Nucleotide substitution models and estimation of phylogeny

The nucleotide substitution matrix inferred from avian data sets using cytochrome b differs considerably from the models commonly used in phylogenetic analyses. To analyze the possible effects of this particular pattern of change in phylogeny estimation we performed a computer simulation in which we started with a real sequence and used the inferred model of change to produce a tree of 10 species. Maximum parsimony (MP), maximum likelihood (ML), and various distance methods were then used to recover the topology and the branch lengths. We used two kinds of data with varying levels of variation. In addition, we tested with the removal of third positions and different weighting schemes. At low levels of variation, MP was outstanding in recovering the topology (90% correct), while unweighted pair-group method, arithmetic average (UPGMA), regardless of distances used, was poor (40%). At the higher level, most methods had a chance of around 40%-58% of finding the true tree. However, in most cases, the trees found were only slightly wrong, with only one or a few branches misplaced. On the other hand, the use of a "wrong" model had serious effects on the estimation of branch lengths (distances). Although precision was high, accuracy was poor with most methods, giving branch lengths that were biased downward. When seeded with the true distance matrix, Fitch and NJ always found the true tree, while UPGMA frequently failed to do so. The effect of removing third positions was dramatic at low levels of variation, because only one MP program was able to find a true tree at all, albeit rarely, while none of the others ever did so. At higher levels, the situation was better, but still much worse than with the whole data set.     

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.      

Phylogenetic relationships of agaric fungi based on nuclear large subunit ribosomal DNA sequences

Phylogenetic relationships of mushrooms and their relatives within the order Agaricales were addressed by using nuclear large subunit ribosomal DNA sequences. Approximately 900 bases of the 5' end of the nucleus-encoded large subunit RNA gene were sequenced for 154 selected taxa representing most families within the Agaricales. Several phylogenetic methods were used, including weighted and equally weighted parsimony (MP), maximum likelihood (ML), and distance methods (NJ). The starting tree for branch swapping in the ML analyses was the tree with the highest ML score among previously produced MP and NJ trees. A high degree of consensus was observed between phylogenetic estimates obtained through MP and ML. NJ trees differed according to the distance model that was used; however, all NJ trees still supported most of the same terminal groupings as the MP and ML trees did. NJ trees were always significantly suboptimal when evaluated against the best MP and ML trees, by both parsimony and likelihood tests. Our analyses suggest that weighted MP and ML provide the best estimates of Agaricales phylogeny. Similar support was observed between bootstrapping and jackknifing methods for evaluation of tree robustness. Phylogenetic analyses revealed many groups of agaricoid fungi that are supported by moderate to high bootstrap or jackknife values or are consistent with morphology-based classification schemes. Analyses also support separate placement of the boletes and russules, which are basal to the main core group of gilled mushrooms (the Agaricineae of Singer). Examples of monophyletic groups include the families Amanitaceae, Coprinaceae (excluding Coprinus comatus and subfamily Panaeolideae), Agaricaceae (excluding the Cystodermateae), and Strophariaceae pro parte (Stropharia, Pholiota, and Hypholoma); the mycorrhizal species of Tricholoma (including Leucopaxillus, also mycorrhizal); Mycena and Resinomycena; Termitomyces, Podabrella, and Lyophyllum; and Pleurotus with Hohenbuehelia. Several groups revealed by these data to be nonmonophyletic include the families Tricholomataceae, Cortinariaceae, and Hygrophoraceae and the genera Clitocybe, Omphalina, and Marasmius. This study provides a framework for future systematics studies in the Agaricales and suggestions for analyzing large molecular data sets.     

Limitations of the evolutionary parsimony method of phylogenetic analysis [published erratum appears in Mol Biol Evol 1990 Mar;7(2):201]

