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Thi-Hau Nguyen. Réconciliations: corriger des arbres de gènes et inférer la fiabilité des événements évolutifs. PhD thesis, Université Montpellier 2, France, 2013. Keywords: duplication, explicit network, from rooted trees, heuristic, lateral gene transfer, phylogenetic network, phylogeny, Program Mowgli, Program MowgliNNI, reconstruction. Note: http://www.biu-montpellier.fr/florabium/servlet/DocumentFileManager?source=ged&document=ged:IDOCS:247665&resolution=&recordId=theses%3ABIU_THESE%3A1789&file=.
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Chris Whidden. Efficient Computation and Application of Maximum Agreement Forests. PhD thesis, Dalhousie University, Canada, 2013. Keywords: agreement forest, explicit network, FPT, from rooted trees, minimum number, phylogenetic network, phylogeny, reconstruction. Note: http://hdl.handle.net/10222/35349.
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Sarah Bastkowski. From Trees to Networks and Back. PhD thesis, University of East Anglia, 2013. Keywords: abstract network, NeighborNet, phylogenetic network, phylogeny, Program FlatNJ, Program QNet, Program SplitsTree, reconstruction, software, split network. Note: http://spectre-suite-of-phylogenetic-tools-for-reticulate-evolution.readthedocs.io/en/latest/_downloads/spectre_bastkowskis_thesis.pdf.
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Hoa Vu,
Francis Chin,
Wing-Kai Hon,
Henry Leung,
Kunihiko Sadakane,
Wing-Kin Sung and
Siu-Ming Yiu. Reconstructing k-Reticulated Phylogenetic Network from a Set of Gene Trees. In ISBRA13, Vol. 7875:112-124 of LNCS, springer, 2013. Keywords: from rooted trees, k-reticulated, phylogenetic network, phylogeny, polynomial, Program ARTNET, Program CMPT, reconstruction. Note: http://grid.cs.gsu.edu/~xguo9/publications/2013_Cloud%20computing%20for%20de%20novo%20metagenomic%20sequence%20assembly.pdf#page=123.
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"The time complexity of existing algorithms for reconstructing a level-x phylogenetic network increases exponentially in x. In this paper, we propose a new classification of phylogenetic networks called k-reticulated network. A k-reticulated network can model all level-k networks and some level-x networks with x > k. We design algorithms for reconstructing k-reticulated network (k = 1 or 2) with minimum number of hybrid nodes from a set of m binary trees, each with n leaves in O(mn 2) time. The implication is that some level-x networks with x > k can now be reconstructed in a faster way. We implemented our algorithm (ARTNET) and compared it with CMPT. We show that ARTNET outperforms CMPT in terms of running time and accuracy. We also consider the case when there does not exist a 2-reticulated network for the input trees. We present an algorithm computing a maximum subset of the species set so that a new set of subtrees can be combined into a 2-reticulated network. © 2013 Springer-Verlag."
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Yufeng Wu. An Algorithm for Constructing Parsimonious Hybridization Networks with Multiple Phylogenetic Trees. In RECOMB13, Vol. 7821:291-303 of LNCS, springer, 2013. Keywords: explicit network, exponential algorithm, from rooted trees, phylogenetic network, phylogeny, Program PIRN, reconstruction. Note: http://www.engr.uconn.edu/~ywu/Papers/ExactNetRecomb2013.pdf.
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"Phylogenetic network is a model for reticulate evolution. Hybridization network is one type of phylogenetic network for a set of discordant gene trees, and "displays" each gene tree. A central computational problem on hybridization networks is: given a set of gene trees, reconstruct the minimum (i.e. most parsimonious) hybridization network that displays each given gene tree. This problem is known to be NP-hard, and existing approaches for this problem are either heuristics or make simplifying assumptions (e.g. work with only two input trees or assume some topological properties). In this paper, we develop an exact algorithm (called PIRNC ) for inferring the minimum hybridization networks from multiple gene trees. The PIRNC algorithm does not rely on structural assumptions. To the best of our knowledge, PIRN C is the first exact algorithm for this formulation. When the number of reticulation events is relatively small (say four or fewer), PIRNC runs reasonably efficient even for moderately large datasets. For building more complex networks, we also develop a heuristic version of PIRNC called PIRNCH. Simulation shows that PIRNCH usually produces networks with fewer reticulation events than those by an existing method. © 2013 Springer-Verlag."
