IQPNNI: moving fast through tree space and stopping in time

An efficient tree reconstruction method (IQPNNI) is introduced to reconstruct a phylogenetic tree based on DNA or amino acid sequence data. Our approach combines various fast algorithms to generate a list of potential candidate trees. The key ingredient is the definition of so-called important quartets (IQs), which allow the computation of an intermediate tree in O(n(2)) time for n sequences. The resulting tree is then further optimized by applying the nearest neighbor interchange (NNI) operation. Subsequently a random fraction of the sequences is deleted from the best tree found so far. The deleted sequences are then re-inserted in the smaller tree using the important quartet puzzling (IQP) algorithm. These steps are repeated several times and the best tree, with respect to the likelihood criterion, is considered as the inferred phylogenetic tree. Moreover, we suggest a rule which indicates when to stop the search. Simulations show that IQPNNI gives a slightly better accuracy than other programs tested. Moreover, we applied the approach to 218 small subunit rRNA sequences and 500 rbcL sequences. We found trees with higher likelihood compared to the results by others. A program to reconstruct DNA or amino acid based phylogenetic trees is available online (http://www.bi.uni-duesseldorf.de/software/iqpnni).     

Optimal algorithms for local vertex quartet cleaning

MOTIVATION: Reconstructing evolutionary trees is an important problem in biology. A response to the computational intractability of most of the traditional criteria for inferring evolutionary trees has been a focus on new criteria, particularly quartet-based methods that seek to merge trees derived on subsets of four species from a given species-set into a tree for that entire set. Unfortunately, most of these methods are very sensitive to errors in the reconstruction of the trees for individual quartets of species. A recently developed technique called quartet cleaning can alleviate this difficulty in certain cases by using redundant information in the complete set of quartet topologies for a given species-set to correct such errors. RESULTS: In this paper, we describe two new local vertex quartet cleaning algorithms which have optimal time complexity and error-correction bound, respectively. These are the first known local vertex quartet cleaning algorithms that are optimal with respect to either of these attributes.     

Quartet MaxCut: A fast algorithm for amalgamating quartet trees

Accurate phylogenetic reconstruction methods are inherently computationally heavy and therefore are limited to relatively small numbers of taxa. Supertree construction is the task of amalgamating small trees over partial sets into a big tree over the complete taxa set. The need for fast and accurate supertree methods has become crucial due to the enormous number of new genomic sequences generated by modern technology and the desire to use them for classification purposes. In particular, the Assembling the Tree of Life (ATOL) program aims at constructing the evolutionary history of all living organisms on Earth. When dealing with unrooted trees, a quartet - an unrooted tree over four taxa - is the most basic piece of phylogenetic information. Therefore, quartet amalgamation stands at the heart of any supertree problem as it concerns combining many minimal pieces of information into a single, coherent, and more comprehensive piece of information.We have devised an extremely fast algorithm for quartet amalgamation and implemented it in a very efficient code. The new code can handle over a hundred millions of quartet trees over several hundreds of taxa with very high accuracy.     

Fast local fragment chaining using sum-of-pair gap costs

Background

When inferring phylogenetic trees different algorithms may give different trees. To study such effects a measure for the distance between two trees is useful. Quartet distance is one such measure, and is the number of quartet topologies that differ between two trees.

Results

We have derived a new algorithm for computing the quartet distance between a pair of general trees, i.e. trees where inner nodes can have any degree ≥ 3. The time and space complexity of our algorithm is sub-cubic in the number of leaves and does not depend on the degree of the inner nodes. This makes it the fastest algorithm so far for computing the quartet distance between general trees independent of the degree of the inner nodes.

Conclusions

We have implemented our algorithm and two of the best competitors. Our new algorithm is significantly faster than the competition and seems to run in close to quadratic time in practice.     

