Species trees from gene trees: reconstructing Bayesian posterior distributions of a species phylogeny using estimated gene tree distributions

The desire to infer the evolutionary history of a group of species should be more viable now that a considerable amount of multilocus molecular data is available. However, the current molecular phylogenetic paradigm still reconstructs gene trees to represent the species tree. Further, commonly used methods of combining data, such as the concatenation method, are known to be inconsistent in some circumstances. In this paper, we propose a Bayesian hierarchical model to estimate the phylogeny of a group of species using multiple estimated gene tree distributions, such as those that arise in a Bayesian analysis of DNA sequence data. Our model employs substitution models used in traditional phylogenetics but also uses coalescent theory to explain genealogical signals from species trees to gene trees and from gene trees to sequence data, thereby forming a complete stochastic model to estimate gene trees, species trees, ancestral population sizes, and species divergence times simultaneously. Our model is founded on the assumption that gene trees, even of unlinked loci, are correlated due to being derived from a single species tree and therefore should be estimated jointly. We apply the method to two multilocus data sets of DNA sequences. The estimates of the species tree topology and divergence times appear to be robust to the prior of the population size, whereas the estimates of effective population sizes are sensitive to the prior used in the analysis. These analyses also suggest that the model is superior to the concatenation method in fitting these data sets and thus provides a more realistic assessment of the variability in the distribution of the species tree that may have produced the molecular information at hand. Future improvements of our model and algorithm should include consideration of other factors that can cause discordance of gene trees and species trees, such as horizontal transfer or gene duplication.     

ASTRAL-Pro: Quartet-Based Species-Tree Inference despite Paralogy

Phylogenetic inference from genome-wide data (phylogenomics) has revolutionized the study of evolution because it enables accounting for discordance among evolutionary histories across the genome. To this end, summary methods have been developed to allow accurate and scalable inference of species trees from gene trees. However, most of these methods, including the widely used ASTRAL, can only handle single-copy gene trees and do not attempt to model gene duplication and gene loss. As a result, most phylogenomic studies have focused on single-copy genes and have discarded large parts of the data. Here, we first propose a measure of quartet similarity between single-copy and multicopy trees that accounts for orthology and paralogy. We then introduce a method called ASTRAL-Pro (ASTRAL for PaRalogs and Orthologs) to find the species tree that optimizes our quartet similarity measure using dynamic programing. By studying its performance on an extensive collection of simulated data sets and on real data sets, we show that ASTRAL-Pro is more accurate than alternative methods.     

How Bayes tests of molecular phylogenies compare with frequentist approaches

MOTIVATION: The desire to compare molecular phylogenies has stimulated the design of numerous tests. Most of these tests are formulated in a frequentist framework, and it is not known how they compare with Bayes procedures. I propose here two new Bayes tests that either compare pairs of trees (Bayes hypothesis test, BHT), or test each tree against an average of the trees included in the analysis (Bayes significance test, BST). RESULTS: The algorithm, based on a standard Metropolis-Hastings sampler, integrates nuisance parameters out and estimates the probability of the data under each topology. These quantities are used to estimate Bayes factors for composite vs. composite hypotheses. Based on two data sets, the BHT and BST are shown to construct similar confidence sets to the bootstrap and the Shimodaira Hasegawa test, respectively. This suggests that the known difference among previous tests is mainly due to the null hypothesis considered.     

Supertree bootstrapping methods for assessing phylogenetic variation among genes in genome-scale data sets

Nonparamtric bootstrapping methods may be useful for assessing confidence in a supertree inference. We examined the performance of two supertree bootstrapping methods on four published data sets that each include sequence data from more than 100 genes. In "input tree bootstrapping," input gene trees are sampled with replacement and then combined in replicate supertree analyses; in "stratified bootstrapping," trees from each gene's separate (conventional) bootstrap tree set are sampled randomly with replacement and then combined. Generally, support values from both supertree bootstrap methods were similar or slightly lower than corresponding bootstrap values from a total evidence, or supermatrix, analysis. Yet, supertree bootstrap support also exceeded supermatrix bootstrap support for a number of clades. There was little overall difference in support scores between the input tree and stratified bootstrapping methods. Results from supertree bootstrapping methods, when compared to results from corresponding supermatrix bootstrapping, may provide insights into patterns of variation among genes in genome-scale data sets.     

Application of phylogenetic networks in evolutionary studies

The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a tree-like manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees.     

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.     

