Who is Who in Phylogenetic Networks

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1 Victoria Kusherbaeva and Nikolay Vyahhi. Stochastic Approach to Binary Matrix Partitioning for Phylogenetic Networks. In Proceedings of the SYRCODIS 2008 Colloquium on Databases and Information Systems (SYRCoDIS'08), Vol. 355 of CEUR Workshop Proceedings, 2008.   Keywords: clustering, phylogenetic network, phylogeny, reconstruction. Note: http://ftp.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-355/kusherbaeva.pdf.

2 Sergey Bereg and Kathryn Bean. Constructing Phylogenetic Networks from Trees. In BIBE05, Pages 299-305, 2005. 1 comment   Keywords: evaluation, from distances, phylogenetic network, phylogeny, Program SplitsTree, Program T REX, reconstruction, split, split network. Note: http://dx.doi.org/10.1109/BIBE.2005.19.         Toggle abstract We present a new method of constructing a phylogenetic network from a given phylogenetic tree. It is based on a procedure that locally improves the tree. The procedure is quite general and can be applied to phylogenetic networks. By repeating local improvements user can introduce a given number of recombination cycles. A sequence of networks with decreasing distance deviation can be generated. The algorithm is efficient and shows a good performance on an example with plants. This is due to the fact that the update in every step is local and optimal. © 2005 IEEE. 3 Hans-Jürgen Bandelt and Andreas W. M. Dress. A relational approach to split decomposition. In H.-H. Bock, W. Lenski and M. M. Richter editors, Information Systems and Data Analysis, Proceedings of the 17th Annual Conference of the Gesellschaft Für Klassifikation (GFKL93), Vol. 42:123-131 of Studies in Classification, Data Analysis, and Knowledge Organization, springer, 1994.   Keywords: characterization, from quartets, phylogenetic network, weakly compatible.

4 Juan Wang and Maozu Guo. IGNet: Constructing Rooted Phylogenetic Networks Based on Incompatible Graphs. In ICNC-FSKD19, Vol. 1075:894-900 of Advances in Intelligent Systems and Computing, Springer, 2019.   Keywords: explicit network, from rooted trees, phylogenetic network, phylogeny, Program BIMLR, Program IGNet, Program LNetwork, reconstruction, software.         5 Ruzbeh Tusserkani, Hadi Poormohammadi, Azin Azadi and Changiz Eslahchi. Inferring phylogenies from minimal information. In AEEICB17, Pages 202-206, IEEE, 2017.   Keywords: from triplets, phylogenetic network, phylogeny, Program TripNet, reconstruction.         6 Quan Nguyen and Teemu Roos. Likelihood-based inference of phylogenetic networks from sequence data by PhyloDAG. In AlCoB15, Vol. 9199:126-140 of LNCS, springer, 2015.   Keywords: BIC, explicit network, from sequences, likelihood, phylogenetic network, phylogeny, Program PhyloDAG, reconstruction, software. Note: http://www.cs.helsinki.fi/u/ttonteri/pub/alcob2015.pdf.         7 Hyun Jung Park and Luay Nakhleh. Inference of reticulate evolutionary histories by maximum likelihood: The performance of information criteria. In RECOMB-CG'12, Vol. 13(suppl 19):S12 of BMCB, 2012.   Keywords: AIC, BIC, explicit network, heuristic, likelihood, phylogenetic network, phylogeny, reconstruction, statistical model. Note: http://www.biomedcentral.com/1471-2105/13/S19/S12.         8 Gabriel Cardona, Mercè Llabrés, Francesc Rosselló and Gabriel Valiente. Path lengths in tree-child time consistent hybridization networks. In Information Sciences, Vol. 180(3):366-383, 2010.   Keywords: distance between networks, phylogenetic network, phylogeny, time consistent network, tree-child network. Note: http://arxiv.org/abs/0807.0087?context=cs.CE.         Toggle abstract "Hybridization networks are representations of evolutionary histories that allow for the inclusion of reticulate events like recombinations, hybridizations, or lateral gene transfers. The recent growth in the number of hybridization network reconstruction algorithms has led to an increasing interest in the definition of metrics for their comparison that can be used to assess the accuracy or robustness of these methods. In this paper we establish some basic results that make it possible the generalization to tree-child time consistent (TCTC) hybridization networks of some of the oldest known metrics for phylogenetic trees: those based on the comparison of the vectors of path lengths between leaves. More specifically, we associate to each hybridization network a suitably defined vector of 'splitted' path lengths between its leaves, and we prove that if two TCTC hybridization networks have the same such vectors, then they must be isomorphic. Thus, comparing these vectors by means of a metric for real-valued vectors defines a metric for TCTC hybridization networks. We also consider the case of fully resolved hybridization networks, where we prove that simpler, 'non-splitted' vectors can be used. © 2009 Elsevier Inc. All rights reserved." 9 Luay Nakhleh, Derek Ruths and Hideki Innan. Gene Trees, Species Trees, and Species Networks. In R. Guerra, D. B. Allison and D. Goldstein editors, Meta-analysis and Combining Information in Genetics and Genomics, 2009.   Keywords: coalescent, explicit network, from rooted trees, from species tree, phylogenetic network, phylogeny, reconstruction. Note: http://www.cs.rice.edu/~nakhleh/Papers/GuerraGoldsteinBookChapter.pdf.         10 Bui Quang Minh, Fabio Pardi, Steffen Klaere and Arndt von Haeseler. Budgeted Phylogenetic Diversity on Circular Split Systems. In TCBB, Vol. 6(1):22-29, 2009.   Keywords: abstract network, circular split system, dynamic programming, from network, phylogenetic network, polynomial, split, split network. Note: http://dx.doi.org/10.1109/TCBB.2008.54.         Toggle abstract "In the last 15 years, Phylogenetic Diversity (PD) has gained interest in the community of conservation biologists as a surrogate measure for assessing biodiversity. We have recently proposed two approaches to select taxa for maximizing PD, namely PD with budget constraints and PD on split systems. In this paper, we will unify these two strategies and present a dynamic programming algorithm to solve the unified framework of selecting taxa with maximal PD under budget constraints on circular split systems. An improved algorithm will also be given if the underlying split system is a tree. © 2006 IEEE." 11 Leo van Iersel, Judith Keijsper, Steven Kelk, Leen Stougie, Ferry Hagen and Teun Boekhout. Constructing level-2 phylogenetic networks from triplets. In RECOMB08, Vol. 4955:450-462 of LNCS, springer, 2008.   Keywords: explicit network, from triplets, level k phylogenetic network, NP complete, phylogenetic network, phylogeny, polynomial, Program Level2, reconstruction. Note: http://homepages.cwi.nl/~iersel/level2full.pdf. An appendix with proofs can be found here http://arxiv.org/abs/0707.2890.         Toggle abstract "Jansson and Sung showed that, given a dense set of input triplets T (representing hypotheses about the local evolutionary relationships of triplets of taxa), it is possible to determine in polynomial time whether there exists a level-1 network consistent with T, and if so, to construct such a network [24]. Here, we extend this work by showing that this problem is even polynomial time solvable for the construction of level-2 networks. This shows that, assuming density, it is tractable to construct plausible evolutionary histories from input triplets even when such histories are heavily nontree-like. This further strengthens the case for the use of triplet-based methods in the construction of phylogenetic networks. We also implemented the algorithm and applied it to yeast data. © 2009 IEEE." 12 Andreas Spillner, Binh T. Nguyen and Vincent Moulton. Computing phylogenetic diversity for split systems. In TCBB, Vol. 5(2):235-244, 2008.   Keywords: abstract network, diversity, phylogenetic network, phylogeny, split. Note: http://dx.doi.org/10.1109/TCBB.2007.70260, slides available at http://www.newton.cam.ac.uk/webseminars/pg+ws/2007/plg/plgw01/0906/spillner/.         Toggle abstract "In conservation biology it is a central problem to measure, predict, and preserve biodiversity as species face extinction. In 1992 Faith proposed measuring the diversity of a collection of species in terms of their relationships on a phylogenetic tree, and to use this information to identify collections of species with high diversity. Here we are interested in some variants of the resulting optimization problem that arise when considering species whose evolution is better represented by a network rather than a tree. More specifically, we consider the problem of computing phylogenetic diversity relative to a split system on a collection of species of size $n$. We show that for general split systems this problem is NP-hard. In addition we provide some efficient algorithms for some special classes of split systems, in particular presenting an optimal $O(n)$ time algorithm for phylogenetic trees and an $O(nlog n + n k)$ time algorithm for choosing an optimal subset of size $k$ relative to a circular split system. © 2006 IEEE." 13 Rune Lyngsø, Yun S. Song and Jotun Hein. Accurate Computation of Likelihoods in the Coalescent with Recombination via Parsimony. In RECOMB08, Vol. 4955:463-477 of LNCS, springer, 2008.   Keywords: coalescent, likelihood, phylogenetic network, phylogeny, recombination, statistical model. Note: http://dx.doi.org/10.1007/978-3-540-78839-3_41.         