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1.  Phylogenetic and Functional Assessment of Orthologs Inference Projects and Methods 
PLoS Computational Biology  2009;5(1):e1000262.
Accurate genome-wide identification of orthologs is a central problem in comparative genomics, a fact reflected by the numerous orthology identification projects developed in recent years. However, only a few reports have compared their accuracy, and indeed, several recent efforts have not yet been systematically evaluated. Furthermore, orthology is typically only assessed in terms of function conservation, despite the phylogeny-based original definition of Fitch. We collected and mapped the results of nine leading orthology projects and methods (COG, KOG, Inparanoid, OrthoMCL, Ensembl Compara, Homologene, RoundUp, EggNOG, and OMA) and two standard methods (bidirectional best-hit and reciprocal smallest distance). We systematically compared their predictions with respect to both phylogeny and function, using six different tests. This required the mapping of millions of sequences, the handling of hundreds of millions of predicted pairs of orthologs, and the computation of tens of thousands of trees. In phylogenetic analysis or in functional analysis where high specificity is required, we find that OMA and Homologene perform best. At lower functional specificity but higher coverage level, OrthoMCL outperforms Ensembl Compara, and to a lesser extent Inparanoid. Lastly, the large coverage of the recent EggNOG can be of interest to build broad functional grouping, but the method is not specific enough for phylogenetic or detailed function analyses. In terms of general methodology, we observe that the more sophisticated tree reconstruction/reconciliation approach of Ensembl Compara was at times outperformed by pairwise comparison approaches, even in phylogenetic tests. Furthermore, we show that standard bidirectional best-hit often outperforms projects with more complex algorithms. First, the present study provides guidance for the broad community of orthology data users as to which database best suits their needs. Second, it introduces new methodology to verify orthology. And third, it sets performance standards for current and future approaches.
Author Summary
The identification of orthologs, pairs of homologous genes in different species that started diverging through speciation events, is a central problem in genomics with applications in many research areas, including comparative genomics, phylogenetics, protein function annotation, and genome rearrangement. An increasing number of projects aim at inferring orthologs from complete genomes, but little is known about their relative accuracy or coverage. Because the exact evolutionary history of entire genomes remains largely unknown, predictions can only be validated indirectly, that is, in the context of the different applications of orthology. The few comparison studies published so far have asssessed orthology exclusively from the expectation that orthologs have conserved protein function. In the present work, we introduce methodology to verify orthology in terms of phylogeny and perform a comprehensive comparison of nine leading ortholog inference projects and two methods using both phylogenetic and functional tests. The results show large variations among the different projects in terms of performances, which indicates that the choice of orthology database can have a strong impact on any downstream analysis.
doi:10.1371/journal.pcbi.1000262
PMCID: PMC2612752  PMID: 19148271
2.  Inferring species trees from incongruent multi-copy gene trees using the Robinson-Foulds distance 
Background
Constructing species trees from multi-copy gene trees remains a challenging problem in phylogenetics. One difficulty is that the underlying genes can be incongruent due to evolutionary processes such as gene duplication and loss, deep coalescence, or lateral gene transfer. Gene tree estimation errors may further exacerbate the difficulties of species tree estimation.
Results
We present a new approach for inferring species trees from incongruent multi-copy gene trees that is based on a generalization of the Robinson-Foulds (RF) distance measure to multi-labeled trees (mul-trees). We prove that it is NP-hard to compute the RF distance between two mul-trees; however, it is easy to calculate this distance between a mul-tree and a singly-labeled species tree. Motivated by this, we formulate the RF problem for mul-trees (MulRF) as follows: Given a collection of multi-copy gene trees, find a singly-labeled species tree that minimizes the total RF distance from the input mul-trees. We develop and implement a fast SPR-based heuristic algorithm for the NP-hard MulRF problem.
We compare the performance of the MulRF method (available at http://genome.cs.iastate.edu/CBL/MulRF/) with several gene tree parsimony approaches using gene tree simulations that incorporate gene tree error, gene duplications and losses, and/or lateral transfer. The MulRF method produces more accurate species trees than gene tree parsimony approaches. We also demonstrate that the MulRF method infers in minutes a credible plant species tree from a collection of nearly 2,000 gene trees.
Conclusions
Our new phylogenetic inference method, based on a generalized RF distance, makes it possible to quickly estimate species trees from large genomic data sets. Since the MulRF method, unlike gene tree parsimony, is based on a generic tree distance measure, it is appealing for analyses of genomic data sets, in which many processes such as deep coalescence, recombination, gene duplication and losses as well as phylogenetic error may contribute to gene tree discord. In experiments, the MulRF method estimated species trees accurately and quickly, demonstrating MulRF as an efficient alternative approach for phylogenetic inference from large-scale genomic data sets.
doi:10.1186/1748-7188-8-28
PMCID: PMC3874668  PMID: 24180377
3.  Assessing the evolutionary rate of positional orthologous genes in prokaryotes using synteny data 
Background
Comparison of completely sequenced microbial genomes has revealed how fluid these genomes are. Detecting synteny blocks requires reliable methods to determining the orthologs among the whole set of homologs detected by exhaustive comparisons between each pair of completely sequenced genomes. This is a complex and difficult problem in the field of comparative genomics but will help to better understand the way prokaryotic genomes are evolving.
Results
We have developed a suite of programs that automate three essential steps to study conservation of gene order, and validated them with a set of 107 bacteria and archaea that cover the majority of the prokaryotic taxonomic space. We identified the whole set of shared homologs between two or more species and computed the evolutionary distance separating each pair of homologs. We applied two strategies to extract from the set of homologs a collection of valid orthologs shared by at least two genomes. The first computes the Reciprocal Smallest Distance (RSD) using the PAM distances separating pairs of homologs. The second method groups homologs in families and reconstructs each family's evolutionary tree, distinguishing bona fide orthologs as well as paralogs created after the last speciation event. Although the phylogenetic tree method often succeeds where RSD fails, the reverse could occasionally be true. Accordingly, we used the data obtained with either methods or their intersection to number the orthologs that are adjacent in for each pair of genomes, the Positional Orthologous Genes (POGs), and to further study their properties. Once all these synteny blocks have been detected, we showed that POGs are subject to more evolutionary constraints than orthologs outside synteny groups, whichever the taxonomic distance separating the compared organisms.
