Cuong Than

PhyloNet: a software package for analyzing and reconstructing reticulate evolutionary relationships

BackgroundPhylogenies, i.e., the evolutionary histories of groups of taxa, play a major role in representing the interrelationships among biological entities. Many software tools for reconstructing and evaluating such phylogenies have been proposed, almost all of which assume the underlying evolutionary history to be a tree. While trees give a satisfactory first-order approximation for many families of organisms, other families exhibit evolutionary mechanisms that cannot be represented by trees. Processes such as horizontal gene transfer (HGT), hybrid speciation, and interspecific recombination, collectively referred to as reticulate evolutionary events, result in networks, rather than trees, of relationships. Various software tools have been recently developed to analyze reticulate evolutionary relationships, which include SplitsTree4, LatTrans, EEEP, HorizStory, and T-REX.ResultsIn this paper, we report on the PhyloNet software package, which is a suite of tools for analyzing reticulate evolutionary relationships, or evolutionary networks, which are rooted, directed, acyclic graphs, leaf-labeled by a set of taxa. These tools can be classified into four categories: (1) evolutionary network representation: reading/writing evolutionary networks in a newly devised compact form; (2) evolutionary network characterization: analyzing evolutionary networks in terms of three basic building blocks – trees, clusters, and tripartitions; (3) evolutionary network comparison: comparing two evolutionary networks in terms of topological dissimilarities, as well as fitness to sequence evolution under a maximum parsimony criterion; and (4) evolutionary network reconstruction: reconstructing an evolutionary network from a species tree and a set of gene trees.ConclusionThe software package, PhyloNet, offers an array of utilities to allow for efficient and accurate analysis of evolutionary networks. The software package will help significantly in analyzing large data sets, as well as in studying the performance of evolutionary network reconstruction methods. Further, the software package supports the proposed eNewick format for compact representation of evolutionary networks, a feature that allows for efficient interoperability of evolutionary network software tools. Currently, all utilities in PhyloNet are invoked on the command line.

Species tree inference by minimizing deep coalescences.

In a 1997 seminal paper, W. Maddison proposed minimizing deep coalescences, or MDC, as an optimization criterion for inferring the species tree from a set of incongruent gene trees, assuming the incongruence is exclusively due to lineage sorting. In a subsequent paper, Maddison and Knowles provided and implemented a search heuristic for optimizing the MDC criterion, given a set of gene trees. However, the heuristic is not guaranteed to compute optimal solutions, and its hill-climbing search makes it slow in practice. In this paper, we provide two exact solutions to the problem of inferring the species tree from a set of gene trees under the MDC criterion. In other words, our solutions are guaranteed to find the tree that minimizes the total number of deep coalescences from a set of gene trees. One solution is based on a novel integer linear programming (ILP) formulation, and another is based on a simple dynamic programming (DP) approach. Powerful ILP solvers, such as CPLEX, make the first solution appealing, particularly for very large-scale instances of the problem, whereas the DP-based solution eliminates dependence on proprietary tools, and its simplicity makes it easy to integrate with other genomic events that may cause gene tree incongruence. Using the exact solutions, we analyze a data set of 106 loci from eight yeast species, a data set of 268 loci from eight Apicomplexan species, and several simulated data sets. We show that the MDC criterion provides very accurate estimates of the species tree topologies, and that our solutions are very fast, thus allowing for the accurate analysis of genome-scale data sets. Further, the efficiency of the solutions allow for quick exploration of sub-optimal solutions, which is important for a parsimony-based criterion such as MDC, as we show. We show that searching for the species tree in the compatibility graph of the clusters induced by the gene trees may be sufficient in practice, a finding that helps ameliorate the computational requirements of optimization solutions. Further, we study the statistical consistency and convergence rate of the MDC criterion, as well as its optimality in inferring the species tree. Finally, we show how our solutions can be used to identify potential horizontal gene transfer events that may have caused some of the incongruence in the data, thus augmenting Maddisons original framework. We have implemented our solutions in the PhyloNet software package, which is freely available at: http://bioinfo.cs.rice.edu/phylonet.

