A random effects branch-site model for detecting episodic diversifying selection

Adaptive evolution frequently occurs in episodic bursts, localized to a few sites in a gene, and to a small number of lineages in a phylogenetic tree. A popular class of "branch-site" evolutionary models provides a statistical framework to search for evidence of such episodic selection. For computational tractability, current branch-site models unrealistically assume that all branches in the tree can be partitioned a priori into two rigid classes--"foreground" branches that are allowed to undergo diversifying selective bursts and "background" branches that are negatively selected or neutral. We demonstrate that this assumption leads to unacceptably high rates of false positives or false negatives when the evolutionary process along background branches strongly deviates from modeling assumptions. To address this problem, we extend Felsenstein's pruning algorithm to allow efficient likelihood computations for models in which variation over branches (and not just sites) is described in the random effects likelihood framework. This enables us to model the process at every branch-site combination as a mixture of three Markov substitution models--our model treats the selective class of every branch at a particular site as an unobserved state that is chosen independently of that at any other branch. When benchmarked on a previously published set of simulated sequences, our method consistently matched or outperformed existing branch-site tests in terms of power and error rates. Using three empirical data sets, previously analyzed for episodic selection, we discuss how modeling assumptions can influence inference in practical situations.     

Weighted parsimony outperforms other methods of phylogenetic inference under models appropriate for morphology

One of the lasting controversies in phylogenetic inference is the degree to which specific evolutionary models should influence the choice of methods. Model‐based approaches to phylogenetic inference (likelihood, Bayesian) are defended on the premise that without explicit statistical models there is no science, and parsimony is defended on the grounds that it provides the best rationalization of the data, while refraining from assigning specific probabilities to trees or character‐state reconstructions. Authors who favour model‐based approaches often focus on the statistical properties of the methods and models themselves, but this is of only limited use in deciding the best method for phylogenetic inference—such decision also requires considering the conditions of evolution that prevail in nature. Another approach is to compare the performance of parsimony and model‐based methods in simulations, which traditionally have been used to defend the use of models of evolution for DNA sequences. Some recent papers, however, have promoted the use of model‐based approaches to phylogenetic inference for discrete morphological data as well. These papers simulated data under models already known to be unfavourable to parsimony, and modelled morphological evolution as if it evolved just like DNA, with probabilities of change for all characters changing in concert along tree branches. The present paper discusses these issues, showing that under reasonable and less restrictive models of evolution for discrete characters, equally weighted parsimony performs as well or better than model‐based methods, and that parsimony under implied weights clearly outperforms all other methods.     

SPIn: model selection for phylogenetic mixtures via linear invariants

In phylogenetic inference, an evolutionary model describes the substitution processes along each edge of a phylogenetic tree. Misspecification of the model has important implications for the analysis of phylogenetic data. Conventionally, however, the selection of a suitable evolutionary model is based on heuristics or relies on the choice of an approximate input tree. We introduce a method for model Selection in Phylogenetics based on linear INvariants (SPIn), which uses recent insights on linear invariants to characterize a model of nucleotide evolution for phylogenetic mixtures on any number of components. Linear invariants are constraints among the joint probabilities of the bases in the operational taxonomic units that hold irrespective of the tree topologies appearing in the mixtures. SPIn therefore requires no input tree and is designed to deal with nonhomogeneous phylogenetic data consisting of multiple sequence alignments showing different patterns of evolution, for example, concatenated genes, exons, and/or introns. Here, we report on the results of the proposed method evaluated on multiple sequence alignments simulated under a variety of single-tree and mixture settings for both continuous- and discrete-time models. In the simulations, SPIn successfully recovers the underlying evolutionary model and is shown to perform better than existing approaches.     