Toggle abstract "Understanding the variation of recombination rates across a given genome is crucial for disease gene mapping and for detecting signatures of selection, to name just a couple of applications. A widely-used method of estimating recombination rates is the maximum likelihood approach, and the problem of accurately computing likelihoods in the coalescent with recombination has received much attention in the past. A variety of sampling and approximation methods have been proposed, but no single method seems to perform consistently better than the rest, and there still is great value in developing better statistical methods for accurately computing likelihoods. So far, with the exception of some two-locus models, it has remained unknown how the true likelihood exactly behaves as a function of model parameters, or how close estimated likelihoods are to the true likelihood. In this paper, we develop a deterministic, parsimony-based method of accurately computing the likelihood for multi-locus input data of moderate size. We first find the set of all ancestral configurations (ACs) that occur in evolutionary histories with at most k crossover recombinations. Then, we compute the likelihood by summing over all evolutionary histories that can be constructed only using the ACs in that set. We allow for an arbitrary number of crossing over, coalescent and mutation events in a history, as long as the transitions stay within that restricted set of ACs. For given parameter values, by gradually increasing the bound k until the likelihood stabilizes, we can obtain an accurate estimate of the likelihood. At least for moderate crossover rates, the algorithm-based method described here opens up a new window of opportunities for testing and fine-tuning statistical methods for computing likelihoods. © 2008 Springer-Verlag Berlin Heidelberg." 14 Steven M. Woolley, David Posada and Keith A. Crandall. A Comparison of Phylogenetic Network Methods Using Computer Simulation. In PLoS ONE, Vol. 3(4):e1913, 2008.   Keywords: abstract network, distance between networks, evaluation, median network, MedianJoining, minimum spanning network, NeighborNet, parsimony, phylogenetic network, phylogeny, Program Arlequin, Program CombineTrees, Program Network, Program SHRUB, Program SplitsTree, Program TCS, split decomposition. Note: http://dx.doi.org/10.1371/journal.pone.0001913.         Toggle abstract "Background: We present a series of simulation studies that explore the relative performance of several phylogenetic network approaches (statistical parsimony, split decomposition, union of maximum parsimony trees, neighbor-net, simulated history recombination upper bound, median-joining, reduced median joining and minimum spanning network) compared to standard tree approaches (neighbor-joining and maximum parsimony) in the presence and absence of recombination. Principal Findings: In the absence of recombination, all methods recovered the correct topology and branch lengths nearly all of the time when the subtitution rate was low, except for minimum spanning networks, which did considerably worse. At a higher substitution rate, maximum parsimony and union of maximum parsimony trees were the most accurate. With recombination, the ability to infer the correct topology was halved for all methods and no method could accurately estimate branch lengths. Conclusions: Our results highlight the need for more accurate phylogenetic network methods and the importance of detecting and accounting for recombination in phylogenetic studies. Furthermore, we provide useful information for choosing a network algorithm and a framework in which to evaluate improvements to existing methods and novel algorithms developed in the future. © 2008 Woolley et al." 15 Leo van Iersel and Steven Kelk. Constructing the Simplest Possible Phylogenetic Network from Triplets. In ISAAC08, Vol. 5369:472-483 of LNCS, springer, 2008.   Keywords: explicit network, from triplets, galled tree, level k phylogenetic network, minimum number, phylogenetic network, phylogeny, polynomial, Program Marlon, Program Simplistic. Note: http://arxiv.org/abs/0805.1859.         16 Cuong Than and Luay Nakhleh. SPR-based Tree Reconciliation: Non-binary Trees and Multiple Solutions. In APBC08, Pages 251-260, 2008.   Keywords: evaluation, from rooted trees, lateral gene transfer, phylogenetic network, phylogeny, Program LatTrans, Program PhyloNet, reconstruction, SPR distance. Note: http://www.cs.rice.edu/~nakhleh/Papers/apbc08.pdf.         17 Daniel H. Huson and Regula Rupp. Summarizing Multiple Gene Trees Using Cluster Networks. In WABI08, Vol. 5251:296-305 of LNCS, springer, 2008.   Keywords: abstract network, from clusters, from rooted trees, phylogenetic network, phylogeny, polynomial, Program Dendroscope. Note: http://dx.doi.org/10.1007/978-3-540-87361-7_25, slides from the MIEP Conference available at http://www.lirmm.fr/MIEP08/slides/11_13_rupp.pdf.         Toggle abstract "The result of a multiple gene tree analysis is usually a number of different tree topologies that are each supported by a significant proportion of the genes. We introduce the concept of a cluster network that can be used to combine such trees into a single rooted network, which can be drawn either as a cladogram or phylogram. In contrast to split networks, which can grow exponentially in the size of the input, cluster networks grow only quadratically. A cluster network is easily computed using a modification of the tree-popping algorithm, which we call network-popping. The approach has been implemented as part of the Dendroscope tree-drawing program and its application is illustrated using data and results from three recent studies on large numbers of gene trees. © 2008 Springer-Verlag Berlin Heidelberg." 18 Lichen Bao and Sergey Bereg. Clustered SplitsNetworks. In COCOA08, Vol. 5165:469-478 of LNCS, springer, 2008.   Keywords: abstract network, from distances, NeighborNet, realization, reconstruction. Note: http://dx.doi.org/10.1007/978-3-540-85097-7_44, slides available at http://www.utdallas.edu/~besp/cocoa08talk.pdf.         Toggle abstract "We address the problem of constructing phylogenetic networks using two criteria: the number of cycles and the fit value of the network. Traditionally the fit value is the main objective for evaluating phylogenetic networks. However, a small number of cycles in a network is desired and pointed out in several publications. We propose a new phylogenetic network called CS-network and a method for constructing it. The method is based on the well-known splitstree method. A CS-network contains a face which is k-cycle, k ≥ 3 (not as splitstree). We discuss difficulties of using non-parallelogram faces in splitstree networks. Our method involves clustering and optimization of weights of the network edges. The algorithm for constructing the underlying graph (except the optimization step) has a polynomial time. Experimental results show a good performance of our algorithm. © Springer-Verlag Berlin Heidelberg 2008." 19 Sagi Snir and Tamir Tuller. Novel Phylogenetic Network Inference by Combining Maximum Likelihood and Hidden Markov Models. In WABI08, Vol. 5251:354-368 of LNCS, springer, 2008.   Keywords: explicit network, from sequences, HMM, lateral gene transfer, likelihood, phylogenetic network, phylogeny, statistical model. Note: http://dx.doi.org/10.1007/978-3-540-87361-7_30.         Toggle abstract "Horizontal Gene Transfer (HGT) is the event of transferring genetic material from one lineage in the evolutionary tree to a different lineage. HGT plays a major role in bacterial genome diversification and is a significant mechanism by which bacteria develop resistance to antibiotics. Although the prevailing assumption is of complete HGT, cases of partial HGT (which are also named chimeric HGT) where only part of a gene is horizontally transferred, have also been reported, albeit less frequently. In this work we suggest a new probabilistic model for analyzing and modeling phylogenetic networks, the NET-HMM. This new model captures the biologically realistic assumption that neighboring sites of DNA or amino acid sequences are not independent, which increases the accuracy of the inference. The model describes the phylogenetic network as a Hidden Markov Model (HMM), where each hidden state is related to one of the network's trees. One of the advantages of the NET-HMM is its ability to infer partial HGT as well as complete HGT. We describe the properties of the NET-HMM, devise efficient algorithms for solving a set of problems related to it, and implement them in software. We also provide a novel complementary significance test for evaluating the fitness of a model (NET-HMM) to a given data set. Using NET-HMM we are able to answer interesting biological questions, such as inferring the length of partial HGT's and the affected nucleotides in the genomic sequences, as well as inferring the exact location of HGT events along the tree branches. These advantages are demonstrated through the analysis of synthetical inputs and two different biological inputs. © 2008 Springer-Verlag Berlin Heidelberg." 20 Stefan Grünewald, Andreas Spillner, Kristoffer Forslund and Vincent Moulton. Constructing Phylogenetic Supernetworks from Quartets. In WABI08, Vol. 5251:284-295 of LNCS, springer, 2008.   Keywords: abstract network, from quartets, from unrooted trees, phylogenetic network, phylogeny, Program QNet, Program SplitsTree, reconstruction, split network. Note: http://dx.doi.org/10.1007/978-3-540-87361-7_24.         Toggle abstract "In phylogenetics it is common practice to summarize collections of partial phylogenetic trees in the form of supertrees. Recently it has been proposed to construct phylogenetic supernetworks as an alternative to supertrees as these allow the representation of conflicting information in the trees, information that may not be representable in a single tree. Here we introduce SuperQ, a new method for constructing such supernetworks. It works by breaking the input trees into quartet trees, and stitching together the resulting set to form a network. The stitching process is performed using an adaptation of the QNet method for phylogenetic network reconstruction. In addition to presenting the new method, we illustrate the applicability of SuperQ to three data sets and discuss future directions for testing and development. © 2008 Springer-Verlag Berlin Heidelberg." 21 Gabriel Cardona, Mercè Llabrés, Francesc Rosselló and Gabriel Valiente. Phylogenetic Networks: Justification, Models, Distances and Algorithms. In VI Jornadas de Matemática Discreta y Algorítmica (JMDA'08), 2008.   