A comprehensive analysis of mammalian mitochondrial genome base composition and improved phylogenetic methods

Phylogenetic analysis of mammalian species using mitochondrial protein genes has proved to be problematic in many previous studies. The high mutation rate of mitochondrial DNA and unusual base composition of several species has prompted us to conduct a detailed study of the composition of 69 mammalian mitochondrial genomes. Most major changes in base composition between lineages can be attributed to shifts between the proportions of C and T on the L-strand. These changes are significant at all codon positions and are shown to affect amino acid composition. Correlated changes in the base composition of the RNA loops and stems are also observed. Following up from previous studies, we investigate changes in the base composition of all 12 H-strand proteins and find that variability in proportions of C and T is correlated with location on the genome. Variation in base composition across genes and species is known to adversely affect the performance of phylogenetic inference methods. We have, therefore, developed a customized three-state general time-reversible DNA substitution model, implemented in the PHASE phylogenetic inference package, which lumps C and T into a composite pyrimidine state. We compare the phylogenetic tree obtained using the new three-state model with that obtained using a standard four-state model. Results using the three-state model are more congruent with recent studies using large sets of nuclear genes and help resolve some of the apparent conflicts between studies using nuclear and mitochondrial proteins.     

GenNon-h: Generating multiple sequence alignments on nonhomogeneous phylogenetic trees

ABSTRACT: BACKGROUND: A number of software packages are available to generate DNA multiple sequence alignments (MSAs) evolved under continuous-time Markov processes on phylogenetic trees. On the other hand, methods of simulating the DNA MSA directly from the transition matrices do not exist. Moreover, existing software restricts to the time-reversible models and it is not optimized to generate nonhomogeneous data (i.e. placing distinct substitution rates at different lineages). RESULTS: We present the first package designed to generate MSAs evolving under discrete-time Markov processes on phylogenetic trees, directly from probability substitution matrices. Based on the input model and a phylogenetic tree in the Newick format (with branch lengths measured as the expected number of substitutions per site), the algorithm produces DNA alignments of desired length. GenNon-h is publicly available for download. CONCLUSION: The software presented here is an efficient tool to generate DNA MSAs on a given phylogenetic tree. GenNon-h provides the user with the nonstationary or nonhomogeneous phylogenetic data that is well suited for testing complex biological hypotheses, exploring the limits of the reconstruction algorithms and their robustness to such models.     

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.     

On the use of nucleic acid sequences to infer early branchings in the tree of life

Simplifying assumptions made in various tree reconstruction methods-- notably rate constancy among nucleotide sites, homogeneity, and stationarity of the substitutional processes--are clearly violated when nucleotide sequences are used to infer distant relationships. Use of tree reconstruction methods based on such oversimplified assumptions can lead to misleading results, as pointed out by previous authors. In this paper, we made use of a (discretized) gamma distribution to account for variable rates of substitution among sites and built models that allowed for unequal base frequencies in different sequences. The models were nonhomogeneous Markov-process models, assuming different patterns of substitution in different parts of the tree. Data of the small-subunit rRNAs from four species were analyzed, where base frequencies were quite different among sequences and rates of substitution were highly variable at sites. Parameters in the models were estimated by maximum likelihood, and models were compared by the likelihood-ratio test. The nonhomogeneous models provided significantly better fit to the data than homogeneous models despite their involvement of many parameters. They also appeared to produce reasonable estimation of the phylogenetic tree; in particular, they seemed able to identify the root of the tree.      

Choosing appropriate substitution models for the phylogenetic analysis of protein-coding sequences

Although phylogenetic inference of protein-coding sequences continues to dominate the literature, few analyses incorporate evolutionary models that consider the genetic code. This problem is exacerbated by the exclusion of codon-based models from commonly employed model selection techniques, presumably due to the computational cost associated with codon models. We investigated an efficient alternative to standard nucleotide substitution models, in which codon position (CP) is incorporated into the model. We determined the most appropriate model for alignments of 177 RNA virus genes and 106 yeast genes, using 11 substitution models including one codon model and four CP models. The majority of analyzed gene alignments are best described by CP substitution models, rather than by standard nucleotide models, and without the computational cost of full codon models. These results have significant implications for phylogenetic inference of coding sequences as they make it clear that substitution models incorporating CPs not only are a computationally realistic alternative to standard models but may also frequently be statistically superior.     