Detecting highways of horizontal gene transfer

In a horizontal gene transfer (HGT) event, a gene is transferred between two species that do not have an ancestor-descendant relationship. Typically, no more than a few genes are horizontally transferred between any two species. However, several studies identified pairs of species between which many different genes were horizontally transferred. Such a pair is said to be linked by a highway of gene sharing. We present a method for inferring such highways. Our method is based on the fact that the evolutionary histories of horizontally transferred genes disagree with the corresponding species phylogeny. Specifically, given a set of gene trees and a trusted rooted species tree, each gene tree is first decomposed into its constituent quartet trees and the quartets that are inconsistent with the species tree are identified. Our method finds a pair of species such that a highway between them explains the largest (normalized) fraction of inconsistent quartets. For a problem on n species and m input quartet trees, we give an efficient O(m + n(2))-time algorithm for detecting highways, which is optimal with respect to the quartets input size. An application of our method to a dataset of 1128 genes from 11 cyanobacterial species, as well as to simulated datasets, illustrates the efficacy of our method.     

Fast calculation of the quartet distance between trees of arbitrary degrees

Background  

A number of algorithms have been developed for calculating the quartet distance between two evolutionary trees on the same set of species. The quartet distance is the number of quartets – sub-trees induced by four leaves – that differs between the trees. Mostly, these algorithms are restricted to work on binary trees, but recently we have developed algorithms that work on trees of arbitrary degree.     

An error-correcting map for quartets can improve the signals for phylogenetic trees

From the DNA sequences for N taxa, the (generally unknown) phylogenetic tree T that gave rise to them is to be reconstructed. Various methods give rise, for each quartet J consisting of exactly four taxa, to a predicted tree L(J) based only on the sequences in J, and these are then used to reconstruct T. The author defines an "error-correcting map" (Ec), which replaces each L(J) with a new tree, Ec(L)(J), which has been corrected using other trees, L(K), in the list L. The "quartet distance" between two trees is defined as the number of quartets J on which the two trees differ, and two distinct trees are shown to always have quartet distance of at least N - 3. If L has quartet distance at most (N - 4)/2 from T, then Ec(L) will coincide with the correct list for T; and this result cannot be improved. In general, Ec can correct many more errors in L. Iteration of the map Ec may produce still more accurate lists. Simulations are reported which often show improvement even when the quartet distance considerably exceeds (N - 4)/2. Moreover, the Buneman tree for Ec(L) is shown to refine the Buneman tree for L, so that strongly supported edges for L remain strongly supported for Ec(L). Simulations show that if methods such as the C-tree or hypercleaning are applied to Ec(L), the resulting trees often have more resolution than when the methods are applied only to L.     

An algebraic analysis of the two state Markov model on tripod trees

Methods of phylogenetic inference use more and more complex models to generate trees from data. However, even simple models and their implications are not fully understood. Here, we investigate the two-state Markov model on a tripod tree, inferring conditions under which a given set of observations gives rise to such a model. This type of investigation has been undertaken before by several scientists from different fields of research. In contrast to other work we fully analyse the model, presenting conditions under which one can infer a model from the observation or at least get support for the tree-shaped interdependence of the leaves considered. We also present all conditions under which the results can be extended from tripod trees to quartet trees, a step necessary to reconstruct at least a topology. Apart from finding conditions under which such an extension works we discuss example cases for which such an extension does not work.     

Fast and accurate phylogeny reconstruction algorithms based on the minimum-evolution principle.

The Minimum Evolution (ME) approach to phylogeny estimation has been shown to be statistically consistent when it is used in conjunction with ordinary least-squares (OLS) fitting of a metric to a tree structure. The traditional approach to using ME has been to start with the Neighbor Joining (NJ) topology for a given matrix and then do a topological search from that starting point. The first stage requires O(n(3)) time, where n is the number of taxa, while the current implementations of the second are in O(p n(3)) or more, where p is the number of swaps performed by the program. In this paper, we examine a greedy approach to minimum evolution which produces a starting topology in O(n(2)) time. Moreover, we provide an algorithm that searches for the best topology using nearest neighbor interchanges (NNIs), where the cost of doing p NNIs is O(n(2) + p n), i.e., O(n(2)) in practice because p is always much smaller than n. The Greedy Minimum Evolution (GME) algorithm, when used in combination with NNIs, produces trees which are fairly close to NJ trees in terms of topological accuracy. We also examine ME under a balanced weighting scheme, where sibling subtrees have equal weight, as opposed to the standard "unweighted" OLS, where all taxa have the same weight so that the weight of a subtree is equal to the number of its taxa. The balanced minimum evolution scheme (BME) runs slower than the OLS version, requiring O(n(2) x diam(T)) operations to build the starting tree and O(p n x diam(T)) to perform the NNIs, where diam(T) is the topological diameter of the output tree. In the usual Yule-Harding distribution on phylogenetic trees, the diameter expectation is in log(n), so our algorithms are in practice faster that NJ. Moreover, this BME scheme yields a very significant improvement over NJ and other distance-based algorithms, especially with large trees, in terms of topological accuracy.     

