Assessment of protein distance measures and tree-building methods for phylogenetic tree reconstruction

Distance-based methods are popular for reconstructing evolutionary trees of protein sequences, mainly because of their speed and generality. A number of variants of the classical neighbor-joining (NJ) algorithm have been proposed, as well as a number of methods to estimate protein distances. We here present a large-scale assessment of performance in reconstructing the correct tree topology for the most popular algorithms. The programs BIONJ, FastME, Weighbor, and standard NJ were run using 12 distance estimators, producing 48 tree-building/distance estimation method combinations. These were evaluated on a test set based on real trees taken from 100 Pfam families. Each tree was used to generate multiple sequence alignments with the ROSE program using three evolutionary models. The accuracy of each method was analyzed as a function of both sequence divergence and location in the tree. We found that BIONJ produced the overall best results, although the average accuracy differed little between the tree-building methods (normally less than 1%). A noticeable trend was that FastME performed poorer than the rest on long branches. Weighbor was several orders of magnitude slower than the other programs. Larger differences were observed when using different distance estimators. Protein-adapted Jukes-Cantor and Kimura distance correction produced clearly poorer results than the other methods, even worse than uncorrected distances. We also assessed the recently developed Scoredist measure, which performed equally well as more complex methods.     

Efficient biased estimation of evolutionary distances when substitution rates vary across sites

This paper deals with phylogenetic inference when the variability of substitution rates across sites (VRAS) is modeled by a gamma distribution. We show that underestimating VRAS, which results in underestimates for the evolutionary distances between sequences, usually improves the topological accuracy of phylogenetic tree inference by distance-based methods, especially when the molecular clock holds. We propose a method to estimate the gamma shape parameter value which is most suited for tree topology inference, given the sequences at hand. This method is based on the pairwise evolutionary distances between sequences and allows one to reconstruct the phylogeny of a high number of taxa (>1,000). Simulation results show that the topological accuracy is highly improved when using the gamma shape parameter value given by our method, compared with the true (unknown) value which was used to generate the data. Furthermore, when VRAS is high, the topological accuracy of our distance-based method is better than that of a maximum likelihood approach. Finally, a data set of Maoricicada species sequences is analyzed, which confirms the advantage of our method.     

拓扑树间的通经拓扑距离

给出了一种新的系统树间的拓扑距离,使用NJ,MP,UPGMA等3种方法对13种动物的线粒体中14个基因（含组合的）DNA序列数据进行系统树的构建,利用分割拓扑距离和本文给出的通经拓扑距离对这14种系统树这间及其与真树进行比较。结果显示,NJ法对获得已知树的有效率最高,MP法次之,UPGMA法最低。这14种DNA序列所构建的系统树与已知树的拓扑距离基本上是随其DNA序列长度增加而减小,但两者的相关系数并未达到显著水平,分割拓扑距离在总体上可反映树间的拓扑结构差异,但其测度精确度比通经拓扑距离要低。     

Stochastic errors vs. modeling errors in distance based phylogenetic reconstructions

ABSTRACT: BACKGROUND: Distance-based phylogenetic reconstruction methods use evolutionary distances between species in order to reconstruct the phylogenetic tree spanning them. There are many different methods for estimating distances from sequence data. These methods assume different substitution models and have different statistical properties. Since the true substitution model is typically unknown, it is important to consider the effect of model misspecification on the performance of a distance estimation method. RESULTS: This paper continues the line of research which attempts to adjust to each given set of input sequences a distance function which maximizes the expected topological accuracy of the reconstructed tree. We focus here on the effect of systematic error caused by assuming an inadequate model, but consider also the stochastic error caused by using short sequences. We introduce a theoretical framework for analyzing both sources of error based on the notion of deviation from additivity, which quantifies the contribution of model misspecification to the estimation error. We demonstrate this framework by studying the behavior of the Jukes-Cantor distance function when applied to data generated according to Kimura's two-parameter model with a transition-transversion bias. We provide both a theoretical derivation for this case, and a detailed simulation study on quartet trees. CONCLUSIONS: We demonstrate both analytically and experimentally that by deliberately assuming an oversimplified evolutionary model, it is possible to increase the topological accuracy of reconstruction. Our theoretical framework provides new insights into the mechanisms that enables statistically inconsistent reconstruction methods to outperform consistent methods.     

