The effect of heterotachy in multigene analysis using the neighbor joining method

Sequence alignments of multiple genes are routinely used to infer phylogenetic relationships among species. The analysis of their concatenation is more likely to give correct results under an assumption of homotachy (i.e., the evolutionary rates within lineages in each of the concatenated genes are constant during evolution). Here, we examine how the violation of homotachy (i.e., presence of within-site rate variation, called heterotachy) distorts species phylogenies. A theoretical examination has been conducted using a four taxon case and the neighbor joining (NJ) method, concluding that NJ recovers the incorrect tree when concatenated genes exhibit heterotachy. The application of average and weighted-average distance approaches, where gene boundaries are kept intact, overcomes the detrimental effect of heterotachy in multigene analysis using the NJ method.     

Heterotachy, an important process of protein evolution.

Because of functional constraints, substitution rates vary among the positions of a protein but are usually assumed to be constant at a given site during evolution. The distribution of the rates across the sequence positions generally fits a Gamma distribution. Models of sequence evolution were accordingly designed and led to improved phylogenetic reconstruction. However, it has been convincingly demonstrated that the evolutionary rate of a given position is not always constant throughout time. We called such within-site rate variations heterotachy (for "different speed" in Greek). Yet, heterotachy was found among homologous sequences of distantly related organisms, often with different functions. In such cases, the functional constraints are likely different, which would explain the different distribution of variable sites. To evaluate the importance of heterotachy, we focused on amino acid sequences of mitochondrial cytochrome b, for which the function is likely the same in all vertebrates. Using 2,038 sequences, we demonstrate that 95% of the variable positions are heterotachous, i.e., underwent dramatic variations of substitution rate among vertebrate lineages. Heterotachy even occurs at small evolutionary scale, and in these cases it is very unlikely to be related to functional changes. Since a large number of sequences are required to efficiently detect heterotachy, the extent of this phenomenon could not be estimated for all proteins yet. It could be as large as for cytochrome b, since this protein is not a peculiar case. The observations made here open several new avenues of research, such as the understanding of the evolution of functional constraints or the improvement of phylogenetic reconstruction methods.     

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.     

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.     

A mixed branch length model of heterotachy improves phylogenetic accuracy

Evolutionary relationships are typically inferred from molecular sequence data using a statistical model of the evolutionary process. When the model accurately reflects the underlying process, probabilistic phylogenetic methods recover the correct relationships with high accuracy. There is ample evidence, however, that models commonly used today do not adequately reflect real-world evolutionary dynamics. Virtually all contemporary models assume that relatively fast-evolving sites are fast across the entire tree, whereas slower sites always evolve at relatively slower rates. Many molecular sequences, however, exhibit site-specific changes in evolutionary rates, called "heterotachy." Here we examine the accuracy of 2 phylogenetic methods for incorporating heterotachy, the mixed branch length model--which incorporates site-specific rate changes by summing likelihoods over multiple sets of branch lengths on the same tree--and the covarion model, which uses a hidden Markov process to allow sites to switch between variable and invariable as they evolve. Under a variety of simple heterogeneous simulation conditions, the mixed model was dramatically more accurate than homotachous models, which were subject to topological biases as well as biases in branch length estimates. When data were simulated with strong versions of the types of heterotachy observed in real molecular sequences, the mixed branch length model was more accurate than homotachous techniques. Analyses of empirical data sets confirmed that the mixed branch length model can improve phylogenetic accuracy under conditions that cause homotachous models to fail. In contrast, the covarion model did not improve phylogenetic accuracy compared with homotachous models and was sometimes substantially less accurate. We conclude that a mixed branch length approach, although not the solution to all phylogenetic errors, is a valuable strategy for improving the accuracy of inferred trees.     

A novel comparative method for identifying shifts in the rate of character evolution on trees

Evolutionary biologists since Darwin have been fascinated by differences in the rate of trait-evolutionary change across lineages. Despite this continued interest, we still lack methods for identifying shifts in evolutionary rates on the growing tree of life while accommodating uncertainty in the evolutionary process. Here we introduce a Bayesian approach for identifying complex patterns in the evolution of continuous traits. The method (auteur) uses reversible-jump Markov chain Monte Carlo sampling to more fully characterize the complexity of trait evolution, considering models that range in complexity from those with a single global rate to potentially ones in which each branch in the tree has its own independent rate. This newly introduced approach performs well in recovering simulated rate shifts and simulated rates for datasets nearing the size typical for comparative phylogenetic study (i.e., ≥64 tips). Analysis of two large empirical datasets of vertebrate body size reveal overwhelming support for multiple-rate models of evolution, and we observe exceptionally high rates of body-size evolution in a group of emydid turtles relative to their evolutionary background. auteur will facilitate identification of exceptional evolutionary dynamics, essential to the study of both adaptive radiation and stasis.     