Keywords: distance between networks, mu distance, phylogenetic network, phylogeny, polynomial, survey, time consistent network, tree-child network, tripartition distance, triplet distance. Note: http://bioinfo.uib.es/media/uploaded/jmda2008_submission_61-1.pdf.         22 Ernst Althaus and Rouven Naujoks. Reconstructing Phylogenetic Networks with One Recombination. In Proceedings of the seventh International Workshop on Experimental Algorithms (WEA'08), Vol. 5038:275-288 of LNCS, springer, 2008.   Keywords: enumeration, explicit network, exponential algorithm, from sequences, generation, parsimony, phylogenetic network, phylogeny, reconstruction, unicyclic network. Note: http://dx.doi.org/10.1007/978-3-540-68552-4_21.         Toggle abstract "In this paper we propose a new method for reconstructing phylogenetic networks under the assumption that recombination events have occurred rarely. For a fixed number of recombinations, we give a generalization of the maximum parsimony criterion. Furthermore, we describe an exact algorithm for one recombination event and show that in this case our method is not only able to identify the recombined sequence but also to reliably reconstruct the complete evolutionary history. © 2008 Springer-Verlag Berlin Heidelberg." 23 Supriya Munshaw and Thomas B. Kepler. An Information-Theoretic Method for the Treatment of Plural Ancestry in Phylogenetics. In MBE, Vol. 25(6):1199-1208, 2008.   Keywords: explicit network, from sequences, heuristic, phylogenetic network, reconstruction, simulated annealing, software. Note: http://dx.doi.org/10.1093/molbev/msn066.         Toggle abstract "In the presence of recombination and gene conversion, a given genomic segment may inherit information from 2 distinct immediate ancestors. The importance of this type of molecular inheritance has become increasingly clear over the years, and the potential for erroneous inference when it is not accounted for in the statistical model is well documented. Yet, the inclusion of plural ancestry (PA) in phylogenetic analysis is still not routine. This omission is due to the greater difficulty of phylogenetic inference on general acyclic graphs compared that on with trees and the accompanying computational burden. We have developed a technique for phylogenetic inference in the presence of PA based on the principle of minimum description length, which assigns a cost - the description length - to each network topology given the observed sequence data. The description length combines the cost of poor data fit and model complexity in terms of information. This device allows us to search through network topologies to minimize the total description length. By comparing the best models obtained with and without PA, one can determine whether or not recombination has played an active role in the evolution of the genes under investigation, identify those genes that appear to be mosaic, and infer the phylogenetic network that best represents the history of the alignment. We show that the method performs well on simulated data and demonstrate its application on HIV env gene sequence data from 8 human subjects. The software implementation of the method is available upon request. © The Author 2008. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved." 24 Cuong Than, Guohua Jin and Luay Nakhleh. Integrating Sequence and Topology for Efficient and Accurate Detection of Horizontal Gene Transfer. In Proceedings of the Sixth RECOMB Comparative Genomics Satellite Workshop (RECOMB-CG'08), Vol. 5267:113-127 of LNCS, springer, 2008.   Keywords: bootstrap, explicit network, from rooted trees, from sequences, lateral gene transfer, phylogenetic network, phylogeny, Program Nepal, Program PhyloNet, reconstruction. Note: http://www.cs.rice.edu/~nakhleh/Papers/recombcg-08.pdf, slides available at http://igm.univ-mlv.fr/RCG08/RCG08slides/Cuong_Than_RCG08.pdf.         25 Elena Dubrova. Phylogenetic networks with edge-disjoint recombination cycles. In Proceedings of SPIE Bioengineered and Bioinspired Systems II (SPIE-BBS II), Vol. 5839:381-388, 2005.   Keywords: galled tree, phylogenetic network, polynomial, site consistency. Note: http://dx.doi.org/10.1117/12.607910.         Toggle abstract "Phylogenetic analysis is a branch of biology that establishes the evolutionary relationships between living organisms. The goal of phylogenetic analysis is to determine the order and approximate timing of speciation events in the evolution of a given set of species. Phylogenetic networks allow to represent evolutionary histories that include events like recombination and hybridization. In this paper, we introduce a class of phylogenetic networks called extended galled-trees in which recombination cycles share no edge. We show that the site consistency problem, which is NP-hard in general, can be solved in polynomial time for this class of phylogenetic networks." 26 Mohd Abdul Hai Zahid, Ankush Mittal and Ramesh C. Joshi. A Classification Based Approach for Root Unknown Phylogenetic Networks under Constrained Recombination. In Proceedings of the Second International Conference on Distributed Computing and Internet Technology (ICDCIT'05), Vol. 3816:592-603, 2005.   Note: http://www.isical.ac.in/~zahid_t/publications/papers/paper_ICDCIT.pdf.         27 Jesper Jansson and Wing-Kin Sung. Inferring a level-1 phylogenetic network from a dense set of rooted triplets. In COCOON04, Vol. 3106:462-471 of LNCS, springer, 2004. 1 comment   Keywords: explicit network, from triplets, galled tree, level k phylogenetic network, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://www.df.lth.se/~jj/Publications/ipnrt6_COCOON2004.pdf.         28 Pawel Górecki. Single step reconciliation algorithm for duplication, loss and horizontal gene transfer model. In ECCB03, 2003.   Keywords: duplication, explicit network, from rooted trees, from species tree, lateral gene transfer, NP complete, parsimony, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://www.inra.fr/eccb2003/posters/pdf/short/S_gorecki.ps.         29 Andreas W. M. Dress, Katharina Huber and Vincent Moulton. Hereditarily Optimal Realizations: Why are they Relevant in Phylogenetic Analysis, and how does one Compute them? In Proceedings of the Euroconference on Algebraic Combinatorics and Applications (Alcoma'99), Pages 110-117, springer, 2001.   Keywords: abstract network, from distances, optimal realization, phylogenetic network. Note: http://www.math.uni-bielefeld.de/fsp-math/Preprints/139.pdf.         30 Pierre Legendre and Vladimir Makarenkov. Improving the additive tree representation of a dissimilarity matrix using reticulations. In IFCS00, Pages 35-40, springer, 2000.   Keywords: phylogenetic network, phylogeny, reconstruction, reticulogram. Note: http://www.info2.uqam.ca/~makarenv/makarenv/Article_IFCS.pdf.         31 Bin Ma, Lusheng Wang and Ming Li. Fixed topology alignment with recombination. In CPM98, Vol. 1448:174-188 of LNCS, springer, 1998.   Keywords: approximation, explicit network, from network, from sequences, galled tree, inapproximability, phylogenetic network, phylogeny, recombination. Note: http://dx.doi.org/10.1007/BFb0030789.

32 Andrew R. Francis, Daniel H. Huson and Mike Steel. Normalising phylogenetic networks. 2020.   Keywords: explicit network, from network, normal network, phylogenetic network, phylogeny, polynomial, Program PhyloSketch, reconstruction, tree-child network. Note: https://arxiv.org/abs/2008.07797.         33 Louxin Zhang. Recent Progresses in the Combinatorial and Algorithmic Study of Rooted Phylogenetic Networks. In WALCOM20, Vol. 12049:22-27 of LNCS, Springer, 2020.   Keywords: cluster containment, galled network, galled tree, nearly-stable network, phylogenetic network, phylogeny, polynomial, reticulation-visible network, survey, time consistent network, tree containment, tree-based network, tree-child network.         34 Jonathan Klawitter and Peter Stumpf. Drawing Tree-Based Phylogenetic Networks with Minimum Number of Crossings. 2020.   Keywords: explicit network, FPT, minimum number, NP complete, phylogenetic network, phylogeny, polynomial, visualization. Note: https://arxiv.org/abs/2008.08960.         35 Remie Janssen, Mark Jones and Yukihiro Murakami. Combining Networks Using Cherry Picking Sequences. In AlCoB20, Vol. 12099:77-92 of LNCS, Springer, 2020.   Keywords: cherry-picking, explicit network, FPT, from network, hybridization, orchard network, phylogenetic network, phylogeny, tree-child network.         36 Hannah Brown, Lei Zuo and Dan Gusfield. Comparing Integer Linear Programming to SAT-Solving for Hard Problems in Computational and Systems Biology. In AlCoB2020, Vol. 12099:63-76 of LNCS, Springer, 2020.   Keywords: from binary characters, History bound, integer linear programming, minimum number, phylogeny, SAT. Note: https://doi.org/10.1007/978-3-030-42266-0_6.         37 Remie Janssen and Yukihiro Murakami. Linear Time Algorithm for Tree-Child Network Containment. In AlCoB20, Vol. 12099:93-107 of LNCS, Springer, 2020.   Keywords: explicit network, from network, isomorphism, phylogenetic network, phylogeny, polynomial, reconstruction, tree-child network, tree-child sequence. Note: https://doi.org/10.1007/978-3-030-42266-0_8.         38 Jesper Jansson, Konstantinos Mampentzidis, Ramesh Rajaby and Wing-Kin Sung. Computing the Rooted Triplet Distance Between Phylogenetic Networks. In IWOCA19, Vol. 11638:290-303 of LNCS, Springer, 2019.   Keywords: distance between networks, from network, phylogenetic network, phylogeny, polynomial, triplet distance.         39 Mathias Weller. Linear-Time Tree Containment in Phylogenetic Networks. In RECOMB-CG18, Vol. 11183:309-323 of LNCS, Springer, 2018.   Keywords: explicit network, from network, from rooted trees, nearly-stable network, phylogenetic network, phylogeny, polynomial, reconstruction, reticulation-visible network, tree containment. Note: https://arxiv.org/abs/1702.06364.         40 Hussein A. Hejase, Natalie VandePol, Gregory A. Bonito and Kevin J. Liu. Fast and accurate statistical inference of phylogenetic networks using large-scale genomic sequence data. In RECOMB-CG18, Vol. 11183:242-259 of LNCS, Springer, 2018.   