Testing for covarion-like evolution in protein sequences

The covarion hypothesis of molecular evolution proposes that selective pressures on an amino acid or nucleotide site change through time, thus causing changes of evolutionary rate along the edges of a phylogenetic tree. Several kinds of Markov models for the covarion process have been proposed. One model, proposed by Huelsenbeck (2002), has 2 substitution rate classes: the substitution process at a site can switch between a single variable rate, drawn from a discrete gamma distribution, and a zero invariable rate. A second model, suggested by Galtier (2001), assumes rate switches among an arbitrary number of rate classes but switching to and from the invariable rate class is not allowed. The latter model allows for some sites that do not participate in the rate-switching process. Here we propose a general covarion model that combines features of both models, allowing evolutionary rates not only to switch between variable and invariable classes but also to switch among different rates when they are in a variable state. We have implemented all 3 covarion models in a maximum likelihood framework for amino acid sequences and tested them on 23 protein data sets. We found significant likelihood increases for all data sets for the 3 models, compared with a model that does not allow site-specific rate switches along the tree. Furthermore, we found that the general model fit the data better than the simpler covarion models in the majority of the cases, highlighting the complexity in modeling the covarion process. The general covarion model can be used for comparing tree topologies, molecular dating studies, and the investigation of protein adaptation.     

Fast statistical tests for detecting heterotachy in protein evolution

The w statistic introduced by Lockhart et al. (1998. A covariotide model explains apparent phylogenetic structure of oxygenic photosynthetic lineages. Mol Biol Evol. 15:1183-1188) is a simple and easily calculated statistic intended to detect heterotachy by comparing amino acid substitution patterns between two monophyletic groups of protein sequences. It is defined as the difference between the fraction of varied sites in both groups and the fraction of varied sites in each group. The w test has been used to distinguish a covarion process from equal rates and rates variation across sites processes. Using simulation we show that the w test is effective for small data sets and for data sets that have low substitution rates in the groups but can have difficulties when these conditions are not met. Using site entropy as a measure of variability of a sequence site, we modify the w statistic to a w' statistic by assigning as varied in one group those sites that are actually varied in both groups but have a large entropy difference. We show that the w' test has more power to detect two kinds of heterotachy processes (covarion and bivariate rate shifts) in large and variable data. We also show that a test of Pearson's correlation of the site entropies between two monophyletic groups can be used to detect heterotachy and has more power than the w' test. Furthermore, we demonstrate that there are settings where the correlation test as well as w and w' tests do not detect heterotachy signals in data simulated under a branch length mixture model. In such cases, it is sometimes possible to detect heterotachy through subselection of appropriate taxa. Finally, we discuss the abilities of the three statistical tests to detect a fourth mode of heterotachy: lineage-specific changes in proportion of variable sites.     

A test for heterotachy using multiple pairs of sequences

Heterotachy is a general term to describe positions that evolve at different rates in different lineages. Heterotachy also can generally be viewed as multivariate rates-across-sites variation, which can be described as randomly drawing rates (or branch lengths) from a multivariate distribution for each branch at each site (Wu J, Susko E. 2009. General heterotachy and distance method adjustments. Mol Biol Evol. 26:2689-2697). Motivated by this result, we propose three new distance-based tests: a heterogeneity test, a heterotachy test, and a within-gene heterotachy test and demonstrate with simulations that they perform well under a wide range of conditions. We also applied the first two tests to two real data sets and found that although all these data sets showed significant evidence of heterotachy, there were subtrees for which the data were consistent with an equal rates or rates-across-sites model.heterogeneity, heterotachy, within-gene heterotachy, covarion model, distance method, hypothesis test.     

Topological Estimation Biases with Covarion Evolution

Covarion processes allow changes in evolutionary rates at sites along the branches of a phylogenetic tree. Covarion-like evolution is increasingly recognized as an important mode of protein evolution. Several recent reports suggest that maximum likelihood estimation employing covarion models may support different optimal topologies than estimation using standard rates-across-sites (RAS) models. However, it remains to be demonstrated that ignoring covarion evolution will generally result in topological misestimation. In this study we performed analytical and theoretical studies of limiting distances under the covarion model and four-taxon tree simulations to investigate the extent to which the covarion process impacts on phylogenetic estimation. In particular, we assessed the limits of an RAS model-based maximum likelihood method to recover the phylogenies when the sequence data were simulated under the covarion processes. We find that, when ignored, covarion processes can induce systematic errors in phylogeny reconstruction. Surprisingly, when sequences are evolved under a covarion process but an RAS model is used for estimation, we find that a long branch repel bias occurs.     

