Majority-rule supertrees

Most supertree methods proposed to date are essentially ad hoc, rather than designed with particular properties in mind. Although the supertree problem remains difficult, one promising avenue is to develop from better understood consensus methods to the more general supertree setting. Here, we generalize the widely used majority-rule consensus method to the supertree setting. The majority-rule consensus tree is the strict consensus of the median trees under the symmetric-difference metric, so we can generalize the consensus method by generalizing this metric to trees with differing leaf sets. There are two different natural generalizations, based on pruning or grafting leaves to produce comparable trees, and these two generalizations produce two different, but related, majority-rule supertree methods.     

Summarizing a posterior distribution of trees using agreement subtrees

Bayesian inference of phylogeny is unique among phylogenetic reconstruction methods in that it produces a posterior distribution of trees rather than a point estimate of the best tree. The most common way to summarize this distribution is to report the majority-rule consensus tree annotated with the marginal posterior probabilities of each partition. Reporting a single tree discards information contained in the full underlying distribution and reduces the Bayesian analysis to simply another method for finding a point estimate of the tree. Even when a point estimate of the phylogeny is desired, the majority-rule consensus tree is only one possible method, and there may be others that are more appropriate for the given data set and application. We present a method for summarizing the distribution of trees that is based on identifying agreement subtrees that are frequently present in the posterior distribution. This method provides fully resolved binary trees for subsets of taxa with high marginal posterior probability on the entire tree and includes additional information about the spread of the distribution.     

Majority-rule reduced consensus trees and their use in bootstrapping

Bootstrap analyses are usually summarized with majority-rule component consensus trees. This consensus method is based on replicated components and, like all component consensus methods, it is insensitive to other kinds of agreement between trees. Recently developed reduced consensus methods can be used to summarize much additional agreement on hypothesised phylogenetic relationships among multiple trees. The new methods are "strict" in the sense that they require agreement among all the trees being compared for any relationships to be represented in a consensus tree. Majority-rule reduced consensus methods are described and their use in bootstrap analyses is illustrated with a hypothetical and a real example. The new methods provide summaries of the bootstrap proportions of all n-taxon statements/partitions and facilitate the identification of hypotheses of relationships that are supported by high bootstrap proportions, in spite of a lack of support for particular components or clades. In practice majority-rule reduced consensus profiles may contain many trees. The size of the profile can be reduced by constraints on minimal bootstrap proportions and/or cardinality of the included trees. Majority-rule reduced consensus trees can also be selected a posteriori from the profile. Surrogates to the majority-rule reduced consensus methods using partition tables or tree pruning options provided by widely used phylogenetic inference software are also described. The methods are designed to produce more informative summaries of bootstrap analyses and thereby foster more informed assessment of the strengths and weaknesses of complex phylogenetic hypotheses.      

鲤科盘鮈属鱼类系统发育及其历史地理分布格局解析

以盘鮈属鱼类作为内群,以巴马拟缨鱼作为外群。通过形态比较共筛选出85个稳定的特征,形成形态特征状态矩阵表。以PAUP4.0b软件,采用均权方式,在无序和有序状态下分别按Heuristic、Branch-and-Bound以及Bootstrap等3种方式计算和构树。每种方法计算均得到唯一的1棵树,最大简约树与严格一致树、Bootstrap值检测树呈现微小差异。但仅最大简约树体现了各种之间先后分化的次序以及各姐妹群之间的关系,所以选择最大简约树作为盘鮈鱼类的系统发育树。其结果显示,盘鮈具小吸盘的种类与具大吸盘的种类分别构成了A、B两支。B支又可分为C、D两支。其中,C支的种类以吻端形成1对明显珠星,甚至形成吻突而区别于同属中具大吸盘的其他种类。运用Component(2.0)软件计算,得到盘鮈属种类分布河流的唯一分支树,其结构基本与水系的地理分布成对应关系。盘鮈属鱼类祖先的形成时期应为第4纪中期之初或更早。古云贵高原是盘鮈属鱼类的起源、分布和分化中心。云贵高原面的抬升与河流的袭夺促成了盘鮈属鱼类的多次分化和扩散,由此形成了该属鱼类的现今分布格局。     

Majority Does Not Rule: The Trouble with Majority-Rule Consensus Trees

The use of majority-rule consensus trees as a means of resolving ambiguity in phylogenetic analyses is investigated. It is shown to be an inappropriate method for this purpose.     