Conclusion
The suite of programs described in this paper allows a reliable detection of orthologs and is useful for evaluating gene order conservation in prokaryotes whichever their taxonomic distance. Thus, our approach will make easy the rapid identification of POGS in the next few years as we are expecting to be inundated with thousands of completely sequenced microbial genomes.
doi:10.1186/1471-2148-7-237
PMCID: PMC2238764  PMID: 18047665
4.  Phylogenetic Reconstruction of Orthology, Paralogy, and Conserved Synteny for Dog and Human 
PLoS Computational Biology  2006;2(9):e133.
Accurate predictions of orthology and paralogy relationships are necessary to infer human molecular function from experiments in model organisms. Previous genome-scale approaches to predicting these relationships have been limited by their use of protein similarity and their failure to take into account multiple splicing events and gene prediction errors. We have developed PhyOP, a new phylogenetic orthology prediction pipeline based on synonymous rate estimates, which accurately predicts orthology and paralogy relationships for transcripts, genes, exons, or genomic segments between closely related genomes. We were able to identify orthologue relationships to human genes for 93% of all dog genes from Ensembl. Among 1:1 orthologues, the alignments covered a median of 97.4% of protein sequences, and 92% of orthologues shared essentially identical gene structures. PhyOP accurately recapitulated genomic maps of conserved synteny. Benchmarking against predictions from Ensembl and Inparanoid showed that PhyOP is more accurate, especially in its predictions of paralogy. Nearly half (46%) of PhyOP paralogy predictions are unique. Using PhyOP to investigate orthologues and paralogues in the human and dog genomes, we found that the human assembly contains 3-fold more gene duplications than the dog. Species-specific duplicate genes, or “in-paralogues,” are generally shorter and have fewer exons than 1:1 orthologues, which is consistent with selective constraints and mutation biases based on the sizes of duplicated genes. In-paralogues have experienced elevated amino acid and synonymous nucleotide substitution rates. Duplicates possess similar biological functions for either the dog or human lineages. Having accounted for 2,954 likely pseudogenes and gene fragments, and after separating 346 erroneously merged genes, we estimated that the human genome encodes a minimum of 19,700 protein-coding genes, similar to the gene count of nematode worms. PhyOP is a fast and robust approach to orthology prediction that will be applicable to whole genomes from multiple closely related species. PhyOP will be particularly useful in predicting orthology for mammalian genomes that have been incompletely sequenced, and for large families of rapidly duplicating genes.
Synopsis
Biologists often exploit the evolutionary relationships between proteins in order to explain how their findings are relevant to the biology of other species, including Homo sapiens. The most natural way to define these relationships is to draw family trees showing, for example, which human protein is the counterpart (“orthologue”) of a protein in dog, and which human proteins have arisen by recent duplication of existing genes (“paralogues”). On a small-scale this is relatively straightforward, but it is difficult to do this automatically on a genome-wide scale. In this paper the authors describe a new approach to drawing a giant family tree of all proteins from humans and dogs. They show how this tree allows them to refine some protein predictions and discard others that are likely to be nonfunctional dead sequences. Family relationships can show how the dog and human genomes have been rearranged since their last common ancestor. In addition, they help to identify the proteins that are specific to either dog or human, and which contribute to these species' biological differences. Giant trees, drawn from this method, will help to associate the differences, duplications, and evolution of proteins in different mammals with their distinctive physiologies and behaviours.
doi:10.1371/journal.pcbi.0020133
PMCID: PMC1584324  PMID: 17009864
5.  An approach of orthology detection from homologous sequences under minimum evolution 
Nucleic Acids Research  2008;36(17):e110.
In the field of phylogenetics and comparative genomics, it is important to establish orthologous relationships when comparing homologous sequences. Due to the slight sequence dissimilarity between orthologs and paralogs, it is prone to regarding paralogs as orthologs. For this reason, several methods based on evolutionary distance, phylogeny and BLAST have tried to detect orthologs with more precision. Depending on their algorithmic implementations, each of these methods sometimes has increased false negative or false positive rates. Here, we developed a novel algorithm for orthology detection that uses a distance method based on the phylogenetic criterion of minimum evolution. Our algorithm assumes that sets of sequences exhibiting orthologous relationships are evolutionarily less costly than sets that include one or more paralogous relationships. Calculation of evolutionary cost requires the reconstruction of a neighbor-joining (NJ) tree, but calculations are unaffected by the topology of any given NJ tree. Unlike tree reconciliation, our algorithm appears free from the problem of incorrect topologies of species and gene trees. The reliability of the algorithm was tested in a comparative analysis with two other orthology detection methods using 95 manually curated KOG datasets and 21 experimentally verified EXProt datasets. Sensitivity and specificity estimates indicate that the concept of minimum evolution could be valuable for the detection of orthologs.
doi:10.1093/nar/gkn485
PMCID: PMC2553584  PMID: 18676448
6.  PhyloTreePruner: A Phylogenetic Tree-Based Approach for Selection of Orthologous Sequences for Phylogenomics 
Molecular phylogenetics relies on accurate identification of orthologous sequences among the taxa of interest. Most orthology inference programs available for use in phylogenomics rely on small sets of pre-defined orthologs from model organisms or phenetic approaches such as all-versus-all sequence comparisons followed by Markov graph-based clustering. Such approaches have high sensitivity but may erroneously include paralogous sequences. We developed PhyloTreePruner, a software utility that uses a phylogenetic approach to refine orthology inferences made using phenetic methods. PhyloTreePruner checks single-gene trees for evidence of paralogy and generates a new alignment for each group containing only sequences inferred to be orthologs. Importantly, PhyloTreePruner takes into account support values on the tree and avoids unnecessarily deleting sequences in cases where a weakly supported tree topology incorrectly indicates paralogy. A test of PhyloTreePruner on a dataset generated from 11 completely sequenced arthropod genomes identified 2,027 orthologous groups sampled for all taxa. Phylogenetic analysis of the concatenated supermatrix yielded a generally well-supported topology that was consistent with the current understanding of arthropod phylogeny. PhyloTreePruner is freely available from http://sourceforge.net/projects/phylotreepruner/.
doi:10.4137/EBO.S12813
PMCID: PMC3825643  PMID: 24250218
phylogenomic; orthology; paralogy; gene tree
7.  Genome trees constructed using five different approaches suggest new major bacterial clades 
Background
The availability of multiple complete genome sequences from diverse taxa prompts the development of new phylogenetic approaches, which attempt to incorporate information derived from comparative analysis of complete gene sets or large subsets thereof. Such attempts are particularly relevant because of the major role of horizontal gene transfer and lineage-specific gene loss, at least in the evolution of prokaryotes.