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Mukul S. Bansal,
Eric J. Alm and
Manolis Kellis. Reconciliation Revisited: Handling Multiple Optima when Reconciling with Duplication, Transfer, and Loss. In RECOMB13, Vol. 7821:1-13 of LNCS, springer, 2013. Keywords: duplication, from rooted trees, from species tree, loss, phylogenetic network, phylogeny, polynomial, Program RANGER-DTL, reconstruction. Note: http://people.csail.mit.edu/mukul/Bansal_RECOMB2013.pdf.
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"Phylogenetic tree reconciliation is a powerful approach for inferring evolutionary events like gene duplication, horizontal gene transfer, and gene loss, which are fundamental to our understanding of molecular evolution. While Duplication-Loss (DL) reconciliation leads to a unique maximum-parsimony solution, Duplication-Transfer-Loss (DTL) reconciliation yields a multitude of optimal solutions, making it difficult the infer the true evolutionary history of the gene family. Here, we present an effective, efficient, and scalable method for dealing with this fundamental problem in DTL reconciliation. Our approach works by sampling the space of optimal reconciliations uniformly at random and aggregating the results. We present an algorithm to efficiently sample the space of optimal reconciliations uniformly at random in O(mn 2) time, where m and n denote the number of genes and species, respectively. We use these samples to understand how different optimal reconciliations vary in their node mapping and event assignments, and to investigate the impact of varying event costs. © 2013 Springer-Verlag."
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Katharina Huber and
Vincent Moulton. Encoding and Constructing 1-Nested Phylogenetic Networks with Trinets. In ALG, Vol. 66(3):714-738, 2013. Keywords: explicit network, from subnetworks, from trinets, phylogenetic network, phylogeny, reconstruction, uniqueness. Note: http://arxiv.org/abs/1110.0728.
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"Phylogenetic networks are a generalization of phylogenetic trees that are used in biology to represent reticulate or non-treelike evolution. Recently, several algorithms have been developed which aim to construct phylogenetic networks from biological data using triplets, i.e. binary phylogenetic trees on 3-element subsets of a given set of species. However, a fundamental problem with this approach is that the triplets displayed by a phylogenetic network do not necessarily uniquely determine or encode the network. Here we propose an alternative approach to encoding and constructing phylogenetic networks, which uses phylogenetic networks on 3-element subsets of a set, or trinets, rather than triplets. More specifically, we show that for a special, well-studied type of phylogenetic network called a 1-nested network, the trinets displayed by a 1-nested network always encode the network. We also present an efficient algorithm for deciding whether a dense set of trinets (i.e. one that contains a trinet on every 3-element subset of a set) can be displayed by a 1-nested network or not and, if so, constructs that network. In addition, we discuss some potential new directions that this new approach opens up for constructing and comparing phylogenetic networks. © 2012 Springer Science+Business Media, LLC."
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Alberto Apostolico,
Matteo Comin,
Andreas W. M. Dress and
Laxmi Parida. Ultrametric networks: a new tool for phylogenetic analysis. In Algorithms for Molecular Biology, Vol. 8(7):1-10, 2013. Keywords: abstract network, from distances, phylogenetic network, phylogeny, Program Ultranet. Note: http://dx.doi.org/10.1186/1748-7188-8-7.
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"Background: The large majority of optimization problems related to the inference of distance-based trees used in phylogenetic analysis and classification is known to be intractable. One noted exception is found within the realm of ultrametric distances. The introduction of ultrametric trees in phylogeny was inspired by a model of evolution driven by the postulate of a molecular clock, now dismissed, whereby phylogeny could be represented by a weighted tree in which the sum of the weights of the edges separating any given leaf from the root is the same for all leaves. Both, molecular clocks and rooted ultrametric trees, fell out of fashion as credible representations of evolutionary change. At the same time, ultrametric dendrograms have shown good potential for purposes of classification in so far as they have proven to provide good approximations for additive trees. Most of these approximations are still intractable, but the problem of finding the nearest ultrametric distance matrix to a given distance matrix with respect to the L∞ distance has been long known to be solvable in polynomial time, the solution being incarnated in any minimum spanning tree for the weighted graph subtending to the matrix.Results: This paper expands this subdominant ultrametric perspective by studying ultrametric networks, consisting of the collection of all edges involved in some minimum spanning tree. It is shown that, for a graph with n vertices, the construction of such a network can be carried out by a simple algorithm in optimal time O(n2) which is faster by a factor of n than the direct adaptation of the classical O(n3) paradigm by Warshall for computing the transitive closure of a graph. This algorithm, called UltraNet, will be shown to be easily adapted to compute relaxed networks and to support the introduction of artificial points to reduce the maximum distance between vertices in a pair. Finally, a few experiments will be discussed to demonstrate the applicability of subdominant ultrametric networks.Availability: http://www.dei.unipd.it/~ciompin/main/Ultranet/Ultranet.html. © 2013 Apostolico et al.; licensee BioMed Central Ltd."