ImOSM: intermittent evolution and robustness of phylogenetic methods

Among the criteria to evaluate the performance of a phylogenetic method, robustness to model violation is of particular practical importance as complete a priori knowledge of evolutionary processes is typically unavailable. For studies of robustness in phylogenetic inference, a utility to add well-defined model violations to the simulated data would be helpful. We therefore introduce ImOSM, a tool to imbed intermittent evolution as model violation into an alignment. Intermittent evolution refers to extra substitutions occurring randomly on branches of a tree, thus changing alignment site patterns. This means that the extra substitutions are placed on the tree after the typical process of sequence evolution is completed. We then study the robustness of widely used phylogenetic methods: maximum likelihood (ML), maximum parsimony (MP), and a distance-based method (BIONJ) to various scenarios of model violation. Violation of rates across sites (RaS) heterogeneity and simultaneous violation of RaS and the transition/transversion ratio on two nonadjacent external branches hinder all the methods recovery of the true topology for a four-taxon tree. For an eight-taxon balanced tree, the violations cause each of the three methods to infer a different topology. Both ML and MP fail, whereas BIONJ, which calculates the distances based on the ML estimated parameters, reconstructs the true tree. Finally, we report that a test of model homogeneity and goodness of fit tests have enough power to detect such model violations. The outcome of the tests can help to actually gain confidence in the inferred trees. Therefore, we recommend using these tests in practical phylogenetic analyses.     

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent

The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.     

Long-Branch Attraction Bias and Inconsistency in Bayesian Phylogenetics

Bayesian inference (BI) of phylogenetic relationships uses the same probabilistic models of evolution as its precursor maximum likelihood (ML), so BI has generally been assumed to share ML''s desirable statistical properties, such as largely unbiased inference of topology given an accurate model and increasingly reliable inferences as the amount of data increases. Here we show that BI, unlike ML, is biased in favor of topologies that group long branches together, even when the true model and prior distributions of evolutionary parameters over a group of phylogenies are known. Using experimental simulation studies and numerical and mathematical analyses, we show that this bias becomes more severe as more data are analyzed, causing BI to infer an incorrect tree as the maximum a posteriori phylogeny with asymptotically high support as sequence length approaches infinity. BI''s long branch attraction bias is relatively weak when the true model is simple but becomes pronounced when sequence sites evolve heterogeneously, even when this complexity is incorporated in the model. This bias—which is apparent under both controlled simulation conditions and in analyses of empirical sequence data—also makes BI less efficient and less robust to the use of an incorrect evolutionary model than ML. Surprisingly, BI''s bias is caused by one of the method''s stated advantages—that it incorporates uncertainty about branch lengths by integrating over a distribution of possible values instead of estimating them from the data, as ML does. Our findings suggest that trees inferred using BI should be interpreted with caution and that ML may be a more reliable framework for modern phylogenetic analysis.     

Detecting the node-density artifact in phylogeny reconstruction

The node-density effect is an artifact of phylogeny reconstruction that can cause branch lengths to be underestimated in areas of the tree with fewer taxa. Webster, Payne, and Pagel (2003, Science 301:478) introduced a statistical procedure (the "delta" test) to detect this artifact, and here we report the results of computer simulations that examine the test's performance. In a sample of 50,000 random data sets, we find that the delta test detects the artifact in 94.4% of cases in which it is present. When the artifact is not present (n = 10,000 simulated data sets) the test showed a type I error rate of approximately 1.69%, incorrectly reporting the artifact in 169 data sets. Three measures of tree shape or "balance" failed to predict the size of the node-density effect. This may reflect the relative homogeneity of our randomly generated topologies, but emphasizes that nearly any topology can suffer from the artifact, the effect not being confined only to highly unevenly sampled or otherwise imbalanced trees. The ability to screen phylogenies for the node-density artifact is important for phylogenetic inference and for researchers using phylogenetic trees to infer evolutionary processes, including their use in molecular clock dating.     

Disparity index: a simple statistic to measure and test the homogeneity of substitution patterns between molecular sequences.