Results
Five largely independent approaches were employed to construct trees for completely sequenced bacterial and archaeal genomes: i) presence-absence of genomes in clusters of orthologous genes; ii) conservation of local gene order (gene pairs) among prokaryotic genomes; iii) parameters of identity distribution for probable orthologs; iv) analysis of concatenated alignments of ribosomal proteins; v) comparison of trees constructed for multiple protein families. All constructed trees support the separation of the two primary prokaryotic domains, bacteria and archaea, as well as some terminal bifurcations within the bacterial and archaeal domains. Beyond these obvious groupings, the trees made with different methods appeared to differ substantially in terms of the relative contributions of phylogenetic relationships and similarities in gene repertoires caused by similar life styles and horizontal gene transfer to the tree topology. The trees based on presence-absence of genomes in orthologous clusters and the trees based on conserved gene pairs appear to be strongly affected by gene loss and horizontal gene transfer. The trees based on identity distributions for orthologs and particularly the tree made of concatenated ribosomal protein sequences seemed to carry a stronger phylogenetic signal. The latter tree supported three potential high-level bacterial clades,: i) Chlamydia-Spirochetes, ii) Thermotogales-Aquificales (bacterial hyperthermophiles), and ii) Actinomycetes-Deinococcales-Cyanobacteria. The latter group also appeared to join the low-GC Gram-positive bacteria at a deeper tree node. These new groupings of bacteria were supported by the analysis of alternative topologies in the concatenated ribosomal protein tree using the Kishino-Hasegawa test and by a census of the topologies of 132 individual groups of orthologous proteins. Additionally, the results of this analysis put into question the sister-group relationship between the two major archaeal groups, Euryarchaeota and Crenarchaeota, and suggest instead that Euryarchaeota might be a paraphyletic group with respect to Crenarchaeota.
Conclusions
We conclude that, the extensive horizontal gene flow and lineage-specific gene loss notwithstanding, extension of phylogenetic analysis to the genome scale has the potential of uncovering deep evolutionary relationships between prokaryotic lineages.
doi:10.1186/1471-2148-1-8
PMCID: PMC60490  PMID: 11734060
8.  Identification of mammalian orthologs using local synteny 
BMC Genomics  2009;10:630.
Background
Accurate determination of orthology is central to comparative genomics. For vertebrates in particular, very large gene families, high rates of gene duplication and loss, multiple mechanisms of gene duplication, and high rates of retrotransposition all combine to make inference of orthology between genes difficult. Many methods have been developed to identify orthologous genes, mostly based upon analysis of the inferred protein sequence of the genes. More recently, methods have been proposed that use genomic context in addition to protein sequence to improve orthology assignment in vertebrates. Such methods have been most successfully implemented in fungal genomes and have long been used in prokaryotic genomes, where gene order is far less variable than in vertebrates. However, to our knowledge, no explicit comparison of synteny and sequence based definitions of orthology has been reported in vertebrates, or, more specifically, in mammals.
Results
We test a simple method for the measurement and utilization of gene order (local synteny) in the identification of mammalian orthologs by investigating the agreement between coding sequence based orthology (Inparanoid) and local synteny based orthology. In the 5 mammalian genomes studied, 93% of the sampled inter-species pairs were found to be concordant between the two orthology methods, illustrating that local synteny is a robust substitute to coding sequence for identifying orthologs. However, 7% of pairs were found to be discordant between local synteny and Inparanoid. These cases of discordance result from evolutionary events including retrotransposition and genome rearrangements.
Conclusions
By analyzing cases of discordance between local synteny and Inparanoid we show that local synteny can distinguish between true orthologs and recent retrogenes, can resolve ambiguous many-to-many orthology relationships into one-to-one ortholog pairs, and might be used to identify cases of non-orthologous gene displacement by retroduplicated paralogs.
doi:10.1186/1471-2164-10-630
PMCID: PMC2807883  PMID: 20030836
9.  COCO-CL: hierarchical clustering of homology relations based on evolutionary correlations 
Bioinformatics (Oxford, England)  2006;22(7):779-788.
Motivation
Determining orthology relations among genes across multiple genomes is an important problem in the post-genomic era. Identifying orthologous genes can not only help predict functional annotations for newly sequenced or poorly characterized genomes, but can also help predict new protein–protein interactions. Unfortunately, determining orthology relation through computational methods is not straightforward due to the presence of paralogs. Traditional approaches have relied on pairwise sequence comparisons to construct graphs, which were then partitioned into putative clusters of orthologous groups. These methods do not attempt to preserve the non-transitivity and hierarchic nature of the orthology relation.
Results
We propose a new method, COCO-CL, for hierarchical clustering of homology relations and identification of orthologous groups of genes. Unlike previous approaches, which are based on pairwise sequence comparisons, our method explores the correlation of evolutionary histories of individual genes in a more global context. COCO-CL can be used as a semi-independent method to delineate the orthology/paralogy relation for a refined set of homologous proteins obtained using a less-conservative clustering approach, or as a refiner that removes putative out-paralogs from clusters computed using a more inclusive approach. We analyze our clustering results manually, with support from literature and functional annotations. Since our orthology determination procedure does not employ a species tree to infer duplication events, it can be used in situations when the species tree is unknown or uncertain.
doi:10.1093/bioinformatics/btl009
PMCID: PMC1620014  PMID: 16434444
10.  MultiMSOAR 2.0: An Accurate Tool to Identify Ortholog Groups among Multiple Genomes 
PLoS ONE  2011;6(6):e20892.
