MOTIVATION: Despite the widespread occurrence of polyploids across the Tree of Life, especially in the plant kingdom, very few computational methods have been developed to handle the specific complexities introduced by polyploids in phylogeny estimation. Furthermore, methods that are designed to account for polyploidy often disregard incomplete lineage sorting (ILS), a major source of heterogeneous gene histories, or are computationally very demanding. Therefore, there is a great need for efficient and robust methods to accurately reconstruct polyploid phylogenies. RESULTS: We introduce Polyphest (POLYploid PHylogeny ESTimation), a new method for efficiently and accurately inferring species phylogenies in the presence of both polyploidy and ILS. Polyphest bypasses the need for extensive network space searches by first generating a multilabeled tree based on gene trees, which is then converted into a (uniquely labeled) species phylogeny. We compare the performance of Polyphest to that of two polyploid phylogeny estimation methods, one of which does not account for ILS, namely PADRE, and another that accounts for ILS, namely MPAllopp. Polyphest is more accurate than PADRE and achieves comparable accuracy to MPAllopp, while being significantly faster. We also demonstrate the application of Polyphest to empirical data from the hexaploid bread wheat and confirm the allopolyploid origin of bread wheat along with the closest relatives for each of its subgenomes. AVAILABILITY AND IMPLEMENTATION: Polyphest is available at https://github.com/NakhlehLab/Polyphest.

MOTIVATION: Single-nucleotide variants (SNVs) are the most common variations in the human genome. Recently developed methods for SNV detection from single-cell DNA sequencing data, such as SCIΦ and scVILP, leverage the evolutionary history of the cells to overcome the technical errors associated with single-cell sequencing protocols. Despite being accurate, these methods are not scalable to the extensive genomic breadth of single-cell whole-genome (scWGS) and whole-exome sequencing (scWES) data. RESULTS: Here, we report on a new scalable method, Phylovar, which extends the phylogeny-guided variant calling approach to sequencing datasets containing millions of loci. Through benchmarking on simulated datasets under different settings, we show that, Phylovar outperforms SCIΦ in terms of running time while being more accurate than Monovar (which is not phylogeny-aware) in terms of SNV detection. Furthermore, we applied Phylovar to two real biological datasets: an scWES triple-negative breast cancer data consisting of 32 cells and 3375 loci as well as an scWGS data of neuron cells from a normal human brain containing 16 cells and approximately 2.5 million loci. For the cancer data, Phylovar detected somatic SNVs with high or moderate functional impact that were also supported by bulk sequencing dataset and for the neuron dataset, Phylovar identified 5745 SNVs with non-synonymous effects some of which were associated with neurodegenerative diseases. AVAILABILITY AND IMPLEMENTATION: Phylovar is implemented in Python and is publicly available at https://github.com/NakhlehLab/Phylovar.

SUMMARY: We report on a new single-cell DNA sequence simulator, SimSCSnTree, which generates an evolutionary tree of cells and evolves single nucleotide variants (SNVs) and copy number aberrations (CNAs) along its branches. Data generated by the simulator can be used to benchmark tools for single-cell genomic analyses, particularly in cancer where SNVs and CNAs are ubiquitous. AVAILABILITY AND IMPLEMENTATION: SimSCSnTree is now on BioConda and also is freely available for download at https://github.com/compbiofan/SimSCSnTree.git with detailed documentation.

Phylogenomic studies of prokaryotic taxa often assume conserved marker genes are homologous across their length. However, processes such as horizontal gene transfer or gene duplication and loss may disrupt this homology by recombining only parts of genes, causing gene fission or fusion. We show using simulation that it is necessary to delineate homology groups in a set of bacterial genomes without relying on gene annotations to define the boundaries of homologous regions. To solve this problem, we have developed a graph-based algorithm to partition a set of bacterial genomes into Maximal Homologous Groups of sequences (MHGs) where each MHG is a maximal set of maximum-length sequences which are homologous across the entire sequence alignment. We applied our algorithm to a dataset of 19 Enterobacteriaceae species and found that MHGs cover much greater proportions of genomes than markers and, relatedly, are less biased in terms of the functions of the genes they cover. We zoomed in on the correlation between each individual marker and their overlapping MHGs, and show that few phylogenetic splits supported by the markers are supported by the MHGs while many marker-supported splits are contradicted by the MHGs. A comparison of the species tree inferred from marker genes with the species tree inferred from MHGs suggests that the increased bias and lack of genome coverage by markers causes incorrect inferences as to the overall relationship between bacterial taxa.