Lake's evolutionary parsimony (EP) method of constructing a phylogenetic tree is primarily applied to four DNA sequences. In this method, three quantities--X, Y, and Z--that correspond to three possible unrooted trees are computed, and an invariance property of these quantities is used for choosing the best tree. However, Lake's method depends on a number of unrealistic assumptions. We therefore examined the theoretical basis of his method and reached the following conclusions: (1) When the rates of two transversional changes from a nucleotide are unequal, his invariance property breaks down. (2) Even if the rates of two transversional changes are equal, the invariance property requires some additional conditions. (3) When Kimura's two- parameter model of nucleotide substitution applies and the rate of nucleotide substitution varies greatly with branch, the EP method is generally better than the standard maximum-parsimony (MP) method in recovering the correct tree but is inferior to the neighbor-joining (NJ) and a few other distance matrix methods. (4) When the rate of nucleotide substitution is the same or nearly the same for all branches, the EP method is inferior to the MP method even if the proportion of transitional changes is high. (5) When Lake's assumptions fail, his chi2 test may identify an erroneous tree as the correct tree. This happens because the test is not for comparing different trees. (6) As long as a proper distance measure is used, the NJ method is better than the EP and MP methods whether there is a transition/transversion bias or whether there is variation in substitution rate among different nucleotide sites.      

Relative efficiencies of the maximum parsimony and distance-matrix methods in obtaining the correct phylogenetic tree

The relative efficiencies of the maximum parsimony (MP) and distance-matrix methods in obtaining the correct tree (topology) were studied by using computer simulation. The distance-matrix methods examined are the neighbor-joining, distance-Wagner, Tateno et al. modified Farris, Faith, and Li methods. In the computer simulation, six or eight DNA sequences were assumed to evolve following a given model tree, and the evolutionary changes of the sequences were followed. Both constant and varying rates of nucleotide substitution were considered. From the sequences thus obtained, phylogenetic trees were constructed using the six tree-making methods and compared with the model (true) tree. This process was repeated 300 times for each different set of parameters. The results obtained indicate that when the number of nucleotide substitutions per site is small and a relatively small number of nucleotides are used, the probability of obtaining the correct topology (P1) is generally lower in the MP method than in the distance-matrix methods. The P1 value for the MP method increases with increasing number of nucleotides but is still generally lower than the value for the NJ or DW method. Essentially the same conclusion was obtained whether or not the rate of nucleotide substitution was constant or whether or not a transition bias in nucleotide substitution existed. The relatively poor performance of the MP method for these cases is due to the fact that information from singular sites is not used in this method. The MP method also showed a relatively low P1 value when the model of varying rate of nucleotide substitution was used and the number of substitutions per site was large. However, the MP method often produced cases in which the correct tree was one of several equally parsimonious trees. When these cases were included in the class of "success," the MP method performed better than the other methods, provided that the number of nucleotide substitutions per site was small.     

The consistency of several phylogeny-inference methods under varying evolutionary rates.

A phylogenetic method is a consistent estimator of phylogeny if and only if it is guaranteed to give the correct tree, given that sufficient (possibly infinite) independent data are examined. The following methods are examined for consistency: UPGMA (unweighted pair-group method, averages), NJ (neighbor joining), MF (modified Farris), and P (parsimony). A two-parameter model of nucleotide sequence substitution is used, and the expected distribution of character states is calculated. Without perfect correction for superimposed substitutions, all four methods may be inconsistent if there is but one branch evolving at a faster rate than the other branches. Partial correction of observed distances improves the robustness of the NJ method to rate variation, and perfect correction makes the NJ method a consistent estimator for all combinations of rates that were examined. The sensitivity of all the methods to unequal rates varies over a wide range, so relative-rate tests are unlikely to be a reliable guide for accepting or rejecting phylogenies based on parsimony analysis.     

ImOSM: intermittent evolution and robustness of phylogenetic methods

Among the criteria to evaluate the performance of a phylogenetic method, robustness to model violation is of particular practical importance as complete a priori knowledge of evolutionary processes is typically unavailable. For studies of robustness in phylogenetic inference, a utility to add well-defined model violations to the simulated data would be helpful. We therefore introduce ImOSM, a tool to imbed intermittent evolution as model violation into an alignment. Intermittent evolution refers to extra substitutions occurring randomly on branches of a tree, thus changing alignment site patterns. This means that the extra substitutions are placed on the tree after the typical process of sequence evolution is completed. We then study the robustness of widely used phylogenetic methods: maximum likelihood (ML), maximum parsimony (MP), and a distance-based method (BIONJ) to various scenarios of model violation. Violation of rates across sites (RaS) heterogeneity and simultaneous violation of RaS and the transition/transversion ratio on two nonadjacent external branches hinder all the methods recovery of the true topology for a four-taxon tree. For an eight-taxon balanced tree, the violations cause each of the three methods to infer a different topology. Both ML and MP fail, whereas BIONJ, which calculates the distances based on the ML estimated parameters, reconstructs the true tree. Finally, we report that a test of model homogeneity and goodness of fit tests have enough power to detect such model violations. The outcome of the tests can help to actually gain confidence in the inferred trees. Therefore, we recommend using these tests in practical phylogenetic analyses.     