Multipolar consensus for phylogenetic trees

Collections of phylogenetic trees are usually summarized using consensus methods. These methods build a single tree, supposed to be representative of the collection. However, in the case of heterogeneous collections of trees, the resulting consensus may be poorly resolved (strict consensus, majority-rule consensus, ...), or may perform arbitrary choices among mutually incompatible clades, or splits (greedy consensus). Here, we propose an alternative method, which we call the multipolar consensus (MPC). Its aim is to display all the splits having a support above a predefined threshold, in a minimum number of consensus trees, or poles. We show that the problem is equivalent to a graph-coloring problem, and propose an implementation of the method. Finally, we apply the MPC to real data sets. Our results indicate that, typically, all the splits down to a weight of 10% can be displayed in no more than 4 trees. In addition, in some cases, biologically relevant secondary signals, which would not have been present in any of the classical consensus trees, are indeed captured by our method, indicating that the MPC provides a convenient exploratory method for phylogenetic analysis. The method was implemented in a package freely available at http://www.lirmm.fr/~cbonnard/MPC.html     

Phylogenetic relationships among Phytophthora species inferred from sequence analysis of mitochondrially encoded cytochrome oxidase I and II genes

The phylogenetic relationships of 51 isolates representing 27 species of Phytophthora were assessed by sequence alignment of 568 bp of the mitochondrially encoded cytochrome oxidase II gene. A total of 1299 bp of the cytochrome oxidase I gene also were examined for a subset of 13 species. The cox II gene trees constructed by a heuristic search, based on maximum parsimony for a bootstrap 50% majority-rule consensus tree, revealed 18 species grouping into seven clades and nine species unaffiliated with a specific clade. The phylogenetic relationships among species observed on cox II gene trees did not exhibit consistent similarities in groupings for morphology, pathogenicity, host range or temperature optima. The topology of cox I gene trees, constructed by a heuristic search based on maximum parsimony for a bootstrap 50% majority-rule consensus tree for 13 species of Phytophthora, revealed 10 species grouping into three clades and three species unaffiliated with a specific clade. The groupings in general agreed with what was observed in the cox II tree. Species relationships observed for the cox II gene tree were in agreement with those based on ITS regions, with several notable exceptions. Some of these differences were noted in species in which the same isolates were used for both ITS and cox II analysis, suggesting either a differential rate of evolutionary divergence for these two regions or incorrect assumptions about alignment of ITS sequences. Analysis of combined data sets of ITS and cox II sequences generated a tree that did not differ substantially from analysis of ITS data alone, however, the results of a partition homogeneity test suggest that combining data sets may not be valid.     

Investigating deep phylogenetic relationships among cyanobacteria and plastids by small subunit rRNA sequence analysis.

Small subunit rRNA sequence data were generated for 27 strains of cyanobacteria and incorporated into a phylogenetic analysis of 1,377 aligned sequence positions from a diverse sampling of 53 cyanobacteria and 10 photosynthetic plastids. Tree inference was carried out using a maximum likelihood method with correction for site-to-site variation in evolutionary rate. Confidence in the inferred phylogenetic relationships was determined by construction of a majority-rule consensus tree based on alternative topologies not considered to be statistically significantly different from the optimal tree. The results are in agreement with earlier studies in the assignment of individual taxa to specific sequence groups. Several relationships not previously noted among sequence groups are indicated, whereas other relationships previously supported are contradicted. All plastids cluster as a strongly supported monophyletic group arising near the root of the cyanobacterial line of descent.     

Molecular phytogeny of conifers using RFLP analysis of PCR-amplified specific chloroplast genes