Single-cell DNA sequencing technologies are enabling the study of mutations and their evolutionary trajectories in cancer. Somatic copy number aberrations (CNAs) have been implicated in the development and progression of various types of cancer. A wide array of methods for CNA detection has been either developed specifically for or adapted to single-cell DNA sequencing data. Understanding the strengths and limitations that are unique to each of these methods is very important for obtaining accurate copy number profiles from single-cell DNA sequencing data. We benchmarked three widely used methods-Ginkgo, HMMcopy, and CopyNumber-on simulated as well as real datasets. To facilitate this, we developed a novel simulator of single-cell genome evolution in the presence of CNAs. Furthermore, to assess performance on empirical data where the ground truth is unknown, we introduce a phylogeny-based measure for identifying potentially erroneous inferences. While single-cell DNA sequencing is very promising for elucidating and understanding CNAs, our findings show that even the best existing method does not exceed 80% accuracy. New methods that significantly improve upon the accuracy of these three methods are needed. Furthermore, with the large datasets being generated, the methods must be computationally efficient.

Phylogenetic networks extend the phylogenetic tree structure and allow for modeling vertical and horizontal evolution in a single framework. Statistical inference of phylogenetic networks is prohibitive and currently limited to small networks. An approach that could significantly improve phylogenetic network space exploration is based on first inferring an evolutionary tree of the species under consideration, and then augmenting the tree into a network by adding a set of "horizontal" edges to better fit the data. In this paper, we study the performance of such an approach on networks generated under a birth-hybridization model and explore its feasibility as an alternative to approaches that search the phylogenetic network space directly (without relying on a fixed underlying tree). We find that the concatenation method does poorly at obtaining a "backbone" tree that could be augmented into the correct network, whereas the popular species tree inference method ASTRAL does significantly better at such a task. We then evaluated the tree-to-network augmentation phase under the minimizing deep coalescence and pseudo-likelihood criteria. We find that even though this is a much faster approach than the direct search of the network space, the accuracy is much poorer, even when the backbone tree is a good starting tree. Our results show that tree-based inference of phylogenetic networks could yield very poor results. As exploration of the network space directly in search of maximum likelihood estimates or a representative sample of the posterior is very expensive, significant improvements to the computational complexity of phylogenetic network inference are imperative if analyses of large data sets are to be performed. We show that a recently developed divide-and-conquer approach significantly outperforms tree-based inference in terms of accuracy, albeit still at a higher computational cost.

Single-cell sequencing provides a powerful approach for elucidating intratumor heterogeneity by resolving cell-to-cell variability. However, it also poses additional challenges including elevated error rates, allelic dropout and non-uniform coverage. A recently introduced single-cell-specific mutation detection algorithm leverages the evolutionary relationship between cells for denoising the data. However, due to its probabilistic nature, this method does not scale well with the number of cells. Here, we develop a novel combinatorial approach for utilizing the genealogical relationship of cells in detecting mutations from noisy single-cell sequencing data. Our method, called scVILP, jointly detects mutations in individual cells and reconstructs a perfect phylogeny among these cells. We employ a novel Integer Linear Program algorithm for deterministically and efficiently solving the joint inference problem. We show that scVILP achieves similar or better accuracy but significantly better runtime over existing methods on simulated data. We also applied scVILP to an empirical human cancer dataset from a high grade serous ovarian cancer patient.

MOTIVATION: Reticulate evolutionary histories, such as those arising in the presence of hybridization, are best modeled as phylogenetic networks. Recently developed methods allow for statistical inference of phylogenetic networks while also accounting for other processes, such as incomplete lineage sorting. However, these methods can only handle a small number of loci from a handful of genomes. RESULTS: In this article, we introduce a novel two-step method for scalable inference of phylogenetic networks from the sequence alignments of multiple, unlinked loci. The method infers networks on subproblems and then merges them into a network on the full set of taxa. To reduce the number of trinets to infer, we formulate a Hitting Set version of the problem of finding a small number of subsets, and implement a simple heuristic to solve it. We studied their performance, in terms of both running time and accuracy, on simulated as well as on biological datasets. The two-step method accurately infers phylogenetic networks at a scale that is infeasible with existing methods. The results are a significant and promising step towards accurate, large-scale phylogenetic network inference. AVAILABILITY AND IMPLEMENTATION: We implemented the algorithms in the publicly available software package PhyloNet (https://bioinfocs.rice.edu/PhyloNet). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Summary: The evolutionary histories of individual regions across a genomic alignment-called 'local genealogies'-can differ from each other, due to processes such as recombination. Elucidating and analyzing these local genealogies are important for a large number of inference tasks, including those pertaining to species phylogenies, evolutionary processes and trait mapping. In this paper, we present a toolkit for automated local phylogenomic analyses, or ALPHA. The purpose of this toolkit is to provide a wide array of functionalities for automated inference of local genealogies as well as analyses based on these local genealogies. The toolkit uses sliding windows to construct local genealogies and can compute a wide array of local phylogeny based statistics, such as the D-statistic. The toolkit comes with a graphical user interface and several import/export functionalities. Over the last few decades, much emphasis in phylogenomics has been put on developing tools for inferring species phylogenies. This toolkit complements those efforts by emphasizing the 'local' aspect of phylogenomics. Availability and implementation: ALPHA is freely available for installation and use, including source code, at https://github.com/chilleo/ALPHA.