Keywords: explicit network, from rooted trees, heuristic, phylogenetic network, phylogeny, Program FastNet, reconstruction. Note: http://biorxiv.org/content/early/2017/05/01/132795.         41 Andreas Gunawan. Solving the Tree Containment Problem for Reticulation-visible Networks in Linear Time. In AlCoB18, Vol. 10849:24-36 of LNCS, Springer, 2018.   Keywords: explicit network, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, reticulation-visible network, tree containment. Note: https://arxiv.org/abs/1702.04088.         42 Sebastien Roch and Kun-Chieh Wang. Circular Networks from Distorted Metrics. In RECOMB18, Vol. 10812:167-176 of LNCS, Springer, 2018.   Keywords: abstract network, circular split system, from distances, NeighborNet, phylogenetic network, phylogeny, reconstruction, split network. Note: https://arxiv.org/abs/1707.05722.         43 Magnus Bordewich, Katharina Huber, Vincent Moulton and Charles Semple. Recovering normal networks from shortest inter-taxa distance information. In JOMB, Vol. 77(3):571-594, 2018.   Keywords: explicit network, from distances, normal network, phylogenetic network, phylogeny, polynomial, reconstruction, uniqueness. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/BHMS18.pdf.         44 Kuang-Yu Chang, Wing-Kai Hon and Sharma V. Thankachan. Compact Encoding for Galled-Trees and its Applications. In 2018 Data Compression Conference, Pages 297-306, 2018.   Keywords: compression, counting, explicit network, galled tree, phylogenetic network, polynomial.         45 Leo van Iersel, Remie Janssen, Mark Jones, Yukihiro Murakami and Norbert Zeh. Polynomial-Time Algorithms for Phylogenetic Inference Problems. In AlCoB18, Vol. 10849:37-49 of LNCS, Springer, 2018.   Keywords: hybridization, minimum number, parental hybridization, phylogenetic network, phylogeny, polynomial, reconstruction, weakly displaying. Note: https://research.tudelft.nl/files/53686721/10.1007_978_3_319_91938_6_4.pdf.         46 Andreas Gunawan, Bhaskar DasGupta and Louxin Zhang. A decomposition theorem and two algorithms for reticulation-visible networks. In Information and Computation, Vol. 252:161-175, 2017.   Keywords: cluster containment, explicit network, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, reticulation-visible network, tree containment. Note: https://www.cs.uic.edu/~dasgupta/resume/publ/papers/Infor_Comput_IC4848_final.pdf.         47 Bingxin Lu, Louxin Zhang and Hon Wai Leong. A program to compute the soft Robinson-Foulds distance between phylogenetic networks. In APBC17, Vol. 18(Suppl. 2):111 of BMC Genomics, 2017.   Keywords: cluster containment, distance between networks, explicit network, exponential algorithm, from network, phylogenetic network, phylogeny, Program icelu-PhyloNetwork. Note: http://dx.doi.org/10.1186/s12864-017-3500-5.         48 Jesper Jansson, Ramesh Rajaby and Wing-Kin Sung. An Efficient Algorithm for the Rooted Triplet Distance Between Galled Trees. In AlCoB17, Vol. 10252:115-126 of LNCS, Springer, 2017.   Keywords: distance between networks, from network, phylogenetic network, phylogeny, polynomial, reconstruction, triplet distance. Note: .         49 Han Lai, Maureen Stolzer and Dannie Durand. Fast Heuristics for Resolving Weakly Supported Branches Using Duplication, Transfers, and Losses. In RECOMB-CG17, Vol. 10562:298-320 of LNCS, Springer, 2017.   Keywords: duplication, explicit network, from rooted trees, from species tree, lateral gene transfer, loss, phylogenetic network, phylogeny, Program Notung, reconstruction.         50 Kuang-Yu Chang, Yun Cui, Siu-Ming Yiu and Wing-Kai Hon. Reconstructing One-Articulated Networks with Distance Matrices. In ISBRA17, Vol. 10330:34-45 of LNCS, Springer, 2017.   Keywords: explicit network, from distances, k-reticulated, phylogenetic network, phylogeny, reconstruction. Note: https://link.springer.com/content/pdf/10.1007%2F978-3-319-59575-7.pdf#page=100.         51 Andreas Gunawan, Bhaskar DasGupta and Louxin Zhang. Locating a Tree in a Reticulation-Visible Network in Cubic Time. In RECOMB16, Vol. 9649:266 of LNBI, Springer, 2016.   Keywords: cluster containment, explicit network, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, reticulation-visible network, tree containment. Note: http://arxiv.org/abs/1507.02119.         52 Philippe Gambette, Andreas Gunawan, Anthony Labarre, Stéphane Vialette and Louxin Zhang. Solving the Tree Containment Problem for Genetically Stable Networks in Quadratic Time. In IWOCA15, Vol. 9538:197-208 of LNCS, springer, 2016.   Keywords: explicit network, from network, from rooted trees, genetically stable network, phylogenetic network, phylogeny, polynomial, tree containment. Note: https://hal-upec-upem.archives-ouvertes.fr/hal-01226035 .         53 Andreas Gunawan, Bingxin Lu and Louxin Zhang. A program for verification of phylogenetic network models. In ECCB16, Vol. 32(17):i503-i510 of BIO, 2016.   Keywords: exponential algorithm, from network, from rooted trees, phylogenetic network, phylogeny, software, tree containment. Note: http://dx.doi.org/10.1093/bioinformatics/btw467.         54 Ioannis G. Tollis and Konstantinos G. Kakoulis. Algorithms for Visualizing Phylogenetic Networks. In GD16, Vol. 9801:183-195 of LNCS, springer, 2016.   Keywords: explicit network, galled network, galled tree, NP complete, planar, visualization. Note: http://arxiv.org/abs/1609.00755.         55 Nikita Alexeev and Max A. Alekseyev. Combinatorial Scoring of Phylogenetic Networks. In COCOON16, Vol. 9797:560-572 of LNCS, Springer, 2016.   Keywords: cactus graph, counting, explicit network, galled tree, phylogenetic network, phylogeny. Note: http://arxiv.org/abs/1602.02841.         56 Jiafan Zhu, Yun Yu and Luay Nakhleh. In the Light of Deep Coalescence: Revisiting Trees Within Networks. In RECOMB-CG16, Vol. 17(suppl. 14):415.271-282 of BMCB, 2016.   Keywords: branch length, evaluation, explicit network, incomplete lineage sorting, phylogenetic network, phylogeny, statistical model, tree-based network, weakly displaying. Note: http://arxiv.org/abs/1606.07350.         57 Katharina Huber, Leo van Iersel, Vincent Moulton and Taoyang Wu. How much information is needed to infer reticulate evolutionary histories? In Systematic Biology, Vol. 64(1):102-111, 2015.   Keywords: explicit network, from network, from rooted trees, from subnetworks, from trinets, identifiability, phylogenetic network, phylogeny, reconstruction, uniqueness. Note: http://dx.doi.org/10.1093/sysbio/syu076.         58 Philippe Gambette, Andreas Gunawan, Anthony Labarre, Stéphane Vialette and Louxin Zhang. Locating a Tree in A Phylogenetic Network in Quadratic Time. In RECOMB15, Vol. 9029:96-107 of LNCS, Springer, 2015.   Keywords: evaluation, explicit network, from network, from rooted trees, genetically stable network, nearly-stable network, phylogenetic network, phylogeny, polynomial, tree containment. Note: https://hal.archives-ouvertes.fr/hal-01116231/en.         59 Dan Gusfield. Persistent Phylogeny: A Galled-Tree and Integer Linear Programming Approach. In BCB15, Pages 443-451, 2015.   Keywords: explicit network, from binary characters, galled tree, integer linear programming, phylogenetic network, phylogeny, reconstruction. Note: http://arxiv.org/abs/1506.00678.         60 Quan Nguyen. Likelihood-based Phylogenetic Network Inference by Approximate Structural Expectation Maximization. Master's thesis, University of Helsinki, 2015.   Keywords: BIC, likelihood, phylogenetic network, phylogeny, Program PhyloDAG, reconstruction, software. Note: http://urn.fi/URN:NBN:fi-fe2015062910525.         61 Vladimir Ulyantsev and Mikhail Melnik. Constructing Parsimonious Hybridization Networks from Multiple Phylogenetic Trees Using a SAT-solver. In AlCoB15, Vol. 9199:141-153 of LNCS, springer, 2015.   Keywords: explicit network, from rooted trees, from trees, phylogenetic network, phylogeny, Program PIRN, reconstruction. Note: https://www.researchgate.net/profile/Vladimir_Ulyantsev/publication/282816862_Constructing_Parsimonious_Hybridization_Networks_from_Multiple_Phylogenetic_Trees_Using_a_SAT-Solver/links/561d372c08aecade1acb3699/Constructing-Parsimonious-Hybridization-Networks-from-Multiple-Phylogenetic-Trees-Using-a-SAT-Solver.pdf.         62 Jittat Fakcharoenphol, Tanee Kumpijit and Attakorn Putwattana. A Faster Algorithm for the Tree Containment Problem for Binary Nearly Stable Phylogenetic Networks. In Proceedings of the The 12th International Joint Conference on Computer Science and Software Engineering (JCSSE'15), Pages 337-342, IEEE, 2015.   Keywords: dynamic programming, explicit network, from network, from rooted trees, nearly-stable network, phylogenetic network, phylogeny, polynomial, tree containment.         63 Misagh Kordi and Mukul S. Bansal. On the Complexity of Duplication-Transfer-Loss Reconciliation with Non-Binary Gene Trees. In ISBRA15, Vol. 9096:187-198 of LNCS, springer, 2015.   Keywords: duplication, from rooted trees, from species tree, lateral gene transfer, loss, NP complete, phylogenetic network, phylogeny, reconstruction. Note: http://compbio.engr.uconn.edu/papers/Kordi_ISBRA2015.pdf.         64 Yun Yu and Luay Nakhleh. A Distance-Based Method for Inferring Phylogenetic Networks in the Presence of Incomplete Lineage Sorting. In ISBRA15, Vol. 9096:378-389 of LNCS, springer, 2015.   Keywords: bootstrap, explicit network, from distances, heuristic, incomplete lineage sorting, phylogenetic network, phylogeny, reconstruction. Note: http://bioinfo.cs.rice.edu/sites/bioinfo.cs.rice.edu/files/YuNakhleh-ISBRA15.pdf.         65 Johannes Fischer and Daniel Peters. A Practical Succinct Data Structure for Tree-Like Graphs. In WALCOM15, Vol. 8973:65-76 of LNCS, springer, 2015.   Keywords: compression, from network, phylogenetic network, phylogeny.         66 Yun Yu and Luay Nakhleh. A maximum pseudo-likelihood approach for phylogenetic networks. In RECOMB-CG15, Vol. 16(Suppl 10)(S10):1-10 of BMC Genomics, BioMed Central, 2015.   Keywords: explicit network, from rooted trees, hybridization, incomplete lineage sorting, likelihood, phylogenetic network, phylogeny, Program PhyloNet, reconstruction, tripartition distance. Note: http://dx.doi.org/10.1186/1471-2164-16-S10-S10.         