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Jialiang Yang,
Stefan Grünewald,
Yifei Xu and
Xiu-Feng Wan. Quartet-based methods to reconstruct phylogenetic networks. In BMC Systems Biology, Vol. 80(21), 2014. Keywords: abstract network, from quartets, phylogenetic network, phylogeny, Program QuartetMethods, Program QuartetNet, Program SplitsTree, reconstruction. Note: http://dx.doi.org/10.1186/1752-0509-8-21
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"Background: Phylogenetic networks are employed to visualize evolutionary relationships among a group of nucleotide sequences, genes or species when reticulate events like hybridization, recombination, reassortant and horizontal gene transfer are believed to be involved. In comparison to traditional distance-based methods, quartet-based methods consider more information in the reconstruction process and thus have the potential to be more accurate.Results: We introduce QuartetSuite, which includes a set of new quartet-based methods, namely QuartetS, QuartetA, and QuartetM, to reconstruct phylogenetic networks from nucleotide sequences. We tested their performances and compared them with other popular methods on two simulated nucleotide sequence data sets: one generated from a tree topology and the other from a complicated evolutionary history containing three reticulate events. We further validated these methods to two real data sets: a bacterial data set consisting of seven concatenated genes of 36 bacterial species and an influenza data set related to recently emerging H7N9 low pathogenic avian influenza viruses in China.Conclusion: QuartetS, QuartetA, and QuartetM have the potential to accurately reconstruct evolutionary scenarios from simple branching trees to complicated networks containing many reticulate events. These methods could provide insights into the understanding of complicated biological evolutionary processes such as bacterial taxonomy and reassortant of influenza viruses. © 2014 Yang et al.; licensee BioMed Central Ltd."
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Stefan Grünewald,
Andreas Spillner,
Sarah Bastkowski,
Anja Bögershausen and
Vincent Moulton. SuperQ: Computing Supernetworks from Quartets. In TCBB, Vol. 10(1):151-160, 2013. Keywords: abstract network, circular split system, from quartets, heuristic, phylogenetic network, phylogeny, Program QNet, Program SplitsTree, Program SuperQ, software, split network.
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"Supertrees are a commonly used tool in phylogenetics to summarize collections of partial phylogenetic trees. As a generalization of supertrees, phylogenetic supernetworks allow, in addition, the visual representation of conflict between the trees that is not possible to observe with a single tree. Here, we introduce SuperQ, a new method for constructing such supernetworks (SuperQ is freely available at >www.uea.ac.uk/computing/superq.). It works by first breaking the input trees into quartet trees, and then stitching these together to form a special kind of phylogenetic network, called a split network. This stitching process is performed using an adaptation of the QNet method for split network reconstruction employing a novel approach to use the branch lengths from the input trees to estimate the branch lengths in the resulting network. Compared with previous supernetwork methods, SuperQ has the advantage of producing a planar network. We compare the performance of SuperQ to the Z-closure and Q-imputation supernetwork methods, and also present an analysis of some published data sets as an illustration of its applicability. © 2004-2012 IEEE."
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Jialiang Yang,
Stefan Grünewald and
Xiu-Feng Wan. Quartet-Net: A Quartet Based Method to Reconstruct Phylogenetic Networks. In MBE, Vol. 30(5):1206-1217, 2013. Keywords: from quartets, phylogenetic network, phylogeny, Program QuartetNet, reconstruction.
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"Phylogenetic networks can model reticulate evolutionary events such as hybridization, recombination, and horizontal gene transfer. However, reconstructing such networks is not trivial. Popular character-based methods are computationally inefficient, whereas distance-based methods cannot guarantee reconstruction accuracy because pairwise genetic distances only reflect partial information about a reticulate phylogeny. To balance accuracy and computational efficiency, here we introduce a quartet-based method to construct a phylogenetic network from a multiple sequence alignment. Unlike distances that only reflect the relationship between a pair of taxa, quartets contain information on the relationships among four taxa; these quartets provide adequate capacity to infer a more accurate phylogenetic network. In applications to simulated and biological data sets, we demonstrate that this novel method is robust and effective in reconstructing reticulate evolutionary events and it has the potential to infer more accurate phylogenetic distances than other conventional phylogenetic network construction methods such as Neighbor-Joining, Neighbor-Net, and Split Decomposition. This method can be used in constructing phylogenetic networks from simple evolutionary events involving a few reticulate events to complex evolutionary histories involving a large number of reticulate events. A software called Quartet-Net is implemented and available at http://sysbio.cvm.msstate.edu/QuartetNet/. © 2013 The Author."
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Stefan Grünewald,
Vincent Moulton and
Andreas Spillner. Consistency of the QNet algorithm for generating planar split networks from weighted quartets. In DAM, Vol. 157(10):2325-2334, 2009. Keywords: abstract network, consistency, from quartets, phylogenetic network, phylogeny, Program QNet, reconstruction, software. Note: http://dx.doi.org/10.1016/j.dam.2008.06.038.
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"Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that allow the representation of conflicting signals or alternative evolutionary histories in a single diagram. Recently the Quartet-Net or "QNet" method was introduced, a method for computing a special kind of phylogenetic network called a split network from a collection of weighted quartet trees (i.e. phylogenetic trees with 4 leaves). This can be viewed as a quartet analogue of the distance-based Neighbor-Net (NNet) method for constructing outer-labeled planar split networks. In this paper, we prove that QNet is a consistent method, that is, we prove that if QNet is applied to a collection of weighted quartets arising from a circular split weight function, then it will return precisely this function. This key property of QNet not only ensures that it is guaranteed to produce a tree if the input corresponds to a tree, and an outer-labeled planar split network if the input corresponds to such a network, but also provides the main guiding principle for the design of the method. © 2008 Elsevier B.V. All rights reserved."