Motivation: Species and gene trees represent how species and individual loci within their genomes evolve from their most recent common ancestors. These trees are central to addressing several questions in biology relating to, among other issues, species conservation, trait evolution and gene function. Consequently, their accurate inference from genomic data is a major endeavor. One approach to their inference is to co-estimate species and gene trees from genome-wide data. Indeed, Bayesian methods based on this approach already exist. However, these methods are very slow, limiting their applicability to datasets with small numbers of taxa. The more commonly used approach is to first infer gene trees individually, and then use gene tree estimates to infer the species tree. Methods in this category rely significantly on the accuracy of the gene trees which is often not high when the dataset includes closely related species. Results: In this work, we introduce a simple, yet effective, iterative method for co-estimating gene and species trees from sequence data of multiple, unlinked loci. In every iteration, the method estimates a species tree, uses it as a generative process to simulate a collection of gene trees, and then selects gene trees for the individual loci from among the simulated gene trees by making use of the sequence data. We demonstrate the accuracy and efficiency of our method on simulated as well as biological data, and compare them to those of existing competing methods. Availability and implementation: The method has been implemented in PhyloNet, which is publicly available at http://bioinfocs.rice.edu/phylonet.

Motivation: Phylogenetic networks represent reticulate evolutionary histories. Statistical methods for their inference under the multispecies coalescent have recently been developed. A particularly powerful approach uses data that consist of bi-allelic markers (e.g. single nucleotide polymorphism data) and allows for exact likelihood computations of phylogenetic networks while numerically integrating over all possible gene trees per marker. While the approach has good accuracy in terms of estimating the network and its parameters, likelihood computations remain a major computational bottleneck and limit the method's applicability. Results: In this article, we first demonstrate why likelihood computations of networks take orders of magnitude more time when compared to trees. We then propose an approach for inference of phylogenetic networks based on pseudo-likelihood using bi-allelic markers. We demonstrate the scalability and accuracy of phylogenetic network inference via pseudo-likelihood computations on simulated data. Furthermore, we demonstrate aspects of robustness of the method to violations in the underlying assumptions of the employed statistical model. Finally, we demonstrate the application of the method to biological data. The proposed method allows for analyzing larger datasets in terms of the numbers of taxa and reticulation events. While pseudo-likelihood had been proposed before for data consisting of gene trees, the work here uses sequence data directly, offering several advantages as we discuss. Availability and implementation: The methods have been implemented in PhyloNet (http://bioinfocs.rice.edu/phylonet).

Phylogenetic networks are rooted, directed, acyclic graphs that model reticulate evolutionary histories. Recently, statistical methods were devised for inferring such networks from either gene tree estimates or the sequence alignments of multiple unlinked loci. Bi-allelic markers, most notably single nucleotide polymorphisms (SNPs) and amplified fragment length polymorphisms (AFLPs), provide a powerful source of genome-wide data. In a recent paper, a method called SNAPP was introduced for statistical inference of species trees from unlinked bi-allelic markers. The generative process assumed by the method combined both a model of evolution for the bi-allelic markers, as well as the multispecies coalescent. A novel component of the method was a polynomial-time algorithm for exact computation of the likelihood of a fixed species tree via integration over all possible gene trees for a given marker. Here we report on a method for Bayesian inference of phylogenetic networks from bi-allelic markers. Our method significantly extends the algorithm for exact computation of phylogenetic network likelihood via integration over all possible gene trees. Unlike the case of species trees, the algorithm is no longer polynomial-time on all instances of phylogenetic networks. Furthermore, the method utilizes a reversible-jump MCMC technique to sample the posterior of phylogenetic networks given bi-allelic marker data. Our method has a very good performance in terms of accuracy and robustness as we demonstrate on simulated data, as well as a data set of multiple New Zealand species of the plant genus Ourisia (Plantaginaceae). We implemented the method in the publicly available, open-source PhyloNet software package.