Heterogeneity of nucleotide frequencies among evolutionary lineages and phylogenetic inference

A major assumption of many molecular phylogenetic methods is the homogeneity of nucleotide frequencies among taxa, which refers to the equality of the nucleotide frequency bias among species. Changes in nucleotide frequency among different lineages in a data set are thought to lead to erroneous phylogenetic inference because unrelated clades may appear similar because of evolutionarily unrelated similarities in nucleotide frequencies. We tested the effects of the heterogeneity of nucleotide frequency bias on phylogenetic inference, along with the interaction between this heterogeneity and stratified taxon sampling, by means of computer simulations using evolutionary parameters derived from genomic databases. We found that the phylogenetic trees inferred from data sets simulated under realistic, observed levels of heterogeneity for mammalian genes were reconstructed with accuracy comparable to those simulated with homogeneous nucleotide frequencies; the results hold for Neighbor-Joining, minimum evolution, maximum parsimony, and maximum-likelihood methods. The LogDet distance method, specifically designed to deal with heterogeneous nucleotide frequencies, does not perform better than distance methods that assume substitution pattern homogeneity among sequences. In these specific simulation conditions, we did not find a significant interaction between phylogenetic accuracy and substitution pattern heterogeneity among lineages, even when the taxon sampling is increased.     

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.     

Tests of applicability of several substitution models for DNA sequence data

Using linear invariants for various models of nucleotide substitution, we developed test statistics for examining the applicability of a specific model to a given dataset in phylogenetic inference. The models examined are those developed by Jukes and Cantor (1969), Kimura (1980), Tajima and Nei (1984), Hasegawa et al. (1985), Tamura (1992), Tamura and Nei (1993), and a new model called the eight-parameter model. The first six models are special cases of the last model. The test statistics developed are independent of evolutionary time and phylogeny, although the variances of the statistics contain phylogenetic information. Therefore, these statistics can be used before a phylogenetic tree is estimated. Our objective is to find the simplest model that is applicable to a given dataset, keeping in mind that a simple model usually gives an estimate of evolutionary distance (number of nucleotide substitutions per site) with a smaller variance than a complicated model when the simple model is correct. We have also developed a statistical test of the homogeneity of nucleotide frequencies of a sample of several sequences that takes into account possible phylogenetic correlations. This test is used to examine the stationarity in time of the base frequencies in the sample. For Hasegawa et al.'s and the eight-parameter models, analytical formulas for estimating evolutionary distances are presented. Application of the above tests to several sets of real data has shown that the assumption of stationarity of base composition is usually acceptable when the sequences studied are closely related but otherwise it is rejected. Similarly, the simple models of nucleotide substitution are almost always rejected when actual genes are distantly related and/or the total number of nucleotides examined is large.      

Pitfalls of heterogeneous processes for phylogenetic reconstruction

Different genes often have different phylogenetic histories. Even within regions having the same phylogenetic history, the mutation rates often vary. We investigate the prospects of phylogenetic reconstruction when all the characters are generated from the same tree topology, but the branch lengths vary (with possibly different tree shapes). Furthering work of Kolaczkowski and Thornton (2004, Nature 431: 980-984) and Chang (1996, Math. Biosci. 134: 189-216), we show examples where maximum likelihood (under a homogeneous model) is an inconsistent estimator of the tree. We then explore the prospects of phylogenetic inference under a heterogeneous model. In some models, there are examples where phylogenetic inference under any method is impossible - despite the fact that there is a common tree topology. In particular, there are nonidentifiable mixture distributions, i.e., multiple topologies generate identical mixture distributions. We address which evolutionary models have nonidentifiable mixture distributions and prove that the following duality theorem holds for most DNA substitution models. The model has either: (i) nonidentifiability - two different tree topologies can produce identical mixture distributions, and hence distinguishing between the two topologies is impossible; or (ii) linear tests - there exist linear tests which identify the common tree topology for character data generated by a mixture distribution. The theorem holds for models whose transition matrices can be parameterized by open sets, which includes most of the popular models, such as Tamura-Nei and Kimura's 2-parameter model. The duality theorem relies on our notion of linear tests, which are related to Lake's linear invariants.     

Bayesian phylogenetics using an RNA substitution model applied to early mammalian evolution

We study the phylogeny of the placental mammals using molecular data from all mitochondrial tRNAs and rRNAs of 54 species. We use probabilistic substitution models specific to evolution in base paired regions of RNA. A number of these models have been implemented in a new phylogenetic inference software package for carrying out maximum likelihood and Bayesian phylogenetic inferences. We describe our Bayesian phylogenetic method which uses a Markov chain Monte Carlo algorithm to provide samples from the posterior distribution of tree topologies. Our results show support for four primary mammalian clades, in agreement with recent studies of much larger data sets mainly comprising nuclear DNA. We discuss some issues arising when using Bayesian techniques on RNA sequence data.     

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.     

