Partitionfinder: combined selection of partitioning schemes and substitution models for phylogenetic analyses

In phylogenetic analyses of molecular sequence data, partitioning involves estimating independent models of molecular evolution for different sets of sites in a sequence alignment. Choosing an appropriate partitioning scheme is an important step in most analyses because it can affect the accuracy of phylogenetic reconstruction. Despite this, partitioning schemes are often chosen without explicit statistical justification. Here, we describe two new objective methods for the combined selection of best-fit partitioning schemes and nucleotide substitution models. These methods allow millions of partitioning schemes to be compared in realistic time frames and so permit the objective selection of partitioning schemes even for large multilocus DNA data sets. We demonstrate that these methods significantly outperform previous approaches, including both the ad hoc selection of partitioning schemes (e.g., partitioning by gene or codon position) and a recently proposed hierarchical clustering method. We have implemented these methods in an open-source program, PartitionFinder. This program allows users to select partitioning schemes and substitution models using a range of information-theoretic metrics (e.g., the Bayesian information criterion, akaike information criterion [AIC], and corrected AIC). We hope that PartitionFinder will encourage the objective selection of partitioning schemes and thus lead to improvements in phylogenetic analyses. PartitionFinder is written in Python and runs under Mac OSX 10.4 and above. The program, source code, and a detailed manual are freely available from www.robertlanfear.com/partitionfinder.     

Phylogenetic relationship among horseshoe crab species: effect of substitution models on phylogenetic analyses

The horseshoe crabs, known as living fossils, have maintained their morphology almost unchanged for the past 150 million years. The little morphological differentiation among horseshoe crab lineages has resulted in substantial controversy concerning the phylogenetic relationship among the extant species of horseshoe crabs, especially among the three species in the Indo-Pacific region. Previous studies suggest that the three species constitute a phylogenetically unresolvable trichotomy, the result of a cladogenetic process leading to the formation of all three Indo-Pacific species in a short geological time. Data from two mitochondrial genes (for 16S ribosomal rRNA and cytochrome oxidase subunit I) and one nuclear gene (for coagulogen) in the four species of horseshoe crabs and outgroup species were used in a phylogenetic analysis with various substitution models. All three genes yield the same tree topology, with Tachypleus-gigas and Carcinoscorpius-rotundicauda grouped together as a monophyletic taxon. This topology is significantly better than all the alternatives when evaluated with the RELL (resampling estimated log-likelihood) method.     

Estimation of rates-across-sites distributions in phylogenetic substitution models

Previous work has shown that it is often essential to account for the variation in rates at different sites in phylogenetic models in order to avoid phylogenetic artifacts such as long branch attraction. In most current models, the gamma distribution is used for the rates-across-sites distributions and is implemented as an equal-probability discrete gamma. In this article, we introduce discrete distribution estimates with large numbers of equally spaced rate categories allowing us to investigate the appropriateness of the gamma model. With large numbers of rate categories, these discrete estimates are flexible enough to approximate the shape of almost any distribution. Likelihood ratio statistical tests and a nonparametric bootstrap confidence-bound estimation procedure based on the discrete estimates are presented that can be used to test the fit of a parametric family. We applied the methodology to several different protein data sets, and found that although the gamma model often provides a good parametric model for this type of data, rate estimates from an equal-probability discrete gamma model with a small number of categories will tend to underestimate the largest rates. In cases when the gamma model assumption is in doubt, rate estimates coming from the discrete rate distribution estimate with a large number of rate categories provide a robust alternative to gamma estimates. An alternative implementation of the gamma distribution is proposed that, for equal numbers of rate categories, is computationally more efficient during optimization than the standard gamma implementation and can provide more accurate estimates of site rates.     

Testing substitution models within a phylogenetic tree

Phylogenetic tree reconstruction frequently assumes the homogeneity of the substitution process over the whole tree. To test this assumption statistically, we propose a test based on the sample covariance matrix of the set of substitution rate matrices estimated from pairwise sequence comparison. The sample covariance matrix is condensed into a one-dimensional test statistic Delta = sum ln(1 + delta(i)), where delta(i) are the eigenvalues of the sample covariance matrix. The test does not assume a specific mutational model. It analyses the variation in the estimated rate matrices. The distribution of this test statistic is determined by simulations based on the phylogeny estimated from the data. We study the power of the test under various scenarios and apply the test to X chromosome and mtDNA primate sequence data. Finally, we demonstrate how to include rate variation in the test.     

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.     

Rooting a phylogenetic tree with nonreversible substitution models

Background  

We compared two methods of rooting a phylogenetic tree: the stationary and the nonstationary substitution processes. These methods do not require an outgroup.     