The identification of orthologous genes shared by multiple genomes plays an important role in evolutionary studies and gene functional analyses. Based on a recently developed accurate tool, called MSOAR 2.0, for ortholog assignment between a pair of closely related genomes based on genome rearrangement, we present a new system MultiMSOAR 2.0, to identify ortholog groups among multiple genomes in this paper. In the system, we construct gene families for all the genomes using sequence similarity search and clustering, run MSOAR 2.0 for all pairs of genomes to obtain the pairwise orthology relationship, and partition each gene family into a set of disjoint sets of orthologous genes (called super ortholog groups or SOGs) such that each SOG contains at most one gene from each genome. For each such SOG, we label the leaves of the species tree using 1 or 0 to indicate if the SOG contains a gene from the corresponding species or not. The resulting tree is called a tree of ortholog groups (or TOGs). We then label the internal nodes of each TOG based on the parsimony principle and some biological constraints. Ortholog groups are finally identified from each fully labeled TOG. In comparison with a popular tool MultiParanoid on simulated data, MultiMSOAR 2.0 shows significantly higher prediction accuracy. It also outperforms MultiParanoid, the Roundup multi-ortholog repository and the Ensembl ortholog database in real data experiments using gene symbols as a validation tool. In addition to ortholog group identification, MultiMSOAR 2.0 also provides information about gene births, duplications and losses in evolution, which may be of independent biological interest. Our experiments on simulated data demonstrate that MultiMSOAR 2.0 is able to infer these evolutionary events much more accurately than a well-known software tool Notung. The software MultiMSOAR 2.0 is available to the public for free.
doi:10.1371/journal.pone.0020892
PMCID: PMC3119667  PMID: 21712981
11.  Orthology Inference in Nonmodel Organisms Using Transcriptomes and Low-Coverage Genomes: Improving Accuracy and Matrix Occupancy for Phylogenomics 
Molecular Biology and Evolution  2014;31(11):3081-3092.
Orthology inference is central to phylogenomic analyses. Phylogenomic data sets commonly include transcriptomes and low-coverage genomes that are incomplete and contain errors and isoforms. These properties can severely violate the underlying assumptions of orthology inference with existing heuristics. We present a procedure that uses phylogenies for both homology and orthology assignment. The procedure first uses similarity scores to infer putative homologs that are then aligned, constructed into phylogenies, and pruned of spurious branches caused by deep paralogs, misassembly, frameshifts, or recombination. These final homologs are then used to identify orthologs. We explore four alternative tree-based orthology inference approaches, of which two are new. These accommodate gene and genome duplications as well as gene tree discordance. We demonstrate these methods in three published data sets including the grape family, Hymenoptera, and millipedes with divergence times ranging from approximately 100 to over 400 Ma. The procedure significantly increased the completeness and accuracy of the inferred homologs and orthologs. We also found that data sets that are more recently diverged and/or include more high-coverage genomes had more complete sets of orthologs. To explicitly evaluate sources of conflicting phylogenetic signals, we applied serial jackknife analyses of gene regions keeping each locus intact. The methods described here can scale to over 100 taxa. They have been implemented in python with independent scripts for each step, making it easy to modify or incorporate them into existing pipelines. All scripts are available from https://bitbucket.org/yangya/phylogenomic_dataset_construction.
doi:10.1093/molbev/msu245
PMCID: PMC4209138  PMID: 25158799
Diplopoda; phylotranscriptomics; RNA-seq; Vitaceae
12.  Evola: Ortholog database of all human genes in H-InvDB with manual curation of phylogenetic trees 
Nucleic Acids Research  2007;36(Database issue):D787-D792.
Orthologs are genes in different species that evolved from a common ancestral gene by speciation. Currently, with the rapid growth of transcriptome data of various species, more reliable orthology information is prerequisite for further studies. However, detection of orthologs could be erroneous if pairwise distance-based methods, such as reciprocal BLAST searches, are utilized. Thus, as a sub-database of H-InvDB, an integrated database of annotated human genes (http://h-invitational.jp/), we constructed a fully curated database of evolutionary features of human genes, called ‘Evola’. In the process of the ortholog detection, computational analysis based on conserved genome synteny and transcript sequence similarity was followed by manual curation by researchers examining phylogenetic trees. In total, 18 968 human genes have orthologs among 11 vertebrates (chimpanzee, mouse, cow, chicken, zebrafish, etc.), either computationally detected or manually curated orthologs. Evola provides amino acid sequence alignments and phylogenetic trees of orthologs and homologs. In ‘dN/dS view’, natural selection on genes can be analyzed between human and other species. In ‘Locus maps’, all transcript variants and their exon/intron structures can be compared among orthologous gene loci. We expect the Evola to serve as a comprehensive and reliable database to be utilized in comparative analyses for obtaining new knowledge about human genes. Evola is available at http://www.h-invitational.jp/evola/.
doi:10.1093/nar/gkm878
PMCID: PMC2238928  PMID: 17982176
13.  Genome Trees from Conservation Profiles 
PLoS Computational Biology  2005;1(7):e75.
The concept of the genome tree depends on the potential evolutionary significance in the clustering of species according to similarities in the gene content of their genomes. In this respect, genome trees have often been identified with species trees. With the rapid expansion of genome sequence data it becomes of increasing importance to develop accurate methods for grasping global trends for the phylogenetic signals that mutually link the various genomes. We therefore derive here the methodological concept of genome trees based on protein conservation profiles in multiple species. The basic idea in this derivation is that the multi-component “presence-absence” protein conservation profiles permit tracking of common evolutionary histories of genes across multiple genomes. We show that a significant reduction in informational redundancy is achieved by considering only the subset of distinct conservation profiles. Beyond these basic ideas, we point out various pitfalls and limitations associated with the data handling, paving the way for further improvements. As an illustration for the methods, we analyze a genome tree based on the above principles, along with a series of other trees derived from the same data and based on pair-wise comparisons (ancestral duplication-conservation and shared orthologs). In all trees we observe a sharp discrimination between the three primary domains of life: Bacteria, Archaea, and Eukarya. The new genome tree, based on conservation profiles, displays a significant correspondence with classically recognized taxonomical groupings, along with a series of departures from such conventional clusterings.