BACKGROUND: Phylogenetic networks model reticulate evolutionary histories. The last two decades have seen an increased interest in establishing mathematical results and developing computational methods for inferring and analyzing these networks. A salient concept underlying a great majority of these developments has been the notion that a network displays a set of trees and those trees can be used to infer, analyze, and study the network. RESULTS: In this paper, we show that in the presence of coalescence effects, the set of displayed trees is not sufficient to capture the network. We formally define the set of parental trees of a network and make three contributions based on this definition. First, we extend the notion of anomaly zone to phylogenetic networks and report on anomaly results for different networks. Second, we demonstrate how coalescence events could negatively affect the ability to infer a species tree that could be augmented into the correct network. Third, we demonstrate how a phylogenetic network can be viewed as a mixture model that lends itself to a novel inference approach via gene tree clustering. CONCLUSIONS: Our results demonstrate the limitations of focusing on the set of trees displayed by a network when analyzing and inferring the network. Our findings can form the basis for achieving higher accuracy when inferring phylogenetic networks and open up new venues for research in this area, including new problem formulations based on the notion of a network's parental trees.

BACKGROUND: Recent advances in deep digital sequencing have unveiled an unprecedented degree of clonal heterogeneity within a single tumor DNA sample. Resolving such heterogeneity depends on accurate estimation of fractions of alleles that harbor somatic mutations. Unlike substitutions or small indels, structural variants such as deletions, duplications, inversions and translocations involve segments of DNAs and are potentially more accurate for allele fraction estimations. However, no systematic method exists that can support such analysis. RESULTS: In this paper, we present a novel maximum-likelihood method that estimates allele fractions of structural variants integratively from various forms of alignment signals. We develop a tool, BreakDown, to estimate the allele fractions of most structural variants including medium size (from 1 kilobase to 1 megabase) deletions and duplications, and balanced inversions and translocations. CONCLUSIONS: Evaluation based on both simulated and real data indicates that our method systematically enables structural variants for clonal heterogeneity analysis and can greatly enhance the characterization of genomically instable tumors.

One outcome of interspecific hybridization and subsequent effects of evolutionary forces is introgression, which is the integration of genetic material from one species into the genome of an individual in another species. The evolution of several groups of eukaryotic species has involved hybridization, and cases of adaptation through introgression have been already established. In this work, we report on PhyloNet-HMM-a new comparative genomic framework for detecting introgression in genomes. PhyloNet-HMM combines phylogenetic networks with hidden Markov models (HMMs) to simultaneously capture the (potentially reticulate) evolutionary history of the genomes and dependencies within genomes. A novel aspect of our work is that it also accounts for incomplete lineage sorting and dependence across loci. Application of our model to variation data from chromosome 7 in the mouse (Mus musculus domesticus) genome detected a recently reported adaptive introgression event involving the rodent poison resistance gene Vkorc1, in addition to other newly detected introgressed genomic regions. Based on our analysis, it is estimated that about 9% of all sites within chromosome 7 are of introgressive origin (these cover about 13 Mbp of chromosome 7, and over 300 genes). Further, our model detected no introgression in a negative control data set. We also found that our model accurately detected introgression and other evolutionary processes from synthetic data sets simulated under the coalescent model with recombination, isolation, and migration. Our work provides a powerful framework for systematic analysis of introgression while simultaneously accounting for dependence across sites, point mutations, recombination, and ancestral polymorphism.

BACKGROUND: Forward-time population genetic simulations play a central role in deriving and testing evolutionary hypotheses. Such simulations may be data-intensive, depending on the settings to the various parameters controlling them. In particular, for certain settings, the data footprint may quickly exceed the memory of a single compute node. RESULTS: We develop a novel and general method for addressing the memory issue inherent in forward-time simulations by compressing and decompressing, in real-time, active and ancestral genotypes, while carefully accounting for the time overhead. We propose a general graph data structure for compressing the genotype space explored during a simulation run, along with efficient algorithms for constructing and updating compressed genotypes which support both mutation and recombination. We tested the performance of our method in very large-scale simulations. Results show that our method not only scales well, but that it also overcomes memory issues that would cripple existing tools. CONCLUSIONS: As evolutionary analyses are being increasingly performed on genomes, pathways, and networks, particularly in the era of systems biology, scaling population genetic simulators to handle large-scale simulations is crucial. We believe our method offers a significant step in that direction. Further, the techniques we provide are generic and can be integrated with existing population genetic simulators to boost their performance in terms of memory usage.