Accurate estimation of substitution rates with neighbor-dependent models in a phylogenetic context

Most models and algorithms developed to perform statistical inference from DNA data make the assumption that substitution processes affecting distinct nucleotide sites are stochastically independent. This assumption ensures both mathematical and computational tractability but is in disagreement with observed data in many situations--one well-known example being CpG dinucleotide hypermutability in mammalian genomes. In this paper, we consider the class of RN95 + YpR substitution models, which allows neighbor-dependent effects--including CpG hypermutability--to be taken into account, through transitions between pyrimidine-purine dinucleotides. We show that it is possible to adapt inference methods originally developed under the assumption of independence between sites to RN95 + YpR models, using a mathematically rigorous framework provided by specific structural properties of this class of models. We assess how efficient this approach is at inferring the CpG hypermutability rate from aligned DNA sequences. The method is tested on simulated data and compared against several alternatives; the results suggest that it delivers a high degree of accuracy at a low computational cost. We then apply our method to an alignment of 10 DNA sequences from primate species. Model comparisons within the RN95 + YpR class show the importance of taking into account neighbor-dependent effects. An application of the method to the detection of hypomethylated islands is discussed.     

Comparison of models for nucleotide substitution used in maximum- likelihood phylogenetic estimation

Using real sequence data, we evaluate the adequacy of assumptions made in evolutionary models of nucleotide substitution and the effects that these assumptions have on estimation of evolutionary trees. Two aspects of the assumptions are evaluated. The first concerns the pattern of nucleotide substitution, including equilibrium base frequencies and the transition/transversion-rate ratio. The second concerns the variation of substitution rates over sites. The maximum-likelihood estimate of tree topology appears quite robust to both these aspects of the assumptions of the models, but evaluation of the reliability of the estimated tree by using simpler, less realistic models can be misleading. Branch lengths are underestimated when simpler models of substitution are used, but the underestimation caused by ignoring rate variation over nucleotide sites is much more serious. The goodness of fit of a model is reduced by ignoring spatial rate variation, but unrealistic assumptions about the pattern of nucleotide substitution can lead to an extraordinary reduction in the likelihood. It seems that evolutionary biologists can obtain accurate estimates of certain evolutionary parameters even with an incorrect phylogeny, while systematists cannot get the right tree with confidence even when a realistic, and more complex, model of evolution is assumed.      

An examination of phylogenetic models of substitution rate variation among lineages

Molecular evolutionary rates can show significant variation among lineages, complicating the task of estimating substitution rates and divergence times using phylogenetic methods. Accordingly, relaxed molecular clock models have been developed to accommodate such rate heterogeneity, but these often make the assumption of rate autocorrelation among lineages. In this paper, I examine the validity of this assumption.     

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.     

HIV-1 subtypes in Russia in 1987-1988

The subtyping of 350 isolates of HIV-1, isolated on the territories of 38 subjects of the Russian Federation, was carried out. The analysis was made by the method of the comparative heteroduplex mobility assay, as well as by the determination of the sequence of genes env [correction of ens] (gp 120) and gag (p17-p24). The study revealed that more than 50% of all cases of HIV-1 infection were caused by closely related variants of subtype A virus. The number of cases of HIV-1 infection caused by recombinant virus A/B was not less than 25%. The total number of cases caused by viruses of subtypes C, D, E, F and H was not more than 5%.     

Genetic analysis of HIV-1 subtypes in Nairobi, Kenya

Background

Genetic analysis of a viral infection helps in following its spread in a given population, in tracking the routes of infection and, where applicable, in vaccine design. Additionally, sequence analysis of the viral genome provides information about patterns of genetic divergence that may have occurred during viral evolution.

Objective

In this study we have analyzed the subtypes of Human Immunodeficiency Virus -1 (HIV-1) circulating in a diverse sample population of Nairobi, Kenya.

Methodology

69 blood samples were collected from a diverse subject population attending the Aga Khan University Hospital in Nairobi, Kenya. Total DNA was extracted from peripheral blood mononuclear cells (PBMCs), and used in a Polymerase Chain Reaction (PCR) to amplify the HIV gag gene. The PCR amplimers were partially sequenced, and alignment and phylogenetic analysis of these sequences was performed using the Los Alamos HIV Database.

Results

Blood samples from 69 HIV-1 infected subjects from varying ethnic backgrounds were analyzed. Sequence alignment and phylogenetic analysis showed 39 isolates to be subtype A, 13 subtype D, 7 subtype C, 3 subtype AD and CRF01_AE, 2 subtype G and 1 subtype AC and 1 AG. Deeper phylogenetic analysis revealed HIV subtype A sequences to be highly divergent as compared to subtypes D and C.