Synopsis
Since Darwin's Origin of Species and Haeckel's Tree of Life, systematic biology has attempted to classify species into “family trees.” Genomics has provided a new framework permitting descriptions of sibling relations between species on the basis of their complete genetic blueprints. While trees based on single genes (rRNA), or limited numbers of genes have been useful, genome trees derived from complete genome comparisons should lead to more complete pictures of phylogenetic relations between various organisms. In order to reach such a global vision, procedures to establish sibling relationships should depend on an overall comparison that captures the evolutionary fates of proteins jointly in multiple genomes. This paper aims to establish a methodological basis to use genuine multidimensional procedures in the construction of genome trees. This approach completes the derivation of trees based on more classical techniques of pair-wise comparison between species. The authors survey classification schemes emerging from this approach, which either supports traditional views, such as the separation between the three phylogenetic domains Bacteria, Archaea, and Eukarya, or challenges them by suggesting, for example, intermingled clusterings of Proteobacteria with various other bacterial species.
doi:10.1371/journal.pcbi.0010075
PMCID: PMC1314884  PMID: 16362074
14.  Species Tree Inference by Minimizing Deep Coalescences 
PLoS Computational Biology  2009;5(9):e1000501.
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.
Author Summary
Inferring the evolutionary history of a set of species, known as the species tree, is a task of utmost significance in biology and beyond. The traditional approach to accomplishing this task from molecular sequences entails sequencing a gene in the set of species under consideration, reconstructing the gene's evolutionary history, and declaring it to be the species tree. However, recent analyses of multiple gene data sets, made available thanks to advances in sequencing technologies, have indicated that gene trees in the same group of species may disagree with each other, as well as with the species tree. Therefore, the development of methods for inferring the species tree despite such disagreements is imperative.
In this paper, we propose such a method, which seeks the tree that minimizes the amount of disagreement between the input set of gene trees and the inferred one. We have implemented our method and studied its performance, in terms of accuracy and computational efficiency, on two biological data sets and a large number of simulated data sets. Our analyses, of both the biological and synthetic data sets, indicate high accuracy of the method, as well as computationally efficient solutions in practice. Hence, our method makes a good candidate for inferring accurate species trees, despite gene tree disagreements, at a genomic scale.
doi:10.1371/journal.pcbi.1000501
PMCID: PMC2729383  PMID: 19749978
15.  MSOAR 2.0: Incorporating tandem duplications into ortholog assignment based on genome rearrangement 
BMC Bioinformatics  2010;11:10.
Background
Ortholog assignment is a critical and fundamental problem in comparative genomics, since orthologs are considered to be functional counterparts in different species and can be used to infer molecular functions of one species from those of other species. MSOAR is a recently developed high-throughput system for assigning one-to-one orthologs between closely related species on a genome scale. It attempts to reconstruct the evolutionary history of input genomes in terms of genome rearrangement and gene duplication events. It assumes that a gene duplication event inserts a duplicated gene into the genome of interest at a random location (i.e., the random duplication model). However, in practice, biologists believe that genes are often duplicated by tandem duplications, where a duplicated gene is located next to the original copy (i.e., the tandem duplication model).
Results
In this paper, we develop MSOAR 2.0, an improved system for one-to-one ortholog assignment. For a pair of input genomes, the system first focuses on the tandemly duplicated genes of each genome and tries to identify among them those that were duplicated after the speciation (i.e., the so-called inparalogs), using a simple phylogenetic tree reconciliation method. For each such set of tandemly duplicated inparalogs, all but one gene will be deleted from the concerned genome (because they cannot possibly appear in any one-to-one ortholog pairs), and MSOAR is invoked. Using both simulated and real data experiments, we show that MSOAR 2.0 is able to achieve a better sensitivity and specificity than MSOAR. In comparison with the well-known genome-scale ortholog assignment tool InParanoid, Ensembl ortholog database, and the orthology information extracted from the well-known whole-genome multiple alignment program MultiZ, MSOAR 2.0 shows the highest sensitivity. Although the specificity of MSOAR 2.0 is slightly worse than that of InParanoid in the real data experiments, it is actually better than that of InParanoid in the simulation tests.
Conclusions
Our preliminary experimental results demonstrate that MSOAR 2.0 is a highly accurate tool for one-to-one ortholog assignment between closely related genomes. The software is available to the public for free and included as online supplementary material.
doi:10.1186/1471-2105-11-10
PMCID: PMC2821317  PMID: 20053291
16.  Orthology and paralogy constraints: satisfiability and consistency 
BMC Genomics  2014;15(Suppl 6):S12.
Background
A variety of methods based on sequence similarity, reconciliation, synteny or functional characteristics, can be used to infer orthology and paralogy relations between genes of a given gene family  G. But is a given set  C of orthology/paralogy constraints possible, i.e., can they simultaneously co-exist in an evolutionary history for  G? While previous studies have focused on full sets of constraints, here we consider the general case where  C does not necessarily involve a constraint for each pair of genes. The problem is subdivided in two parts: (1) Is  C satisfiable, i.e. can we find an event-labeled gene tree G inducing  C? (2) Is there such a G which is consistent, i.e., such that all displayed triplet phylogenies are included in a species tree?