Phylogenetics of Chondrichthyes and the problem of rooting phylogenies with distant outgroups

Erroneous estimates of ingroup relationships can be caused by attributes in the outgroup chosen to root the tree. Phylogenetic analyses of DNA sequences frequently yield incorrect estimates of ingroup relationships when the outgroup used to "root" the tree is highly divergent from the ingroup. This is especially the case when the outgroup has a different base composition than the ingroup. Unfortunately, in many instances, alternative less divergent outgroups are not available. In such cases, investigators must either target genes with attributes that minimize the problem (slowly evolving genes with stationary base compositions--which are often not ideal for estimating relationships among the more closely related ingroup taxa) or use inference models that are explicitly tailored to deal with an attenuated historical signal with a superimposed non-stationary base composition. In this paper we explore the problem both empirically and through simulation. For the empirical component we looked at the phylogenetic relationships among elasmobranch fishes (sharks and rays), a group whose closest living outgroup, the holocephalan Ghost fishes, are separated from the elasmobranchs by more than 100 million years of evolution. We compiled a data set for analysis comprising 10 single-copy nuclear protein-coding genes (12,096 bp) for representatives of the major lineages within elasmobranchs and holocephalans. For the simulation, we used an evolutionary model on a fixed tree topology to generate DNA sequence data sets which varied both in their distance to the outgroup, and in their base compositional difference between ingroup and outgroup. Results from both the empirical data set and the simulation, support the idea that deviation from base compositional stationarity, in conjunction with distance from the root can act in concert to compromise accuracy of estimated relationships within the ingroup. We tested several approaches to mitigate such problems. We found, that excluding genes with overall faster rates and heterogeneous base compositions, while the least sophisticated of the methods evaluated, seemed to be the most effective.     

On the correlation between composition and site-specific evolutionary rate: implications for phylogenetic inference

Model-based phylogenetic reconstruction methods traditionally assume homogeneity of nucleotide frequencies among sequence sites and lineages. Yet, heterogeneity in base composition is a characteristic shared by most biological sequences. Compositional variation in time, reflected in the compositional biases among contemporary sequences, has already been extensively studied, and its detrimental effects on phylogenetic estimates are known. However, fewer studies have focused on the effects of spatial compositional heterogeneity within genes. We show here that different sites in an alignment do not always share a unique compositional pattern, and we provide examples where nucleotide frequency trends are correlated with the site-specific rate of evolution in RNA genes. Spatial compositional heterogeneity is shown to affect the estimation of evolutionary parameters. With standard phylogenetic methods, estimates of equilibrium frequencies are found to be biased towards the composition observed at fast-evolving sites. Conversely, the ancestral composition estimates of some time-heterogeneous but spatially homogeneous methods are found to be biased towards frequencies observed at invariant and slow-evolving sites. The latter finding challenges the result of a previous study arguing against a hyperthermophilic last universal ancestor from the low apparent G + C content of its rRNA sequences. We propose a new model to account for compositional variation across sites. A Gaussian process prior is used to allow for a smooth change in composition with evolutionary rate. The model has been implemented in the phylogenetic inference software PHASE, and Bayesian methods can be used to obtain the model parameters. The results suggest that this model can accurately capture the observed trends in present-day RNA sequences.     

The origin and diversification of eukaryotes: problems with molecular phylogenetics and molecular clock estimation

Determining the relationships among and divergence times for the major eukaryotic lineages remains one of the most important and controversial outstanding problems in evolutionary biology. The sequencing and phylogenetic analyses of ribosomal RNA (rRNA) genes led to the first nearly comprehensive phylogenies of eukaryotes in the late 1980s, and supported a view where cellular complexity was acquired during the divergence of extant unicellular eukaryote lineages. More recently, however, refinements in analytical methods coupled with the availability of many additional genes for phylogenetic analysis showed that much of the deep structure of early rRNA trees was artefactual. Recent phylogenetic analyses of a multiple genes and the discovery of important molecular and ultrastructural phylogenetic characters have resolved eukaryotic diversity into six major hypothetical groups. Yet relationships among these groups remain poorly understood because of saturation of sequence changes on the billion-year time-scale, possible rapid radiations of major lineages, phylogenetic artefacts and endosymbiotic or lateral gene transfer among eukaryotes. Estimating the divergence dates between the major eukaryote lineages using molecular analyses is even more difficult than phylogenetic estimation. Error in such analyses comes from a myriad of sources including: (i) calibration fossil dates, (ii) the assumed phylogenetic tree, (iii) the nucleotide or amino acid substitution model, (iv) substitution number (branch length) estimates, (v) the model of how rates of evolution change over the tree, (vi) error inherent in the time estimates for a given model and (vii) how multiple gene data are treated. By reanalysing datasets from recently published molecular clock studies, we show that when errors from these various sources are properly accounted for, the confidence intervals on inferred dates can be very large. Furthermore, estimated dates of divergence vary hugely depending on the methods used and their assumptions. Accurate dating of divergence times among the major eukaryote lineages will require a robust tree of eukaryotes, a much richer Proterozoic fossil record of microbial eukaryotes assignable to extant groups for calibration, more sophisticated relaxed molecular clock methods and many more genes sampled from the full diversity of microbial eukaryotes.     