Conclusion

Our analysis indicates that HIV-1 subtypes in the Nairobi province of Kenya are dominated by a genetically diverse clade A. Additionally, the prevalence of highly divergent, complex subtypes, intersubtypes, and the recombinant forms indicates viral mixing in Kenyan population, possibly as a result of dual infections.     

Efficiencies of maximum likelihood methods of phylogenetic inferences when different substitution models are used

Choice of a substitution model is a crucial step in the maximum likelihood (ML) method of phylogenetic inference, and investigators tend to prefer complex mathematical models to simple ones. However, when complex models with many parameters are used, the extent of noise in statistical inferences increases, and thus complex models may not produce the true topology with a higher probability than simple ones. This problem was studied using computer simulation. When the number of nucleotides used was relatively large (1000 bp), the HKY+Gamma model showed smaller d(T) topological distance between the inferred and the true trees) than the JC and Kimura models. In the cases of shorter sequences (300 bp) simpler model and search algorithm such as JC model and SA+NNI search were found to be as efficient as more complicated searches and models in terms of topological distances, although the topologies obtained under HKY+Gamma model had the highest likelihood values. The performance of relatively simple search algorithm SA+NNI was found to be essentially the same as that of more extensive SA+TBR search under all models studied. Similarly to the conclusions reached by Takahashi and Nei [Mol. Biol. Evol. 17 (2000) 1251], our results indicate that simple models can be as efficient as complex models, and that use of complex models does not necessarily give more reliable trees compared with simple models.     

The distribution of HIV-1 subtypes in Fukuoka, Japan.

To determine the incidence of human immunodeficiency virus type-1 (HIV-1) subtypes in Fukuoka, Japan, viruses from 41 HIV-1 infected individuals were subtyped. Subtyping by V3-loop enzyme-linked immunosorbent assay (ELISA) showed 31 of the 41 subjects as subtype B (MN type), one as subtype A, one as subtype C, and eight untypable. The subject infected with subtype C was identified as a foreigner; the subtype A subject was Japanese. A phylogenetic analysis of nucleic acid sequences from the env C2-V3 region was also conducted. Genetic subtyping was successful for 25 samples: 23 samples were determined as subtype B, one subtype A and one subtype E. One of the individuals infected with subtype B, as well as the subtype A and subtype E subjects, were not Japanese. This study indicated that subtype B (USA and European type) is still dominant among HIV-1 infections in Fukuoka. Further, no Japanese were subtype E positive, which is increasing in the Kanto region. It is notable, however, that subtype A and subtype C infections, which are rare in Japan, were found in Fukuoka, located far from the metropolitan area of Tokyo.     

RAxML-VI-HPC: maximum likelihood-based phylogenetic analyses with thousands of taxa and mixed models

RAxML-VI-HPC (randomized axelerated maximum likelihood for high performance computing) is a sequential and parallel program for inference of large phylogenies with maximum likelihood (ML). Low-level technical optimizations, a modification of the search algorithm, and the use of the GTR+CAT approximation as replacement for GTR+Gamma yield a program that is between 2.7 and 52 times faster than the previous version of RAxML. A large-scale performance comparison with GARLI, PHYML, IQPNNI and MrBayes on real data containing 1000 up to 6722 taxa shows that RAxML requires at least 5.6 times less main memory and yields better trees in similar times than the best competing program (GARLI) on datasets up to 2500 taxa. On datasets > or =4000 taxa it also runs 2-3 times faster than GARLI. RAxML has been parallelized with MPI to conduct parallel multiple bootstraps and inferences on distinct starting trees. The program has been used to compute ML trees on two of the largest alignments to date containing 25,057 (1463 bp) and 2182 (51,089 bp) taxa, respectively. AVAILABILITY: icwww.epfl.ch/~stamatak     

Frequentist properties of Bayesian posterior probabilities of phylogenetic trees under simple and complex substitution models

What does the posterior probability of a phylogenetic tree mean?This simulation study shows that Bayesian posterior probabilities have the meaning that is typically ascribed to them; the posterior probability of a tree is the probability that the tree is correct, assuming that the model is correct. At the same time, the Bayesian method can be sensitive to model misspecification, and the sensitivity of the Bayesian method appears to be greater than the sensitivity of the nonparametric bootstrap method (using maximum likelihood to estimate trees). Although the estimates of phylogeny obtained by use of the method of maximum likelihood or the Bayesian method are likely to be similar, the assessment of the uncertainty of inferred trees via either bootstrapping (for maximum likelihood estimates) or posterior probabilities (for Bayesian estimates) is not likely to be the same. We suggest that the Bayesian method be implemented with the most complex models of those currently available, as this should reduce the chance that the method will concentrate too much probability on too few trees.     

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.