Mukul S. Bansal

Efficient algorithms for the reconciliation problem with gene duplication, horizontal transfer and loss

Motivation: Gene family evolution is driven by evolutionary events such as speciation, gene duplication, horizontal gene transfer and gene loss, and inferring these events in the evolutionary history of a given gene family is a fundamental problem in comparative and evolutionary genomics with numerous important applications. Solving this problem requires the use of a reconciliation framework, where the input consists of a gene family phylogeny and the corresponding species phylogeny, and the goal is to reconcile the two by postulating speciation, gene duplication, horizontal gene transfer and gene loss events. This reconciliation problem is referred to as duplication-transfer-loss (DTL) reconciliation and has been extensively studied in the literature. Yet, even the fastest existing algorithms for DTL reconciliation are too slow for reconciling large gene families and for use in more sophisticated applications such as gene tree or species tree reconstruction. Results: We present two new algorithms for the DTL reconciliation problem that are dramatically faster than existing algorithms, both asymptotically and in practice. We also extend the standard DTL reconciliation model by considering distance-dependent transfer costs, which allow for more accurate reconciliation and give an efficient algorithm for DTL reconciliation under this extended model. We implemented our new algorithms and demonstrated up to 100 000-fold speed-up over existing methods, using both simulated and biological datasets. This dramatic improvement makes it possible to use DTL reconciliation for performing rigorous evolutionary analyses of large gene families and enables its use in advanced reconciliation-based gene and species tree reconstruction methods. Availability: Our programs can be freely downloaded from http://compbio.mit.edu/ranger-dtl/. Contact: mukul@csail.mit.edu; manoli@mit.edu Supplementary information: Supplementary data are available at Bioinformatics online.

DupTree: a program for large-scale phylogenetic analyses using gene tree parsimony

UNLABELLED DupTree is a new software program for inferring rooted species trees from collections of gene trees using the gene tree parsimony approach. The program implements a novel algorithm that significantly improves upon the run time of standard search heuristics for gene tree parsimony, and enables the first truly genome-scale phylogenetic analyses. In addition, DupTree allows users to examine alternate rootings and to weight the reconciliation costs for gene trees. DupTree is an open source project written in C++. AVAILABILITY DupTree for Mac OS X, Windows, and Linux along with a sample dataset and an on-line manual are available at http://genome.cs.iastate.edu/CBL/DupTree

Genome-Scale Phylogenetics: Inferring the Plant Tree of Life from 18,896 Gene Trees

Phylogenetic analyses using genome-scale data sets must confront incongruence among gene trees, which in plants is exacerbated by frequent gene duplications and losses. Gene tree parsimony (GTP) is a phylogenetic optimization criterion in which a species tree that minimizes the number of gene duplications induced among a set of gene trees is selected. The run time performance of previous implementations has limited its use on large-scale data sets. We used new software that incorporates recent algorithmic advances to examine the performance of GTP on a plant data set consisting of 18,896 gene trees containing 510,922 protein sequences from 136 plant taxa (giving a combined alignment length of >2.9 million characters). The relationships inferred from the GTP analysis were largely consistent with previous large-scale studies of backbone plant phylogeny and resolved some controversial nodes. The placement of taxa that were present in few gene trees generally varied the most among GTP bootstrap replicates. Excluding these taxa either before or after the GTP analysis revealed high levels of phylogenetic support across plants. The analyses supported magnoliids sister to a eudicot + monocot clade and did not support the eurosid I and II clades. This study presents a nuclear genomic perspective on the broad-scale phylogenic relationships among plants, and it demonstrates that nuclear genes with a history of duplication and loss can be phylogenetically informative for resolving the plant tree of life.