BACKGROUND: Phylogenomic analyses involving whole-genome or multi-locus data often entail dealing with incongruent gene trees. In this paper, we consider two causes of such incongruence, namely, incomplete lineage sorting (ILS) and hybridization, and consider both parsimony and probabilistic criteria for dealing with them. RESULTS: Under the assumption of ILS, computing the probability of a gene tree given a species tree is a very hard problem. We present a heuristic for speeding up the computation, and demonstrate how it scales up computations to data sizes that are not feasible to analyze using current techniques, while achieving very good accuracy. Further, under the assumption of both ILS and hybridization, computing the probability of a gene tree and parsimoniously reconciling it with a phylogenetic network are both very hard problems. We present two exact algorithms for these two problems that speed up existing techniques significantly and enable analyses of much larger data sets than is currently feasible. CONCLUSION: Our heuristics and algorithms enable phylogenomic analyses of larger (in terms of numbers of taxa) data sets than is currently feasible. Further, our methods account for ILS and hybridization, thus allowing analyses of reticulate evolutionary histories.

The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM) that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them using such more detailed mathematical models.

Recent advances in high-throughput technologies and an increased knowledge of biochemical systems have enabled the reconstruction of cellular regulatory networks. While these reconstructions often consist of the connectivity patterns among the network's components, an important task in this area is to derive values for the kinetic parameters of the system so that its dynamics can be elucidated and testable hypotheses can be generated. The problem here is to reverse engineer the model (in our case, values of kinetic parameters) given the data that consists of a network connectivity and time-series data. Particle swarm optimization (PSO) has been recently used for this reverse engineering task. In this paper, we introduce three scoring metrics for assessing the optimality of the solution found by PSO. Using biological data sets, we study the performance of the PSO framework under the three scoring metrics. Our results show that PSO achieves very good parameterization of the cellular networks we consider, regardless of the complexity of the dynamics patterns generated by the underlying kinetics. Given the flexibility of the PSO framework, as well as its natural amenability to parallelization and general high-performance implementations and execution, our results indicate PSO may be a good candidate for parameterizing cellular networks.

BACKGROUND: Maximum likelihood has been widely used for over three decades to infer phylogenetic trees from molecular data. When reticulate evolutionary events occur, several genomic regions may have conflicting evolutionary histories, and a phylogenetic network may provide a more adequate model for representing the evolutionary history of the genomes or species. A maximum likelihood (ML) model has been proposed for this case and accounts for both mutation within a genomic region and reticulation across the regions. However, the performance of this model in terms of inferring information about reticulate evolution and properties that affect this performance have not been studied. RESULTS: In this paper, we study the effect of the evolutionary diameter and height of a reticulation event on its identifiability under ML. We find both of them, particularly the diameter, have a significant effect. Further, we find that the number of genes (which can be generalized to the concept of "non-recombining genomic regions") that are transferred across a reticulation edge affects its detectability. Last but not least, a fundamental challenge with phylogenetic networks is that they allow an arbitrary level of complexity, giving rise to the model selection problem. We investigate the performance of two information criteria, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), for addressing this problem. We find that BIC performs well in general for controlling the model complexity and preventing ML from grossly overestimating the number of reticulation events. CONCLUSION: Our results demonstrate that BIC provides a good framework for inferring reticulate evolutionary histories. Nevertheless, the results call for caution when interpreting the accuracy of the inference particularly for data sets with particular evolutionary features.

MOTIVATION: A metabolic graph represents the connectivity patterns of a metabolic system, and provides a powerful framework within which the organization of metabolic reactions can be analyzed and elucidated. A common practice is to prune (i.e. remove nodes and edges) the metabolic graph prior to any analysis in order to eliminate confounding signals from the representation. Currently, this pruning process is carried out in an ad hoc fashion, resulting in discrepancies and ambiguities across studies. RESULTS: We propose a biochemically informative criterion, the strength of chemical linkage (SCL), for a systematic pruning of metabolic graphs. By analyzing the metabolic graph of Escherichia coli, we show that thresholding SCL is powerful in selecting the conventional pathways' connectivity out of the raw network connectivity when the network is restricted to the reactions collected from these pathways. Further, we argue that the root of ambiguity in pruning metabolic graphs is in the continuity of the amount of chemical content that can be conserved in reaction transformation patterns. Finally, we demonstrate how biochemical pathways can be inferred efficiently if the search procedure is guided by SCL.