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.     

Assessing an unknown evolutionary process: effect of increasing site-specific knowledge through taxon addition

Assessment of the evolutionary process is crucial for understanding the effect of protein structure and function on sequence evolution and for many other analyses in molecular evolution. Here, we used simulations to study how taxon sampling affects accuracy of parameter estimation and topological inference in the absence of branch length asymmetry. With maximum-likelihood analysis, we find that adding taxa dramatically improves both support for the evolutionary model and accurate assessment of its parameters when compared with increasing the sequence length. Using a method we call "doppelg?nger trees," we distinguish the contributions of two sources of improved topological inference: greater knowledge about internal nodes and greater knowledge of site-specific rate parameters. Surprisingly, highly significant support for the correct general model does not lead directly to improved topological inference. Instead, substantial improvement occurs only with accurate assessment of the evolutionary process at individual sites. Although these results are based on a simplified model of the evolutionary process, they indicate that in general, assuming processes are not independent and identically distributed among sites, more extensive sampling of taxonomic biodiversity will greatly improve analytical results in many current sequence data sets with moderate sequence lengths.     

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.     

Directional biases in phylogenetic structure quantification: a Mediterranean case study

Recent years have seen an increasing effort to incorporate phylogenetic hypotheses to the study of community assembly processes. The incorporation of such evolutionary information has been eased by the emergence of specialized software for the automatic estimation of partially resolved supertrees based on published phylogenies. Despite this growing interest in the use of phylogenies in ecological research, very few studies have attempted to quantify the potential biases related to the use of partially resolved phylogenies and to branch length accuracy, and no work has examined how tree shape may affect inference of community phylogenetic metrics. In this study, we tested the influence of phylogenetic resolution and branch length information on the quantification of phylogenetic structure, and also explored the impact of tree shape (stemminess) on the loss of accuracy in phylogenetic structure quantification due to phylogenetic resolution. For this purpose, we used 9 sets of phylogenetic hypotheses of varying resolution and branch lengths to calculate three indices of phylogenetic structure: the mean phylogenetic distance (NRI), the mean nearest taxon distance (NTI) and phylogenetic diversity (stdPD) metrics. The NRI metric was the less sensitive to phylogenetic resolution, stdPD showed an intermediate sensitivity, and NTI was the most sensitive one; NRI was also less sensitive to branch length accuracy than NTI and stdPD, the degree of sensitivity being strongly dependent on the dating method and the sample size. Directional biases were generally towards type II errors. Interestingly, we detected that tree shape influenced the accuracy loss derived from the lack of phylogenetic resolution, particularly for NRI and stdPD. We conclude that well‐resolved molecular phylogenies with accurate branch length information are needed to identify the underlying phylogenetic structure of communities, and also that sensitivity of phylogenetic structure measures to low phylogenetic resolution can strongly vary depending on phylogenetic tree shape.     

Evaluation of the models handling heterotachy in phylogenetic inference

Background  

The evolutionary rate at a given homologous position varies across time. When sufficiently pronounced, this phenomenon – called heterotachy – may produce artefactual phylogenetic reconstructions under the commonly used models of sequence evolution. These observations have motivated the development of models that explicitly recognize heterotachy, with research directions proposed along two main axes: 1) the covarion approach, where sites switch from variable to invariable states; and 2) the mixture of branch lengths (MBL) approach, where alignment patterns are assumed to arise from one of several sets of branch lengths, under a given phylogeny.     

Mathematical Elegance with Biochemical Realism: The Covarion Model of Molecular Evolution

There is an apparent paradox in our understanding of molecular evolution. Current biochemically based models predict that evolutionary trees should not be recoverable for divergences beyond a few hundred million years. In practice, however, trees often appear to be recovered from much older times. Mathematical models, such as those assuming that sites evolve at different rates [including a Γ distribution of rates across sites (RAS)] may in theory allow the recovery of some ancient divergences. However, such models require that each site maintain its characteristic rate over the whole evolutionary period. This assumption, however, contradicts the knowledge that tertiary structures diverge with time, invalidating the rate-constancy assumption of purely mathematical models. We report here that a hidden Markov version of the covarion model can meet both biochemical and statistical requirements for the analysis of sequence data. The model was proposed on biochemical grounds and can be implemented with only two additional parameters. The two hidden parts of this model are the proportion of sites free to vary (covarions) and the rate of interchange between fixed sites and these variable sites. Simulation results are consistent with this approach, providing a better framework for understanding anciently diverged sequences than the standard RAS models. However, a Γ distribution of rates may approximate a covarion model and may possibly be justified on these grounds. The accurate reconstruction of older divergences from sequence data is still a major problem, and molecular evolution still requires mathematical models that also have a sound biochemical basis. Received: 13 February 2001 / Accepted: 22 May 2001     