Robinson-Foulds Supertrees

BackgroundSupertree methods synthesize collections of small phylogenetic trees with incomplete taxon overlap into comprehensive trees, or supertrees, that include all taxa found in the input trees. Supertree methods based on the well established Robinson-Foulds (RF) distance have the potential to build supertrees that retain much information from the input trees. Specifically, the RF supertree problem seeks a binary supertree that minimizes the sum of the RF distances from the supertree to the input trees. Thus, an RF supertree is a supertree that is consistent with the largest number of clusters (or clades) from the input trees.ResultsWe introduce efficient, local search based, hill-climbing heuristics for the intrinsically hard RF supertree problem on rooted trees. These heuristics use novel non-trivial algorithms for the SPR and TBR local search problems which improve on the time complexity of the best known (naïve) solutions by a factor of Θ(n) and Θ(n2) respectively (where n is the number of taxa, or leaves, in the supertree). We use an implementation of our new algorithms to examine the performance of the RF supertree method and compare it to matrix representation with parsimony (MRP) and the triplet supertree method using four supertree data sets. Not only did our RF heuristic provide fast estimates of RF supertrees in all data sets, but the RF supertrees also retained more of the information from the input trees (based on the RF distance) than the other supertree methods.ConclusionsOur heuristics for the RF supertree problem, based on our new local search algorithms, make it possible for the first time to estimate large supertrees by directly optimizing the RF distance from rooted input trees to the supertrees. This provides a new and fast method to build accurate supertrees. RF supertrees may also be useful for estimating majority-rule(-) supertrees, which are a generalization of majority-rule consensus trees.

iGTP: A software package for large-scale gene tree parsimony analysis

BackgroundThe ever-increasing wealth of genomic sequence information provides an unprecedented opportunity for large-scale phylogenetic analysis. However, species phylogeny inference is obfuscated by incongruence among gene trees due to evolutionary events such as gene duplication and loss, incomplete lineage sorting (deep coalescence), and horizontal gene transfer. Gene tree parsimony (GTP) addresses this issue by seeking a species tree that requires the minimum number of evolutionary events to reconcile a given set of incongruent gene trees. Despite its promise, the use of gene tree parsimony has been limited by the fact that existing software is either not fast enough to tackle large data sets or is restricted in the range of evolutionary events it can handle.ResultsWe introduce iGTP, a platform-independent software program that implements state-of-the-art algorithms that greatly speed up species tree inference under the duplication, duplication-loss, and deep coalescence reconciliation costs. iGTP significantly extends and improves the functionality and performance of existing gene tree parsimony software and offers advanced features such as building effective initial trees using stepwise leaf addition and the ability to have unrooted gene trees in the input. Moreover, iGTP provides a user-friendly graphical interface with integrated tree visualization software to facilitate analysis of the results.ConclusionsiGTP enables, for the first time, gene tree parsimony analyses of thousands of genes from hundreds of taxa using the duplication, duplication-loss, and deep coalescence reconciliation costs, all from within a convenient graphical user interface.

TreeFix: statistically informed gene tree error correction using species trees.

Accurate gene tree reconstruction is a fundamental problem in phylogenetics, with many important applications. However, sequence data alone often lack enough information to confidently support one gene tree topology over many competing alternatives. Here, we present a novel framework for combining sequence data and species tree information, and we describe an implementation of this framework in TreeFix, a new phylogenetic program for improving gene tree reconstructions. Given a gene tree (preferably computed using a maximum-likelihood phylogenetic program), TreeFix finds a “statistically equivalent” gene tree that minimizes a species tree-based cost function. We have applied TreeFix to 2 clades of 12 Drosophila and 16 fungal genomes, as well as to simulated phylogenies and show that it dramatically improves reconstructions compared with current state-of-the-art programs. Given its accuracy, speed, and simplicity, TreeFix should be applicable to a wide range of analyses and have many important implications for future investigations of gene evolution. The source code and a sample data set are available at http://compbio.mit.edu/treefix.

Heuristics for the gene-duplication problem: a Θ(n) speed-up for the local search

The gene-duplication problem is to infer a species supertree from a collection of gene trees that are confounded by complex histories of gene duplications. This problem is NP-hard and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. We show how this local search problem can be solved efficiently by reusing previously computed information. This improves the running time of the current solution by a factor of n, where n is the number of species in the resulting supertree solution, and makes the gene-duplication problem more tractable for large-scale phylogenetic analyses. We verify the exceptional performance of our solution in a comparison study using sets of large randomly generated gene trees. Furthermore, we demonstrate the utility of our solution by incorporating large genomic data sets from GenBank into a supertree analysis of plants.