Heterogeneity in the rate of molecular sequence evolution substantially impacts the accuracy of detecting shifts in diversification rates

As species richness varies along the tree of life, there is a great interest in identifying factors that affect the rates by which lineages speciate or go extinct. To this end, theoretical biologists have developed a suite of phylogenetic comparative methods that aim to identify where shifts in diversification rates had occurred along a phylogeny and whether they are associated with some traits. Using these methods, numerous studies have predicted that speciation and extinction rates vary across the tree of life. In this study, we show that asymmetric rates of sequence evolution lead to systematic biases in the inferred phylogeny, which in turn lead to erroneous inferences regarding lineage diversification patterns. The results demonstrate that as the asymmetry in sequence evolution rates increases, so does the tendency to select more complicated models that include the possibility of diversification rate shifts. These results thus suggest that any inference regarding shifts in diversification pattern should be treated with great caution, at least until any biases regarding the molecular substitution rate have been ruled out.     

Difficulties in testing for covarion-like properties of sequences under the confounding influence of changing proportions of variable sites

The covarion (COV)-like properties of sequences are poorly described and their impact on phylogenetic analyses poorly understood. We demonstrate using simulations that, under an evolutionary model where the proportion of variable sites changes in nonadjacent lineages, log likelihood values for rates across site (RAS) and COV models become similar, making models difficult to distinguish. Further, although COV and RAS models provide a great improvement in likelihood scores over a homogeneous model with these simulated data, reconstruction accuracy of tree building is low, suggesting caution when it is suspected that proportions of variable sites differ in different evolutionary lineages. We study the performance of a recently developed contingency test that detects the presence of COV-type evolution modified for protein data. We report that if proportions of variable sites (p(var)) change in a lineage-specific manner such that their distributions in different lineages become sufficiently nonoverlapping, then the contingency test can incorrectly suggest a homogeneous model. Also of concern is the possibility of different proportions of variable sites between the groups being studied. In a study of chloroplast proteins, interpretation of the test is found to be susceptible to different partitioning of taxon groups, making the test very subjective in its implementation. Extreme intergroup differences in the extent of divergence and difference in proportions of variable sites could be contributing to this effect.     

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.     

Rates of molecular evolution in tree ferns are associated with body size,environmental temperature,and biological productivity

Variation in rates of molecular evolution (heterotachy) is a common phenomenon among plants. Although multiple theoretical models have been proposed, fundamental questions remain regarding the combined effects of ecological and morphological traits on rate heterogeneity. Here, we used tree ferns to explore the correlation between rates of molecular evolution in chloroplast DNA sequences and several morphological and environmental factors within a Bayesian framework. We revealed direct and indirect effects of body size, biological productivity, and temperature on substitution rates, where smaller tree ferns living in warmer and less productive environments tend to have faster rates of molecular evolution. In addition, we found that variation in the ratio of nonsynonymous to synonymous substitution rates (dN/dS) in the chloroplast rbcL gene was significantly correlated with ecological and morphological variables. Heterotachy in tree ferns may be influenced by effective population size associated with variation in body size and productivity. Macroevolutionary hypotheses should go beyond explaining heterotachy in terms of mutation rates and instead, should integrate population‐level factors to better understand the processes affecting the tempo of evolution at the molecular level.     

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.     

Maximum likelihood outperforms maximum parsimony even when evolutionary rates are heterotachous

Heterotachy occurs when the relative evolutionary rates among sites are not the same across lineages. Sequence alignments are likely to exhibit heterotachy with varying severity because the intensity of purifying selection and adaptive forces at a given amino acid or DNA sequence position is unlikely to be the same in different species. In a recent study, the influence of heterotachy on the performance of different phylogenetic methods was examined using computer simulation for a four-species phylogeny. Maximum parsimony (MP) was reported to generally outperform maximum likelihood (ML). However, our comparisons of MP and ML methods using the methods and evaluation criteria employed in that study, but considering the possible range of proportions of sites involved in heterotachy, contradict their findings and indicate that, in fact, ML is significantly superior to MP even under heterotachy.     

Ancestral inference and the study of codon bias evolution: implications for molecular evolutionary analyses of the Drosophila melanogaster subgroup

