topology. A branch-length set that is best for one site may differ from the branch-length set that is best for some other site, thereby allowing different sites to have different rates of change throughout the tree. Because rate variation may not be present in all branches, we use a reversible-jump Markov chain Monte Carlo algorithm to identify those branches in which reliable amounts of heterotachy occur. We implement the method in combination with our 'pattern-heterogeneity' mixture model, applying it to simulated data and five published datasets. We find that complex evolutionary signals of heterotachy are routinely present over and above variation in the rate or pattern of evolution across sites, that the reversible-jump method requires far fewer parameters than conventional mixture models to describe it, and serves to identify the regions of the tree in which heterotachy is most pronounced. The reversible-jump procedure also removes the need for a posteriori tests of 'significance' such as the Akaike or Bayesian information criterion tests, or Bayes factors. Heterotachy has important consequences for the correct reconstruction of phylogenies as well as for tests of hypotheses that rely on accurate branch-length information. These include molecular clocks, analyses of tempo and mode of evolution, comparative studies and ancestral state reconstruction. The model is available from the authors' website, and can be used for the analysis of both nucleotide and morphological data.     

Phylogeny of shorebirds, gulls, and alcids (Aves: Charadrii) from the cytochrome-b gene: parsimony, Bayesian inference, minimum evolution, and quartet puzzling

Charadrii (shorebirds, gulls, and alcids) have exceptional diversity in ecological, behavioral, and life-history traits. A phylogenetic framework is necessary to fully understand the relationships among these traits. Despite several attempts to resolve the phylogeny of the Charadrii, none have comprehensively utilized molecular sequence data. Complete and partial cytochrome-b gene sequences for 86 Charadrii and five Falconides species (as outgroup taxa) were obtained from GenBank and aligned. We analyzed the resulting matrices using parsimony, Bayesian inference, minimum evolution, and quartet puzzling methods. Posterior probabilities, decay indices, and bootstrapping provide strong support for four major lineages consisting of gulls, alcids, plovers, and sandpipers, respectively. The broad structure of the trees differ significantly from all previous hypotheses of Charadrii phylogeny in placing the plovers at the base of the tree below the sandpipers in a pectinate sequence towards a large clade of gulls and alcids. The parsimony, Bayesian, and minimum evolution models provide strong evidence for this phylogenetic hypothesis. This is further corroborated by non-tree based measures of support and conflict (Lento plots). The quartet puzzling trees are poorly resolved and inconclusive.     

A mitogenomic timescale for birds detects variable phylogenetic rates of molecular evolution and refutes the standard molecular clock

Current understanding of the diversification of birds is hindered by their incomplete fossil record and uncertainty in phylogenetic relationships and phylogenetic rates of molecular evolution. Here we performed the first comprehensive analysis of mitogenomic data of 48 vertebrates, including 35 birds, to derive a Bayesian timescale for avian evolution and to estimate rates of DNA evolution. Our approach used multiple fossil time constraints scattered throughout the phylogenetic tree and accounts for uncertainties in time constraints, branch lengths, and heterogeneity of rates of DNA evolution. We estimated that the major vertebrate lineages originated in the Permian; the 95% credible intervals of our estimated ages of the origin of archosaurs (258 MYA), the amniote-amphibian split (356 MYA), and the archosaur-lizard divergence (278 MYA) bracket estimates from the fossil record. The origin of modern orders of birds was estimated to have occurred throughout the Cretaceous beginning about 139 MYA, arguing against a cataclysmic extinction of lineages at the Cretaceous/Tertiary boundary. We identified fossils that are useful as time constraints within vertebrates. Our timescale reveals that rates of molecular evolution vary across genes and among taxa through time, thereby refuting the widely used mitogenomic or cytochrome b molecular clock in birds. Moreover, the 5-Myr divergence time assumed between 2 genera of geese (Branta and Anser) to originally calibrate the standard mitochondrial clock rate of 0.01 substitutions per site per lineage per Myr (s/s/l/Myr) in birds was shown to be underestimated by about 9.5 Myr. Phylogenetic rates in birds vary between 0.0009 and 0.012 s/s/l/Myr, indicating that many phylogenetic splits among avian taxa also have been underestimated and need to be revised. We found no support for the hypothesis that the molecular clock in birds "ticks" according to a constant rate of substitution per unit of mass-specific metabolic energy rather than per unit of time, as recently suggested. Our analysis advances knowledge of rates of DNA evolution across birds and other vertebrates and will, therefore, aid comparative biology studies that seek to infer the origin and timing of major adaptive shifts in vertebrates.     