An approach of orthology detection from homologous sequences under minimum evolution

In the field of phylogenetics and comparative genomics, it is important to establish orthologous relationships when comparing homologous sequences. Due to the slight sequence dissimilarity between orthologs and paralogs, it is prone to regarding paralogs as orthologs. For this reason, several methods based on evolutionary distance, phylogeny and BLAST have tried to detect orthologs with more precision. Depending on their algorithmic implementations, each of these methods sometimes has increased false negative or false positive rates. Here, we developed a novel algorithm for orthology detection that uses a distance method based on the phylogenetic criterion of minimum evolution. Our algorithm assumes that sets of sequences exhibiting orthologous relationships are evolutionarily less costly than sets that include one or more paralogous relationships. Calculation of evolutionary cost requires the reconstruction of a neighbor-joining (NJ) tree, but calculations are unaffected by the topology of any given NJ tree. Unlike tree reconciliation, our algorithm appears free from the problem of incorrect topologies of species and gene trees. The reliability of the algorithm was tested in a comparative analysis with two other orthology detection methods using 95 manually curated KOG datasets and 21 experimentally verified EXProt datasets. Sensitivity and specificity estimates indicate that the concept of minimum evolution could be valuable for the detection of orthologs.     

Relative efficiencies of the maximum-parsimony and distance-matrix methods of phylogeny construction for restriction data.

The relative efficiencies of the maximum-parsimony (MP), UPGMA, and neighbor-joining (NJ) methods in obtaining the correct tree (topology) for restriction-site and restriction-fragment data were studied by computer simulation. In this simulation, six DNA sequences of 16,000 nucleotides were assumed to evolve following a given model tree. The recognition sequences of 20 different six-base restriction enzymes were used to identify the restriction sites of the DNA sequences generated. The restriction-site data and restriction-fragment data thus obtained were used to reconstruct a phylogenetic tree, and the tree obtained was compared with the model tree. This process was repeated 300 times. The results obtained indicate that when the rate of nucleotide substitution is constant the probability of obtaining the correct tree (Pc) is generally higher in the NJ method than in the MP method. However, if we use the average topological deviation from the model tree (dT) as the criterion of comparison, the NJ and MP methods are nearly equally efficient. When the rate of nucleotide substitution varies with evolutionary lineage, the NJ method is better than the MP method, whether Pc or dT is used as the criterion of comparison. With 500 nucleotides and when the number of nucleotide substitutions per site was very small, restriction-site data were, contrary to our expectation, more useful than sequence data. Restriction-fragment data were less useful than restriction-site data, except when the sequence divergence was very small. UPGMA seems to be useful only when the rate of nucleotide substitution is constant and sequence divergence is high.     

Efficiency of the Neighbor-Joining Method in Reconstructing Deep and Shallow Evolutionary Relationships in Large Phylogenies

The neighbor-joining (NJ) method is widely used in reconstructing large phylogenies because of its computational speed and the high accuracy in phylogenetic inference as revealed in computer simulation studies. However, most computer simulation studies have quantified the overall performance of the NJ method in terms of the percentage of branches inferred correctly or the percentage of replications in which the correct tree is recovered. We have examined other aspects of its performance, such as the relative efficiency in correctly reconstructing shallow (close to the external branches of the tree) and deep branches in large phylogenies; the contribution of zero-length branches to topological errors in the inferred trees; and the influence of increasing the tree size (number of sequences), evolutionary rate, and sequence length on the efficiency of the NJ method. Results show that the correct reconstruction of deep branches is no more difficult than that of shallower branches. The presence of zero-length branches in realized trees contributes significantly to the overall error observed in the NJ tree, especially in large phylogenies or slowly evolving genes. Furthermore, the tree size does not influence the efficiency of NJ in reconstructing shallow and deep branches in our simulation study, in which the evolutionary process is assumed to be homogeneous in all lineages. Received: 7 March 2000 / Accepted: 2 August 2000     