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Thi-Hau Nguyen,
Vincent Ranwez,
Stéphanie Pointet,
Anne-Muriel Chifolleau Arigon,
Jean-Philippe Doyon and
Vincent Berry. Reconciliation and local gene tree rearrangement can be of mutual profit. In ALMOB, Vol. 8(12), 2013. Keywords: duplication, explicit network, from rooted trees, heuristic, lateral gene transfer, phylogenetic network, phylogeny, Program Mowgli, Program MowgliNNI, Program Prunier, reconstruction, software.
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"Background: Reconciliation methods compare gene trees and species trees to recover evolutionary events such as duplications, transfers and losses explaining the history and composition of genomes. It is well-known that gene trees inferred from molecular sequences can be partly erroneous due to incorrect sequence alignments as well as phylogenetic reconstruction artifacts such as long branch attraction. In practice, this leads reconciliation methods to overestimate the number of evolutionary events. Several methods have been proposed to circumvent this problem, by collapsing the unsupported edges and then resolving the obtained multifurcating nodes, or by directly rearranging the binary gene trees. Yet these methods have been defined for models of evolution accounting only for duplications and losses, i.e. can not be applied to handle prokaryotic gene families.Results: We propose a reconciliation method accounting for gene duplications, losses and horizontal transfers, that specifically takes into account the uncertainties in gene trees by rearranging their weakly supported edges. Rearrangements are performed on edges having a low confidence value, and are accepted whenever they improve the reconciliation cost. We prove useful properties on the dynamic programming matrix used to compute reconciliations, which allows to speed-up the tree space exploration when rearrangements are generated by Nearest Neighbor Interchanges (NNI) edit operations. Experiments on synthetic data show that gene trees modified by such NNI rearrangements are closer to the correct simulated trees and lead to better event predictions on average. Experiments on real data demonstrate that the proposed method leads to a decrease in the reconciliation cost and the number of inferred events. Finally on a dataset of 30 k gene families, this reconciliation method shows a ranking of prokaryotic phyla by transfer rates identical to that proposed by a different approach dedicated to transfer detection [BMCBIOINF 11:324, 2010, PNAS 109(13):4962-4967, 2012].Conclusions: Prokaryotic gene trees can now be reconciled with their species phylogeny while accounting for the uncertainty of the gene tree. More accurate and more precise reconciliations are obtained with respect to previous parsimony algorithms not accounting for such uncertainties [LNCS 6398:93-108, 2010, BIOINF 28(12): i283-i291, 2012].A software implementing the method is freely available at http://www.atgc-montpellier.fr/Mowgli/. © 2013 Nguyen et al.; licensee BioMed Central Ltd."
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Mukul S. Bansal,
Guy Banay,
Timothy J. Harlow,
J. Peter Gogarten and
Ron Shamir. Systematic inference of highways of horizontal gene transfer in prokaryotes. In BIO, Vol. 29(5):571-579, 2013. Keywords: duplication, explicit network, from species tree, from unrooted trees, lateral gene transfer, phylogenetic network, phylogeny, Program HiDe, Program RANGER-DTL, reconstruction. Note: http://people.csail.mit.edu/mukul/Bansal_Highways_Bioinformatics_2013.pdf.
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Juan Wang,
Maozu Guo,
Xiaoyan Liu,
Yang Liu,
Chunyu Wang,
Linlin Xing and
Kai Che. LNETWORK: An Efficient and Effective Method for Constructing Phylogenetic Networks. In BIO, Vol. 29(18):2269-2276, 2013. Keywords: explicit network, from rooted trees, phylogenetic network, phylogeny, Program LNetwork, reconstruction, software.
