Phylogenetic mixtures on a single tree can mimic a tree of another topology

Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data are generated by a mixture model has stimulated considerable recent debate. Much of the controversy stems from simulations of mixture model data on a given tree topology for which reconstruction algorithms output a tree of a different topology; these findings were held up to show the shortcomings of particular tree reconstruction methods. In so doing, the underlying assumption was that mixture model data on one topology can be distinguished from data evolved on an unmixed tree of another topology given enough data and the "correct" method. Here we show that this assumption can be false. For biologists, our results imply that, for example, the combined data from two genes whose phylogenetic trees differ only in terms of branch lengths can perfectly fit a tree of a different topology.     

ggtreeExtra: Compact Visualization of Richly Annotated Phylogenetic Data

We present the ggtreeExtra package for visualizing heterogeneous data with a phylogenetic tree in a circular or rectangular layout (https://www.bioconductor.org/packages/ggtreeExtra). The package supports more data types and visualization methods than other tools. It supports using the grammar of graphics syntax to present data on a tree with richly annotated layers and allows evolutionary statistics inferred by commonly used software to be integrated and visualized with external data. GgtreeExtra is a universal tool for tree data visualization. It extends the applications of the phylogenetic tree in different disciplines by making more domain-specific data to be available to visualize and interpret in the evolutionary context.     

Constructing splits graphs

Phylogenetic trees correspond one-to-one to compatible systems of splits and so splits play an important role in theoretical and computational aspects of phylogeny. Whereas any tree reconstruction method can be thought of as producing a compatible system of splits, an increasing number of phylogenetic algorithms are available that compute split systems that are not necessarily compatible and, thus, cannot always be represented by a tree. Such methods include the split decomposition, Neighbor-Net, consensus networks, and the Z-closure method. A more general split system of this kind can be represented graphically by a so-called splits graph, which generalizes the concept of a phylogenetic tree. This paper addresses the problem of computing a splits graph for a given set of splits. We have implemented all presented algorithms in a new program called SplitsTree4.     

Drawing Rooted Phylogenetic Networks

The evolutionary history of a collection of species is usually represented by a phylogenetic tree. Sometimes, phylogenetic networks are used as a means of representing reticulate evolution or of showing uncertainty and incompatibilities in evolutionary datasets. This is often done using unrooted phylogenetic networks such as split networks, due in part, to the availability of software (SplitsTree) for their computation and visualization. In this paper we discuss the problem of drawing rooted phylogenetic networks as cladograms or phylograms in a number of different views that are commonly used for rooted trees. Implementations of the algorithms are available in new releases of the Dendroscope and SplitsTree programs.     

A structural EM algorithm for phylogenetic inference.

A central task in the study of molecular evolution is the reconstruction of a phylogenetic tree from sequences of current-day taxa. The most established approach to tree reconstruction is maximum likelihood (ML) analysis. Unfortunately, searching for the maximum likelihood phylogenetic tree is computationally prohibitive for large data sets. In this paper, we describe a new algorithm that uses Structural Expectation Maximization (EM) for learning maximum likelihood phylogenetic trees. This algorithm is similar to the standard EM method for edge-length estimation, except that during iterations of the Structural EM algorithm the topology is improved as well as the edge length. Our algorithm performs iterations of two steps. In the E-step, we use the current tree topology and edge lengths to compute expected sufficient statistics, which summarize the data. In the M-Step, we search for a topology that maximizes the likelihood with respect to these expected sufficient statistics. We show that searching for better topologies inside the M-step can be done efficiently, as opposed to standard methods for topology search. We prove that each iteration of this procedure increases the likelihood of the topology, and thus the procedure must converge. This convergence point, however, can be a suboptimal one. To escape from such "local optima," we further enhance our basic EM procedure by incorporating moves in the flavor of simulated annealing. We evaluate these new algorithms on both synthetic and real sequence data and show that for protein sequences even our basic algorithm finds more plausible trees than existing methods for searching maximum likelihood phylogenies. Furthermore, our algorithms are dramatically faster than such methods, enabling, for the first time, phylogenetic analysis of large protein data sets in the maximum likelihood framework.     

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.      

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.     