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     

STBase: One Million Species Trees for Comparative Biology

Comprehensively sampled phylogenetic trees provide the most compelling foundations for strong inferences in comparative evolutionary biology. Mismatches are common, however, between the taxa for which comparative data are available and the taxa sampled by published phylogenetic analyses. Moreover, many published phylogenies are gene trees, which cannot always be adapted immediately for species level comparisons because of discordance, gene duplication, and other confounding biological processes. A new database, STBase, lets comparative biologists quickly retrieve species level phylogenetic hypotheses in response to a query list of species names. The database consists of 1 million single- and multi-locus data sets, each with a confidence set of 1000 putative species trees, computed from GenBank sequence data for 413,000 eukaryotic taxa. Two bodies of theoretical work are leveraged to aid in the assembly of multi-locus concatenated data sets for species tree construction. First, multiply labeled gene trees are pruned to conflict-free singly-labeled species-level trees that can be combined between loci. Second, impacts of missing data in multi-locus data sets are ameliorated by assembling only decisive data sets. Data sets overlapping with the user’s query are ranked using a scheme that depends on user-provided weights for tree quality and for taxonomic overlap of the tree with the query. Retrieval times are independent of the size of the database, typically a few seconds. Tree quality is assessed by a real-time evaluation of bootstrap support on just the overlapping subtree. Associated sequence alignments, tree files and metadata can be downloaded for subsequent analysis. STBase provides a tool for comparative biologists interested in exploiting the most relevant sequence data available for the taxa of interest. It may also serve as a prototype for future species tree oriented databases and as a resource for assembly of larger species phylogenies from precomputed trees.     

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]     

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.     

A conditional probability of reconstruction measure for internal cladogram branches

The conditional probability of reconstruction is a measure of the robustness of cladogram internodes and, unlike Bremer support and bootstrapping values, directly gauges probability. The new method compares the three putative branch lengths (the optimal and two alternatives) obtained through branch recalculation after nearest neighbor interchange and recalculation under constraint. With rooted trees, one switches the two free lineages attached at the distal end of an internal branch with the basal lineage. Probabilistic reconstruction of a branch for small data sets (e.g., morphological) is defined as having no contrary support for the two alternative branches and, when sufficient data are available (e.g., molecular studies), as meeting a selected confidence limit in chi-squared analysis. The exact probability that the internal branch is reconstructed is the same as the preselected confidence level met with chi-squared analysis; alternatively, it is a simple calculation of the length of the optimal branch divided by the sum of the lengths of all three putative branches. This new measure of robustness allows calculation of summary probabilities of subclade and tree reconstruction. The measure is conditional on a particular data set and optimization method but may also compare support from conflicting gene trees. Examples are provided by a morphological data set (the bryophyte Didymodon) and a molecular data set (primates).     

Proceedings of the SMBE Tri-National Young Investigators' Workshop 2005. Improved consensus network techniques for genome-scale phylogeny

Although recent studies indicate that estimating phylogenies from alignments of concatenated genes greatly reduces the stochastic error, the potential for systematic error still remains, heightening the need for reliable methods to analyze multigene data sets. Consensus methods provide an alternative, more inclusive, approach for analyzing collections of trees arising from multiple genes. We extend a previously described consensus network method for genome-scale phylogeny (Holland, B. R., K. T. Huber, V. Moulton, and P. J. Lockhart. 2004. Using consensus networks to visualize contradictory evidence for species phylogeny. Mol. Biol. Evol. 21:1459-1461) to incorporate additional information. This additional information could come from bootstrap analysis, Bayesian analysis, or various methods to find confidence sets of trees. The new methods can be extended to include edge weights representing genetic distance. We use three data sets to illustrate the approach: 61 genes from 14 angiosperm taxa and one gymnosperm, 106 genes from eight yeast taxa, and 46 members of a gene family from 15 vertebrate taxa.     