67 Thu-Hien To and Celine Scornavacca. Efficient algorithms for reconciling gene trees and species networks via duplication and loss events. In RECOMB-CG15, Vol. 16(Suppl 10)(S6):1-14 of BMC Genomics, BioMed Central, 2015.   Keywords: explicit network, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://dx.doi.org/10.1186/1471-2164-16-S10-S6.         68 Gabriel Cardona, Mercè Llabrés, Francesc Rosselló and Gabriel Valiente. The comparison of tree-sibling time consistent phylogenetic networks is graph-isomorphism complete. In The Scientific World Journal, Vol. 2014(254279):1-6, 2014.   Keywords: abstract network, distance between networks, from network, isomorphism, phylogenetic network, tree sibling network. Note: http://arxiv.org/abs/0902.4640.         Toggle abstract "Several polynomial time computable metrics on the class of semibinary tree-sibling time consistent phylogenetic networks are available in the literature; in particular, the problem of deciding if two networks of this kind are isomorphic is in P. In this paper, we show that if we remove the semibinarity condition, then the problem becomes much harder. More precisely, we prove that the isomorphism problem for generic tree-sibling time consistent phylogenetic networks is polynomially equivalent to the graph isomorphism problem. Since the latter is believed not to belong to P, the chances are that it is impossible to define a metric on the class of all tree-sibling time consistent phylogenetic networks that can be computed in polynomial time. © 2014 Gabriel Cardona et al." 69 Leo van Iersel and Steven Kelk. Kernelizations for the hybridization number problem on multiple nonbinary trees. In WG14, Vol. 8747:299-311 of LNCS, springer, 2014.   Keywords: explicit network, from rooted trees, kernelization, minimum number, phylogenetic network, phylogeny, Program Treeduce, reconstruction. Note: http://arxiv.org/abs/1311.4045.         70 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 .         Toggle abstract "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." 71 Ran Libeskind-Hadas, Yi-Chieh Wu, Mukul S. Bansal and Manolis Kellis. Pareto-optimal phylogenetic tree reconciliation. In ISMB14, Vol. 30:i87-i95 of BIO, 2014.   Keywords: duplication, lateral gene transfer, loss, phylogenetic network, phylogeny, polynomial, Program Xscape, reconstruction. Note: http://dx.doi.org/10.1093/bioinformatics/btu289.         Toggle abstract "Motivation: Phylogenetic tree reconciliation is a widely used method for reconstructing the evolutionary histories of gene families and species, hosts and parasites and other dependent pairs of entities. Reconciliation is typically performed using maximum parsimony, in which each evolutionary event type is assigned a cost and the objective is to find a reconciliation of minimum total cost. It is generally understood that reconciliations are sensitive to event costs, but little is understood about the relationship between event costs and solutions. Moreover, choosing appropriate event costs is a notoriously difficult problem. Results: We address this problem by giving an efficient algorithm for computing Pareto-optimal sets of reconciliations, thus providing the first systematic method for understanding the relationship between event costs and reconciliations. This, in turn, results in new techniques for computing event support values and, for cophylogenetic analyses, performing robust statistical tests. We provide new software tools and demonstrate their use on a number of datasets from evolutionary genomic and cophylogenetic studies. © 2014 The Author. Published by Oxford University Press. All rights reserved." 72 Adrià Alcalà Mena, Mercè Llabrés, Francesc Rosselló and Pau Rullan. Tree-Child Cluster Networks. In Fundamenta Informaticae, Vol. 134(1-2):1-15, 2014.   Keywords: explicit network, from clusters, phylogenetic network, phylogeny, Program PhyloNetwork, reconstruction, tree-child network.         73 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.         Toggle abstract "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." 74 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.         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 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." 75 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.         Toggle abstract "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." 76 Yun Yu, Nikola Ristic and Luay Nakhleh. Fast algorithms and heuristics for phylogenomics under ILS and hybridization. In RECOMB-CG'13, Vol. 14(Suppl 15):S6 of BMCB, 2013.   Keywords: from network, from rooted trees, heuristic, phylogenetic network, phylogeny, Program PhyloNet, reconstruction.         77 Zhi-Zhong Chen, Fei Deng and Lusheng Wang. Identifying Duplications and Lateral Gene Transfers Simultaneously and Rapidly. In CIBCB13, Pages 128-135, 2013.   Keywords: duplication, FPT, from rooted trees, from species tree, phylogenetic network, phylogeny, reconstruction. Note: http://www.cs.cityu.edu.hk/~lwang/research/singaporet2013.pdf.         78 Paul Phipps and Sergey Bereg. Optimizing Phylogenetic Networks for Circular Split Systems. In TCBB, Vol. 9(2):535-547, 2012.   Keywords: abstract network, from distances, from splits, phylogenetic network, phylogeny, Program PhippsNetwork, reconstruction, software.         Toggle abstract "We address the problem of realizing a given distance matrix by a planar phylogenetic network with a minimum number of faces. With the help of the popular software SplitsTree4, we start by approximating the distance matrix with a distance metric that is a linear combination of circular splits. The main results of this paper are the necessary and sufficient conditions for the existence of a network with a single face. We show how such a network can be constructed, and we present a heuristic for constructing a network with few faces using the first algorithm as the base case. Experimental results on biological data show that this heuristic algorithm can produce phylogenetic networks with far fewer faces than the ones computed by SplitsTree4, without affecting the approximation of the distance matrix. © 2012 IEEE." 79 Magnus Bordewich and Charles Semple. Budgeted Nature Reserve Selection with diversity feature loss and arbitrary split systems. In JOMB, Vol. 64(1):69-85, 2012.   Keywords: abstract network, approximation, diversity, phylogenetic network, polynomial, split network. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/BS11.pdf.         Toggle abstract "Arising in the context of biodiversity conservation, the Budgeted Nature Reserve Selection (BNRS) problem is to select, subject to budgetary constraints, a set of regions to conserve so that the phylogenetic diversity (PD) of the set of species contained within those regions is maximized. Here PD is measured across either a single rooted tree or a single unrooted tree. Nevertheless, in both settings, this problem is NP-hard. However, it was recently shown that, for each setting, there is a polynomial-time (1-1/e)-approximation algorithm for it and that this algorithm is tight. In the first part of the paper, we consider two extensions of BNRS. In the rooted setting we additionally allow for the disappearance of features, for varying survival probabilities across species, and for PD to be measured across multiple trees. In the unrooted setting, we extend to arbitrary split systems. We show that, despite these additional allowances, there remains a polynomial-time (1-1/e)-approximation algorithm for each extension. In the second part of the paper, we resolve a complexity problem on computing PD across an arbitrary split system left open by Spillner et al. © 2011 Springer-Verlag." 80 Yun Yu, James H. Degnan and Luay Nakhleh. The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection. In PLoS Genetics, Vol. 8(4):e1002660, 2012.   Keywords: AIC, BIC, explicit network, hybridization, phylogenetic network, phylogeny, statistical model. Note: http://dx.doi.org/10.1371/journal.pgen.1002660.         Toggle abstract "Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa. © 2012 Yu et al." 81 Hyun Jung Park and Luay Nakhleh. MURPAR: A fast heuristic for inferring parsimonious phylogenetic networks from multiple gene trees. In ISBRA12, Vol. 7292:213-224 of LNCS, springer, 2012.   Keywords: explicit network, from unrooted trees, heuristic, phylogenetic network, phylogeny, reconstruction, software. Note: https://www.researchgate.net/profile/Hyun_Jung_Park2/publication/262318595_MURPAR_A_Fast_Heuristic_for_Inferring_Parsimonious_Phylogenetic_Networks_from_Multiple_Gene_Trees/links/54b7e7b50cf269d8cbf58cc4.pdf.         Toggle abstract "Phylogenetic networks provide a graphical representation of evolutionary histories that involve non-treelike evolutionary events, such as horizontal gene transfer (HGT). One approach for inferring phylogenetic networks is based on reconciling gene trees, assuming all incongruence among the gene trees is due to HGT. Several mathematical results and algorithms, both exact and heuristic, have been introduced to construct and analyze phylogenetic networks. Here, we address the computational problem of inferring phylogenetic networks with minimum reticulations from a collection of gene trees. As this problem is known to be NP-hard even for a pair of gene trees, the problem at hand is very hard. In this paper, we present an efficient heuristic, MURPAR, for inferring a phylogenetic network from a collection of gene trees by using pairwise reconciliations of trees in the collection. Given the development of efficient and accurate methods for pairwise gene tree reconciliations, MURPAR inherits this efficiency and accuracy. Further, the method includes a formulation for combining pairwise reconciliations that is naturally amenable to an efficient integer linear programming (ILP) solution. We show that MURPAR produces more accurate results than other methods and is at least as fast, when run on synthetic and biological data. We believe that our method is especially important for rapidly obtaining estimates of genome-scale evolutionary histories that can be further refined by more detailed and compute-intensive methods. © 2012 Springer-Verlag." 