We investigated the molecular phylogeny of conifers using restriction endonuclease fragment length polymorphism of six polymerase chain reaction-amplified chloroplast genes — frxC, rbcL, psbA, psbD, trnK, and 16S. We detected 227 total site changes among species, representing 23, 26, 38, 48, 67, and 25 site changes in frxC, psbA, psbD, rbcL, trnK and 16S, respectively. The mean nucleotide substitution was 10.75% (SD 0.573) among species in five families. Forty maximally parsimonious trees were obtained using the Wagner parsimony method, and a 50% majority-rule consensus tree was obtained from them. Data analysis produced similar basic patterns when both the Wagner parsimony and the neighbor-joining methods were applied, and the main lineages were clearly separated. Taxaceae and Cephalotaxaceae species were used as the out-groups when applying Wagner parsimony methods. With the Wagner method, the consistency index was 0.510, the retention index was 0.879, and tree length was 435 steps. Our results indicated that Cupressaceae and Taxodiaceae are closely related families and that Sciadopitys verticillata is the basal lineage of Cupressaceae and Taxodiaceae. The neighbor-joining tree is similar to the 50% majority-rule consensus of the 40 Wagner parsimony trees except for the position of Keteleeria daversifolia, the Picea and Cedrus group, and the divergence within Cupressaceae.     

Threshold consensus methods for molecular sequences.

We introduce a parameterized threshold consensus method (th chi) for molecular sequences which is based on a majority-rule voting principle. In contrast to other frequency-based methods, the th chi method uses a single criterion to return ambiguity codes of different lengths. We derive basic features of the method and establish that it returns at most two ambiguity codes at any position of the consensus sequence. We bound from below the size of the frequency gap that exists when the th chi method returns an ambiguity code. Using such properties, we compare the th chi method to other consensus methods for molecular sequences which are defined in terms of threshold or gap criteria.     

Assessing reliability of gene clusters from gene expression data

The rapid development of microarray technologies has raised many challenging problems in experiment design and data analysis. Although many numerical algorithms have been successfully applied to analyze gene expression data, the effects of variations and uncertainties in measured gene expression levels across samples and experiments have been largely ignored in the literature. In this article, in the context of hierarchical clustering algorithms, we introduce a statistical resampling method to assess the reliability of gene clusters identified from any hierarchical clustering method. Using the clustering trees constructed from the resampled data, we can evaluate the confidence value for each node in the observed clustering tree. A majority-rule consensus tree can be obtained, showing clusters that only occur in a majority of the resampled trees. We illustrate our proposed methods with applications to two published data sets. Although the methods are discussed in the context of hierarchical clustering methods, they can be applied with other cluster-identification methods for gene expression data to assess the reliability of any gene cluster of interest. Electronic Publication     

Imputing supertrees and supernetworks from quartets

Inferring species phylogenies is an important part of understanding molecular evolution. Even so, it is well known that an accurate phylogenetic tree reconstruction for a single gene does not always necessarily correspond to the species phylogeny. One commonly accepted strategy to cope with this problem is to sequence many genes; the way in which to analyze the resulting collection of genes is somewhat more contentious. Supermatrix and supertree methods can be used, although these can suppress conflicts arising from true differences in the gene trees caused by processes such as lineage sorting, horizontal gene transfer, or gene duplication and loss. In 2004, Huson et al. (IEEE/ACM Trans. Comput. Biol. Bioinformatics 1:151-158) presented the Z-closure method that can circumvent this problem by generating a supernetwork as opposed to a supertree. Here we present an alternative way for generating supernetworks called Q-imputation. In particular, we describe a method that uses quartet information to add missing taxa into gene trees. The resulting trees are subsequently used to generate consensus networks, networks that generalize strict and majority-rule consensus trees. Through simulations and application to real data sets, we compare Q-imputation to the matrix representation with parsimony (MRP) supertree method and Z-closure, and demonstrate that it provides a useful complementary tool.     

A supertree approach to shorebird phylogeny

Background

Order Charadriiformes (shorebirds) is an ideal model group in which to study a wide range of behavioural, ecological and macroevolutionary processes across species. However, comparative studies depend on phylogeny to control for the effects of shared evolutionary history. Although numerous hypotheses have been presented for subsets of the Charadriiformes none to date include all recognised species. Here we use the matrix representation with parsimony method to produce the first fully inclusive supertree of Charadriiformes. We also provide preliminary estimates of ages for all nodes in the tree.

Results

Three main lineages are revealed: i) the plovers and allies; ii) the gulls and allies; and iii) the sandpipers and allies. The relative position of these clades is unresolved in the strict consensus tree but a 50% majority-rule consensus tree indicates that the sandpiper clade is sister group to the gulls and allies whilst the plover group is placed at the base of the tree. The overall topology is highly consistent with recent molecular hypotheses of shorebird phylogeny.