The effects of nucleotide substitution model assumptions on estimates of nonparametric bootstrap support

The use of parameter-rich substitution models in molecular phylogenetics has been criticized on the basis that these models can cause a reduction both in accuracy and in the ability to discriminate among competing topologies. We have explored the relationship between nucleotide substitution model complexity and nonparametric bootstrap support under maximum likelihood (ML) for six data sets for which the true relationships are known with a high degree of certainty. We also performed equally weighted maximum parsimony analyses in order to assess the effects of ignoring branch length information during tree selection. We observed that maximum parsimony gave the lowest mean estimate of bootstrap support for the correct set of nodes relative to the ML models for every data set except one. For several data sets, we established that the exact distribution used to model among-site rate variation was critical for a successful phylogenetic analysis. Site-specific rate models were shown to perform very poorly relative to gamma and invariable sites models for several of the data sets most likely because of the gross underestimation of branch lengths. The invariable sites model also performed poorly for several data sets where this model had a poor fit to the data, suggesting that addition of the gamma distribution can be critical. Estimates of bootstrap support for the correct nodes often increased under gamma and invariable sites models relative to equal rates models. Our observations are contrary to the prediction that such models cause reduced confidence in phylogenetic hypotheses. Our results raise several issues regarding the process of model selection, and we briefly discuss model selection uncertainty and the role of sensitivity analyses in molecular phylogenetics.     

Likelihood, parsimony, and heterogeneous evolution

Evolutionary rates vary among sites and across the phylogenetic tree (heterotachy). A recent analysis suggested that parsimony can be better than standard likelihood at recovering the true tree given heterotachy. The authors recommended that results from parsimony, which they consider to be nonparametric, be reported alongside likelihood results. They also proposed a mixture model, which was inconsistent but better than either parsimony or standard likelihood under heterotachy. We show that their main conclusion is limited to a special case for the type of model they study. Their mixture model was inconsistent because it was incorrectly implemented. A useful nonparametric model should perform well over a wide range of possible evolutionary models, but parsimony does not have this property. Likelihood-based methods are therefore the best way to deal with heterotachy.     

Heterotachy processes in rhodophyte-derived secondhand plastid genes: Implications for addressing the origin and evolution of dinoflagellate plastids

Serial transfer of plastids from one eukaryotic host to another is the key process involved in evolution of secondhand plastids. Such transfers drastically change the environment of the plastids and hence the selection regimes, presumably leading to changes over time in the characteristics of plastid gene evolution and to misleading phylogenetic inferences. About half of the dinoflagellate protists species are photosynthetic and unique in harboring a diversity of plastids acquired from a wide range of eukaryotic algae. They are therefore ideal for studying evolutionary processes of plastids gained through secondary and tertiary endosymbioses. In the light of these processes, we have evaluated the origin of 2 types of dinoflagellate plastids, containing the peridinin or 19'-hexanoyloxyfucoxanthin (19'-HNOF) pigments, by inferring the phylogeny using "covarion" evolutionary models allowing the pattern of among-site rate variation to change over time. Our investigations of genes from secondary and tertiary plastids derived from the rhodophyte plastid lineage clearly reveal "heterotachy" processes characterized as stationary covarion substitution patterns and changes in proportion of variable sites across sequences. Failure to accommodate covarion-like substitution patterns can have strong effects on the plastid tree topology. Importantly, multigene analyses performed with probabilistic methods using among-site rate and covarion models of evolution conflict with proposed single origin of the peridinin- and 19'-HNOF-containing plastids, suggesting that analysis of secondhand plastids can be hampered by convergence in the evolutionary signature of the plastid DNA sequences. Another type of sequence convergence was detected at protein level involving the psaA gene. Excluding the psaA sequence from a concatenated protein alignment grouped the peridinin plastid with haptophytes, congruent with all DNA trees. Altogether, taking account of complex processes involved in the evolution of dinoflagellate plastid sequences (both at the DNA and amino acid level), we demonstrate the difficulty of excluding independent, tertiary origin for both the peridinin and 19'-HNOF plastids involving engulfment of haptophyte-like algae. In addition, the refined topologies suggest the red algal order, Porphyridales, as the endosymbiont ancestor of the secondary plastids in cryptophytes, haptophytes, and heterokonts.     