The performance of phylogenetic algorithms in estimating haplotype genealogies with migration

Genealogies estimated from haplotypic genetic data play a prominent role in various biological disciplines in general and in phylogenetics, population genetics and phylogeography in particular. Several software packages have specifically been developed for the purpose of reconstructing genealogies from closely related, and hence, highly similar haplotype sequence data. Here, we use simulated data sets to test the performance of traditional phylogenetic algorithms, neighbour-joining, maximum parsimony and maximum likelihood in estimating genealogies from nonrecombining haplotypic genetic data. We demonstrate that these methods are suitable for constructing genealogies from sets of closely related DNA sequences with or without migration. As genealogies based on phylogenetic reconstructions are fully resolved, but not necessarily bifurcating, and without reticulations, these approaches outperform widespread 'network' constructing methods. In our simulations of coalescent scenarios involving panmictic, symmetric and asymmetric migration, we found that phylogenetic reconstruction methods performed well, while the statistical parsimony approach as implemented in TCS performed poorly. Overall, parsimony as implemented in the PHYLIP package performed slightly better than other methods. We further point out that we are not making the case that widespread 'network' constructing methods are bad, but that traditional phylogenetic tree finding methods are applicable to haplotypic data and exhibit reasonable performance with respect to accuracy and robustness. We also discuss some of the problems of converting a tree to a haplotype genealogy, in particular that it is nonunique.     

Algorithms for MDC-based multi-locus phylogeny inference: beyond rooted binary gene trees on single alleles

One of the criteria for inferring a species tree from a collection of gene trees, when gene tree incongruence is assumed to be due to incomplete lineage sorting (ILS), is Minimize Deep Coalescence (MDC). Exact algorithms for inferring the species tree from rooted, binary trees under MDC were recently introduced. Nevertheless, in phylogenetic analyses of biological data sets, estimated gene trees may differ from true gene trees, be incompletely resolved, and not necessarily rooted. In this article, we propose new MDC formulations for the cases where the gene trees are unrooted/binary, rooted/non-binary, and unrooted/non-binary. Further, we prove structural theorems that allow us to extend the algorithms for the rooted/binary gene tree case to these cases in a straightforward manner. In addition, we devise MDC-based algorithms for cases when multiple alleles per species may be sampled. We study the performance of these methods in coalescent-based computer simulations.     

On the use of cartographic projections in visualizing phylo-genetic tree space

Phylogenetic analysis is becoming an increasingly important tool for biological research. Applications include epidemiological studies, drug development, and evolutionary analysis. Phylogenetic search is a known NP-Hard problem. The size of the data sets which can be analyzed is limited by the exponential growth in the number of trees that must be considered as the problem size increases. A better understanding of the problem space could lead to better methods, which in turn could lead to the feasible analysis of more data sets. We present a definition of phylogenetic tree space and a visualization of this space that shows significant exploitable structure. This structure can be used to develop search methods capable of handling much larger data sets.     

Direct maximum parsimony phylogeny reconstruction from genotype data

Background  

Maximum parsimony phylogenetic tree reconstruction from genetic variation data is a fundamental problem in computational genetics with many practical applications in population genetics, whole genome analysis, and the search for genetic predictors of disease. Efficient methods are available for reconstruction of maximum parsimony trees from haplotype data, but such data are difficult to determine directly for autosomal DNA. Data more commonly is available in the form of genotypes, which consist of conflated combinations of pairs of haplotypes from homologous chromosomes. Currently, there are no general algorithms for the direct reconstruction of maximum parsimony phylogenies from genotype data. Hence phylogenetic applications for autosomal data must therefore rely on other methods for first computationally inferring haplotypes from genotypes.     

GenNon-h: Generating multiple sequence alignments on nonhomogeneous phylogenetic trees

ABSTRACT: BACKGROUND: A number of software packages are available to generate DNA multiple sequence alignments (MSAs) evolved under continuous-time Markov processes on phylogenetic trees. On the other hand, methods of simulating the DNA MSA directly from the transition matrices do not exist. Moreover, existing software restricts to the time-reversible models and it is not optimized to generate nonhomogeneous data (i.e. placing distinct substitution rates at different lineages). RESULTS: We present the first package designed to generate MSAs evolving under discrete-time Markov processes on phylogenetic trees, directly from probability substitution matrices. Based on the input model and a phylogenetic tree in the Newick format (with branch lengths measured as the expected number of substitutions per site), the algorithm produces DNA alignments of desired length. GenNon-h is publicly available for download. CONCLUSION: The software presented here is an efficient tool to generate DNA MSAs on a given phylogenetic tree. GenNon-h provides the user with the nonstationary or nonhomogeneous phylogenetic data that is well suited for testing complex biological hypotheses, exploring the limits of the reconstruction algorithms and their robustness to such models.     