Coalescent Histories on Phylogenetic Networks and Detection of Hybridization Despite Incomplete Lineage Sorting

Analyses of the increasingly available genomic data continue to reveal the extent of hybridization and its role in the evolutionary diversification of various groups of species. We show, through extensive coalescent-based simulations of multilocus data sets on phylogenetic networks, how divergence times before and after hybridization events can result in incomplete lineage sorting with gene tree incongruence signatures identical to those exhibited by hybridization. Evolutionary analysis of such data under the assumption of a species tree model can miss all hybridization events, whereas analysis under the assumption of a species network model would grossly overestimate hybridization events. These issues necessitate a paradigm shift in evolutionary analysis under these scenarios, from a model that assumes a priori a single source of gene tree incongruence to one that integrates multiple sources in a unifying framework. We propose a framework of coalescence within the branches of a phylogenetic network and show how this framework can be used to detect hybridization despite incomplete lineage sorting. We apply the model to simulated data and show that the signature of hybridization can be revealed as long as the interval between the divergence times of the species involved in hybridization is not too small. We reanalyze a data set of 106 loci from 7 in-group Saccharomyces species for which a species tree with no hybridization has been reported in the literature. Our analysis supports the hypothesis that hybridization occurred during the evolution of this group, explaining a large amount of the incongruence in the data. Our findings show that an integrative approach to gene tree incongruence and its reconciliation is needed. Our framework will help in systematically analyzing genomic data for the occurrence of hybridization and elucidating its evolutionary role.

Confounding Factors in HGT Detection: Statistical Error, Coalescent Effects, and Multiple Solutions

Prokaryotic organisms share genetic material across species boundaries by means of a process known as horizontal gene transfer (HGT). This process has great significance for understanding prokaryotic genome diversification and unraveling their complexities. Phylogeny-based detection of HGT is one of the most commonly used methods for this task, and is based on the fundamental fact that HGT may cause gene trees to disagree with one another, as well as with the species phylogeny. Using these methods, we can compare gene and species trees, and infer a set of HGT events to reconcile the differences among these trees. In this paper, we address three factors that confound the detection of the true HGT events, including the donors and recipients of horizontally transferred genes. First, we study experimentally the effects of error in the estimated gene trees (statistical error) on the accuracy of inferred HGT events. Our results indicate that statistical error leads to overestimation of the number of HGT events, and that HGT detection methods should be designed with unresolved gene trees in mind. Second, we demonstrate, both theoretically and empirically, that based on topological comparison alone, the number of HGT scenarios that reconcile a pair of species/gene trees may be exponential. This number may be reduced when branch lengths in both trees are estimated correctly. This set of results implies that in the absence of additional biological information, and/or a biological model of how HGT occurs, multiple HGT scenarios must be sought, and efficient strategies for how to enumerate such solutions must be developed. Third, we address the issue of lineage sorting, how it confounds HGT detection, and how to incorporate it with HGT into a single stochastic framework that distinguishes between the two events by extending population genetics theories. This result is very important, particularly when analyzing closely related organisms, where coalescent effects may not be ignored when reconciling gene trees. In addition to these three confounding factors, we consider the problem of enumerating all valid coalescent scenarios that constitute plausible species/gene tree reconciliations, and develop a polynomial-time dynamic programming algorithm for solving it. This result bears great significance on reducing the search space for heuristics that seek reconciliation scenarios. Finally, we show, empirically, that the locality of incongruence between a pair of trees has an impact on the numbers of HGT and coalescent reconciliation scenarios.

Seeing the trees and their branches in the network is hard

Phylogenetic networks are a restricted class of directed acyclic graphs that model evolutionary histories in the presence of reticulate evolutionary events, such as horizontal gene transfer, hybrid speciation, and recombination. Characterizing a phylogenetic network as a collection of trees and their branches has long been the basis for several methods of reconstructing and evaluating phylogenetic networks. Further, these characterizations have been used to understand molecular sequence evolution on phylogenetic networks. In this paper, we address theoretical questions with regard to phylogenetic networks, their characterizations, and sequence evolution on them. In particular, we prove that the problem of deciding whether a given tree is contained inside a network is NP-complete. Further, we prove that the problem of deciding whether a branch of a given tree is also a branch of a given network is polynomially equivalent to that of deciding whether the evolution of a molecular character (site) on a network is governed by the infinite site model. Exploiting this equivalence, we establish the NP-completeness of both problems, and provide a parameterized algorithm that runs in time O(2^k^/^2n^2), where n is the total number of nodes and k is the number of recombination nodes in the network, which significantly improves upon the trivial brute-force O(2^kn) time algorithm for the problem. This reduction in time is significant, particularly when analyzing recombination hotspots.

Mathematical Properties of the Deep Coalescence Cost

In the minimizing-deep-coalescences (MDC) approach for species tree inference, a tree that has the minimal deep coalescence cost for reconciling a collection of gene trees is taken as an estimate of the species tree topology. The MDC method possesses the desirable Pareto property, and in practice it is quite accurate and computationally efficient. Here, in order to better understand the MDC method, we investigate some properties of the deep coalescence cost. We prove that the unit neighborhood of either a rooted species tree or a rooted gene tree under the deep coalescence cost is exactly the same as the trees unit neighborhood under the rooted nearest-neighbor interchange (NNI) distance. Next, for a fixed species tree, we obtain the maximum deep coalescence cost across all gene trees as well as the number of gene trees that achieve the maximum cost. We also study corresponding problems for a fixed gene tree.