TreeSnatcher: coding trees from images

TreeSnatcher is a GUI-driven JAVA application for the semi-automatic recognition of multifurcating phylogenetic trees in pixel images. The program accepts an image file as input and analyzes the topology and the metrics of a tree depicted. The analysis is carried out in a multiple-stage process using algorithms from image analysis. In the end, TreeSnatcher produces a Newick tree code that represents the tree structure optionally including branch lengths. TreeSnatcher can process trees with 100 leaves or more in a few seconds. AVAILABILITY: TreeSnatcher was developed in JAVA under Mac OS X and is executable on UNIX/Linux, Windows and Mac OS X systems. The application and its documentation can be freely downloaded from http://www.cibiv.at/software/treesnatcher.     

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.     

Computing the all-pairs quartet distance on a set of evolutionary trees

We present two algorithms for calculating the quartet distance between all pairs of trees in a set of binary evolutionary trees on a common set of species. The algorithms exploit common substructure among the trees to speed up the pairwise distance calculations, thus performing significantly better on large sets of trees compared to performing distinct pairwise distance calculations, as we illustrate experimentally, where we see a speedup factor of around 130 in the best case.     

Quartets MaxCut: a divide and conquer quartets algorithm

Accurate phylogenetic reconstruction methods are currently limited to a maximum of few dozens of taxa. Supertree methods construct a large tree over a large set of taxa, from a set of small trees over overlapping subsets of the complete taxa set. Hence, in order to construct the tree of life over a million and a half different species, the use of a supertree method over the product of accurate methods, is inevitable. Perhaps the simplest version of this task that is still widely applicable, yet quite challenging, is quartet-based reconstruction. This problem lies at the root of many tree reconstruction methods and theoretical as well as experimental results have been reported. Nevertheless, dealing with false, conflicting quartet trees remains problematic. In this paper, we describe an algorithm for constructing a tree from a set of input quartet trees even with a significant fraction of errors. We show empirically that conflicts in the inputs are handled satisfactorily and that it significantly outperforms and outraces the Matrix Representation with Parsimony (MRP) methods that have previously been most successful in dealing with supertrees. Our algorithm is based on a divide and conquer algorithm where our divide step uses a semidefinite programming (SDP) formulation of MaxCut. We remark that this builds on previous work of ours for piecing together trees from rooted triplet trees. The recursion for unrooted quartets, however, is more complicated in that even with completely consistent set of quartet trees the problem is NP-hard, as opposed to the problem for triples where there is a linear time algorithm. This complexity leads to several issues and some solutions of possible independent interest.     

Phylogenetic analyses of amino acid variation in the serpin proteins

Phylogenetic analyses of 110 serpin protein sequences revealed clades consistent with independent phylogenetic analyses based on exon-intron structure and diagnostic amino acid sites. Trees were estimated by maximum likelihood, neighbor joining, and partial split decomposition using both the BLOSUM 62 and Jones-Taylor-Thornton substitution matrices. Neighbor-joining trees gave results closest to those based on independent analyses using genomic and chromosomal data. The maximum-likelihood trees derived using the quartet puzzling algorithm were very conservative, producing many small clades that separated groups of proteins that other results suggest were related. Independent analyses based on exon-intron structure suggested that a neighbor-joining tree was more accurate than maximum-likelihood trees obtained using the quartet puzzling algorithm.     

Fast recovery of evolutionary trees with thousands of nodes.

We present a novel distance-based algorithm for evolutionary tree reconstruction. Our algorithm reconstructs the topology of a tree with n leaves in O(n(2)) time using O(n) working space. In the general Markov model of evolution, the algorithm recovers the topology successfully with (1 - o(1)) probability from sequences with polynomial length in n. Moreover, for almost all trees, our algorithm achieves the same success probability on polylogarithmic sample sizes. The theoretical results are supported by simulation experiments involving trees with 500, 1,895, and 3,135 leaves. The topologies of the trees are recovered with high success from 2,000 bp DNA sequences.     