BACKGROUND: Standard graphs, where each edge links two nodes, have been extensively used to represent the connectivity of metabolic networks. It is based on this representation that properties of metabolic networks, such as hierarchical and small-world structures, have been elucidated and null models have been proposed to derive biological organization hypotheses. However, these graphs provide a simplistic model of a metabolic network's connectivity map, since metabolic reactions often involve more than two reactants. In other words, this map is better represented as a hypergraph. Consequently, a question that naturally arises in this context is whether these properties truly reflect biological organization or are merely an artifact of the representation. RESULTS: In this paper, we address this question by reanalyzing topological properties of the metabolic network of Escherichia coli under a hypergraph representation, as well as standard graph abstractions. We find that when clustering is properly defined for hypergraphs and subsequently used to analyze metabolic networks, the scaling of clustering, and thus the hierarchical structure hypothesis in metabolic networks, become unsupported. Moreover, we find that incorporating the distribution of reaction sizes into the null model further weakens the support for the scaling patterns. CONCLUSIONS: These results combined suggest that the reported scaling of the clustering coefficients in the metabolic graphs and its specific power coefficient may be an artifact of the graph representation, and may not be supported when biochemical reactions are atomically treated as hyperedges. This study highlights the implications of the way a biological system is represented and the null model employed on the elucidated properties, along with their support, of the system.

Phylogenetic networks are leaf-labeled, rooted, acyclic, and directed graphs that are used to model reticulate evolutionary histories. Several measures for quantifying the topological dissimilarity between two phylogenetic networks have been devised, each of which was proven to be a metric on certain restricted classes of phylogenetic networks. A biologically motivated class of phylogenetic networks, namely, reduced phylogenetic networks, was recently introduced. None of the existing measures is a metric on the space of reduced phylogenetic networks. In this paper, we provide a metric on the space of reduced phylogenetic networks that is computable in time polynomial in the size of the networks.

MOTIVATION: The growing availability of genome-scale datasets has attracted increasing attention to the development of computational methods for automated inference of functional similarities among genes and their products. One class of such methods measures the functional similarity of genes based on their distance in the Gene Ontology (GO). To measure the functional relatedness of a gene set, these measures consider every pair of genes in the set, and the average of all pairwise distances is calculated. However, as more data becomes available and gene sets used for analysis become larger, such pair-based calculation becomes prohibitive. RESULTS: In this article, we propose GS(2) (GO-based similarity of gene sets), a novel GO-based measure of gene set similarity that is computable in linear time in the size of the gene set. The measure quantifies the similarity of the GO annotations among a set of genes by averaging the contribution of each gene's GO terms and their ancestor terms with respect to the GO vocabulary graph. To study the performance of our method, we compared our measure with an established pair-based measure when run on gene sets with varying degrees of functional similarities. In addition to a significant speed improvement, our method produced comparable similarity scores to the established method. Our method is available as a web-based tool and an open-source Python library. AVAILABILITY: The web-based tools and Python code are available at: http://bioserver.cs.rice.edu/gs2.

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 Maddison's original framework. We have implemented our solutions in the PhyloNet software package, which is freely available at: http://bioinfo.cs.rice.edu/phylonet.

Phylogenies-the evolutionary histories of groups of organisms-play a major role in representing the interrelationships among biological entities. Many methods for reconstructing and studying such phylogenies have been proposed, almost all of which assume that the underlying history of a given set of species can be represented by a binary tree. Although many biological processes can be effectively modeled and summarized in this fashion, others cannot: recombination, hybrid speciation, and horizontal gene transfer result in networks of relationships rather than trees of relationships. In previous works, we formulated a maximum parsimony (MP) criterion for reconstructing and evaluating phylogenetic networks, and demonstrated its quality on biological as well as synthetic data sets. In this paper, we provide further theoretical results as well as a very fast heuristic algorithm for the MP criterion of phylogenetic networks. In particular, we provide a novel combinatorial definition of phylogenetic networks in terms of "forbidden cycles," and provide detailed hardness and hardness of approximation proofs for the "small" MP problem. We demonstrate the performance of our heuristic in terms of time and accuracy on both biological and synthetic data sets. Finally, we explain the difference between our model and a similar one formulated by Nguyen et al., and describe the implications of this difference on the hardness and approximation results.