SPR-BASED TREE RECONCILIATION: NON-BINARY TREES AND MULTIPLE SOLUTIONS

The SPR (subtree prune and regraft) operation is used as the basis for reconciling incongruent phylogenetic trees, particularly for detecting and analyzing non-treelike evolutionary histories such as horizontal gene transfer, hybrid speciation, and recombination. The SPR-based tree reconciliation problem has been shown to be NP-hard, and several efficient heuristics have been designed to solve it. A major drawback of these heuristics is that for the most part they do not handle non-binary trees appropriately. Further, their computational efficiency suffers significantly when computing multiple optimal reconciliations. In this paper, we present algorithmic techniques for efficient SPR-based reconciliation of trees that are not necessarily binary. Further, we present divide-and-conquer approaches that enable efficient computing of multiple optimal reconciliations. We have implemented our techniques in the PhyloNet software package, which is publicly available at http://bioinfo.cs.rice.edu. The resulting method outperforms all existing methods in terms of speed, and performs at least as well as those methods in terms of accuracy.

Identifiability issues in phylogeny-based detection of horizontal gene transfer

Prokaryotic organisms share genetic material across species boundaries by means of a process known as horizontal gene transfer (HGT). Detecting this process bears great significance on understanding prokaryotic genome diversification and unraveling their complexities. Phylogeny-based detection of HGT is one of the most commonly used approaches for this task, and is based on the fundamental fact that HGT may cause gene trees to disagree with one another, as well as with the species phylogeny. Hence, methods that adopt this approach compare gene and species trees, and infer a set of HGT events to reconcile the differences among these trees. In this paper, we address some of the identifiability issues that face phylogeny-based detection of HGT. In particular, we show the effect of inaccuracies in the reconstructed (species and gene) trees on inferring the correct number of HGT events. Further, we show that a large number of maximally parsimonious HGT scenarios may exist. These results indicate that accurate detection of HGT requires accurate reconstruction of individual trees, and necessitates the search for more than a single scenario to explain gene tree disagreements. Finally, we show that disagreements among trees may be a result of not only HGT, but also lineage sorting, and make initial progress on incorporating HGT into the coalescent model, so as to stochastically distinguish between the two and make an accurate reconciliation. This contribution is very significant, particularly when analyzing closely related organisms.

Integrating Sequence and Topology for Efficient and Accurate Detection of Horizontal Gene Transfer

One phylogeny-based approach to horizontal gene transfer (HGT) detection entails comparing the topology of a gene tree to that of the species tree, and using their differences to locate HGT events. Another approach is based on augmenting a species tree into a phylogenetic network to improve the fitness of the evolution of the gene sequence data under an optimization criterion, such as maximum parsimony (MP). One major problem with the first approach is that gene tree estimates may have wrong branches, which result in false positive estimates of HGT events, and the second approach is accurate, yet suffers from the computational complexity of searching through the space of possible phylogenetic networks. The contributions of this paper are two-fold. First, we present a measure that computes the support of HGT events inferred from pairs of species and gene trees. The measure uses the bootstrap values of the gene tree branches. Second, we present an integrative method to speed up the approaches for augmenting species trees into phylogenetic networks. We conducted data analysis and performance study of our methods on a data set of 20 genes from the Amborellamitochondrial genome, in which Jeffrey Palmer and his co-workers postulated a massive amount of horizontal gene transfer. As expected, we found that including poorly supported gene tree branches in the analysis results in a high rate of false positive gene transfer events. Further, the bootstrap-based support measure assessed, with high accuracy, the support of the inferred gene transfer events. Further, we obtained very promising results, in terms of both speed and accuracy, when applying our integrative method on these data sets (we are currently studying the performance in extensive simulations). All methods have been implemented in the PhyloNet and NEPAL tools, which are available in the form of executable code from http://bioinfo.cs.rice.edu .

Mean deep coalescence cost under exchangeable probability distributions

Abstract We derive formulas for mean deep coalescence cost, for either a fixed species tree or a fixed gene tree, under probability distributions that satisfy the exchangeability property. We then apply the formulas to study mean deep coalescence cost under two commonly used exchangeable models—the uniform and Yule models. We find that mean deep coalescence cost, for either a fixed species tree or a fixed gene tree, tends to be larger for unbalanced trees than for balanced trees. These results provide a better understanding of the deep coalescence cost, as well as allow for the development of new species tree inference criteria.