Brassicaceae phylogeny inferred from phytochrome A and ndhF sequence data: tribes and trichomes revisited

The family Brassicaceae comprises 3710 species in 338 genera, 25 recently delimited tribes, and three major lineages based on phylogenetic results from the chloroplast gene ndhF. To assess the credibility of the lineages and newly delimited tribes, we sequenced an approximately 1.8-kb region of the nuclear phytochrome A (PHYA) gene for taxa previously sampled for the chloroplast gene ndhF. Using parsimony, likelihood, and Bayesian methods, we reconstructed the phylogeny of the gene and used the approximately unbiased (AU) test to compare phylogenetic results from PHYA with findings from ndhF. We also combined ndhF and PHYA data and used a Bayesian mixed model approach to infer phylogeny. PHYA and combined analyses recovered the same three large lineages as those recovered in ndhF trees, increasing confidence in these lineages. The combined tree confirms the monophyly of most of the recently delimited tribes (only Alysseae, Anchonieae, and Descurainieae are not monophyletic), while 13 of the 23 sampled tribes are monophyletic in PHYA trees. In addition to phylogenetic results, we documented the trichome branching morphology of species across the phylogeny and explored the evolution of different trichome morphologies using the AU test. Our results indicate that dendritic, medifixed, and stellate trichomes likely evolved independently several times in the Brassicaceae.     

The accuracy of species tree estimation under simulation: a comparison of methods

Numerous simulation studies have investigated the accuracy of phylogenetic inference of gene trees under maximum parsimony, maximum likelihood, and Bayesian techniques. The relative accuracy of species tree inference methods under simulation has received less study. The number of analytical techniques available for inferring species trees is increasing rapidly, and in this paper, we compare the performance of several species tree inference techniques at estimating recent species divergences using computer simulation. Simulating gene trees within species trees of different shapes and with varying tree lengths (T) and population sizes (), and evolving sequences on those gene trees, allows us to determine how phylogenetic accuracy changes in relation to different levels of deep coalescence and phylogenetic signal. When the probability of discordance between the gene trees and the species tree is high (i.e., T is small and/or is large), Bayesian species tree inference using the multispecies coalescent (BEST) outperforms other methods. The performance of all methods improves as the total length of the species tree is increased, which reflects the combined benefits of decreasing the probability of discordance between species trees and gene trees and gaining more accurate estimates for gene trees. Decreasing the probability of deep coalescences by reducing also leads to accuracy gains for most methods. Increasing the number of loci from 10 to 100 improves accuracy under difficult demographic scenarios (i.e., coalescent units ≤ 4N(e)), but 10 loci are adequate for estimating the correct species tree in cases where deep coalescence is limited or absent. In general, the correlation between the phylogenetic accuracy and the posterior probability values obtained from BEST is high, although posterior probabilities are overestimated when the prior distribution for is misspecified.     

Computer comparison of new and existing criteria for constructing evolutionary trees from sequence data

Summary Three new methods for constructing evolutionary trees from molecular sequence data are presented. These methods are based on a theory for correcting for non-constant evolutionary rates (Klotz et al. 1979; Klotz and Blanken 1981). Extensive computer simulations were run to compare these new methods to the commonly used criteria of Dayhoff (1978) and Fitch and Margoliash (1967). The results of these simulations showed that two of the new methods performed as well as Dayhoff's criterion, significantly better than that of Fitch and Margoliash, and as well as a simple variation of the latter (Prager and Wilson 1978) where any topology containing negative branch mutations is discarded. However, no method yielded the correct topology all of the time, which demonstrated the need to determine confidence estimates in a particular result when evolutionary trees are determined from sequence data.     

Molecular phylogeny of the hominoids: inferences from multiple independent DNA sequence data sets

Consensus on the evolutionary relationships of humans, chimpanzees, and gorillas has not been reached, despite the existence of a number of DNA sequence data sets relating to the phylogeny, partly because not all gene trees from these data sets agree. However, given the well-known phenomenon of gene tree-species tree mismatch, agreement among gene trees is not expected. A majority of gene trees from available DNA sequence data support one hypothesis, but is this evidence sufficient for statistical confidence in the majority hypothesis? All available DNA sequence data sets showing phylogenetic resolution among the hominoids are grouped according to genetic linkage of their corresponding genes to form independent data sets. Of the 14 independent data sets defined in this way, 11 support a human- chimpanzee clade, 2 support a chimpanzee-gorilla clade, and one supports a human-gorilla clade. The hypothesis of a trichotomous speciation event leading to Homo; Pan, and Gorilla can be firmly rejected on the basis of this data set distribution. The multiple-locus test (Wu 1991), which evaluates hypotheses using gene tree-species tree mismatch probabilities in a likelihood ratio test, favors the phylogeny with a Homo-Pan clade and rejects the other alternatives with a P value of 0.002. When the probabilities are modified to reflect effective population size differences among different types of genetic loci, the observed data set distribution is even more likely under the Homo-Pan clade hypothesis. Maximum-likelihood estimates for the time between successive hominoid divergences are in the range of 300,000-2,800,000 years, based on a reasonable range of estimates for long-term hominoid effective population size and for generation time. The implication of the multiple-locus test is that existing DNA sequence data sets provide overwhelming and sufficient support for a human-chimpanzee clade: no additional DNA data sets need to be generated for the purpose of estimating hominoid phylogeny. Because DNA hybridization evidence (Caccone and Powell 1989) also supports a Homo-Pan clade, the problem of hominoid phylogeny can be confidently considered solved.      