MOTIVATION: In bacterial evolution, inferring a strain tree, which is the evolutionary history of different strains of the same bacterium, plays a major role in analyzing and understanding the evolution of strongly isolated populations, population divergence and various evolutionary events, such as horizontal gene transfer and homologous recombination. Inferring a strain tree from multilocus data of these strains is exceptionally hard since, at this scale of evolution, processes such as homologous recombination result in a very high degree of gene tree incongruence. RESULTS: In this article we present a novel computational method for inferring the strain tree despite massive gene tree incongruence caused by homologous recombination. Our method operates in three phases, where in phase I a set of candidate strain-tree topologies is computed using the maximal cliques concept, in phase II divergence times for each of the topologies are estimated using mixed integer linear programming (MILP) and in phase III the optimal tree (or trees) is selected based on an optimality criterion. We have analyzed 1898 genes from nine strains of the Staphylococcus aureus bacteria, and identified a fully resolved (binary) strain tree with estimated divergence times, despite the high degrees of sequence identity at the nucleotide level and gene tree incongruence. Our method's efficiency makes it particularly suitable for analysis of genome-scale datasets, including those of strongly isolated populations which are usually very challenging to analyze. AVAILABILITY: We have implemented the algorithms in the PhyloNet software package, which is available publicly at http://bioinfo.cs.rice.edu/phylonet/.

BACKGROUND: Phylogenies, 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. RESULTS: In 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. CONCLUSION: The 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.

Reconstructing cellular signaling networks and understanding how they work are major endeavors in cell biology. The scale and complexity of these networks, however, render their analysis using experimental biology approaches alone very challenging. As a result, computational methods have been developed and combined with experimental biology approaches, producing powerful tools for the analysis of these networks. These computational methods mostly fall on either end of a spectrum of model parameterization. On one end is a class of structural network analysis methods; these typically use the network connectivity alone to generate hypotheses about global properties. On the other end is a class of dynamic network analysis methods; these use, in addition to the connectivity, kinetic parameters of the biochemical reactions to predict the network's dynamic behavior. These predictions provide detailed insights into the properties that determine aspects of the network's structure and behavior. However, the difficulty of obtaining numerical values of kinetic parameters is widely recognized to limit the applicability of this latter class of methods. Several researchers have observed that the connectivity of a network alone can provide significant insights into its dynamics. Motivated by this fundamental observation, we present the signaling Petri net, a non-parametric model of cellular signaling networks, and the signaling Petri net-based simulator, a Petri net execution strategy for characterizing the dynamics of signal flow through a signaling network using token distribution and sampling. The result is a very fast method, which can analyze large-scale networks, and provide insights into the trends of molecules' activity-levels in response to an external stimulus, based solely on the network's connectivity. We have implemented the signaling Petri net-based simulator in the PathwayOracle toolkit, which is publicly available at http://bioinfo.cs.rice.edu/pathwayoracle. Using this method, we studied a MAPK1,2 and AKT signaling network downstream from EGFR in two breast tumor cell lines. We analyzed, both experimentally and computationally, the activity level of several molecules in response to a targeted manipulation of TSC2 and mTOR-Raptor. The results from our method agreed with experimental results in greater than 90% of the cases considered, and in those where they did not agree, our approach provided valuable insights into discrepancies between known network connectivities and experimental observations.

MOTIVATION: Phylogenies--the evolutionary histories of groups of organisms-play a major role in representing relationships among biological entities. Although many biological processes can be effectively modeled as tree-like relationships, others, such as hybrid speciation and horizontal gene transfer (HGT), result in networks, rather than trees, of relationships. Hybrid speciation is a significant evolutionary mechanism in plants, fish and other groups of species. HGT plays a major role in bacterial genome diversification and is a significant mechanism by which bacteria develop resistance to antibiotics. Maximum parsimony is one of the most commonly used criteria for phylogenetic tree inference. Roughly speaking, inference based on this criterion seeks the tree that minimizes the amount of evolution. In 1990, Jotun Hein proposed using this criterion for inferring the evolution of sequences subject to recombination. Preliminary results on small synthetic datasets. Nakhleh et al. (2005) demonstrated the criterion's application to phylogenetic network reconstruction in general and HGT detection in particular. However, the naive algorithms used by the authors are inapplicable to large datasets due to their demanding computational requirements. Further, no rigorous theoretical analysis of computing the criterion was given, nor was it tested on biological data. RESULTS: In the present work we prove that the problem of scoring the parsimony of a phylogenetic network is NP-hard and provide an improved fixed parameter tractable algorithm for it. Further, we devise efficient heuristics for parsimony-based reconstruction of phylogenetic networks. We test our methods on both synthetic and biological data (rbcL gene in bacteria) and obtain very promising results.