基于COI基因序列的九种真蝽属昆虫的分子系统学研究(半翅目:蝽科)

通过对真蝽属Pentatoma 9种昆虫线粒体COI基因约798bp的序列进行分子进化分析,并以同蝽科宽铗同蝽Acanthosoma labiduroides为外群,采用最大简约法、最大似然法和邻接法构建了分子系统树,来探讨真蝽属的系统发育关系.研究结果支持褐真蝽群P. semiannulata-group的划分,绿角真蝽Pentatoma viridicornuta应划归到褐真蝽群P. Semiannulata-group;红足真蝽群中的角肩真蝽P. angulata与红足真蝽P. rufipes遗传距离较小,它们是否为1个物种值得关注;真蝽属各群之间的系统发育关系以及是否可分为3个属值得进一步研究.     

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.     

Reanalysis of Murphy et al.'s data gives various mammalian phylogenies and suggests overcredibility of Bayesian trees

Murphy and colleagues reported that the mammalian phylogeny was resolved by Bayesian phylogenetics. However, the DNA sequences they used had many alignment gaps and undetermined nucleotide sites. We therefore reanalyzed their data by minimizing unshared nucleotide sites and retaining as many species as possible (13 species). In constructing phylogenetic trees, we used the Bayesian, maximum likelihood (ML), maximum parsimony (MP), and neighbor-joining (NJ) methods with different substitution models. These trees were constructed by using both protein and DNA sequences. The results showed that the posterior probabilities for Bayesian trees were generally much higher than the bootstrap values for ML, MP, and NJ trees. Two different Bayesian topologies for the same set of species were sometimes supported by high posterior probabilities, implying that two different topologies can be judged to be correct by Bayesian phylogenetics. This suggests that the posterior probability in Bayesian analysis can be excessively high as an indication of statistical confidence and therefore Murphy et al.'s tree, which largely depends on Bayesian posterior probability, may not be correct.     

Property and efficiency of the maximum likelihood method for molecular phylogeny

Summary The maximum likelihood (ML) method for constructing phylogenetic trees (both rooted and unrooted trees) from DNA sequence data was studied. Although there is some theoretical problem in the comparison of ML values conditional for each topology, it is possible to make a heuristic argument to justify the method. Based on this argument, a new algorithm for estimating the ML tree is presented. It is shown that under the assumption of a constant rate of evolution, the ML method and UPGMA always give the same rooted tree for the case of three operational taxonomic units (OTUs). This also seems to hold approximately for the case with four OTUs. When we consider unrooted trees with the assumption of a varying rate of nucleotide substitution, the efficiency of the ML method in obtaining the correct tree is similar to those of the maximum parsimony method and distance methods. The ML method was applied to Brown et al.'s data, and the tree topology obtained was the same as that found by the maximum parsimony method, but it was different from those obtained by distance methods.     

Statistical properties of bootstrap estimation of phylogenetic variability from nucleotide sequences: II. Four taxa without a molecular clock

Summary The statistical properties of sample estimation and bootstrap estimation of phylogenetic variability from a sample of nucleotide sequences were studied by considering model trees of three taxa with an outgroup. The cases of constant and varying rates of nucleotide substitution were compared. From sequences obtained by simulation, phylogenetic trees were constructed by using the maximum parsimony (MP) and neighbor joining (NJ) methods. The effectiveness and consistency of the MP method were studied in terms of proportions of informative sites. The results of simulation showed that bootstrap estimation of the confidence level for an inferred phylogeny can be used even under unequal rates of evolution if the rate differences are not large so that the MP method is not misleading. The condition under which the MP method becomes misleading (inconsistent) is more stringent for slowly evolving sequences than for rapidly evolving ones, and it also depends on the length of the internal branch. If the rate differences are large so that the MP method becomes consistently misleading, then bootstrap estimation will reinforce an erroneous conclusion on topology. Similar conclusions apply to the NJ method with uncorrected distances. The NJ method with corrected distances performs poorly when the sequence length is short but can avoid the inconsistency problem if the sequence length is long and if the distances can be estimated accurately.Offprint requests to: W.-H. Li     