A common assumption in comparative sequence analysis is that the sequences have evolved with the same pattern of nucleotide substitution (homogeneity of the evolutionary process). Violation of this assumption is known to adversely impact the accuracy of phylogenetic inference and tests of evolutionary hypotheses. Here we propose a disparity index, ID, which measures the observed difference in evolutionary patterns for a pair of sequences. On the basis of this index, we have developed a Monte Carlo procedure to test the homogeneity of the observed patterns. This test does not require a priori knowledge of the pattern of substitutions, extent of rate heterogeneity among sites, or the evolutionary relationship among sequences. Computer simulations show that the ID-test is more powerful than the commonly used chi2-test under a variety of biologically realistic models of sequence evolution. An application of this test in an analysis of 3789 pairs of orthologous human and mouse protein-coding genes reveals that the observed evolutionary patterns in neutral sites are not homogeneous in 41% of the genes, apparently due to shifts in G + C content. Thus, the proposed test can be used as a diagnostic tool to identify genes and lineages that have evolved with substantially different evolutionary processes as reflected in the observed patterns of change. Identification of such genes and lineages is an important early step in comparative genomics and molecular phylogenetic studies to discover evolutionary processes that have shaped organismal genomes.     

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.     

When phylogenetic assumptions are violated: base compositional heterogeneity and among‐site rate variation in beetle mitochondrial phylogenomics

The ability to generate large molecular datasets for phylogenetic studies benefits biologists, but such data expansion introduces numerous analytical problems. A typical molecular phylogenetic study implicitly assumes that sequences evolve under stationary, reversible and homogeneous conditions, but this assumption is often violated in real datasets. When an analysis of large molecular datasets results in unexpected relationships, it often reflects violation of phylogenetic assumptions, rather than a correct phylogeny. Molecular evolutionary phenomena such as base compositional heterogeneity and among‐site rate variation are known to affect phylogenetic inference, resulting in incorrect phylogenetic relationships. The ability of methods to overcome such bias has not been measured on real and complex datasets. We investigated how base compositional heterogeneity and among‐site rate variation affect phylogenetic inference in the context of a mitochondrial genome phylogeny of the insect order Coleoptera. We show statistically that our dataset is affected by base compositional heterogeneity regardless of how the data are partitioned or recoded. Among‐site rate variation is shown by comparing topologies generated using models of evolution with and without a rate variation parameter in a Bayesian framework. When compared for their effectiveness in dealing with systematic bias, standard phylogenetic methods tend to perform poorly, and parsimony without any data transformation performs worst. Two methods designed specifically to overcome systematic bias, LogDet and a Bayesian method implementing variable composition vectors, can overcome some level of base compositional heterogeneity, but are still affected by among‐site rate variation. A large degree of variation in both noise and phylogenetic signal among all three codon positions is observed. We caution and argue that more data exploration is imperative, especially when many genes are included in an analysis.     

Dependence among sites in RNA evolution

Although probabilistic models of genotype (e.g., DNA sequence) evolution have been greatly elaborated, less attention has been paid to the effect of phenotype on the evolution of the genotype. Here we propose an evolutionary model and a Bayesian inference procedure that are aimed at filling this gap. In the model, RNA secondary structure links genotype and phenotype by treating the approximate free energy of a sequence folded into a secondary structure as a surrogate for fitness. The underlying idea is that a nucleotide substitution resulting in a more stable secondary structure should have a higher rate than a substitution that yields a less stable secondary structure. This free energy approach incorporates evolutionary dependencies among sequence positions beyond those that are reflected simply by jointly modeling change at paired positions in an RNA helix. Although there is not a formal requirement with this approach that secondary structure be known and nearly invariant over evolutionary time, computational considerations make these assumptions attractive and they have been adopted in a software program that permits statistical analysis of multiple homologous sequences that are related via a known phylogenetic tree topology. Analyses of 5S ribosomal RNA sequences are presented to illustrate and quantify the strong impact that RNA secondary structure has on substitution rates. Analyses on simulated sequences show that the new inference procedure has reasonable statistical properties. Potential applications of this procedure, including improved ancestral sequence inference and location of functionally interesting sites, are discussed.     