Bioinformatics (2006) 22(21), 2604–2611 The authors would like to apologize for errors of graph misplacement in Figures 4–6, and an error in the caption of Figure 6. The correct figures and their captions are shown below. The species tree of the 14 organisms, as reported by Tailliez et al. (2002), and the four HGT edges inferred by our heuristic for the big ML problem. Likelihood criterion = ancestral, and tree criterion = all. The improvement in the likelihood score as a function of the number of HGT edges added to the species tree (shown in Fig. 4). The improvement achieved by adding the fourth HGT edge is smaller compared to that achieved by adding the first three events, which indicates that three HGT events suffice to model the evolution of the ribosomal protein rpl12e gene for these 14 archaea. Likelihood criterion = ancestral, and tree criterion = all. The improvement in the likelihood score as a function of the number of HGT edges added to the species tree (shown in Fig. 3). The improvement achieved by adding the sixth HGT edge is smaller compared to that achieved by adding the first five events, which indicates that five HGT events suffice to model the evolution of the rbcL gene for these 15 organisms. Likelihood criterion = ancestral, and tree criterion = all.

MOTIVATION: Horizontal gene transfer (HGT) is believed to be ubiquitous among bacteria, and plays a major role in their genome diversification as well as their ability to develop resistance to antibiotics. In light of its evolutionary significance and implications for human health, developing accurate and efficient methods for detecting and reconstructing HGT is imperative. RESULTS: In this article we provide a new HGT-oriented likelihood framework for many problems that involve phylogeny-based HGT detection and reconstruction. Beside the formulation of various likelihood criteria, we show that most of these problems are NP-hard, and offer heuristics for efficient and accurate reconstruction of HGT under these criteria. We implemented our heuristics and used them to analyze biological as well as synthetic data. In both cases, our criteria and heuristics exhibited very good performance with respect to identifying the correct number of HGT events as well as inferring their correct location on the species tree. AVAILABILITY: Implementation of the criteria as well as heuristics and hardness proofs are available from the authors upon request. Hardness proofs can also be downloaded at http://www.cs.tau.ac.il/~tamirtul/MLNET/Supp-ML.pdf

We present new methods for reconstructing reticulate evolution of species due to events such as horizontal transfer or hybrid speciation; both methods are based upon extensions of Wayne Maddison's approach in his seminal 1997 paper. Our first method is a polynomial time algorithm for constructing phylogenetic networks from two gene trees contained inside the network. We allow the network to have an arbitrary number of reticulations, but we limit the reticulation in the network so that the cycles in network are node-disjoint (galled); we prove accuracy guarantees for our first method by presenting a formal characterization of the set of gene trees defined by a species network. Our second method is a polynomial time algorithm for constructing networks with one reticulation, where we allow for errors in the estimated gene trees. Using simulations, we demonstrate improved performance of this method over both NeighborNet and Maddison's method.

Phylogenetic networks model the evolutionary history of sets of organisms when events such as hybrid speciation and horizontal gene transfer occur. In spite of their widely acknowledged importance in evolutionary biology, phylogenetic networks have so far been studied mostly for specific data sets. We present a general definition of phylogenetic networks in terms of directed acyclic graphs (DAGs) and a set of conditions. Further, we distinguish between model networks and reconstructible ones and characterize the effect of extinction and taxon sampling on the reconstructibility of the network. Simulation studies are a standard technique for assessing the performance of phylogenetic methods. A main step in such studies entails quantifying the topological error between the model and inferred phylogenies. While many measures of tree topological accuracy have been proposed, none exist for phylogenetic networks. Previously, we proposed the first such measure, which applied only to a restricted class of networks. In this paper, we extend that measure to apply to all networks, and prove that it is a metric on the space of phylogenetic networks. Our results allow for the systematic study of existing network methods, and for the design of new accurate ones.

We examine the organizational impact on phylogenetic databases of the increasing sophistication in the need and use of phylogenetic data. A primary issue is the use of the unnormalized representation of phylogenies in Newick format as a primitive data type in existing phylogenetic databases. In particular we identify and enumerate a list of potential applications of such databases and queries (use-cases) that biologists may wish to see integrated into a phylogenetic database management system. We show there are many queries that would best be supported by a normalized data model where phylogenies are stored as lists of edges. Since many of the queries require transitive traversals of the phylogenies we demonstrate, constructively, that complex phylogenetic queries can be conveniently constructed as Datalog programs. We address concerns with respect to the cost and performance of the normalized representation by developing and empirically evaluating a feasibility prototype.