82 Pawel Górecki and Jerzy Tiuryn. Inferring evolutionary scenarios in the duplication, loss and horizontal gene transfer model. In Logic and Program Semantics, Vol. 7230:83-105 of LNCS, springer, 2012.   Keywords: duplication, explicit network, lateral gene transfer, loss, phylogenetic network, phylogeny, reconstruction. Note: http://dx.doi.org/10.1007/978-3-642-29485-3_7.         Toggle abstract "An H-tree is a formal model of evolutionary scenario. It can be used to represent any processes with gene duplication and loss, horizontal gene transfer (HGT) and speciation events. The model of H-trees, introduced in [26], is an extension of the duplication-loss model (DL-model). Similarly to its ancestor, it has a number of interesting mathematical and biological properties. It is, however, more computationally complex than the DL-model. In this paper, we primarily address the problem of inferring H-trees that are compatible with a given gene tree and a given phylogeny of species with HGTs. These results create a mathematical and computational foundation for a more general and practical problem of inferring HGTs from given gene and species trees with HGTs. We also demonstrate how our model can be used to support HGT hypotheses based on empirical data sets. © 2012 Springer-Verlag Berlin Heidelberg." 83 Mukul S. Bansal, Eric J. Alm and Manolis Kellis. Efficient Algorithms for the Reconciliation Problem with Gene Duplication, Horizontal Transfer, and Loss. In ISMB12, Vol. 28(12):i283-i291 of BIO, 2012.   Keywords: duplication, explicit network, from rooted trees, from species tree, lateral gene transfer, loss, phylogenetic network, phylogeny, Program Angst, Program Mowgli, Program RANGER-DTL, reconstruction. Note: http://dx.doi.org/10.1093/bioinformatics/bts225.         Toggle abstract "Motivation: Gene family evolution is driven by evolutionary events such as speciation, gene duplication, horizontal gene transfer and gene loss, and inferring these events in the evolutionary history of a given gene family is a fundamental problem in comparative and evolutionary genomics with numerous important applications. Solving this problem requires the use of a reconciliation framework, where the input consists of a gene family phylogeny and the corresponding species phylogeny, and the goal is to reconcile the two by postulating speciation, gene duplication, horizontal gene transfer and gene loss events. This reconciliation problem is referred to as duplication-transfer-loss (DTL) reconciliation and has been extensively studied in the literature. Yet, even the fastest existing algorithms for DTL reconciliation are too slow for reconciling large gene families and for use in more sophisticated applications such as gene tree or species tree reconstruction.Results: We present two new algorithms for the DTL reconciliation problem that are dramatically faster than existing algorithms, both asymptotically and in practice. We also extend the standard DTL reconciliation model by considering distance-dependent transfer costs, which allow for more accurate reconciliation and give an efficient algorithm for DTL reconciliation under this extended model. We implemented our new algorithms and demonstrated up to 100 000-fold speed-up over existing methods, using both simulated and biological datasets. This dramatic improvement makes it possible to use DTL reconciliation for performing rigorous evolutionary analyses of large gene families and enables its use in advanced reconciliation-based gene and species tree reconstruction methods. © The Author(s) 2012. Published by Oxford University Press." 84 An-Chiang Chu, Jesper Jansson, Richard Lemence, Alban Mancheron and Kun-Mao Chao. Asymptotic Limits of a New Type of Maximization Recurrence with an Application to Bioinformatics. In TAMC12, Vol. 7287:177-188 of LNCS, springer, 2012.   Keywords: from triplets, galled network, level k phylogenetic network, phylogenetic network. Note: preliminary version.         Toggle abstract "We study the asymptotic behavior of a new type of maximization recurrence, defined as follows. Let k be a positive integer and p k(x) a polynomial of degree k satisfying p k(0) = 0. Define A 0 = 0 and for n ≥ 1, let A n = max 0≤i<n{A i+n kp k(i/n)}. We prove that lim n→∞A n/n n = sup{pk(x)/1-x k : 0≤x<1}. We also consider two closely related maximization recurrences S n and S′ n, defined as S 0 = S′ 0 = 0, and for n ≥ 1, S n = max 0≤i<n{S i + i(n-i)(n-i-1)/2} and S′ n = max 0≤i<n{S′ i + ( 3 n-i) + 2i( 2 n-i) + (n-i)( 2 i)}. We prove that lim n→∞ S′n/3( 3 n) = 2(√3-1)/3 ≈ 0.488033..., resolving an open problem from Bioinformatics about rooted triplets consistency in phylogenetic networks. © 2012 Springer-Verlag." 85 Marco Alves, Joãd Alves, Rui Camacho, Pedro Soares and Luísa Pereira. From Networks to Trees. In PACBB'12, Vol. 154:129-136 of Advances in Intelligent and Soft Computing, springer, 2012.   Keywords: from network, phylogenetic network, phylogeny.         86 Jesper Jansson and Andrzej Lingas. Computing the rooted triplet distance between galled trees by counting triangles. In CPM12, Vol. 7354:385-398 of LNCS, springer, 2012.   Keywords: distance between networks, explicit network, from network, galled tree, phylogenetic network, phylogeny, polynomial, triplet distance. Note: http://www.df.lth.se/~jj/Publications/d_rt_for_Galled_Trees5_CPM_2012.pdf.         Toggle abstract "We consider a generalization of the rooted triplet distance between two phylogenetic trees to two phylogenetic networks. We show that if each of the two given phylogenetic networks is a so-called galled tree with n leaves then the rooted triplet distance can be computed in o(n 2.688) time. Our upper bound is obtained by reducing the problem of computing the rooted triplet distance to that of counting monochromatic and almost- monochromatic triangles in an undirected, edge-colored graph. To count different types of colored triangles in a graph efficiently, we extend an existing technique based on matrix multiplication and obtain several new related results that may be of independent interest. © 2012 Springer-Verlag." 87 Tetsuo Asano, Jesper Jansson, Kunihiko Sadakane, Ryuhei Uehara and Gabriel Valiente. Faster computation of the Robinson–Foulds distance between phylogenetic networks. In Information Sciences, Vol. 197:77-90, 2012.   Keywords: distance between networks, explicit network, level k phylogenetic network, phylogenetic network, polynomial, spread.         Toggle abstract "The Robinson-Foulds distance, a widely used metric for comparing phylogenetic trees, has recently been generalized to phylogenetic networks. Given two phylogenetic networks N 1, N 2 with n leaf labels and at most m nodes and e edges each, the Robinson-Foulds distance measures the number of clusters of descendant leaves not shared by N 1 and N 2. The fastest known algorithm for computing the Robinson-Foulds distance between N 1 and N 2 runs in O(me) time. In this paper, we improve the time complexity to O(ne/log n) for general phylogenetic networks and O(nm/log n) for general phylogenetic networks with bounded degree (assuming the word RAM model with a word length of ⌈logn⌉ bits), and to optimal O(m) time for leaf-outerplanar networks as well as optimal O(n) time for level-1 phylogenetic networks (that is, galled-trees). We also introduce the natural concept of the minimum spread of a phylogenetic network and show how the running time of our new algorithm depends on this parameter. As an example, we prove that the minimum spread of a level-k network is at most k + 1, which implies that for one level-1 and one level-k phylogenetic network, our algorithm runs in O((k + 1)e) time. © 2012 Elsevier Inc. All rights reserved." 88 Leo van Iersel, Steven Kelk, Nela Lekic and Celine Scornavacca. A practical approximation algorithm for solving massive instances of hybridization number. In WABI12, Vol. 7534(430-440) of LNCS, springer, 2012.   Keywords: agreement forest, approximation, explicit network, from rooted trees, hybridization, phylogenetic network, phylogeny, Program CycleKiller, Program Dendroscope, Program HybridNET, reconstruction, software. Note: http://arxiv.org/abs/1205.3417.         Toggle abstract "Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. In practice, exact solvers struggle to solve instances with reticulation number larger than 40. For such instances, one has to resort to heuristics and approximation algorithms. Here we present the algorithm CycleKiller which is the first approximation algorithm that can produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Theoretically, the algorithm is an exponential-time 2-approximation (or 4-approximation in its fastest mode). However, using simulations we demonstrate that in practice the algorithm runs quickly for large and difficult instances, producing solutions within one percent of optimality. An implementation of this algorithm, which extends the theoretical work of [14], has been made publicly available. © 2012 Springer-Verlag." 89 Maureen Stolzer, Han Lai, Minli Xu, Deepa Sathaye, Benjamin Vernot and Dannie Durand. Inferring Duplications, Losses, Transfers, and Incomplete Lineage Sorting with Non-Binary Species Trees. In ECCB12, Vol. 28(18):i409-i415 of BIO, 2012.   Keywords: duplication, explicit network, from rooted trees, lateral gene transfer, loss, phylogenetic network, phylogeny, Program Notung, reconstruction. Note: http://dx.doi.org/10.1093/bioinformatics/bts386.         