Toggle abstract
"Motivation: The evolutionary history of species is traditionally represented with a rooted phylogenetic tree. Each tree comprises a set of clusters, i.e. subsets of the species that are descended from a common ancestor. When rooted phylogenetic trees are built from several different datasets (e.g. from different genes), the clusters are often conflicting. These conflicting clusters cannot be expressed as a simple phylogenetic tree; however, they can be expressed in a phylogenetic network. Phylogenetic networks are a generalization of phylogenetic trees that can account for processes such as hybridization, horizontal gene transfer and recombination, which are difficult to represent in standard tree-like models of evolutionary histories. There is currently a large body of research aimed at developing appropriate methods for constructing phylogenetic networks from cluster sets. The Cass algorithm can construct a much simpler network than other available methods, but is extremely slow for large datasets or for datasets that need lots of reticulate nodes. The networks constructed by Cass are also greatly dependent on the order of input data, i.e. it generally derives different phylogenetic networks for the same dataset when different input orders are used.Results: In this study, we introduce an improved Cass algorithm, Lnetwork, which can construct a phylogenetic network for a given set of clusters. We show that Lnetwork is significantly faster than Cass and effectively weakens the influence of input data order. Moreover, we show that Lnetwork can construct a much simpler network than most of the other available methods. © The Author 2013."
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Stephen J. Willson. Reconstruction of certain phylogenetic networks from their tree-average distances. In BMB, Vol. 75(10):1840-1878, 2013. Keywords: explicit network, from distances, galled tree, normal network, phylogenetic network, phylogeny, unicyclic network. Note: http://www.public.iastate.edu/~swillson/Tree-AverageReconPaper9.pdf.
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"Trees are commonly utilized to describe the evolutionary history of a collection of biological species, in which case the trees are called phylogenetic trees. Often these are reconstructed from data by making use of distances between extant species corresponding to the leaves of the tree. Because of increased recognition of the possibility of hybridization events, more attention is being given to the use of phylogenetic networks that are not necessarily trees. This paper describes the reconstruction of certain such networks from the tree-average distances between the leaves. For a certain class of phylogenetic networks, a polynomial-time method is presented to reconstruct the network from the tree-average distances. The method is proved to work if there is a single reticulation cycle. © 2013 Society for Mathematical Biology."
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Peter J. Humphries,
Simone Linz and
Charles Semple. Cherry picking: a characterization of the temporal hybridization number for a set of phylogenies. In BMB, Vol. 75(10):1879-1890, 2013. Keywords: characterization, cherry-picking, from rooted trees, hybridization, NP complete, phylogenetic network, phylogeny, reconstruction, time consistent network. Note: http://ab.inf.uni-tuebingen.de/people/linz/publications/CPSpaper.pdf.
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"Recently, we have shown that calculating the minimum-temporal-hybridization number for a set P of rooted binary phylogenetic trees is NP-hard and have characterized this minimum number when P consists of exactly two trees. In this paper, we give the first characterization of the problem for P being arbitrarily large. The characterization is in terms of cherries and the existence of a particular type of sequence. Furthermore, in an online appendix to the paper, we show that this new characterization can be used to show that computing the minimum-temporal hybridization number for two trees is fixed-parameter tractable. © 2013 Society for Mathematical Biology."
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Mehdi Layeghifard,
Pedro R. Peres-Neto and
Vladimir Makarenkov. Inferring explicit weighted consensus networks to represent alternative evolutionary histories. In BMCEB, Vol. 13(274):1-25, 2013. Keywords: explicit network, from rooted trees, from species tree, phylogenetic network, phylogeny, Program ConsensusNetwork, reconstruction. Note: http://dx.doi.org/10.1186/1471-2148-13-274.
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"Background: The advent of molecular biology techniques and constant increase in availability of genetic material have triggered the development of many phylogenetic tree inference methods. However, several reticulate evolution processes, such as horizontal gene transfer and hybridization, have been shown to blur the species evolutionary history by causing discordance among phylogenies inferred from different genes. Methods. To tackle this problem, we hereby describe a new method for inferring and representing alternative (reticulate) evolutionary histories of species as an explicit weighted consensus network which can be constructed from a collection of gene trees with or without prior knowledge of the species phylogeny. Results: We provide a way of building a weighted phylogenetic network for each of the following reticulation mechanisms: diploid hybridization, intragenic recombination and complete or partial horizontal gene transfer. We successfully tested our method on some synthetic and real datasets to infer the above-mentioned evolutionary events which may have influenced the evolution of many species. Conclusions: Our weighted consensus network inference method allows one to infer, visualize and validate statistically major conflicting signals induced by the mechanisms of reticulate evolution. The results provided by the new method can be used to represent the inferred conflicting signals by means of explicit and easy-to-interpret phylogenetic networks. © 2013 Layeghifard et al.; licensee BioMed Central Ltd."