Site-specific time heterogeneity of the substitution process and its impact on phylogenetic inference

Background  

Model violations constitute the major limitation in inferring accurate phylogenies. Characterizing properties of the data that are not being correctly handled by current models is therefore of prime importance. One of the properties of protein evolution is the variation of the relative rate of substitutions across sites and over time, the latter is the phenomenon called heterotachy. Its effect on phylogenetic inference has recently obtained considerable attention, which led to the development of new models of sequence evolution. However, thus far focus has been on the quantitative heterogeneity of the evolutionary process, thereby overlooking more qualitative variations.     

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.     

Testing for differences in rates-across-sites distributions in phylogenetic subtrees

It has long been recognized that the rates of molecular evolution vary amongst sites in proteins. The usual model for rate heterogeneity assumes independent rate variation according to a rate distribution. In such models the rate at a site, although random, is assumed fixed throughout the evolutionary tree. Recent work by several groups has suggested that rates at sites often vary across subtrees of the larger tree as well as across sites. This phenomenon is not captured by most phylogenetic models but instead is more similar to the covarion model of Fitch and coworkers. In this article we present methods that can be useful in detecting whether different rates occur in two different subtrees of the larger tree and where these differences occur. Parametric bootstrapping and orthogonal regression methodologies are used to test for rate differences and to make statements about the general differences in the rates at sites. Confidence intervals based on the conditional distributions of rates at sites are then used to detect where the rate differences occur. Such methods will be helpful in studying the phylogenetic, structural, and functional bases of changes in evolutionary rates at sites, a phenomenon that has important consequences for deep phylogenetic inference.     

Identifying site-specific substitution rates

A maximum likelihood framework for estimating site-specific substitution rates is presented that does not require any prior assumptions about the rate distribution. We show that, when the branching pattern of the underlying tree is known, the analysis of pairs of positions is sufficient to estimate site-specific rates. In the abscense of a known topology, we introduce an iterative procedure to estimate simultaneously the branching pattern, the branch lengths, and site-specific substitution rates. Simulations show that the evolutionary rate of fast-evolving sites can be reliably inferred and that the accuracy of rate estimates depends mainly on the number of sequences in the data set. Thus, large sets of aligned sequences are necessary for reliable site-specific rate estimates. The method is applied to the complete mitochondrial DNA sequence of 53 humans, providing a complete picture of the site-specific substitution rates in human mitochondrial DNA.     

Covarion shifts cause a long-branch attraction artifact that unites microsporidia and archaebacteria in EF-1alpha phylogenies

Microsporidia branch at the base of eukaryotic phylogenies inferred from translation elongation factor 1alpha (EF-1alpha) sequences. Because these parasitic eukaryotes are fungi (or close relatives of fungi), it is widely accepted that fast-evolving microsporidian sequences are artifactually "attracted" to the long branch leading to the archaebacterial (outgroup) sequences ("long-branch attraction," or "LBA"). However, no previous studies have explicitly determined the reason(s) why the artifactual allegiance of microsporidia and archaebacteria ("M + A") is recovered by all phylogenetic methods, including maximum likelihood, a method that is supposed to be resistant to classical LBA. Here we show that the M + A affinity can be attributed to those alignment sites associated with large differences in evolutionary site rates between the eukaryotic and archaebacterial subtrees. Therefore, failure to model the significant evolutionary rate distribution differences (covarion shifts) between the ingroup and outgroup sequences is apparently responsible for the artifactual basal position of microsporidia in phylogenetic analyses of EF-1alpha sequences. Currently, no evolutionary model that accounts for discrete changes in the site rate distribution on particular branches is available for either protein or nucleotide level phylogenetic analysis, so the same artifacts may affect many other "deep" phylogenies. Furthermore, given the relative similarity of the site rate patterns of microsporidian and archaebacterial EF-1alpha proteins ("parallel site rate variation"), we suggest that the microsporidian orthologs may have lost some eukaryotic EF-1alpha-specific nontranslational functions, exemplifying the extreme degree of reduction in this parasitic lineage.     

PROCOV: maximum likelihood estimation of protein phylogeny under covarion models and site-specific covarion pattern analysis

Background  

The covarion hypothesis of molecular evolution holds that selective pressures on a given amino acid or nucleotide site are dependent on the identity of other sites in the molecule that change throughout time, resulting in changes of evolutionary rates of sites along the branches of a phylogenetic tree. At the sequence level, covarion-like evolution at a site manifests as conservation of nucleotide or amino acid states among some homologs where the states are not conserved in other homologs (or groups of homologs). Covarion-like evolution has been shown to relate to changes in functions at sites in different clades, and, if ignored, can adversely affect the accuracy of phylogenetic inference.