Reliable inference of ancestral sequences can be critical to identifying both patterns and causes of molecular evolution. Robustness of ancestral inference is often assumed among closely related species, but tests of this assumption have been limited. Here, we examine the performance of inference methods for data simulated under scenarios of codon bias evolution within the Drosophila melanogaster subgroup. Genome sequence data for multiple, closely related species within this subgroup make it an important system for studying molecular evolutionary genetics. The effects of asymmetric and lineage-specific substitution rates (i.e., varying levels of codon usage bias and departures from equilibrium) on the reliability of ancestral codon usage was investigated. Maximum parsimony inference, which has been widely employed in analyses of Drosophila codon bias evolution, was compared to an approach that attempts to account for uncertainty in ancestral inference by weighting ancestral reconstructions by their posterior probabilities. The latter approach employs maximum likelihood estimation of rate and base composition parameters. For equilibrium and most non-equilibrium scenarios that were investigated, the probabilistic method appears to generate reliable ancestral codon bias inferences for molecular evolutionary studies within the D. melanogaster subgroup. These reconstructions are more reliable than parsimony inference, especially when codon usage is strongly skewed. However, inference biases are considerable for both methods under particular departures from stationarity (i.e., when adaptive evolution is prevalent). Reliability of inference can be sensitive to branch lengths, asymmetry in substitution rates, and the locations and nature of lineage-specific processes within a gene tree. Inference reliability, even among closely related species, can be strongly affected by (potentially unknown) patterns of molecular evolution in lineages ancestral to those of interest.     

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.     

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.     

Heterotachy and tree building: a case study with plastids and eubacteria

The nature of heterotachy at the center of recent controversy over the relative performance of tree-building methods is different from the form of heterotachy that has been inferred in empirical studies. The latter have suggested that proportions of variable sites (p(var)) vary among orthologues and among paralogues. However, the strength of this inference, describing what may be one of the most important evolutionary properties of sequence data, has remained weak. Consequently, other models of sequence evolution have been proposed to explain some long-branch attraction (LBA) problems that could be attributed to differences in p(var). For an empirical case with plastid and eubacterial RNA polymerase sequences, we confirm using capture-recapture estimates and simulations that p(var) can differ among orthologues in anciently diverged evolutionary lineages. We find that parsimony and a least squares distance method that implements an overly simple model of sequence evolution are susceptible to LBA induced by this form of heterotachy. Although homogeneous maximum likelihood inference was found to be robust to model misspecification in our specific example, we caution against assuming that it will always be so.     

A Molecular Genetic Timescale for the Diversification of Autotrophic Stramenopiles (Ochrophyta): Substantive Underestimation of Putative Fossil Ages

Background

Stramenopiles constitute a large and diverse eukaryotic clade that is currently poorly characterized from both phylogenetic and temporal perspectives at deeper taxonomic levels. To better understand this group, and in particular the photosynthetic stramenopiles (Ochrophyta), we analyzed sequence data from 135 taxa representing most major lineages. Our analytical approach utilized several recently developed methods that more realistically model the temporal evolutionary process.

Methodology/Principal Findings

Phylogenetic reconstruction employed a Bayesian joint rate- and pattern-heterogeneity model to reconstruct the evolutionary history of these taxa. Inferred phylogenetic resolution was generally high at all taxonomic levels, sister-class relationships in particular receiving good statistical support. A signal for heterotachy was detected in clustered portions of the tree, although this does not seem to have had a major influence on topological inference. Divergence time estimates, assuming a lognormally-distributed relaxed molecular clock while accommodating topological uncertainty, were broadly congruent over alternative temporal prior distributions. These data suggest that Ochrophyta originated near the Proterozoic-Phanerozoic boundary, diverging from their sister-taxon Oomycota. The evolution of the major ochrophyte lineages appears to have proceeded gradually thereafter, with most lineages coming into existence by ∼200 million years ago.

Conclusions/Significance

The evolutionary timescale of the autotrophic stramenopiles reconstructed here is generally older than previously inferred from molecular clocks. However, this more ancient timescale nevertheless casts serious doubt on the taxonomic validity of putative xanthophyte/phaeophyte fossils from the Proterozoic, which predate by as much as a half billion years or more the age suggested by our molecular genetic data. If these fossils truly represent crown stramenopile lineages, then this would imply that molecular rate evolution in this group proceeds in a fashion that is fundamentally incompatible with the relaxed molecular clock model employed here. A more likely scenario is that there is considerable convergent morphological evolution within Heterokonta, and that these fossils have been taxonomically misdiagnosed.     

Inconsistencies in estimating the age of HIV-1 subtypes due to heterotachy

Rate heterogeneity among lineages is a common feature of molecular evolution, and it has long impeded our ability to accurately estimate the age of evolutionary divergence events. The development of relaxed molecular clocks, which model variable substitution rates among lineages, was intended to rectify this problem. Major subtypes of pandemic HIV-1 group M are thought to exemplify closely related lineages with different substitution rates. Here, we report that inferring the time of most recent common ancestor of all these subtypes in a single phylogeny under a single (relaxed) molecular clock produces significantly different dates for many of the subtypes than does analysis of each subtype on its own. We explore various methods to ameliorate this problem. We conclude that current molecular dating methods are inadequate for dealing with this type of substitution rate variation in HIV-1. Through simulation, we show that heterotachy causes root ages to be overestimated.     

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.     

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.