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Alexey A. Morozov,
Yuri P. Galachyants and
Yelena V. Likhoshway. Inferring Phylogenetic Networks from Gene Order Data. In BMRI, Vol. 2013(503193):1-7, 2013. Keywords: abstract network, from distances, from gene order, NeighborNet, phylogenetic network, phylogeny, Program SplitsTree, reconstruction, split decomposition, split network.
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"Existing algorithms allow us to infer phylogenetic networks from sequences (DNA, protein or binary), sets of trees, and distance matrices, but there are no methods to build them using the gene order data as an input. Here we describe several methods to build split networks from the gene order data, perform simulation studies, and use our methods for analyzing and interpreting different real gene order datasets. All proposed methods are based on intermediate data, which can be generated from genome structures under study and used as an input for network construction algorithms. Three intermediates are used: set of jackknife trees, distance matrix, and binary encoding. According to simulations and case studies, the best intermediates are jackknife trees and distance matrix (when used with Neighbor-Net algorithm). Binary encoding can also be useful, but only when the methods mentioned above cannot be used. © 2013 Alexey Anatolievich Morozov et al."
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Peter J. Humphries,
Simone Linz and
Charles Semple. On the complexity of computing the temporal hybridization number for two phylogenies. In DAM, Vol. 161:871-880, 2013. Keywords: agreement forest, APX hard, characterization, from rooted trees, hybridization, NP complete, phylogenetic network, phylogeny, reconstruction, time consistent network. Note: http://ab.inf.uni-tuebingen.de/people/linz/publications/TAFapx.pdf.
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"Phylogenetic networks are now frequently used to explain the evolutionary history of a set of species for which a collection of gene trees, reconstructed from genetic material of different parts of the species' genomes, reveal inconsistencies. However, in the context of hybridization, the reconstructed networks are often not temporal. If a hybridization network is temporal, then it satisfies the time constraint of instantaneously occurring hybridization events; i.e. all species that are involved in such an event coexist in time. Furthermore, although a collection of phylogenetic trees can often be merged into a hybridization network that is temporal, many algorithms do not necessarily find such a network since their primary optimization objective is to minimize the number of hybridization events. In this paper, we present a characterization for when two rooted binary phylogenetic trees admit a temporal hybridization network. Furthermore, we show that the underlying optimization problem is APX-hard and, therefore, NP-hard. Thus, unless P=NP, it is unlikely that there are efficient algorithms for either computing an exact solution or approximating it within a ratio arbitrarily close to one. © 2012 Elsevier B.V. All rights reserved."
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Juan Wang,
Maozu Guo,
Linlin Xing,
Kai Che,
Xiaoyan Liu and
Chunyu Wang. BIMLR: A Method for Constructing Rooted Phylogenetic Networks from Rooted Phylogenetic Trees. In Gene, Vol. 527(1):344-351, 2013. Keywords: explicit network, from clusters, from rooted trees, phylogenetic network, phylogeny, Program BIMLR, Program Dendroscope, reconstruction, software.
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"Rooted phylogenetic trees constructed from different datasets (e.g. from different genes) are often conflicting with one another, i.e. they cannot be integrated into a single phylogenetic tree. Phylogenetic networks have become an important tool in molecular evolution, and rooted phylogenetic networks are able to represent conflicting rooted phylogenetic trees. Hence, the development of appropriate methods to compute rooted phylogenetic networks from rooted phylogenetic trees has attracted considerable research interest of late. The CASS algorithm proposed by van Iersel et al. is able to construct much simpler networks than other available methods, but it is extremely slow, and the networks it constructs are dependent on the order of the input data. Here, we introduce an improved CASS algorithm, BIMLR. We show that BIMLR is faster than CASS and less dependent on the input data order. Moreover, BIMLR is able to construct much simpler networks than almost all other methods. BIMLR is available at http://nclab.hit.edu.cn/wangjuan/BIMLR/. © 2013 Elsevier B.V."
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Leo van Iersel and
Simone Linz. A quadratic kernel for computing the hybridization number of multiple trees. In IPL, Vol. 113:318-323, 2013. Keywords: explicit network, FPT, from rooted trees, kernelization, minimum number, phylogenetic network, phylogeny, Program Clustistic, Program MaafB, Program PIRN, reconstruction. Note: http://arxiv.org/abs/1203.4067, poster.