Toggle abstract "Motivation: Gene duplication (D), transfer (T), loss (L) and incomplete lineage sorting (I) are crucial to the evolution of gene families and the emergence of novel functions.The history of these events can be inferred via comparison of gene and species trees, a process called reconciliation, yet current reconciliation algorithms model only a subset of these evolutionary processes. Results: We present an algorithm to reconcile a binary gene tree with a nonbinary species tree under a DTLI parsimony criterion. This is the first reconciliation algorithm to capture all four evolutionary processes driving tree incongruence and the first to reconcile nonbinary species trees with a transfer model. Our algorithm infers all optimal solutions and reports complete, temporally feasible event histories, giving the gene and species lineages in which each event occurred. It is fixed-parameter tractable, with polytime complexity when the maximum species outdegree is fixed. Application of our algorithms to prokaryotic and eukaryotic data show that use of an incomplete event model has substantial impact on the events inferred and resulting biological conclusions. © The Author(s) 2012. Published by Oxford University Press." 90 Thi-Hau Nguyen, Jean-Philippe Doyon, Stéphanie Pointet, Anne-Muriel Chifolleau Arigon, Vincent Ranwez and Vincent Berry. Accounting for Gene Tree Uncertainties Improves Gene Trees and Reconciliation Inference. In WABI12, Vol. 7534:123-134 of LNCS, springer, 2012.   Keywords: duplication, heuristic, lateral gene transfer, phylogenetic network, phylogeny, Program Mowgli, reconstruction. Note: http://hal.archives-ouvertes.fr/hal-00718347/en/.         Toggle abstract "We propose a reconciliation heuristic accounting for gene duplications, losses and horizontal transfers that specifically takes into account the uncertainties in the gene tree. Rearrangements are tried for gene tree edges that are weakly supported, 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. Experimental results on simulated and real data confirm that running times are greatly reduced when considering the above-mentioned optimization in comparison to the naïve rearrangement procedure. Results also show that gene trees modified by such NNI rearrangements are closer to the correct (simulated) trees and lead to more correct event predictions on average. The program is available at http://www.atgc-montpellier.fr/ Mowgli/. © 2012 Springer-Verlag." 91 Katharina Huber, Vincent Moulton, Andreas Spillner, Sabine Storandt and Radoslaw Suchecki. Computing a consensus of multilabeled trees. In ALENEX12, Pages 84-92, 2012.   Keywords: duplication, explicit network, exponential algorithm, phylogenetic network, phylogeny. Note: http://siam.omnibooksonline.com/2012ALENEX/data/papers/020.pdf.         Toggle abstract In this paper we consider two challenging problems that arise in the context of computing a consensus of a collection of multilabeled trees, namely (1) selecting a compatible collection of clusters on a multiset from an ordered list of such clusters and (2) optimally refining high degree vertices in a multilabeled tree. Forming such a consensus is part of an approach to reconstruct the evolutionary history of a set of species for which events such as genome duplication and hybridization have occurred in the past. We present exact algorithms for solving (1) and (2) that have an exponential run-time in the worst case. To give some impression of their performance in practice, we apply them to simulated input and to a real biological data set highlighting the impact of several structural properties of the input on the performance. 92 Cayla McBee. Generalizing Fourier Calculus on Evolutionary Trees to Splits Networks. In ISPAN'12, Pages 149-155, 2012.   Keywords: abstract network, from sequences, phylogenetic network, phylogeny, split network, statistical model.         Toggle abstract "Biologists have been interested in Phylogenetics, the study of evolutionary relatedness among various groups of organisms, for more than 140 years. In spite of this, it has only been in the last 40 years that advances in technology and the availability of DNA sequences have led to statistical, computational and algorithmic work on determining evolutionary relatedness between organisms. One method of determining historical relationships between organisms is to assume a group based evolutionary model and use a discrete Fourier transform. The 1993 paper 'Fourier Calculus on Evolutionary Trees' by L.A. Szekely, M.A. Steel and P.L. Erdos outlines this process. The transform presented in Szekely et al provides an invertible relationship between phylogenetic trees and expected frequencies of nucleotide patterns in nucleotide sequences. This implies that given a set of nucleotide sequences from various organisms it is possible to construct a phylogenetic tree that represents the historical relationships of those organisms. Some scenarios are poorly described by phylogenetic trees and there are biological and statistical reasons for using networks to model phylogenetic relationships. Given this motivation I have generalized Szekely et al's result to apply to a specific type of phylogenetic network known as a splits network. © 2012 IEEE." 93 Dan Levy and Lior Pachter. The Neighbor-Net Algorithm. In Advances in Applied Mathematics, Vol. 47(2):240-258, 2011.   Keywords: abstract network, circular split system, evaluation, from distances, NeighborNet, phylogenetic network, phylogeny, split network. Note: http://arxiv.org/abs/math/0702515.         Toggle abstract "The neighbor-joining algorithm is a popular phylogenetics method for constructing trees from dissimilarity maps. The neighbor-net algorithm is an extension of the neighbor-joining algorithm and is used for constructing split networks. We begin by describing the output of neighbor-net in terms of the tessellation of M̄0n(R) by associahedra. This highlights the fact that neighbor-net outputs a tree in addition to a circular ordering and we explain when the neighbor-net tree is the neighbor-joining tree. A key observation is that the tree constructed in existing implementations of neighbor-net is not a neighbor-joining tree. Next, we show that neighbor-net is a greedy algorithm for finding circular split systems of minimal balanced length. This leads to an interpretation of neighbor-net as a greedy algorithm for the traveling salesman problem. The algorithm is optimal for Kalmanson matrices, from which it follows that neighbor-net is consistent and has optimal radius 12. We also provide a statistical interpretation for the balanced length for a circular split system as the length based on weighted least squares estimates of the splits. We conclude with applications of these results and demonstrate the implications of our theorems for a recently published comparison of Papuan and Austronesian languages. © 2010 Elsevier Inc. All rights reserved." 94 Shlomo Moran, Sagi Snir and Wing-Kin Sung. Partial Convex Recolorings of Trees and Galled Networks: Tight Upper and Lower bounds. In ACM Transactions on Algorithms, Vol. 7(4), 2011.   Keywords: evaluation, galled tree, phylogenetic network. Note: http://www.cs.technion.ac.il/~moran/r/PS/gnets-TOA-7Feb2007.pdf.         Toggle abstract "A coloring of a graph is convex if the vertices that pertain to any color induce a connected subgraph; a partial coloring (which assigns colors to a subset of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring has applications in fields such as phylogenetics, communication or transportation networks, etc. When a coloring of a graph is not convex, a natural question is how far it is from a convex one. This problem is denoted as convex recoloring (CR).While the initial works on CR defined and studied the problem on trees, recent efforts aim at either generalizing the underlying graphs or specializing the input colorings. In this work, we extend the underlying graph and the input coloring to partially colored galled networks. We show that although determining whether a coloring is convex on an arbitrary network is hard, it can be found efficiently on galled networks. We present a fixed parameter tractable algorithm that finds the recoloring distance of such a network whose running time is quadratic in the network size and exponential in that distance. This complexity is achieved by amortized analysis that uses a novel technique for contracting colored graphs that seems to be of independent interest. © 2011 ACM." 95 Jean-Philippe Doyon, Celine Scornavacca, Konstantin Yu Gorbunov, Gergely J. Szöllösi, Vincent Ranwez and Vincent Berry. An efficient algorithm for gene/species trees parsimonious reconciliation with losses, duplications, and transfers. In Proceedings of the Eighth RECOMB Comparative Genomics Satellite Workshop (RECOMB-CG'10), Vol. 6398:93-108 of LNCS, springer, 2011.   Keywords: branch length, duplication, dynamic programming, explicit network, from multilabeled tree, from species tree, from unrooted trees, lateral gene transfer, loss, phylogenetic network, phylogeny, polynomial, Program Mowgli, reconstruction. Note: http://www.lirmm.fr/~vberry/Publis/MPR-DoyonEtAl.pdf, software available at http://www.atgc-montpellier.fr/MPR/.         Toggle abstract "Tree reconciliation methods aim at estimating the evolutionary events that cause discrepancy between gene trees and species trees. We provide a discrete computational model that considers duplications, transfers and losses of genes. The model yields a fast and exact algorithm to infer time consistent and most parsimonious reconciliations. Then we study the conditions under which parsimony is able to accurately infer such events. Overall, it performs well even under realistic rates, transfers being in general less accurately recovered than duplications. An implementation is freely available at http://www.atgc- montpellier.fr/MPR. © 2010 Springer-Verlag." 96 Mukul S. Bansal, J. Peter Gogarten and Ron Shamir. Detecting Highways of Horizontal Gene Transfer. In Proceedings of the Eighth RECOMB Comparative Genomics Satellite Workshop (RECOMB-CG'10), Vol. 6398:109-120 of LNCS, springer, 2011.   Keywords: explicit network, from rooted trees, from species tree, lateral gene transfer, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://www.cs.iastate.edu/~bansal/Highways_RCG10.pdf.         