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     

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.     

Comparing and displaying phylogenetic trees using edge union networks

The general problem of representing collections of trees as a single graph has led to many tree summary techniques. Many consensus approaches take sets of trees (either inferred as separate gene trees or gleaned from the posterior of a Bayesian analysis) and produce a single “best” tree. In scenarios where horizontal gene transfer or hybridization are suspected, networks may be preferred, which allow for nodes to have two parents, representing the fusion of lineages. One such construct is the cluster union network (CUN), which is constructed using the union of all clusters in the input trees. The CUN has a number of mathematically desirable properties, but can also present edges not observed in the input trees. In this paper we define a new network construction, the edge union network (EUN), which displays edges if and only if they are contained in the input trees. We also demonstrate that this object can be constructed with polynomial time complexity given arbitrary phylogenetic input trees, and so can be used in conjunction with network analysis techniques for further phylogenetic hypothesis testing.     

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.      

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.     

Weighted compromise trees: a method to summarize competing phylogenetic hypotheses

A new consensus method for summarizing competing phylogenetic hypotheses, weighted compromise, is described. The method corrects for a bias inherent in majority‐rule consensus/compromise trees when the source trees exhibit non‐independence due to ambiguity in terminal clades. Suggestions are given for its employment in parsimony analyses and tree resampling strategies such as bootstrapping and jackknifing. An R function is described that can be used with the programming language R to produce the consensus.     

Metrics on multilabeled trees: interrelationships and diameter bounds

Multilabeled trees or MUL-trees, for short, are trees whose leaves are labeled by elements of some nonempty finite set X such that more than one leaf may be labeled by the same element of X. This class of trees includes phylogenetic trees and tree shapes. MUL-trees arise naturally in, for example, biogeography and gene evolution studies and also in the area of phylogenetic network reconstruction. In this paper, we introduce novel metrics which may be used to compare MUL-trees, most of which generalize well-known metrics on phylogenetic trees and tree shapes. These metrics can be used, for example, to better understand the space of MUL-trees or to help visualize collections of MUL-trees. In addition, we describe some relationships between the MUL-tree metrics that we present and also give some novel diameter bounds for these metrics. We conclude by briefly discussing some open problems as well as pointing out how MUL-tree metrics may be used to define metrics on the space of phylogenetic networks.     

Exploring the effects of phylogenetic uncertainty and consensus trees on stratigraphic consistency scores: a new program and a standardized method

The stratigraphic record of first appearances provides an independent source of data for evaluating and comparing phylogenetic hypotheses that include taxa with fossil histories. However, no standardized method exists for calculating these metrics for polytomous phylogenies, restricting their applicability. Previously proposed methods insufficiently deal with this problem because they skew or restrict the resulting scores. To resolve this issue, we propose a standardized method for treating polytomies when calculating these metrics: the Comprehensive Polytomy approach (ComPoly). This approach accurately describes how phylogenetic uncertainty, indicated by polytomies, affects stratigraphic consistency scores. We also present a new program suite (Assistance with Stratigraphic Consistency Calculations) that incorporates the ComPoly approach and simplifies the calculation of absolute temporal stratigraphic consistency metrics. This study also demonstrates that stratigraphic consistency scores calculated from strict consensus trees can be overly inclusive and those calculated from less‐than‐strict consensus trees inaccurately describe the phylogenetic signal present in the source most‐parsimonious trees (MPTs). Therefore, stratigraphic consistency scores should be calculated directly from the source MPTs whenever possible to ensure their accuracy. Finally, we offer recommendations for standardizing comparisons between molecular divergence dates and the stratigraphic record of first appearances, a promising new application of these methods. © The Willi Hennig Society 2010.     