基于5 993个核基因的被子植物系统发育关系研究

系统发育关系的构建对被子植物分类及进化研究非常重要。长期以来,被子植物系统发育的研究,大多使用质体基因、线粒体基因或少数保守的单拷贝核基因。该研究从已注释基因组或转录组中搜集88种被子植物(包含58目)的核基因集;通过对其进行同源基因聚类及去旁系同源基因,获得了5 993个一对一的直系同源基因家族(即对于每个基因家族,每种植物最多一条序列,最少包含50个物种);使用截取各种不同数目基因集的DNA或氨基酸序列,采用串联法(concatenation)和溯祖法(coalescence),共构建了20棵进化树。比较这些进化树,虽然大部分结果支持APG IV中描述的被子植物主要支系之间的关系[(真双子叶植物,单子叶植物),木兰类植物],但真双子叶植物内部各目分支的演化关系与APG IV有一个很大的不同,即认为檀香目和石竹目是蔷薇类植物的姊妹群。基于这些进化树,估算了被子植物各目分支的分化时间,结果表明被子植物的起源时间为237.78百万年前(95%置信区间为202.6～278.08),与主流观点认为的225百万年至240百万年前一致。以上结果为构建进化树提供了一种可行性策略,这种方法允许使用基因数目更多而计算速度更快。     

Confidence bands for low-dose risk estimation with quantal response data

We study the use of simultaneous confidence bands for low-dose risk estimation with quantal response data, and derive methods for estimating simultaneous upper confidence limits on predicted extra risk under a multistage model. By inverting the upper bands on extra risk, we obtain simultaneous lower bounds on the benchmark dose (BMD). Monte Carlo evaluations explore characteristics of the simultaneous limits under this setting, and a suite of actual data sets are used to compare existing methods for placing lower limits on the BMD.     

Does choice in model selection affect maximum likelihood analysis?

In order to have confidence in model-based phylogenetic analysis, the model of nucleotide substitution adopted must be selected in a statistically rigorous manner. Several model-selection methods are applicable to maximum likelihood (ML) analysis, including the hierarchical likelihood-ratio test (hLRT), Akaike information criterion (AIC), Bayesian information criterion (BIC), and decision theory (DT), but their performance relative to empirical data has not been investigated thoroughly. In this study, we use 250 phylogenetic data sets obtained from TreeBASE to examine the effects that choice in model selection has on ML estimation of phylogeny, with an emphasis on optimal topology, bootstrap support, and hypothesis testing. We show that the use of different methods leads to the selection of two or more models for approximately 80% of the data sets and that the AIC typically selects more complex models than alternative approaches. Although ML estimation with different best-fit models results in incongruent tree topologies approximately 50% of the time, these differences are primarily attributable to alternative resolutions of poorly supported nodes. Furthermore, topologies and bootstrap values estimated with ML using alternative statistically supported models are more similar to each other than to topologies and bootstrap values estimated with ML under the Kimura two-parameter (K2P) model or maximum parsimony (MP). In addition, Swofford-Olsen-Waddell-Hillis (SOWH) tests indicate that ML trees estimated with alternative best-fit models are usually not significantly different from each other when evaluated with the same model. However, ML trees estimated with statistically supported models are often significantly suboptimal to ML trees made with the K2P model when both are evaluated with K2P, indicating that not all models perform in an equivalent manner. Nevertheless, the use of alternative statistically supported models generally does not affect tests of monophyletic relationships under either the Shimodaira-Hasegawa (S-H) or SOWH methods. Our results suggest that although choice in model selection has a strong impact on optimal tree topology, it rarely affects evolutionary inferences drawn from the data because differences are mainly confined to poorly supported nodes. Moreover, since ML with alternative best-fit models tends to produce more similar estimates of phylogeny than ML under the K2P model or MP, the use of any statistically based model-selection method is vastly preferable to forgoing the model-selection process altogether.