Phylogenetic Inference with Weighted Codon Evolutionary Distances

We develop a new approach to estimate a matrix of pairwise evolutionary distances from a codon-based alignment based on a codon evolutionary model. The method first computes a standard distance matrix for each of the three codon positions. Then these three distance matrices are weighted according to an estimate of the global evolutionary rate of each codon position and averaged into a unique distance matrix. Using a large set of both real and simulated codon-based alignments of nucleotide sequences, we show that this approach leads to distance matrices that have a significantly better treelikeness compared to those obtained by standard nucleotide evolutionary distances. We also propose an alternative weighting to eliminate the part of the noise often associated with some codon positions, particularly the third position, which is known to induce a fast evolutionary rate. Simulation results show that fast distance-based tree reconstruction algorithms on distance matrices based on this codon position weighting can lead to phylogenetic trees that are at least as accurate as, if not better, than those inferred by maximum likelihood. Finally, a well-known multigene dataset composed of eight yeast species and 106 codon-based alignments is reanalyzed and shows that our codon evolutionary distances allow building a phylogenetic tree which is similar to those obtained by non-distance-based methods (e.g., maximum parsimony and maximum likelihood) and also significantly improved compared to standard nucleotide evolutionary distance estimates.     

Performance comparison between k-tuple distance and four model-based distances in phylogenetic tree reconstruction

Phylogenetic tree reconstruction requires construction of a multiple sequence alignment (MSA) from sequences. Computationally, it is difficult to achieve an optimal MSA for many sequences. Moreover, even if an optimal MSA is obtained, it may not be the true MSA that reflects the evolutionary history of the underlying sequences. Therefore, errors can be introduced during MSA construction which in turn affects the subsequent phylogenetic tree construction. In order to circumvent this issue, we extend the application of the k-tuple distance to phylogenetic tree reconstruction. The k-tuple distance between two sequences is the sum of the differences in frequency, over all possible tuples of length k, between the sequences and can be estimated without MSAs. It has been traditionally used to build a fast ‘guide tree’ to assist the construction of MSAs. Using the 1470 simulated sets of sequences generated under different evolutionary scenarios, the neighbor-joining trees and BioNJ trees, we compared the performance of the k-tuple distance with four commonly used distance estimators including Jukes–Cantor, Kimura, F84 and Tamura–Nei. These four distance estimators fall into the category of model-based distance estimators, as each of them takes account of a specific substitution model in order to compute the distance between a pair of already aligned sequences. Results show that trees constructed from the k-tuple distance are more accurate than those from other distances most time; when the divergence between underlying sequences is high, the tree accuracy could be twice or higher using the k-tuple distance than other estimators. Furthermore, as the k-tuple distance voids the need for constructing an MSA, it can save tremendous amount of time for phylogenetic tree reconstructions when the data include a large number of sequences.     

Phylogeny reconstruction: increasing the accuracy of pairwise distance estimation using Bayesian inference of evolutionary rates

Distance-based methods for phylogeny reconstruction are the fastest and easiest to use, and their popularity is accordingly high. They are also the only known methods that can cope with huge datasets of thousands of sequences. These methods rely on evolutionary distance estimation and are sensitive to errors in such estimations. In this study, a novel Bayesian method for estimation of evolutionary distances is developed. The proposed method enables the use of a sophisticated evolutionary model that better accounts for among-site rate variation (ASRV), thereby improving the accuracy of distance estimation. Rate variations are estimated within a Bayesian framework by extracting information from the entire dataset of sequences, unlike standard methods that can only use one pair of sequences at a time. We compare the accuracy of a cascade of distance estimation methods, starting from commonly used methods and moving towards the more sophisticated novel method. Simulation studies show significant improvements in the accuracy of distance estimation by the novel method over the commonly used ones. We demonstrate the effect of the improved accuracy on tree reconstruction using both real and simulated protein sequence alignments. An implementation of this method is available as part of the SEMPHY package.     