COMBINED AND SEPARATE ANALYSES OF MORPHOLOGICAL AND MOLECULAR DATA IN THE PLANT FAMILY RUBIACEAE

Abstract— The Rubiaceae are one of the largest of the families of angiosperms, with over 10000 species. The tribal and subfamilial classification is provisional due to the lack of phylogenetic hypotheses. The present study of the Rubiaceae is based on 33 genera and three data sets, one morphological and two molecular from chloroplast DNA, restriction sites andrbcL sequences. There is much congruence between the morphological and the molecular data sets, but also conflict. For parsimony reasons, the best phylogenetic hypothesis is a tree based on an analysis of the combined data sets. The so-called “total evidence” criterion for the combined analysis is simply a reiteration of the principle of parsimony. In this particular study, the classification would be almost the same even if based on the separate analyses instead of the combined. Despite the inapplicability of consensus trees or trees from separate analyses for phylogenetic hypotheses and classification, separate analyses may provide important information. It is the best way to reveal conflicts between different data sets. Knowledge of the conflicts can promote further detailed investigation in order to improve understanding of characters and phylogenetic hypotheses. In this study, the tribe Vanguerieae provides such an example; morphological data support a position in the subfamily Cinchonoideae, but DNA and a tree based on the combined data support a position in subfamily Ixoroideae. The tribe's position in the morphological tree is probably due to missing information concerning the correct pollen presentation system. Bootstrap fractions and K. Bremer's branch support values are used to evaluate the stability of particular nodes in the trees. Interestingly these values are not always correlated, e.g. in the morphological tree, the node with the highest branch support value has very low bootstrap fraction. The reasons for these differences are unclear, but large differences are presumably more likely to occur on short branches.     

Using Confidence Set Heuristics During Topology Search Improves the Robustness of Phylogenetic Inference

We examine the impact of likelihood surface characteristics on phylogenetic inference. Amino acid data sets simulated from topologies with branch length features chosen to represent varying degrees of difficulty for likelihood maximization are analyzed. We present situations where the tree found to achieve the global maximum in likelihood is often not equal to the true tree. We use the program covSEARCH to demonstrate how the use of adaptively sized pools of candidate trees that are updated using confidence tests results in solution sets that are highly likely to contain the true tree. This approach requires more computation than traditional maximum likelihood methods, hence covSEARCH is best suited to small to medium-sized alignments or large alignments with some constrained nodes. The majority rule consensus tree computed from the confidence sets also proves to be different from the generating topology. Although low phylogenetic signal in the input alignment can result in large confidence sets of trees, some biological information can still be obtained based on nodes that exhibit high support within the confidence set. Two real data examples are analyzed: mammal mitochondrial proteins and a small tubulin alignment. We conclude that the technique of confidence set optimization can significantly improve the robustness of phylogenetic inference at a reasonable computational cost. Additionally, when either very short internal branches or very long terminal branches are present, confident resolution of specific bipartitions or subtrees, rather than whole-tree phylogenies, may be the most realistic goal for phylogenetic methods. [Reviewing Editor: Dr. Nicolas Galtier]     

The assembly of tropical tree communities – the advances and shortcomings of phylogenetic and functional trait analyses

Tropical tree communities present one of the most challenging systems for studying the processes underlying community assembly. Most community assembly hypotheses consider the relative importance of the ecological similarity of co‐occurring species. Quantifying this similarity is a daunting and potentially impossible task in species‐rich assemblages. During the past decade tropical tree ecologists have increasingly utilized phylogenetic trees and functional traits to estimate the ecological similarity of species in order to test mechanistic community assembly hypotheses. A large amount of work has resulted with many important advances having been made along the way. That said, there are still many outstanding challenges facing those utilizing phylogenetic and functional trait approaches to study community assembly. Here I review the conceptual background, major advances and major remaining challenges in phylogenetic‐ and trait‐based approaches to community ecology with a specific focus on tropical trees. I argue that both approaches tremendously improve our understanding of tropical tree community ecology, but neither approach has fully reached its potential thus far.     

应用SuperTRI方法重建百合目的系统发育关系

SuperTRI是Ropiquet等(2009)发表的一种新的超树方法,可以通过合并所有系统发育信息来共同组建大的系统发育树.该方法克服了超矩阵法和传统超树法的一些限制,使提出的系统发育假说可信度更高,更具有统计说服力.本文应用SupperTRI方法重建了百合目(Liliales)主要类群的系统发育关系,并与超矩阵法的分析结果进行了比较.结果显示:(1) SuperTRI方法产生了与超矩阵法相似的拓扑结构,但节点支持率相对较低,其中再现性指数对评判分支的可信性更容易理解,在系统树图示方法上也更直观;(2)SuperTRI系统树证实百合科、菝葜科、垂花科和菝葜藤科为一单系分支;黑药花科为一独立分支;秋水仙科、六出花科、刺藤科为一单系分支,但这3个大分支间的关系未明;支持白玉簪科和金梅草科互为姐妹群,是百合目最基部类群.     