Context-Dependent Evolutionary Models for Non-Coding Sequences: An Overview of Several Decades of Research and an Analysis of Laurasiatheria and Primate Evolution

The past decade has seen a growing interest in evolutionary models that relax the assumption of site-independent evolution for non-coding sequences. While phylogenetic inference using such so-called context-dependent models is currently computationally prohibitive, these models have been shown to yield significant increases in model fit compared to site-independent evolutionary models, which remain the most widely used evolutionary models to study substitution patterns and perform phylogenetic inference. Context-dependent models have been shown to be suited to study the spontaneous deamination of cytosine in mammalian sequences. In this paper, I discuss various approaches presented in recent years to model context-dependent evolution. I start with discussing the empirical research and results that have led to the development of these models. To accurately estimate the context-dependent substitution patterns that arise from these models, accurate sampling of substitution histories under such models is required. Further, appropriate model selection techniques to assess model performance has become more important than ever, given the drastic increase in parameters of context-dependent models and the tendency of older model selection techniques to prefer parameter-rich models. I also present new results on two mammalian datasets (Primate and Laurasiatheria data) to shed a light on so-called lineage-dependent context-dependent evolution. I conclude this paper with a discussion on current challenges in the development of context-dependent modeling approaches.     

Escaping from the Felsenstein Zone by Detecting Long Branches in Phylogenetic Data

Long branches in a true phylogeny tend to disrupt hierarchical character covariation (phylogenetic signal) in the distribution of traits among organisms. The distortion of hierarchical structure in character-state matrices can lead to errors in the estimation of phylogenetic relationships and inconsistency of methods of phylogenetic inference. Examination of trees distorted by long-branch attraction will not reveal the identities of problematic taxa, in part because the distortion can mask long branches by reducing inferred branch lengths and through errors in branching order. Here we present a simple method for the detection of taxa whose placement in evolutionary trees is made difficult by the effects of long-branch attraction. The method is an extension of a tree-independent conceptual framework of phylogenetic data exploration (RASA). Taxa that are likely to attract are revealed because long branches leave distinct footprints in the distribution of character states among taxa, and these traces can be directly observed in the error structure of the RASA regression. Problematic taxa are identified using a new diagnostic plot called the taxon variance plot, in which the apparent cladistic and phenetic variances contributed by individual taxa are compared. The procedure for identifying long edges employs algorithms solved in polynomial time and can be applied to morphological, molecular, and mixed characters. The efficacy of the method is demonstrated using simulated evolution and empirical evidence of long branches in a set of recently published sequences. We show that the accuracy of evolutionary trees can be improved by detecting and combating the potentially misleading influences of long-branch taxa.     

Artifactual phylogenies caused by correlated distribution of substitution rates among sites and lineages: the good, the bad, and the ugly

Despite the advances in understanding molecular evolution, current phylogenetic methods barely take account of a fraction of the complexity of evolution. We are chiefly constrained by our incomplete knowledge of molecular evolutionary processes and the limits of computational power. These limitations lead to the establishment of either biologically simplistic models that rarely account for a fraction of the complexity involved or overfitting models that add little resolution to the problem. Such oversimplified models may lead us to assign high confidence to an incorrect tree (inconsistency). Rate-across-site (RAS) models are commonly used evolutionary models in phylogenetic studies. These account for heterogeneity in the evolutionary rates among sites but do not account for changing within-site rates across lineages (heterotachy). If heterotachy is common, using RAS models may lead to systematic errors in tree inference. In this work we show possible misleading effects in tree inference when the assumption of constant within-site rates across lineages is violated using maximum likelihood. Using a simulation study, we explore the ways in which gamma stationary models can lead to wrong topology or to deceptive bootstrap support values when the within-site rates change across lineages. More precisely, we show that different degrees of heterotachy mislead phylogenetic inference when the model assumed is stationary. Finally, we propose a geometry-based approach to visualize and to test for the possible existence of bias due to heterotachy.     

Bayesian model adequacy and choice in phylogenetics

Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global) performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance) of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric bootstrap, accounts for uncertainty in the phylogeny and model parameters.     