Theoretical foundation of the balanced minimum evolution method of phylogenetic inference and its relationship to weighted least-squares tree fitting

Due to its speed, the distance approach remains the best hope for building phylogenies on very large sets of taxa. Recently (R. Desper and O. Gascuel, J. Comp. Biol. 9:687-705, 2002), we introduced a new "balanced" minimum evolution (BME) principle, based on a branch length estimation scheme of Y. Pauplin (J. Mol. Evol. 51:41-47, 2000). Initial simulations suggested that FASTME, our program implementing the BME principle, was more accurate than or equivalent to all other distance methods we tested, with running time significantly faster than Neighbor-Joining (NJ). This article further explores the properties of the BME principle, and it explains and illustrates its impressive topological accuracy. We prove that the BME principle is a special case of the weighted least-squares approach, with biologically meaningful variances of the distance estimates. We show that the BME principle is statistically consistent. We demonstrate that FASTME only produces trees with positive branch lengths, a feature that separates this approach from NJ (and related methods) that may produce trees with branches with biologically meaningless negative lengths. Finally, we consider a large simulated data set, with 5,000 100-taxon trees generated by the Aldous beta-splitting distribution encompassing a range of distributions from Yule-Harding to uniform, and using a covarion-like model of sequence evolution. FASTME produces trees faster than NJ, and much faster than WEIGHBOR and the weighted least-squares implementation of PAUP*. Moreover, FASTME trees are consistently more accurate at all settings, ranging from Yule-Harding to uniform distributions, and all ranges of maximum pairwise divergence and departure from molecular clock. Interestingly, the covarion parameter has little effect on the tree quality for any of the algorithms. FASTME is freely available on the web.     

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.     

Topology improves phylogenetic motif functional site predictions

Prediction of protein functional sites from sequence-derived data remains an open bioinformatics problem. We have developed a phylogenetic motif (PM) functional site prediction approach that identifies functional sites from alignment fragments that parallel the evolutionary patterns of the family. In our approach, PMs are identified by comparing tree topologies of each alignment fragment to that of the complete phylogeny. Herein, we bypass the phylogenetic reconstruction step and identify PMs directly from distance matrix comparisons. In order to optimize the new algorithm, we consider three different distance matrices and 13 different matrix similarity scores. We assess the performance of the various approaches on a structurally nonredundant data set that includes three types of functional site definitions. Without exception, the predictive power of the original approach outperforms the distance matrix variants. While the distance matrix methods fail to improve upon the original approach, our results are important because they clearly demonstrate that the improved predictive power is based on the topological comparisons. Meaning that phylogenetic trees are a straightforward, yet powerful way to improve functional site prediction accuracy. While complementary studies have shown that topology improves predictions of protein-protein interactions, this report represents the first demonstration that trees improve functional site predictions as well.     

Inferring species phylogenies from multiple genes: concatenated sequence tree versus consensus gene tree

Phylogenetic trees from multiple genes can be obtained in two fundamentally different ways. In one, gene sequences are concatenated into a super-gene alignment, which is then analyzed to generate the species tree. In the other, phylogenies are inferred separately from each gene, and a consensus of these gene phylogenies is used to represent the species tree. Here, we have compared these two approaches by means of computer simulation, using 448 parameter sets, including evolutionary rate, sequence length, base composition, and transition/transversion rate bias. In these simulations, we emphasized a worst-case scenario analysis in which 100 replicate datasets for each evolutionary parameter set (gene) were generated, and the replicate dataset that produced a tree topology showing the largest number of phylogenetic errors was selected to represent that parameter set. Both randomly selected and worst-case replicates were utilized to compare the consensus and concatenation approaches primarily using the neighbor-joining (NJ) method. We find that the concatenation approach yields more accurate trees, even when the sequences concatenated have evolved with very different substitution patterns and no attempts are made to accommodate these differences while inferring phylogenies. These results appear to hold true for parsimony and likelihood methods as well. The concatenation approach shows >95% accuracy with only 10 genes. However, this gain in accuracy is sometimes accompanied by reinforcement of certain systematic biases, resulting in spuriously high bootstrap support for incorrect partitions, whether we employ site, gene, or a combined bootstrap resampling approach. Therefore, it will be prudent to report the number of individual genes supporting an inferred clade in the concatenated sequence tree, in addition to the bootstrap support.     