Results
Previous results on the Graph sandwich problem can be used to answer to (1), and we provide polynomial-time algorithms for satisfiability and consistency with a given species tree. We also describe a new polynomial-time algorithm for the case of consistency with an unknown species tree and full knowledge of pairwise orthology/paralogy relationships, as well as a branch-and-bound algorithm in the case when unknown relations are present. We show that our algorithms can be used in combination with ProteinOrtho, a sequence similarity-based orthology detection tool, to extract a set of robust orthology/paralogy relationships.
doi:10.1186/1471-2164-15-S6-S12
PMCID: PMC4240720  PMID: 25572629
orthology; paralogy; gene tree; species tree; satisfiability; consistency
17.  Assessing Performance of Orthology Detection Strategies Applied to Eukaryotic Genomes 
PLoS ONE  2007;2(4):e383.
Orthology detection is critically important for accurate functional annotation, and has been widely used to facilitate studies on comparative and evolutionary genomics. Although various methods are now available, there has been no comprehensive analysis of performance, due to the lack of a genomic-scale ‘gold standard’ orthology dataset. Even in the absence of such datasets, the comparison of results from alternative methodologies contains useful information, as agreement enhances confidence and disagreement indicates possible errors. Latent Class Analysis (LCA) is a statistical technique that can exploit this information to reasonably infer sensitivities and specificities, and is applied here to evaluate the performance of various orthology detection methods on a eukaryotic dataset. Overall, we observe a trade-off between sensitivity and specificity in orthology detection, with BLAST-based methods characterized by high sensitivity, and tree-based methods by high specificity. Two algorithms exhibit the best overall balance, with both sensitivity and specificity>80%: INPARANOID identifies orthologs across two species while OrthoMCL clusters orthologs from multiple species. Among methods that permit clustering of ortholog groups spanning multiple genomes, the (automated) OrthoMCL algorithm exhibits better within-group consistency with respect to protein function and domain architecture than the (manually curated) KOG database, and the homolog clustering algorithm TribeMCL as well. By way of using LCA, we are also able to comprehensively assess similarities and statistical dependence between various strategies, and evaluate the effects of parameter settings on performance. In summary, we present a comprehensive evaluation of orthology detection on a divergent set of eukaryotic genomes, thus providing insights and guides for method selection, tuning and development for different applications. Many biological questions have been addressed by multiple tests yielding binary (yes/no) outcomes but no clear definition of truth, making LCA an attractive approach for computational biology.
doi:10.1371/journal.pone.0000383
PMCID: PMC1849888  PMID: 17440619
18.  SyntenyTracker: a tool for defining homologous synteny blocks using radiation hybrid maps and whole-genome sequence 
BMC Research Notes  2009;2:148.
Background
The recent availability of genomic sequences and BAC libraries for a large number of mammals provides an excellent opportunity for identifying comparatively-anchored markers that are useful for creating high-resolution radiation-hybrid (RH) and BAC-based comparative maps. To use these maps for multispecies genome comparison and evolutionary inference, robust bioinformatic tools are required for the identification of chromosomal regions shared between genomes and to localize the positions of evolutionary breakpoints that are the signatures of chromosomal rearrangements. Here we report an automated tool for the identification of homologous synteny blocks (HSBs) between genomes that tolerates errors common in RH comparative maps and can be used for automated whole-genome analysis of chromosome rearrangements that occur during evolution.
Findings
We developed an algorithm and software tool (SyntenyTracker) that can be used for automated definition of HSBs using pair-wise RH or gene-based comparative maps as input. To verify correct implementation of the underlying algorithm, SyntenyTracker was used to identify HSBs in the cattle and human genomes. Results demonstrated 96% agreement with HSBs defined manually using the same set of rules. A comparison of SyntenyTracker with the AutoGRAPH synteny tool was performed using identical datasets containing 14,380 genes with 1:1 orthology in human and mouse. Discrepancies between the results using the two tools and advantages of SyntenyTracker are reported.
Conclusion
SyntenyTracker was shown to be an efficient and accurate automated tool for defining HSBs using datasets that may contain minor errors resulting from limitations in map construction methodologies. The utility of SyntenyTracker will become more important for comparative genomics as the number of mapped and sequenced genomes increases.
doi:10.1186/1756-0500-2-148
PMCID: PMC2726151  PMID: 19627596
19.  Algorithms: simultaneous error-correction and rooting for gene tree reconciliation and the gene duplication problem 
BMC Bioinformatics  2012;13(Suppl 10):S14.
Background
Evolutionary methods are increasingly challenged by the wealth of fast growing resources of genomic sequence information. Evolutionary events, like gene duplication, loss, and deep coalescence, account more then ever for incongruence between gene trees and the actual species tree. Gene tree reconciliation is addressing this fundamental problem by invoking the minimum number of gene duplication and losses that reconcile a rooted gene tree with a rooted species tree. However, the reconciliation process is highly sensitive to topological error or wrong rooting of the gene tree, a condition that is not met by most gene trees in practice. Thus, despite the promises of gene tree reconciliation, its applicability in practice is severely limited.
Results
We introduce the problem of reconciling unrooted and erroneous gene trees by simultaneously rooting and error-correcting them, and describe an efficient algorithm for this problem. Moreover, we introduce an error-corrected version of the gene duplication problem, a standard application of gene tree reconciliation. We introduce an effective heuristic for our error-corrected version of the gene duplication problem, given that the original version of this problem is NP-hard. Our experimental results suggest that our error-correcting approaches for unrooted input trees can significantly improve on the accuracy of gene tree reconciliation, and the species tree inference under the gene duplication problem. Furthermore, the efficiency of our algorithm for error-correcting reconciliation is capable of handling truly large-scale phylogenetic studies.
Conclusions
Our presented error-correction approach is a crucial step towards making gene tree reconciliation more robust, and thus to improve on the accuracy of applications that fundamentally rely on gene tree reconciliation, like the inference of gene-duplication supertrees.
doi:10.1186/1471-2105-13-S10-S14
PMCID: PMC3382441  PMID: 22759419
20.  Algorithms for computing parsimonious evolutionary scenarios for genome evolution, the last universal common ancestor and dominance of horizontal gene transfer in the evolution of prokaryotes 
Background
Comparative analysis of sequenced genomes reveals numerous instances of apparent horizontal gene transfer (HGT), at least in prokaryotes, and indicates that lineage-specific gene loss might have been even more common in evolution. This complicates the notion of a species tree, which needs to be re-interpreted as a prevailing evolutionary trend, rather than the full depiction of evolution, and makes reconstruction of ancestral genomes a non-trivial task.