Performance of criteria for selecting evolutionary models in phylogenetics: a comprehensive study based on simulated datasets

Background  

Explicit evolutionary models are required in maximum-likelihood and Bayesian inference, the two methods that are overwhelmingly used in phylogenetic studies of DNA sequence data. Appropriate selection of nucleotide substitution models is important because the use of incorrect models can mislead phylogenetic inference. To better understand the performance of different model-selection criteria, we used 33,600 simulated data sets to analyse the accuracy, precision, dissimilarity, and biases of the hierarchical likelihood-ratio test, Akaike information criterion, Bayesian information criterion, and decision theory.     

A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data

We describe a general likelihood-based 'mixture model' for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites "pattern-heterogeneity" to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate-variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program.     

Recent developments in the analysis of comparative data

Comparative methods can be used to test ideas about adaptation by identifying cases of either parallel or convergent evolutionary change across taxa. Phylogenetic relationships must be known or inferred if comparative methods are to separate the cross-taxonomic covariation among traits associated with evolutionary change from that attributable to common ancestry. Only the former can be used to test ideas linking convergent or parallel evolutionary change to some aspect of the environment. The comparative methods that are currently available differ in how they manage the effects brought about by phylogenetic relationships. One method is applicable only to discrete data, and uses cladistic techniques to identify evolutionary events that depart from phylogenetic trends. Techniques for continuous variables attempt to control for phylogenetic effects in a variety of ways. One method examines the taxonomic distribution of variance to identify the taxa within which character variation is small. The method assumes that taxa with small amounts of variation are those in which little evolutionary change has occurred, and thus variation is unlikely to be independent of ancestral trends. Analyses are then concentrated among taxa that show more variation, on the assumption that greater evolutionary change in the character has taken place. Several methods estimate directly the extent to which ancestry can predict the observed variation of a character, and subtract the ancestral effect to reveal variation of phylogeny. Yet another can remove phylogenetic effects if the true phylogeny is known. One class of comparative methods controls for phylogenetic effects by searching for comparative trends within rather than across taxa. With current knowledge of phylogenies, there is a trade-off in the choice of a comparative method: those that control phylogenetic effects with greater certainty are either less applicable to real data, or they make restrictive or untestable assumptions. Those that rely on statistical patterns to infer phylogenetic effects may not control phylogeny as efficiently but are more readily applied to existing data sets.     

Efficient selection of branch-specific models of sequence evolution

The analysis of extant sequences shows that molecular evolution has been heterogeneous through time and among lineages. However, for a given sequence alignment, it is often difficult to uncover what factors caused this heterogeneity. In fact, identifying and characterizing heterogeneous patterns of molecular evolution along a phylogenetic tree is very challenging, for lack of appropriate methods. Users either have to a priori define groups of branches along which they believe molecular evolution has been similar or have to allow each branch to have its own pattern of molecular evolution. The first approach assumes prior knowledge that is seldom available, and the second requires estimating an unreasonably large number of parameters. Here we propose a convenient and reliable approach where branches get clustered by their pattern of molecular evolution alone, with no need for prior knowledge about the data set under study. Model selection is achieved in a statistical framework and therefore avoids overparameterization. We rely on substitution mapping for efficiency and present two clustering approaches, depending on whether or not we expect neighbouring branches to share more similar patterns of sequence evolution than distant branches. We validate our method on simulations and test it on four previously published data sets. We find that our method correctly groups branches sharing similar equilibrium GC contents in a data set of ribosomal RNAs and recovers expected footprints of selection through dN/dS. Importantly, it also uncovers a new pattern of relaxed selection in a phylogeny of Mantellid frogs, which we are able to correlate to life-history traits. This shows that our programs should be very useful to study patterns of molecular evolution and reveal new correlations between sequence and species evolution. Our programs can run on DNA, RNA, codon, or amino acid sequences with a large set of possible models of substitutions and are available at http://biopp.univ-montp2.fr/forge/testnh.