Mitochondrial DNA,morphology, and the phylogenetic relationships of Antarctic icefishes (Notothenioidei: Channichthyidae)

The Channichthyidae is a lineage of 16 species in the Notothenioidei, a clade of fishes that dominate Antarctic near-shore marine ecosystems with respect to both diversity and biomass. Among four published studies investigating channichthyid phylogeny, no two have produced the same tree topology, and no published study has investigated the degree of phylogenetic incongruence between existing molecular and morphological datasets. In this investigation we present an analysis of channichthyid phylogeny using complete gene sequences from two mitochondrial genes (ND2 and 16S) sampled from all recognized species in the clade. In addition, we have scored all 58 unique morphological characters used in three previous analyses of channichthyid phylogenetic relationships. Data partitions were analyzed separately to assess the amount of phylogenetic resolution provided by each dataset, and phylogenetic incongruence among data partitions was investigated using incongruence length difference (ILD) tests. We utilized a parsimony-based version of the Shimodaira-Hasegawa test to determine if alternative tree topologies are significantly different from trees resulting from maximum parsimony analysis of the combined partition dataset. Our results demonstrate that the greatest phylogenetic resolution is achieved when all molecular and morphological data partitions are combined into a single maximum parsimony analysis. Also, marginal to insignificant incongruence was detected among data partitions using the ILD. Maximum parsimony analysis of all data partitions combined results in a single tree, and is a unique hypothesis of phylogenetic relationships in the Channichthyidae. In particular, this hypothesis resolves the phylogenetic relationships of at least two species (Channichthys rhinoceratus and Chaenocephalus aceratus), for which there was no consensus among the previous phylogenetic hypotheses. The combined data partition dataset provides substantial statistical power to discriminate among alternative hypotheses of channichthyid relationships. These findings suggest the optimal strategy for investigating the phylogenetic relationships of channichthyids is one that uses all available phylogenetic data in analyses of combined data partitions.     

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.     

UPGMA树的不惟一性问题及其解决方法

对于一组给定的DNA或蛋白质序列,UPGMA算法构建的二叉进化树可能是不惟一的,其具体拓扑结构与序列输入顺序相关,这一现象通常被称为"tied trees"。提出了UPGMA的一种改进算法——不加权算术平均组群方法(UMGMA),用以解决UPGMA树的不惟一问题。在UPGMA树惟一时,该方法产生的进化树与UPGMA树相同;而在UPGMA树不惟一时,该方法可以产生一棵惟一的、与序列输入顺序无关的多叉进化树,而且该算法还具有一个可调的容差参数,来控制生成进化树的主要分枝结构,这对于突出大规模进化树的总体脉络具有重要意义。     

A maximum pseudo-likelihood approach for estimating species trees under the coalescent model

Background  

Several phylogenetic approaches have been developed to estimate species trees from collections of gene trees. However, maximum likelihood approaches for estimating species trees under the coalescent model are limited. Although the likelihood of a species tree under the multispecies coalescent model has already been derived by Rannala and Yang, it can be shown that the maximum likelihood estimate (MLE) of the species tree (topology, branch lengths, and population sizes) from gene trees under this formula does not exist. In this paper, we develop a pseudo-likelihood function of the species tree to obtain maximum pseudo-likelihood estimates (MPE) of species trees, with branch lengths of the species tree in coalescent units.     

Majority-rule (+) consensus trees

The construction of a consensus tree to summarize the information of a given set of phylogenetic trees is now routinely a part of many studies in systematic biology. One popular method is the majority-rule consensus tree. In this paper we introduce and characterize a new consensus method that refines the majority-rule tree by adding certain compatible clusters satisfying a simple criterion.     

Molecular phylogeny of the brachyuran crab superfamily Majoidea indicates close congruence with trees based on larval morphology

In this study, we constructed the first molecular phylogeny of the diverse crab superfamily Majoidea (Decapoda: Pleocyemata: Brachyura), using three loci (16S, COI, and 28S) from 37 majoid species. We used this molecular phylogeny to evaluate evidence for phylogenetic hypotheses based on larval and adult morphology. Our study supports several relationships predicted from larval morphology. These include a monophyletic Oregoniidae family branching close to the base of the tree; a close phylogenetic association among the Epialtidae, Pisidae, Tychidae, and Mithracidae families; and some support for the monophyly of the Inachidae and Majidae families. However, not all majoid families were monophyletic in our molecular tree, providing weaker support for phylogenetic hypotheses inferred strictly from adult morphology (i.e., monophyly of individual families). This suggests the adult morphological characters traditionally used to classify majoids into different families may be subject to convergence. Furthermore, trees constructed with data from any single locus were more poorly resolved than trees constructed from the combined dataset, suggesting that utilization of multiple loci are necessary to reconstruct relationships in this group.