Encoding phylogenetic trees in terms of weighted quartets

One of the main problems in phylogenetics is to develop systematic methods for constructing evolutionary or phylogenetic trees. For a set of species X, an edge-weighted phylogenetic X-tree or phylogenetic tree is a (graph theoretical) tree with leaf set X and no degree 2 vertices, together with a map assigning a non-negative length to each edge of the tree. Within phylogenetics, several methods have been proposed for constructing such trees that work by trying to piece together quartet trees on X, i.e. phylogenetic trees each having four leaves in X. Hence, it is of interest to characterise when a collection of quartet trees corresponds to a (unique) phylogenetic tree. Recently, Dress and Erdös provided such a characterisation for binary phylogenetic trees, that is, phylogenetic trees all of whose internal vertices have degree 3. Here we provide a new characterisation for arbitrary phylogenetic trees.     

RadCon: phylogenetic tree comparison and consensus

SUMMARY: RadCon is a Macintosh program for manipulating and analysing phylogenetic trees. The program can determine the Cladistic Information Content of individual trees, the stability of leaves across a set of bootstrap trees, produce the strict basic Reduced Cladistic Consensus profile of a set of trees and convert a set of trees into its matrix representation for supertree construction. AVAILABILITY: The program is free and available at http://taxonomy.zoology.gla.ac.uk/ approximately jthorley/radcon/radcon.html.     

A fast algorithm to build a supertree with a set of gene trees

Important desired properties of an algorithm to construct a supertree (species tree) by reconciling input trees are its low complexity and applicability to large biological data. In its common statement the problem is proved to be NP-hard, i.e. to have an exponential complexity in practice. We propose a reformulation of the supertree building problem that allows a computationally effective solution. We introduce a biologically natural requirement that the supertree is sought for such that it does not contain clades incompatible with those existing in the input trees. The algorithm was tested with simulated and biological trees and was shown to possess an almost square complexity even if horizontal transfers are allowed. If HGTs are not assumed, the algorithm is mathematically correct and possesses the longest running time of n3 x[V0]3, where n is the number of input trees and [V0] is the total number of species. The authors are unaware of analogous solutions in published evidence. The corresponding inferring program, its usage examples and manual are freely available at http://lab6.iitp.ru/en/super3gl. The available program does not implement HGTs. The generalized case is described in the publication "A tree nearest in average to a set of trees" (Information Transmission Problems, 2011).     

A Drosophila homolog of bovine smg p25a GDP dissociation inhibitor undergoes a shift in isoelectric point in the developmental mutant quartet.

The Drosophila developmental mutation quartet causes late larval lethality and small imaginal discs and, when expressed in the adult female, has a lethal effect on early embryogenesis. These developmental defects are associated with mitotic defects, which include a low mitotic index in larval brains and incomplete separation of chromosomes in mitosis in the early embryo. quartet mutations also have a biochemical effect, i.e., a basic shift in isoelectric point in three proteins. We have purified one of these proteins, raised an antibody to it, and isolated and sequenced its cDNA. At the amino acid level, the sequence shows 68% identity and 81% similarity to bovine smg p25a GDP dissociation inhibitor (GDI), a regulator of ras-like small GTPases of the rab/SEC4/YPT1 subfamily. The correlation between a basic shift in isoelectric point in Drosophila GDI in quartet mutant tissue and the quartet developmental phenotype raises the possibility that a posttranslational modification of GDI is necessary for its function and that GDI function is essential for development.     

A novel algorithm and web-based tool for comparing two alternative phylogenetic trees

SUMMARY: We describe an algorithm and software tool for comparing alternative phylogenetic trees. The main application of the software is to compare phylogenies obtained using different phylogenetic methods for some fixed set of species or obtained using different gene sequences from those species. The algorithm pairs up each branch in one phylogeny with a matching branch in the second phylogeny and finds the optimum 1-to-1 map between branches in the two trees in terms of a topological score. The software enables the user to explore the corresponding mapping between the phylogenies interactively, and clearly highlights those parts of the trees that differ, both in terms of topology and branch length. AVAILABILITY: The software is implemented as a Java applet at http://www.mrc-bsu.cam.ac.uk/personal/thomas/phylo_comparison/comparison_page.html. It is also available on request from the authors.