Conclusion

The supertree hypothesis presented herein is (to our knowledge) the only complete phylogenetic hypothesis of all extant shorebirds. Despite concerns over the robustness of supertrees (see Discussion), we believe that it provides a valuable framework for testing numerous evolutionary hypotheses relating to the diversity of behaviour, ecology and life-history of the Charadriiformes.

     

Multilocus phylogenetics of a rapid radiation in the genus Thomomys (Rodentia: Geomyidae)

Species complexes undergoing rapid radiation present a challenge in molecular systematics because of the possibility that ancestral polymorphism is retained in component gene trees. Coalescent theory has demonstrated that gene trees often fail to match lineage trees when taxon divergence times are less than the ancestral effective population sizes. Suggestions to increase the number of loci and the number of individuals per taxon have been proposed; however, phylogenetic methods to adequately analyze these data in a coalescent framework are scarce. We compare two approaches to estimating lineage (species) trees using multiple individuals and multiple loci: the commonly used partitioned Bayesian analysis of concatenated sequences and a modification of a newly developed hierarchical Bayesian method (BEST) that simultaneously estimates gene trees and species trees from multilocus data. We test these approaches on a phylogeny of rapidly radiating species wherein divergence times are likely to be smaller than effective population sizes, and incomplete lineage sorting is known, in the rodent genus, Thomomys. We use seven independent noncoding nuclear sequence loci (total approximately 4300 bp) and between 1 and 12 individuals per taxon to construct a phylogenetic hypothesis for eight Thomomys species. The majority-rule consensus tree from the partitioned concatenated analysis included 14 strongly supported bipartitions, corroborating monophyletic species status of five of the eight named species. The BEST tree strongly supported only the split between the two subgenera and showed very low support for any other clade. Comparison of both lineage trees to individual gene trees revealed that the concatenation method appears to ignore conflicting signals among gene trees, whereas the BEST tree considers conflicting signals and downweights support for those nodes. Bayes factor analysis of posterior tree distributions from both analyses strongly favor the model underlying the BEST analysis. This comparison underscores the risks of overreliance on results from concatenation, and ignoring the properties of coalescence, especially in cases of recent, rapid radiations.     

Analyzing and Synthesizing Phylogenies Using Tree Alignment Graphs

Phylogenetic trees are used to analyze and visualize evolution. However, trees can be imperfect datatypes when summarizing multiple trees. This is especially problematic when accommodating for biological phenomena such as horizontal gene transfer, incomplete lineage sorting, and hybridization, as well as topological conflict between datasets. Additionally, researchers may want to combine information from sets of trees that have partially overlapping taxon sets. To address the problem of analyzing sets of trees with conflicting relationships and partially overlapping taxon sets, we introduce methods for aligning, synthesizing and analyzing rooted phylogenetic trees within a graph, called a tree alignment graph (TAG). The TAG can be queried and analyzed to explore uncertainty and conflict. It can also be synthesized to construct trees, presenting an alternative to supertrees approaches. We demonstrate these methods with two empirical datasets. In order to explore uncertainty, we constructed a TAG of the bootstrap trees from the Angiosperm Tree of Life project. Analysis of the resulting graph demonstrates that areas of the dataset that are unresolved in majority-rule consensus tree analyses can be understood in more detail within the context of a graph structure, using measures incorporating node degree and adjacency support. As an exercise in synthesis (i.e., summarization of a TAG constructed from the alignment trees), we also construct a TAG consisting of the taxonomy and source trees from a recent comprehensive bird study. We synthesized this graph into a tree that can be reconstructed in a repeatable fashion and where the underlying source information can be updated. The methods presented here are tractable for large scale analyses and serve as a basis for an alternative to consensus tree and supertree methods. Furthermore, the exploration of these graphs can expose structures and patterns within the dataset that are otherwise difficult to observe.     