切叶蚁亚科七属十二种的分子系统学研究

测定了切叶蚁亚科7属12种的线粒体CO1、CO2的部分基因及完整的tRNA_Leu基因DNA序列,对DNA序列进行了分析,对tRNA_Leu 基因进行了二级结构分析;根据DNA序列数据和氨基酸序列数据,以臭蚁亚科的Forelius chalybaeus作为外群,采用最大似然法(ML)、最大简约法(MP)、邻接法(NJ)、未加权组对算术平均法(UPGMA)构建分子系统树,通过自举检验,得到自举置信水平,以此检验该分子系统树的可靠性。研究结果显示,基于以上基因的分子系统分析与传统分类分析的结果基本一致,且在属级的一致性高于种级的一致性。     

The neighbor-joining method: a new method for reconstructing phylogenetic trees

A new method called the neighbor-joining method is proposed for reconstructing phylogenetic trees from evolutionary distance data. The principle of this method is to find pairs of operational taxonomic units (OTUs [= neighbors]) that minimize the total branch length at each stage of clustering of OTUs starting with a starlike tree. The branch lengths as well as the topology of a parsimonious tree can quickly be obtained by using this method. Using computer simulation, we studied the efficiency of this method in obtaining the correct unrooted tree in comparison with that of five other tree-making methods: the unweighted pair group method of analysis, Farris's method, Sattath and Tversky's method, Li's method, and Tateno et al.'s modified Farris method. The new, neighbor-joining method and Sattath and Tversky's method are shown to be generally better than the other methods.      

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。     

分子系统进化关系分析的一种新方法--贝叶斯法在硬蜱属中的应用

距离矩阵邻接法、最大简约法和最大似然法是重建生物系统关系的3种主要方法。普遍认为最大似然法在原理上优于前二种方法，但其计算复杂费时。由于现行计算机的能力尚达不到其要求而实用性差，特别是在处理大数据集样本(即大于25个分类单元)时，用此方法几乎不可能。新近提出的贝叶斯法(Bayesianmethod)既保留了最大似然法的基本原理，又引进了马尔科夫链的蒙特卡洛方法，并使计算时间大大缩短。本文用贝叶斯法对硬蜱属(Ixodes)19个种的线粒体16S rDNA片段进行了系统进化分析。从总体上看，分析结果与现有的基于形态学的分类体系基本吻合。但与现存的假说相反，莱姆病的主要宿主蓖籽硬蜱复合种组并非单系。通过比较贝叶斯法与其它三种方法的结果，我们认为贝叶斯法是一种系统进化分析的好方法，它既能根据分子进化的现有理论和各种模型用概率重建系统进化关系，又克服了最大似然法计算速度慢、不适用于大数据集样本的缺陷。贝叶斯法根据后验概率直观地表示系统进化关系的分析结果，不需要用自引导法进行检验。可以预料，贝叶斯法将会被广泛地应用到系统进化分析上[动物学报49(3)：380—388，2003]。     

Phylogeny and divergence of the pinnipeds (Carnivora: Mammalia) assessed using a multigene dataset

Background  

Phylogenetic comparative methods are often improved by complete phylogenies with meaningful branch lengths (e.g., divergence dates). This study presents a dated molecular supertree for all 34 world pinniped species derived from a weighted matrix representation with parsimony (MRP) supertree analysis of 50 gene trees, each determined under a maximum likelihood (ML) framework. Divergence times were determined by mapping the same sequence data (plus two additional genes) on to the supertree topology and calibrating the ML branch lengths against a range of fossil calibrations. We assessed the sensitivity of our supertree topology in two ways: 1) a second supertree with all mtDNA genes combined into a single source tree, and 2) likelihood-based supermatrix analyses. Divergence dates were also calculated using a Bayesian relaxed molecular clock with rate autocorrelation to test the sensitivity of our supertree results further.     

A comparison of phylogenetic network methods using computer simulation

Background

We present a series of simulation studies that explore the relative performance of several phylogenetic network approaches (statistical parsimony, split decomposition, union of maximum parsimony trees, neighbor-net, simulated history recombination upper bound, median-joining, reduced median joining and minimum spanning network) compared to standard tree approaches, (neighbor-joining and maximum parsimony) in the presence and absence of recombination.