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Stefan Grünewald,
Katharina Huber,
Vincent Moulton,
Charles Semple and
Andreas Spillner. Characterizing weak compatibility in terms of weighted quartets. In Advances in Applied Mathematics, Vol. 42(3):329-341, 2009. Keywords: abstract network, characterization, from quartets, split network, weak hierarchy. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/GHMSS08.pdf, slides at http://www.lirmm.fr/miep08/slides/12_02_huber.pdf.
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Stefan Grünewald,
Jacobus Koolen and
Woo-Sun Lee. Quartets in maximal weakly compatible split systems. In Applied Mathematics Letters, Vol. 22(6):1604-1608, 2009. Note: http://dx.doi.org/10.1016/j.aml.2009.05.006.
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"Weakly compatible split systems are a generalization of unrooted evolutionary trees and are commonly used to display reticulate evolution or ambiguity in biological data. They are collections of bipartitions of a finite set X of taxa (e.g. species) with the property that, for every four taxa, at least one of the three bipartitions into two pairs (quartets) is not induced by any of the X-splits. We characterize all split systems where exactly two quartets from every quadruple are induced by some split. On the other hand, we construct maximal weakly compatible split systems where the number of induced quartets per quadruple tends to 0 with the number of taxa going to infinity. © 2009."
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Stefan Grünewald,
Katharina Huber and
Qiong Wu. Two novel closure rules for constructing phylogenetic super-networks. In BMB, Vol. 70(7):1906-1924, 2008. Keywords: abstract network, from splits, from unrooted trees, phylogenetic network, phylogeny, Program MY CLOSURE, reconstruction, supernetwork. Note: http://arxiv.org/abs/0709.0283, slides available at http://www.newton.cam.ac.uk/webseminars/pg+ws/2007/plg/plgw01/0904/huber/.
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"A contemporary and fundamental problem faced by many evolutionary biologists is how to puzzle together a collection P of partial trees (leaf-labeled trees whose leaves are bijectively labeled by species or, more generally, taxa, each supported by, e.g., a gene) into an overall parental structure that displays all trees in P. This already difficult problem is complicated by the fact that the trees in P regularly support conflicting phylogenetic relationships and are not on the same but only overlapping taxa sets. A desirable requirement on the sought after parental structure, therefore, is that it can accommodate the observed conflicts. Phylogenetic networks are a popular tool capable of doing precisely this. However, not much is known about how to construct such networks from partial trees, a notable exception being the Z-closure super-network approach, which is based on the Z-closure rule, and the Q-imputation approach. Although attractive approaches, they both suffer from the fact that the generated networks tend to be multidimensional making it necessary to apply some kind of filter to reduce their complexity. To avoid having to resort to a filter, we follow a different line of attack in this paper and develop closure rules for generating circular phylogenetic networks which have the attractive property that they can be represented in the plane. In particular, we introduce the novel Y-(closure) rule and show that this rule on its own or in combination with one of Meacham's closure rules (which we call the M-rule) has some very desirable theoretical properties. In addition, we present a case study based on Rivera et al. "ring of life" to explore the reconstructive power of the M- and Y-rule and also reanalyze an Arabidopsis thaliana data set. © 2008 Society for Mathematical Biology."
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Stefan Grünewald,
Kristoffer Forslund,
Andreas W. M. Dress and
Vincent Moulton. QNet: An agglomerative method for the construction of phylogenetic networks from weighted quartets. In MBE, Vol. 24(2):532-538, 2007. Keywords: abstract network, circular split system, from quartets, phylogenetic network, phylogeny, Program QNet, reconstruction, software. Note: http://mbe.oxfordjournals.org/cgi/content/abstract/24/2/532.
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"We present QNet, a method for constructing split networks from weighted quartet trees. QNet can be viewed as a quartet analogue of the distance-based Neighbor-Net (NNet) method for network construction. Just as NNet, QNet works by agglomeratively computing a collection of circular weighted splits of the taxa set which is subsequently represented by a planar split network. To illustrate the applicability of QNet, we apply it to a previously published Salmonella data set. We conclude that QNet can provide a useful alternative to NNet if distance data are not available or a character-based approach is preferred. Moreover, it can be used as an aid for determining when a quartet-based tree-building method may or may not be appropriate for a given data set. QNet is freely available for download. © The Author 2006. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved."
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Mihaela Baroni,
Stefan Grünewald,
Vincent Moulton and
Charles Semple. Bounding the number of hybridization events for a consistent evolutionary history. In JOMB, Vol. 51(2):171-182, 2005. Keywords: agreement forest, bound, explicit network, from rooted trees, hybridization, minimum number, phylogenetic network, phylogeny, reconstruction, SPR distance. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/BGMS05.pdf.
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"Evolutionary processes such as hybridisation, lateral gene transfer, and recombination are all key factors in shaping the structure of genes and genomes. However, since such processes are not always best represented by trees, there is now considerable interest in using more general networks instead. For example, in recent studies it has been shown that networks can be used to provide lower bounds on the number of recombination events and also for the number of lateral gene transfers that took place in the evolutionary history of a set of molecular sequences. In this paper we describe the theoretical performance of some related bounds that result when merging pairs of trees into networks. © Springer-Verlag 2005."
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