Phylogenetic relationships of the Aurantioideae (Rutaceae) based on the nuclear ribosomal DNA ITS region and three noncoding chloroplast DNA regions, atpB-rbcL spacer, rps16, and trnL-trnF

The tribes and subtribes of Aurantioideae, an economically important subfamily of the Rutaceae, have a controversial taxonomic history because a phylogenetic framework has been lacking. In order to construct an evolutionary history and evaluate the most recent classification system [Swingle and Reece 1967. The botany of Citrus and its wild relatives, in: The Citrus Industry, vol. 1, History, World Distribution, Botany, and Varieties. University of California, Berkeley, pp. 190-430], one nuclear and three noncoding chloroplast genes were sequenced and analyzed phylogenetically along with selected non-molecular characters. Taxa representing tribes Citreae and Clauseneae and their six subtribes were sampled. In all analyses Aurantioideae is monophyletic. The majority-rule consensus tree from the combined analysis indicates that the two tribes are not monophyletic. The combined topology is not congruent with the widely used classification of Aurantioideae by Swingle and Reece (1967). The tribes and subtribes are in need of revision.     

Phylogenetic relationships of neopterygian fishes, inferred from mitochondrial DNA sequences.

To investigate the relationships among the three main groups of extant neopterygian fishes--Amiidae, Lepisosteidae, and Teleostei--we sequenced fragments of three mitochondrial genes from 12 different actinopterygian fishes and translated the nucleotide sequences into amino acid sequences. When all three regions are considered together, Amiidae clusters with Lepisosteidae in the most parsimonious cladograms, but other clades, such as Neopterygii and Teleostei, that are well supported by morphological evidence fail to emerge as monophyletic. When the cytochrome b sequences are analyzed together with previously published sequences for other taxa, the majority-rule consensus tree is consistent with the monophyly of Teleostei and Neopterygii and marginally supports the Amiidae + Lepisosteidae clade. In either analysis, when Neopterygii and Teleostei are constrained to monophyly, all the most-parsimonious cladograms support the Amiidae + Lepisosteidae topology. Where molecules and morphology disagree, provisional morphology-based constraints on the analysis of molecular data offer a practical means of integrating the two types of data.     

MixtureTree: a program for constructing phylogeny

Background  

MixtureTree v1.0 is a Linux based program (written in C++) which implements an algorithm based on mixture models for reconstructing phylogeny from binary sequence data, such as single-nucleotide polymorphisms (SNPs). In addition to the mixture algorithm with three different optimization options, the program also implements a bootstrap procedure with majority-rule consensus.     

Support Measures to Estimate the Reliability of Evolutionary Events Predicted by Reconciliation Methods

The genome content of extant species is derived from that of ancestral genomes, distorted by evolutionary events such as gene duplications, transfers and losses. Reconciliation methods aim at recovering such events and at localizing them in the species history, by comparing gene family trees to species trees. These methods play an important role in studying genome evolution as well as in inferring orthology relationships. A major issue with reconciliation methods is that the reliability of predicted evolutionary events may be questioned for various reasons: Firstly, there may be multiple equally optimal reconciliations for a given species tree–gene tree pair. Secondly, reconciliation methods can be misled by inaccurate gene or species trees. Thirdly, predicted events may fluctuate with method parameters such as the cost or rate of elementary events. For all of these reasons, confidence values for predicted evolutionary events are sorely needed. It was recently suggested that the frequency of each event in the set of all optimal reconciliations could be used as a support measure. We put this proposition to the test here and also consider a variant where the support measure is obtained by additionally accounting for suboptimal reconciliations. Experiments on simulated data show the relevance of event supports computed by both methods, while resorting to suboptimal sampling was shown to be more effective. Unfortunately, we also show that, unlike the majority-rule consensus tree for phylogenies, there is no guarantee that a single reconciliation can contain all events having above 50% support. In this paper, we detail how to rely on the reconciliation graph to efficiently identify the median reconciliation. Such median reconciliation can be found in polynomial time within the potentially exponential set of most parsimonious reconciliations.     

A fully resolved consensus between fully resolved phylogenetic trees

Nowadays, there are many phylogeny reconstruction methods, each with advantages and disadvantages. We explored the advantages of each method, putting together the common parts of trees constructed by several methods, by means of a consensus computation. A number of phylogenetic consensus methods are already known. Unfortunately, there is also a taboo concerning consensus methods, because most biologists see them mainly as comparators and not as phylogenetic tree constructors. We challenged this taboo by defining a consensus method that builds a fully resolved phylogenetic tree based on the most common parts of fully resolved trees in a given collection. We also generated results showing that this consensus is in a way a kind of "median" of the input trees; as such it can be closer to the correct tree in many situations.