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"It has recently been shown that the NP-hard problem of calculating the minimum number of hybridization events that is needed to explain a set of rooted binary phylogenetic trees by means of a hybridization network is fixed-parameter tractable if an instance of the problem consists of precisely two such trees. In this paper, we show that this problem remains fixed-parameter tractable for an arbitrarily large set of rooted binary phylogenetic trees. In particular, we present a quadratic kernel. © 2013 Elsevier B.V."
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Celine Scornavacca,
Paprotny Wojciech,
Vincent Berry and
Vincent Ranwez. Representing a set of reconciliations in a compact way. In JBCB, Vol. 11(2):1250025, 2013. Keywords: duplication, explicit network, from network, from rooted trees, from species tree, phylogeny, Program GraphDTL, Program TERA, visualization. Note: http://hal-lirmm.ccsd.cnrs.fr/lirmm-00818801.
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"Comparative genomic studies are often conducted by reconciliation analyses comparing gene and species trees. One of the issues with reconciliation approaches is that an exponential number of optimal scenarios is possible. The resulting complexity is masked by the fact that a majority of reconciliation software pick up a random optimal solution that is returned to the end-user. However, the alternative solutions should not be ignored since they tell different stories that parsimony considers as viable as the output solution. In this paper, we describe a polynomial space and time algorithm to build a minimum reconciliation graph-a graph that summarizes the set of all most parsimonious reconciliations. Amongst numerous applications, it is shown how this graph allows counting the number of non-equivalent most parsimonious reconciliations. © 2013 Imperial College Press."
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Zhi-Zhong Chen and
Lusheng Wang. An Ultrafast Tool for Minimum Reticulate Networks. In JCB, Vol. 20(1):38-41, 2013. Keywords: agreement forest, explicit network, from rooted trees, phylogenetic network, phylogeny, Program ultra-Net, reconstruction. Note: http://www.cs.cityu.edu.hk/~lwang/research/jcb2013.pdf.
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"Due to hybridization events in evolution, studying different genes of a set of species may yield two or more related but different phylogenetic trees for the set of species. In this case, we want to combine the trees into a reticulate network with the fewest hybridization events. In this article, we develop a software tool (named UltraNet) for several fundamental problems related to the construction of minimum reticulate networks from two or more phylogenetic trees. Our experimental results show that UltraNet is much faster than all previous tools for these problems. © 2013 Mary Ann Liebert, Inc."
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Mukul S. Bansal,
Eric J. Alm and
Manolis Kellis. Reconciliation Revisited: Handling Multiple Optima when Reconciling with Duplication, Transfer, and Loss. In JCB, Vol. 20(10):738-754, 2013. Keywords: duplication, from rooted trees, from species tree, loss, phylogenetic network, phylogeny, Program RANGER-DTL, reconstruction. Note: http://www.engr.uconn.edu/~mukul/Bansal_JCB2013.pdf.
Toggle abstract
"Phylogenetic tree reconciliation is a powerful approach for inferring evolutionary events like gene duplication, horizontal gene transfer, and gene loss, which are fundamental to our understanding of molecular evolution. While duplication-loss (DL) reconciliation leads to a unique maximum-parsimony solution, duplication-transfer-loss (DTL) reconciliation yields a multitude of optimal solutions, making it difficult to infer the true evolutionary history of the gene family. This problem is further exacerbated by the fact that different event cost assignments yield different sets of optimal reconciliations. Here, we present an effective, efficient, and scalable method for dealing with these fundamental problems in DTL reconciliation. Our approach works by sampling the space of optimal reconciliations uniformly at random and aggregating the results. We show that even gene trees with only a few dozen genes often have millions of optimal reconciliations and present an algorithm to efficiently sample the space of optimal reconciliations uniformly at random in O(mn 2) time per sample, where m and n denote the number of genes and species, respectively. We use these samples to understand how different optimal reconciliations vary in their node mappings and event assignments and to investigate the impact of varying event costs. We apply our method to a biological dataset of approximately 4700 gene trees from 100 taxa and observe that 93% of event assignments and 73% of mappings remain consistent across different multiple optima. Our analysis represents the first systematic investigation of the space of optimal DTL reconciliations and has many important implications for the study of gene family evolution. © 2013 Mary Ann Liebert, Inc."
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