Accelerated likelihood surface exploration: the likelihood ratchet

The existence of multiple likelihood maxima necessitates algorithms that explore a large part of the tree space. However, because of computational constraints, stepwise addition-based tree-searching methods do not allow for this exploration in reasonable time. Here, I present an algorithm that increases the speed at which the likelihood landscape can be explored. The iterative algorithm combines the computational speed of distance-based tree construction methods to arrive at approximations of the global optimum with the accuracy of optimality criterion based branch-swapping methods to improve on the result of the starting tree. The algorithm moves between local optima by iteratively perturbing the tree landscape through a process of reweighting randomly drawn samples of the underlying sequence data set. Tests on simulated and real data sets demonstrated that the optimal solution obtained using stepwise addition-based heuristic searches was found faster using the algorithm presented here. Tests on a previously published data set that established the presence of tree islands under maximum likelihood demonstrated that the algorithm identifies the same tree islands in a shorter amount of time than that needed using stepwise addition. The algorithm can be readily applied using standard software for phylogenetic inference.     

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。     

Computationally difficult parsimony problems in phylogenetic systematics

A basic problem in phylogenetic systematics is to construct an evolutionary hypothesis, or phylogenetic tree, from available data for a set of operational taxonomic units (OTUs). Associated with the edges of such trees are weights that usually are interpreted as lengths. Methods proposed for constructing phylogenetic trees attempt to select from among the myriad alternatives a tree that optimizes in some sense the fit of tree topology and edge lengths with the original data. One optimization criterion seeks a most parsimonious tree in which the sum of edge lengths is a minimum. Researchers have failed to develop efficient algorithms to compute optimal solutions for important variations of the parsimonious tree construction problem. Recently Graham & Foulds (1982) proved that a special case of the problem is NP-complete, thus making it unlikely that the computational problem for this case can be solved efficiently. I describe three other parsimonious tree construction problems and prove that they, too, are NP-complete.     

Stochastic search strategy for estimation of maximum likelihood phylogenetic trees

The maximum likelihood (ML) method of phylogenetic tree construction is not as widely used as other tree construction methods (e.g., parsimony, neighbor-joining) because of the prohibitive amount of time required to find the ML tree when the number of sequences under consideration is large. To overcome this difficulty, we propose a stochastic search strategy for estimation of the ML tree that is based on a simulated annealing algorithm. The algorithm works by moving through tree space by way of a "local rearrangement" strategy so that topologies that improve the likelihood are always accepted, whereas those that decrease the likelihood are accepted with a probability that is related to the proportionate decrease in likelihood. Besides greatly reducing the time required to estimate the ML tree, the stochastic search strategy is less likely to become trapped in local optima than are existing algorithms for ML tree estimation. We demonstrate the success of the modified simulated annealing algorithm by comparing it with two existing algorithms (Swofford's PAUP* and Felsenstein's DNAMLK) for several theoretical and real data examples.     

Three-Dimensional Phylogeny Explorer: Distinguishing paralogs,lateral transfer,and violation of "molecular clock" assumption with 3D visualization

Background  

Construction and interpretation of phylogenetic trees has been a major research topic for understanding the evolution of genes. Increases in sequence data and complexity are creating a need for more powerful and insightful tree visualization tools.     

High-throughput peptide quantification using mTRAQ reagent triplex

Background

Continuing research into the global multiple sequence alignment problem has resulted in more sophisticated and principled alignment methods. Unfortunately these new algorithms often require large amounts of time and memory to run, making it nearly impossible to run these algorithms on large datasets. As a solution, we present two general methods, Crumble and Prune, for breaking a phylogenetic alignment problem into smaller, more tractable sub-problems. We call Crumble and Prune meta-alignment methods because they use existing alignment algorithms and can be used with many current alignment programs. Crumble breaks long alignment problems into shorter sub-problems. Prune divides the phylogenetic tree into a collection of smaller trees to reduce the number of sequences in each alignment problem. These methods are orthogonal: they can be applied together to provide better scaling in terms of sequence length and in sequence depth. Both methods partition the problem such that many of the sub-problems can be solved independently. The results are then combined to form a solution to the full alignment problem.

Results

Crumble and Prune each provide a significant performance improvement with little loss of accuracy. In some cases, a gain in accuracy was observed. Crumble and Prune were tested on real and simulated data. Furthermore, we have implemented a system called Job-tree that allows hierarchical sub-problems to be solved in parallel on a compute cluster, significantly shortening the run-time.

Conclusions

These methods enabled us to solve gigabase alignment problems. These methods could enable a new generation of biologically realistic alignment algorithms to be applied to real world, large scale alignment problems.     

PhyloWidget: web-based visualizations for the tree of life

PhyloWidget is a web-based tool for the visualization and manipulation of phylogenetic tree data. It can be accessed online or downloaded as a standalone application. A simple URL-based API allows databases to easily link to and customize PhyloWidget for interactively viewing medium- to large-sized trees. AVAILABILITY: PhyloWidget is available for online use or download at http://www.phylowidget.org/.