Efficient genome-scale phylogenetic analysis under the duplication- loss and deep coalescence cost models

BackgroundGenomic data provide a wealth of new information for phylogenetic analysis. Yet making use of this data requires phylogenetic methods that can efficiently analyze extremely large data sets and account for processes of gene evolution, such as gene duplication and loss, incomplete lineage sorting (deep coalescence), or horizontal gene transfer, that cause incongruence among gene trees. One such approach is gene tree parsimony, which, given a set of gene trees, seeks a species tree that requires the smallest number of evolutionary events to explain the incongruence of the gene trees. However, the only existing algorithms for gene tree parsimony under the duplication-loss or deep coalescence reconciliation cost are prohibitively slow for large datasets.ResultsWe describe novel algorithms for SPR and TBR based local search heuristics under the duplication-loss cost, and we show how they can be adapted for the deep coalescence cost. These algorithms improve upon the best existing algorithms for these problems by a factor of n, where n is the number of species in the collection of gene trees. We implemented our new SPR based local search algorithm for the duplication-loss cost and demonstrate the tremendous improvement in runtime and scalability it provides compared to existing implementations. We also evaluate the performance of our algorithm on three large-scale genomic data sets.ConclusionOur new algorithms enable, for the first time, gene tree parsimony analyses of thousands of genes from hundreds of taxa using the duplication-loss and deep coalescence reconciliation costs. Thus, this work expands both the size of data sets and the range of evolutionary models that can be incorporated into genome-scale phylogenetic analyses.

Reconciliation Revisited: Handling Multiple Optima when Reconciling with Duplication, Transfer, and Loss

Phylogenetic tree reconciliation is a powerful approach for inferring evolutionary events like gene duplication, horizontal gene transfer, and gene loss, which are fundamental to our understanding of molecular evolution. While duplication-loss (DL) reconciliation leads to a unique maximum-parsimony solution, duplication-transfer-loss (DTL) reconciliation yields a multitude of optimal solutions, making it difficult to infer the true evolutionary history of the gene family. This problem is further exacerbated by the fact that different event cost assignments yield different sets of optimal reconciliations. Here, we present an effective, efficient, and scalable method for dealing with these fundamental problems in DTL reconciliation. Our approach works by sampling the space of optimal reconciliations uniformly at random and aggregating the results. We show that even gene trees with only a few dozen genes often have millions of optimal reconciliations and present an algorithm to efficiently sample the space of optimal reconciliations uniformly at random in O(mn(2)) time per sample, where m and n denote the number of genes and species, respectively. We use these samples to understand how different optimal reconciliations vary in their node mappings and event assignments and to investigate the impact of varying event costs. We apply our method to a biological dataset of approximately 4700 gene trees from 100 taxa and observe that 93% of event assignments and 73% of mappings remain consistent across different multiple optima. Our analysis represents the first systematic investigation of the space of optimal DTL reconciliations and has many important implications for the study of gene family evolution.

Comparing and aggregating partially resolved trees

Partially-resolved-that is, non-binary-trees arise frequently in the analysis of species evolution. Non-binary nodes, also called multifurcations, must be treated carefully, since they can be interpreted as reflecting either lack of information or actual evolutionary history. While several distance measures exist for comparing trees, none of them deal explicitly with this dichotomy. Here we introduce two kinds of distance measures between rooted and unrooted partially-resolved phylogenetic trees over the same set of species; the measures address multifurcations directly. For rooted trees, the measures are based on the topologies the input trees induce on triplets; that is, on three-element subsets of the set of species. For unrooted trees, the measures are based on quartets (four-element subsets). The first class of measures are parametric distances, where there is a parameter that weighs the difference between an unresolved triplet/quartet topology and a resolved one. The second class of measures are based on the Hausdorff distance, where each tree is viewed as a set of all possible ways in which the tree can be refined to eliminate unresolved nodes. We give efficient algorithms for computing parametric distances and give conditions under which Hausdorff distances can be calculated approximately in polynomial time. Additionally, we (i) derive the expected value of the parametric distance between two random trees, (ii) characterize the conditions under which parametric distances are near-metrics or metrics, (iii) study the computational and algorithmic properties of consensus tree methods based on the measures, and (iv) analyze the interrelationships among Hausdorff and parametric distances.