New substitution models for rooting phylogenetic trees

The root of a phylogenetic tree is fundamental to its biological interpretation, but standard substitution models do not provide any information on its position. Here, we describe two recently developed models that relax the usual assumptions of stationarity and reversibility, thereby facilitating root inference without the need for an outgroup. We compare the performance of these models on a classic test case for phylogenetic methods, before considering two highly topical questions in evolutionary biology: the deep structure of the tree of life and the root of the archaeal radiation. We show that all three alignments contain meaningful rooting information that can be harnessed by these new models, thus complementing and extending previous work based on outgroup rooting. In particular, our analyses exclude the root of the tree of life from the eukaryotes or Archaea, placing it on the bacterial stem or within the Bacteria. They also exclude the root of the archaeal radiation from several major clades, consistent with analyses using other rooting methods. Overall, our results demonstrate the utility of non-reversible and non-stationary models for rooting phylogenetic trees, and identify areas where further progress can be made.     

The molecular signal for the adaptation to cold temperature during early life on Earth

Several lines of evidence such as the basal location of thermophilic lineages in large-scale phylogenetic trees and the ancestral sequence reconstruction of single enzymes or large protein concatenations support the conclusion that the ancestors of the bacterial and archaeal domains were thermophilic organisms which were adapted to hot environments during the early stages of the Earth. A parsimonious reasoning would therefore suggest that the last universal common ancestor (LUCA) was also thermophilic. Various authors have used branch-wise non-homogeneous evolutionary models that better capture the variation of molecular compositions among lineages to accurately reconstruct the ancestral G + C contents of ribosomal RNAs and the ancestral amino acid composition of highly conserved proteins. They confirmed the thermophilic nature of the ancestors of Bacteria and Archaea but concluded that LUCA, their last common ancestor, was a mesophilic organism having a moderate optimal growth temperature. In this letter, we investigate the unknown nature of the phylogenetic signal that informs ancestral sequence reconstruction to support this non-parsimonious scenario. We find that rate variation across sites of molecular sequences provides information at different time scales by recording the oldest adaptation to temperature in slow-evolving regions and subsequent adaptations in fast-evolving ones.     

Probabilistic phylogenetic inference with insertions and deletions

A fundamental task in sequence analysis is to calculate the probability of a multiple alignment given a phylogenetic tree relating the sequences and an evolutionary model describing how sequences change over time. However, the most widely used phylogenetic models only account for residue substitution events. We describe a probabilistic model of a multiple sequence alignment that accounts for insertion and deletion events in addition to substitutions, given a phylogenetic tree, using a rate matrix augmented by the gap character. Starting from a continuous Markov process, we construct a non-reversible generative (birth-death) evolutionary model for insertions and deletions. The model assumes that insertion and deletion events occur one residue at a time. We apply this model to phylogenetic tree inference by extending the program dnaml in phylip. Using standard benchmarking methods on simulated data and a new "concordance test" benchmark on real ribosomal RNA alignments, we show that the extended program dnamlepsilon improves accuracy relative to the usual approach of ignoring gaps, while retaining the computational efficiency of the Felsenstein peeling algorithm.     

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

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

A Bayesian compound stochastic process for modeling nonstationary and nonhomogeneous sequence evolution

Variations of nucleotidic composition affect phylogenetic inference conducted under stationary models of evolution. In particular, they may cause unrelated taxa sharing similar base composition to be grouped together in the resulting phylogeny. To address this problem, we developed a nonstationary and nonhomogeneous model accounting for compositional biases. Unlike previous nonstationary models, which are branchwise, that is, assume that base composition only changes at the nodes of the tree, in our model, the process of compositional drift is totally uncoupled from the speciation events. In addition, the total number of events of compositional drift distributed across the tree is directly inferred from the data. We implemented the method in a Bayesian framework, relying on Markov Chain Monte Carlo algorithms, and applied it to several nucleotidic data sets. In most cases, the stationarity assumption was rejected in favor of our nonstationary model. In addition, we show that our method is able to resolve a well-known artifact. By Bayes factor evaluation, we compared our model with 2 previously developed nonstationary models. We show that the coupling between speciations and compositional shifts inherent to branchwise models may lead to an overparameterization, resulting in a lesser fit. In some cases, this leads to incorrect conclusions, concerning the nature of the compositional biases. In contrast, our compound model more flexibly adapts its effective number of parameters to the data sets under investigation. Altogether, our results show that accounting for nonstationary sequence evolution may require more elaborate and more flexible models than those currently used.