When is it safe to use an oversimplified substitution model in tree- making?

The choice of an "optimal" mathematical model for computing evolutionary distances from real sequences is not currently supported by easy-to-use software applicable to large data sets, and an investigator frequently selects one of the simplest models available. Here we study properties of the observed proportion of differences (p- distance) between sequences as an estimator of evolutionary distance for tree-making. We show that p-distances allow for consistent tree- making with any of the popular methods working with evolutionary distances if evolution of sequences obeys a "molecular clock" (more precisely, if it follows a stationary time-reversible Markov model of nucleotide substitution). Next, we show that p-distances seem to be efficient in recovering the correct tree topology under a "molecular clock," but produce "statistically supported" wrong trees when substitutions rates vary among evolutionary lineages. Finally, we outline a practical approach for selecting an "optimal" model of nucleotide substitution in a real data analysis, and obtain a crude estimate of a "prior" distribution of the expected tree branch lengths under the Jukes-Cantor model. We conclude that the use of a model that is obviously oversimplified is inadvisable unless it is justified by a preliminary analysis of the real sequences.      

Towards optimal distance functions for stochastic substitution models

Distance based reconstruction methods of phylogenetic trees consist of two independent parts: first, inter-species distances are inferred assuming some stochastic model of sequence evolution; then the inferred distances are used to construct a tree. In this paper we concentrate on the task of inter-species distance estimation. Specifically, we characterize the family of valid distance functions for the assumed substitution model and show that deliberate selection of distance function significantly improves the accuracy of distance estimates and, consequently, also improves the accuracy of the reconstructed tree.Our contribution consists of three parts: first, we present a general framework for constructing families of additive distance functions for stochastic evolutionary models. Then, we present a method for selecting (near) optimal distance functions, and we conclude by presenting simulation results which support our theoretical analysis.     

Efficiencies of different genes and different tree-building methods in recovering a known vertebrate phylogeny

The relative efficiencies of different protein-coding genes of the mitochondrial genome and different tree-building methods in recovering a known vertebrate phylogeny (two whale species, cow, rat, mouse, opossum, chicken, frog, and three bony fish species) was evaluated. The tree-building methods examined were the neighbor joining (NJ), minimum evolution (ME), maximum parsimony (MP), and maximum likelihood (ML), and both nucleotide sequences and deduced amino acid sequences were analyzed. Generally speaking, amino acid sequences were better than nucleotide sequences in obtaining the true tree (topology) or trees close to the true tree. However, when only first and second codon positions data were used, nucleotide sequences produced reasonably good trees. Among the 13 genes examined, Nd5 produced the true tree in all tree-building methods or algorithms for both amino acid and nucleotide sequence data. Genes Cytb and Nd4 also produced the correct tree in most tree-building algorithms when amino acid sequence data were used. By contrast, Co2, Nd1, and Nd41 showed a poor performance. In general, large genes produced better results, and when the entire set of genes was used, all tree-building methods generated the true tree. In each tree-building method, several distance measures or algorithms were used, but all these distance measures or algorithms produced essentially the same results. The ME method, in which many different topologies are examined, was no better than the NJ method, which generates a single final tree. Similarly, an ML method, in which many topologies are examined, was no better than the ML star decomposition algorithm that generates a single final tree. In ML the best substitution model chosen by using the Akaike information criterion produced no better results than simpler substitution models. These results question the utility of the currently used optimization principles in phylogenetic construction. Relatively simple methods such as the NJ and ML star decomposition algorithms seem to produce as good results as those obtained by more sophisticated methods. The efficiencies of the NJ, ME, MP, and ML methods in obtaining the correct tree were nearly the same when amino acid sequence data were used. The most important factor in constructing reliable phylogenetic trees seems to be the number of amino acids or nucleotides used.      