Results
We addressed the problem of constructing parsimonious scenarios for individual sets of orthologous genes given a species tree. The orthologous sets were taken from the database of Clusters of Orthologous Groups of proteins (COGs). We show that the phyletic patterns (patterns of presence-absence in completely sequenced genomes) of almost 90% of the COGs are inconsistent with the hypothetical species tree. Algorithms were developed to reconcile the phyletic patterns with the species tree by postulating gene loss, COG emergence and HGT (the latter two classes of events were collectively treated as gene gains). We prove that each of these algorithms produces a parsimonious evolutionary scenario, which can be represented as mapping of loss and gain events on the species tree. The distribution of the evolutionary events among the tree nodes substantially depends on the underlying assumptions of the reconciliation algorithm, e.g. whether or not independent gene gains (gain after loss after gain) are permitted. Biological considerations suggest that, on average, gene loss might be a more likely event than gene gain. Therefore different gain penalties were used and the resulting series of reconstructed gene sets for the last universal common ancestor (LUCA) of the extant life forms were analysed. The number of genes in the reconstructed LUCA gene sets grows as the gain penalty increases. However, qualitative examination of the LUCA versions reconstructed with different gain penalties indicates that, even with a gain penalty of 1 (equal weights assigned to a gain and a loss), the set of 572 genes assigned to LUCA might be nearly sufficient to sustain a functioning organism. Under this gain penalty value, the numbers of horizontal gene transfer and gene loss events are nearly identical. This result holds true for two alternative topologies of the species tree and even under random shuffling of the tree. Therefore, the results seem to be compatible with approximately equal likelihoods of HGT and gene loss in the evolution of prokaryotes.
Conclusions
The notion that gene loss and HGT are major aspects of prokaryotic evolution was supported by quantitative analysis of the mapping of the phyletic patterns of COGs onto a hypothetical species tree. Algorithms were developed for constructing parsimonious evolutionary scenarios, which include gene loss and gain events, for orthologous gene sets, given a species tree. This analysis shows, contrary to expectations, that the number of predicted HGT events that occurred during the evolution of prokaryotes might be approximately the same as the number of gene losses. The approach to the reconstruction of evolutionary scenarios employed here is conservative with regard to the detection of HGT because only patterns of gene presence-absence in sequenced genomes are taken into account. In reality, horizontal transfer might have contributed to the evolution of many other genes also, which makes it a dominant force in prokaryotic evolution.
doi:10.1186/1471-2148-3-2
PMCID: PMC149225  PMID: 12515582
21.  Phylogenetic identification of lateral genetic transfer events 
Background
Lateral genetic transfer can lead to disagreements among phylogenetic trees comprising sequences from the same set of taxa. Where topological discordance is thought to have arisen through genetic transfer events, tree comparisons can be used to identify the lineages that may have shared genetic information. An 'edit path' of one or more transfer events can be represented with a series of subtree prune and regraft (SPR) operations, but finding the optimal such set of operations is NP-hard for comparisons between rooted trees, and may be so for unrooted trees as well.
Results
Efficient Evaluation of Edit Paths (EEEP) is a new tree comparison algorithm that uses evolutionarily reasonable constraints to identify and eliminate many unproductive search avenues, reducing the time required to solve many edit path problems. The performance of EEEP compares favourably to that of other algorithms when applied to strictly bifurcating trees with specified numbers of SPR operations. We also used EEEP to recover edit paths from over 19 000 unrooted, incompletely resolved protein trees containing up to 144 taxa as part of a large phylogenomic study. While inferred protein trees were far more similar to a reference supertree than random trees were to each other, the phylogenetic distance spanned by random versus inferred transfer events was similar, suggesting that real transfer events occur most frequently between closely related organisms, but can span large phylogenetic distances as well. While most of the protein trees examined here were very similar to the reference supertree, requiring zero or one edit operations for reconciliation, some trees implied up to 40 transfer events within a single orthologous set of proteins.
Conclusion
Since sequence trees typically have no implied root and may contain unresolved or multifurcating nodes, the strategy implemented in EEEP is the most appropriate for phylogenomic analyses. The high degree of consistency among inferred protein trees shows that vertical inheritance is the dominant pattern of evolution, at least for the set of organisms considered here. However, the edit paths inferred using EEEP suggest an important role for genetic transfer in the evolution of microbial genomes as well.
doi:10.1186/1471-2148-6-15
PMCID: PMC1431587  PMID: 16472400
22.  BranchClust: a phylogenetic algorithm for selecting gene families 
BMC Bioinformatics  2007;8:120.
Background
Automated methods for assembling families of orthologous genes include those based on sequence similarity scores and those based on phylogenetic approaches. The first are easy to automate but usually they do not distinguish between paralogs and orthologs or have restriction on the number of taxa. Phylogenetic methods often are based on reconciliation of a gene tree with a known rooted species tree; a limitation of this approach, especially in case of prokaryotes, is that the species tree is often unknown, and that from the analyses of single gene families the branching order between related organisms frequently is unresolved.
Results
Here we describe an algorithm for the automated selection of orthologous genes that recognizes orthologous genes from different species in a phylogenetic tree for any number of taxa. The algorithm is capable of distinguishing complete (containing all taxa) and incomplete (not containing all taxa) families and recognizes in- and outparalogs. The BranchClust algorithm is implemented in Perl with the use of the BioPerl module for parsing trees and is freely available at .
Conclusion
BranchClust outperforms the Reciprocal Best Blast hit method in selecting more sets of putatively orthologous genes. In the test cases examined, the correctness of the selected families and of the identified in- and outparalogs was confirmed by inspection of the pertinent phylogenetic trees.
doi:10.1186/1471-2105-8-120
PMCID: PMC1853112  PMID: 17425803
23.  Inferring Hierarchical Orthologous Groups from Orthologous Gene Pairs 
PLoS ONE  2013;8(1):e53786.