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of auto-correlated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.     

Phylogenetic networks based on the molecular clock hypothesis

A classical result in phylogenetic trees is that a binary phylogenetic tree adhering to the molecular clock hypothesis exists if and only if the matrix of distances between taxa is ultrametric. The ultrametric condition is very restrictive. In this paper we study phylogenetic networks that can be constructed assuming the molecular clock hypothesis. We characterize distance matrices that admit such networks for 3 and 4 taxa. We also design two algorithms for constructing networks optimizing the least-squares fit.     

Phylogeny of sipunculan worms: A combined analysis of four gene regions and morphology

The intra-phyletic relationships of sipunculan worms were analyzed based on DNA sequence data from four gene regions and 58 morphological characters. Initially we analyzed the data under direct optimization using parsimony as optimality criterion. An implied alignment resulting from the direct optimization analysis was subsequently utilized to perform a Bayesian analysis with mixed models for the different data partitions. For this we applied a doublet model for the stem regions of the 18S rRNA. Both analyses support monophyly of Sipuncula and most of the same clades within the phylum. The analyses differ with respect to the relationships among the major groups but whereas the deep nodes in the direct optimization analysis generally show low jackknife support, they are supported by 100% posterior probability in the Bayesian analysis. Direct optimization has been useful for handling sequences of unequal length and generating conservative phylogenetic hypotheses whereas the Bayesian analysis under mixed models provided high resolution in the basal nodes of the tree.     

Inferring the root of a phylogenetic tree

Phylogenetic trees can be rooted by a number of criteria. Here, we introduce a Bayesian method for inferring the root of a phylogenetic tree by using one of several criteria: the outgroup, molecular clock, and nonreversible model of DNA substitution. We perform simulation analyses to examine the relative ability of these three criteria to correctly identify the root of the tree. The outgroup and molecular clock criteria were best able to identify the root of the tree, whereas the nonreversible model was able to identify the root only when the substitution process was highly nonreversible. We also examined the performance of the criteria for a tree of four species for which the topology and root position are well supported. Results of the analyses of these data are consistent with the simulation results.     

Phylogenetic systematics of the colorful, cyanide-producing millipedes of Appalachia (Polydesmida, Xystodesmidae, Apheloriini) using a total evidence Bayesian approach

Here, we provide an exemplar-approach phylogeny of the xystodesmid millipede tribe Apheloriini with a focus on genus-group relationships-particularly of the genus Brachoria. Exemplars for the phylogenetic analysis were chosen to represent the maximum breadth of morphological diversity within all nominal genera in the tribe Apheloriini, and to broadly sample the genus Brachoria. In addition, three closely related tribes were used (Rhysodesmini, Nannariini, and Pachydesmini). Morphological and DNA sequence data were scored for Bayesian inference of phylogeny. Phylogenetic analysis resulted in polyphyletic genera Brachoria and Sigmoria, a monophyletic Apheloriini, and a "southern clade" that contains most of the tribal species diversity. We used this phylogeny to track morphological character histories and reconstruct ancestral states using stochastic character mapping. Based on the findings from the character mapping study, the diagnostic feature of the genus Brachoria, the cingulum, evolved independently in two lineages. We compared our phylogeny against prior classifications using Bayes factor hypothesis-testing and found that our phylogenetic hypothesis is inconsistent with the previous hypotheses underlying the most recent classification. With our preferred total-evidence phylogeny as a framework for taxonomic modifications, we describe a new genus, Appalachioria; supply phylogenetic diagnoses of monophyletic taxa; and provide a phylogeny-based classification for the tribe Apheloriini.