THE ACCURACY OF PHYLOGENETIC ESTIMATION USING THE NEIGHBOR-JOINING METHOD

We studied the factors affecting the accuracy of the neighbor-joining (NJ) method for estimating phylogenies by simulating character change under different evolutionary models applied to twenty different 8-OTU tree topologies that varied widely with respect to tree imbalance and stemminess. The models incorporated three evolutionary rates—constant, varying among lineages, varying among characters—and three evolutionary contexts concerning patterns of character change relative to speciation events—phyletic, speciational, and punctuational. All combinations of the rate and context models were studied. In addition, three different absolute rates of change were investigated. To measure the accuracy, the strict consensus index was computed between the estimated tree and the tree topology along which the data had been generated. The results were analyzed by analysis of variance and compared to a previous study that evaluated UPGMA clustering and maximum parsimony (MP) as phylogenetic estimation techniques. We found evolutionary context and tree imbalance to be the most important factors affecting the accuracy of the NJ method. NJ was more accurate than UPGMA or MP in terms of the average strict consensus index over all treatments. However, no one method was more accurate than the other two for all combinations of treatments. Higher absolute rate of change generally resulted in higher accuracy for all three methods.     

Increasing the efficiency of searches for the maximum likelihood tree in a phylogenetic analysis of up to 150 nucleotide sequences

Even when the maximum likelihood (ML) tree is a better estimate of the true phylogenetic tree than those produced by other methods, the result of a poor ML search may be no better than that of a more thorough search under some faster criterion. The ability to find the globally optimal ML tree is therefore important. Here, I compare a range of heuristic search strategies (and their associated computer programs) in terms of their success at locating the ML tree for 20 empirical data sets with 14 to 158 sequences and 411 to 120,762 aligned nucleotides. Three distinct topics are discussed: the success of the search strategies in relation to certain features of the data, the generation of starting trees for the search, and the exploration of multiple islands of trees. As a starting tree, there was little difference among the neighbor-joining tree based on absolute differences (including the BioNJ tree), the stepwise-addition parsimony tree (with or without nearest-neighbor-interchange (NNI) branch swapping), and the stepwise-addition ML tree. The latter produced the best ML score on average but was orders of magnitude slower than the alternatives. The BioNJ tree was second best on average. As search strategies, star decomposition and quartet puzzling were the slowest and produced the worst ML scores. The DPRml, IQPNNI, MultiPhyl, PhyML, PhyNav, and TreeFinder programs with default options produced qualitatively similar results, each locating a single tree that tended to be in an NNI suboptimum (rather than the global optimum) when the data set had low phylogenetic information. For such data sets, there were multiple tree islands with very similar ML scores. The likelihood surface only became relatively simple for data sets that contained approximately 500 aligned nucleotides for 50 sequences and 3,000 nucleotides for 100 sequences. The RAxML and GARLI programs allowed multiple islands to be explored easily, but both programs also tended to find NNI suboptima. A newly developed version of the likelihood ratchet using PAUP* successfully found the peaks of multiple islands, but its speed needs to be improved.     

重建系统演化树的一种新方法--试错法

重建系统演化树是进化研究的一个极为重要的方面。系统树的构建依赖于一定的方法和数据。在分子系统演化研究中,所使用的数据大多是ＤＮＡ序列、氨基酸序列和分子标记。而就构树方法来说,ＮＪ法、ＭＬ法和ＭＰ法是三种最为普遍使用的方法。本文给出了一种新的建树方法,即试错法。该方法不但具有与ＮＪ法一样好的建树效果,而且不存在难以解释的负枝长问题。