Principal Findings

In the absence of recombination, all methods recovered the correct topology and branch lengths nearly all of the time when the substitution rate was low, except for minimum spanning networks, which did considerably worse. At a higher substitution rate, maximum parsimony and union of maximum parsimony trees were the most accurate. With recombination, the ability to infer the correct topology was halved for all methods and no method could accurately estimate branch lengths.

Conclusions

Our results highlight the need for more accurate phylogenetic network methods and the importance of detecting and accounting for recombination in phylogenetic studies. Furthermore, we provide useful information for choosing a network algorithm and a framework in which to evaluate improvements to existing methods and novel algorithms developed in the future.     

Phylogenetic analysis using parsimony and likelihood methods

The assumptions underlying the maximum-parsimony (MP) method of phylogenetic tree reconstruction were intuitively examined by studying the way the method works. Computer simulations were performed to corroborate the intuitive examination. Parsimony appears to involve very stringent assumptions concerning the process of sequence evolution, such as constancy of substitution rates between nucleotides, constancy of rates across nucleotide sites, and equal branch lengths in the tree. For practical data analysis, the requirement of equal branch lengths means similar substitution rates among lineages (the existence of an approximate molecular clock), relatively long interior branches, and also few species in the data. However, a small amount of evolution is neither a necessary nor a sufficient requirement of the method. The difficulties involved in the application of current statistical estimation theory to tree reconstruction were discussed, and it was suggested that the approach proposed by Felsenstein (1981,J. Mol. Evol. 17: 368–376) for topology estimation, as well as its many variations and extensions, differs fundamentally from the maximum likelihood estimation of a conventional statistical parameter. Evidence was presented showing that the Felsenstein approach does not share the asymptotic efficiency of the maximum likelihood estimator of a statistical parameter. Computer simulations were performed to study the probability that MP recovers the true tree under a hierarchy of models of nucleotide substitution; its performance relative to the likelihood method was especially noted. The results appeared to support the intuitive examination of the assumptions underlying MP. When a simple model of nucleotide substitution was assumed to generate data, the probability that MP recovers the true topology could be as high as, or even higher than, that for the likelihood method. When the assumed model became more complex and realistic, e.g., when substitution rates were allowed to differ between nucleotides or across sites, the probability that MP recovers the true topology, and especially its performance relative to that of the likelihood method, generally deteriorates. As the complexity of the process of nucleotide substitution in real sequences is well recognized, the likelihood method appears preferable to parsimony. However, the development of a statistical methodology for the efficient estimation of the tree topology remains a difficult open problem.     

Exploring among-site rate variation models in a maximum likelihood framework using empirical data: effects of model assumptions on estimates of topology,branch lengths,and bootstrap support

We have investigated the effects of different among-site rate variation models on the estimation of substitution model parameters, branch lengths, topology, and bootstrap proportions under minimum evolution (ME) and maximum likelihood (ML). Specifically, we examined equal rates, invariable sites, gamma-distributed rates, and site-specific rates (SSR) models, using mitochondrial DNA sequence data from three protein-coding genes and one tRNA gene from species of the New Zealand cicada genus Maoricicada. Estimates of topology were relatively insensitive to the substitution model used; however, estimates of bootstrap support, branch lengths, and R-matrices (underlying relative substitution rate matrix) were strongly influenced by the assumptions of the substitution model. We identified one situation where ME and ML tree building became inaccurate when implemented with an inappropriate among-site rate variation model. Despite the fact the SSR models often have a better fit to the data than do invariable sites and gamma rates models, SSR models have some serious weaknesses. First, SSR rate parameters are not comparable across data sets, unlike the proportion of invariable sites or the alpha shape parameter of the gamma distribution. Second, the extreme among-site rate variation within codon positions is problematic for SSR models, which explicitly assume rate homogeneity within each rate class. Third, the SSR models appear to give severe underestimates of R-matrices and branch lengths relative to invariable sites and gamma rates models in this example. We recommend performing phylogenetic analyses under a range of substitution models to test the effects of model assumptions not only on estimates of topology but also on estimates of branch length and nodal support.