Hierarchical orthologous groups are defined as sets of genes that have descended from a single common ancestor within a taxonomic range of interest. Identifying such groups is useful in a wide range of contexts, including inference of gene function, study of gene evolution dynamics and comparative genomics. Hierarchical orthologous groups can be derived from reconciled gene/species trees but, this being a computationally costly procedure, many phylogenomic databases work on the basis of pairwise gene comparisons instead (“graph-based” approach). To our knowledge, there is only one published algorithm for graph-based hierarchical group inference, but both its theoretical justification and performance in practice are as of yet largely uncharacterised. We establish a formal correspondence between the orthology graph and hierarchical orthologous groups. Based on that, we devise GETHOGs (“Graph-based Efficient Technique for Hierarchical Orthologous Groups”), a novel algorithm to infer hierarchical groups directly from the orthology graph, thus without needing gene tree inference nor gene/species tree reconciliation. GETHOGs is shown to correctly reconstruct hierarchical orthologous groups when applied to perfect input, and several extensions with stringency parameters are provided to deal with imperfect input data. We demonstrate its competitiveness using both simulated and empirical data. GETHOGs is implemented as a part of the freely-available OMA standalone package (http://omabrowser.org/standalone). Furthermore, hierarchical groups inferred by GETHOGs (“OMA HOGs”) on >1,000 genomes can be interactively queried via the OMA browser (http://omabrowser.org).
doi:10.1371/journal.pone.0053786
PMCID: PMC3544860  PMID: 23342000
24.  Cinteny: flexible analysis and visualization of synteny and genome rearrangements in multiple organisms 
BMC Bioinformatics  2007;8:82.
Background
Identifying syntenic regions, i.e., blocks of genes or other markers with evolutionary conserved order, and quantifying evolutionary relatedness between genomes in terms of chromosomal rearrangements is one of the central goals in comparative genomics. However, the analysis of synteny and the resulting assessment of genome rearrangements are sensitive to the choice of a number of arbitrary parameters that affect the detection of synteny blocks. In particular, the choice of a set of markers and the effect of different aggregation strategies, which enable coarse graining of synteny blocks and exclusion of micro-rearrangements, need to be assessed. Therefore, existing tools and resources that facilitate identification, visualization and analysis of synteny need to be further improved to provide a flexible platform for such analysis, especially in the context of multiple genomes.
Results
We present a new tool, Cinteny, for fast identification and analysis of synteny with different sets of markers and various levels of coarse graining of syntenic blocks. Using Hannenhalli-Pevzner approach and its extensions, Cinteny also enables interactive determination of evolutionary relationships between genomes in terms of the number of rearrangements (the reversal distance). In particular, Cinteny provides: i) integration of synteny browsing with assessment of evolutionary distances for multiple genomes; ii) flexibility to adjust the parameters and re-compute the results on-the-fly; iii) ability to work with user provided data, such as orthologous genes, sequence tags or other conserved markers. In addition, Cinteny provides many annotated mammalian, invertebrate and fungal genomes that are pre-loaded and available for analysis at .
Conclusion
Cinteny allows one to automatically compare multiple genomes and perform sensitivity analysis for synteny block detection and for the subsequent computation of reversal distances. Cinteny can also be used to interactively browse syntenic blocks conserved in multiple genomes, to facilitate genome annotation and validation of assemblies for newly sequenced genomes, and to construct and assess phylogenomic trees.
doi:10.1186/1471-2105-8-82
PMCID: PMC1821339  PMID: 17343765
25.  Cubic time algorithms of amalgamating gene trees and building evolutionary scenarios 
Biology Direct  2012;7:48.
Background
A long recognized problem is the inference of the supertree S that amalgamates a given set {Gj} of trees Gj, with leaves in each Gj being assigned homologous elements.
We ground on an approach to find the tree S by minimizing the total cost of mappings αj of individual gene trees Gj into S. Traditionally, this cost is defined basically as a sum of duplications and gaps in each αj. The classical problem is to minimize the total cost, where S runs over the set of all trees that contain an exhaustive non-redundant set of species from all input Gj.
Results
We suggest a reformulation of the classical NP-hard problem of building a supertree in terms of the global minimization of the same cost functional but only over species trees S that consist of clades belonging to a fixed set P (e.g., an exhaustive set of clades in all Gj). We developed a deterministic solving algorithm with a low degree polynomial (typically cubic) time complexity with respect to the size of input data.
We define an extensive set of elementary evolutionary events and suggest an original definition of mapping β of tree G into tree S. We introduce the cost functional c(G, S, f ) and define the mapping β as the global minimum of this functional with respect to the variable f, in which sense it is a generalization of classical mapping α.
We suggest a reformulation of the classical NP-hard mapping (reconciliation) problem by introducing time slices into the species tree S and present a cubic time solving algorithm to compute the mapping β. We introduce two novel definitions of the evolutionary scenario based on mapping β or a random process of gene evolution along a species tree.
Conclusions
Developed algorithms are mathematically proved, which justifies the following statements. The supertree building algorithm finds exactly the global minimum of the total cost if only gene duplications and losses are allowed and the given sets of gene trees satisfies a certain condition. The mapping algorithm finds exactly the minimal mapping β, the minimal total cost and the evolutionary scenario as a minimum over all possible distributions of elementary evolutionary events along the edges of tree S.
The algorithms and their effective software implementations provide useful tools in many biological studies. They facilitate processing of voluminous tree data in acceptable time still largely avoiding heuristics. Performance of the tools is tested with artificial and prokaryotic tree data.
Reviewers
This article was reviewed by Prof. Anthony Almudevar, Prof. Alexander Bolshoy (nominated by Prof. Peter Olofsson), and Prof. Marek Kimmel.
doi:10.1186/1745-6150-7-48
PMCID: PMC3577452  PMID: 23259766
Phylogenetics; Fast algorithms; Tree inference; Species tree; Tree amalgamation; Tree reconciliation; Supertree; Evolutionary events; Gene duplication; Gene loss; Horizontal gene transfer; Gene gain; Time slices

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