Toggle abstract "In a horizontal gene transfer (HGT) event a gene is transferred between two species that do not share an ancestor-descendant relationship. Typically, no more than a few genes are horizontally transferred between any two species. However, several studies identified pairs of species between which many different genes were horizontally transferred. Such a pair is said to be linked by a highway of gene sharing. We present a method for inferring such highways. Our method is based on the fact that the evolutionary histories of horizontally transferred genes disagree with the corresponding species phylogeny. Specifically, given a set of gene trees and a trusted rooted species tree, each gene tree is first decomposed into its constituent quartet trees and the quartets that are inconsistent with the species tree are identified. Our method finds a pair of species such that a highway between them explains the largest (normalized) fraction of inconsistent quartets. For a problem on n species, our method requires O(n 4) time, which is optimal with respect to the quartets input size. An application of our method to a dataset of 1128 genes from 11 cyanobacterial species, as well as to simulated datasets, illustrates the efficacy of our method. © 2010 Springer-Verlag." 97 Celine Scornavacca, Franziska Zickmann and Daniel H. Huson. Tanglegrams for Rooted Phylogenetic Trees and Networks. In ISMB11, Vol. 27(13):i248-i256 of BIO, 2011.   Keywords: from network, heuristic, integer linear programming, phylogenetic network, phylogeny, Program Dendroscope, tanglegram, visualization. Note: http://dx.doi.org/10.1093/bioinformatics/btr210.         Toggle abstract "Motivation: In systematic biology, one is often faced with the task of comparing different phylogenetic trees, in particular in multi-gene analysis or cospeciation studies. One approach is to use a tanglegram in which two rooted phylogenetic trees are drawn opposite each other, using auxiliary lines to connect matching taxa. There is an increasing interest in using rooted phylogenetic networks to represent evolutionary history, so as to explicitly represent reticulate events, such as horizontal gene transfer, hybridization or reassortment. Thus, the question arises how to define and compute a tanglegram for such networks. Results: In this article, we present the first formal definition of a tanglegram for rooted phylogenetic networks and present a heuristic approach for computing one, called the NN-tanglegram method. We compare the performance of our method with existing tree tanglegram algorithms and also show a typical application to real biological datasets. For maximum usability, the algorithm does not require that the trees or networks are bifurcating or bicombining, or that they are on identical taxon sets. © The Author(s) 2011. Published by Oxford University Press." 98 Alethea Rea. Statistical approaches to phylogenetic networks, recombination and testing of incongruence. PhD thesis, The University of Auckland, New Zealand, 2011.   Keywords: abstract network, AIC, BIC, phylogenetic network, phylogeny, split, split network, statistical model. Note: https://researchspace.auckland.ac.nz/handle/2292/67624.         99 Changiz Eslahchi and Reza Hassanzadeh. New Algorithm for Constructing Supernetworks from Partial Trees. In MCCMB11, Pages 106-107, 2011.   Keywords: abstract network, from unrooted trees, heuristic, phylogenetic network, phylogeny, Program SNSA, reconstruction, simulated annealing, split network. Note: http://mccmb.belozersky.msu.ru/2011/mccmb11.pdf#page=106.         100 Louxin Zhang, Yen Kaow Ng, Taoyang Wu and Yu Zheng. Network model and efficient method for detecting relative duplications or horizontal gene transfers. In ICCABS11, Pages 214-219, 2011.   Keywords: dynamic programming, explicit network, from network, from rooted trees, from species tree, phylogenetic network, phylogeny, polynomial, reconstruction.         Toggle abstract "Background: Horizontal gene transfer and gene duplication are two significant forces behind genome evolution. As more and more well-supported examples of HGTs are being revealed, there is a growing awareness that HGT is more widespread than previously thought, occurring often not only within bacteria, but also between species remotely related such as bacteria and plants or plants and animals. Although a substantial number of genomic sequences are known, HGT inference remains challenging. Parsimony-based inferences of HGT events are typically NP-hard under the framework of gene tree and species tree comparison; it is even more timeconsuming if the maximum likelihood approach is used. The fact that gene tree and species tree incongruence can be further confounded by gene duplication and gene loss events motivates us to incorporate considerations for these events into our inference of HGT events. Similarly, it will be beneficial if known HGT events are considered in the inference of gene duplications and gene losses. © 2011 IEEE." 101 Jaroslaw Byrka, Pawel Gawrychowski, Katharina Huber and Steven Kelk. Worst-case optimal approximation algorithms for maximizing triplet consistency within phylogenetic networks. In Journal of Discrete Algorithms, Vol. 8(1):65-75, 2010.   Keywords: approximation, explicit network, from triplets, galled tree, level k phylogenetic network, phylogenetic network, phylogeny, reconstruction. Note: http://arxiv.org/abs/0710.3258.         Toggle abstract "The study of phylogenetic networks is of great interest to computational evolutionary biology and numerous different types of such structures are known. This article addresses the following question concerning rooted versions of phylogenetic networks. What is the maximum value of p ∈ [0, 1] such that for every input set T of rooted triplets, there exists some network N such that at least p | T | of the triplets are consistent with N? We call an algorithm that computes such a network (where p is maximum) worst-case optimal. Here we prove that the set containing all triplets (the full triplet set) in some sense defines p. Moreover, given a network N that obtains a fraction p′ for the full triplet set (for any p′), we show how to efficiently modify N to obtain a fraction ≥ p′ for any given triplet set T. We demonstrate the power of this insight by presenting a worst-case optimal result for level-1 phylogenetic networks improving considerably upon the 5/12 fraction obtained recently by Jansson, Nguyen and Sung. For level-2 phylogenetic networks we show that p ≥ 0.61. We emphasize that, because we are taking | T | as a (trivial) upper bound on the size of an optimal solution for each specific input T, the results in this article do not exclude the existence of approximation algorithms that achieve approximation ratio better than p. Finally, we note that all the results in this article also apply to weighted triplet sets. © 2009 Elsevier B.V. All rights reserved." 102 Leo van Iersel, Steven Kelk, Regula Rupp and Daniel H. Huson. Phylogenetic Networks Do not Need to Be Complex: Using Fewer Reticulations to Represent Conflicting Clusters. In ISMB10, Vol. 26(12):i124-i131 of BIO, 2010.   Keywords: from clusters, level k phylogenetic network, Program Dendroscope, Program HybridInterleave, Program HybridNumber, reconstruction. Note: http://dx.doi.org/10.1093/bioinformatics/btq202, with proofs: http://arxiv.org/abs/0910.3082.         Toggle abstract "Phylogenetic trees are widely used to display estimates of how groups of species are evolved. Each phylogenetic tree can be seen as a collection of clusters, subgroups of the species that evolved from a common ancestor. When phylogenetic trees are obtained for several datasets (e.g. for different genes), then their clusters are often contradicting. Consequently, the set of all clusters of such a dataset cannot be combined into a single phylogenetic tree. Phylogenetic networks are a generalization of phylogenetic trees that can be used to display more complex evolutionary histories, including reticulate events, such as hybridizations, recombinations and horizontal gene transfers. Here, we present the new CASS algorithm that can combine any set of clusters into a phylogenetic network. We show that the networks constructed by CASS are usually simpler than networks constructed by other available methods. Moreover, we show that CASS is guaranteed to produce a network with at most two reticulations per biconnected component, whenever such a network exists. We have implemented CASS and integrated it into the freely available Dendroscope software. Contact: l.j.j.v.iersel@gmail.com. Supplementary information: Supplementary data are available at Bioinformatics online. © The Author(s) 2010. Published by Oxford University Press." 103 Tetsuo Asano, Jesper Jansson, Kunihiko Sadakane, Ryuhei Uehara and Gabriel Valiente. Faster Computation of the Robinson-Foulds Distance between Phylogenetic Networks. In CPM10, Vol. 6129:190-201 of LNCS, springer, 2010.   Keywords: distance between networks, explicit network, level k phylogenetic network, phylogenetic network, polynomial, spread. Note: http://hdl.handle.net/10119/9859, slides available at http://cs.nyu.edu/parida/CPM2010/MainPage_files/18.pdf.         Toggle abstract "The Robinson-Foulds distance, which is the most widely used metric for comparing phylogenetic trees, has recently been generalized to phylogenetic networks. Given two networks N1,N2 with n leaves, m nodes, and e edges, the Robinson-Foulds distance measures the number of clusters of descendant leaves that are not shared by N1 and N2. The fastest known algorithm for computing the Robinson-Foulds distance between those networks runs in O(m(m + e)) time. In this paper, we improve the time complexity to O(n(m+ e)/ log n) for general networks and O(nm/log n) for general networks with bounded degree, and to optimal O(m + e) time for planar phylogenetic networks and boundedlevel phylogenetic networks.We also introduce the natural concept of the minimum spread of a phylogenetic network and show how the running time of our new algorithm depends on this parameter. As an example, we prove that the minimum spread of a level-k phylogenetic network is at most k + 1, which implies that for two level-k phylogenetic networks, our algorithm runs in O((k + 1)(m + e)) time. © Springer-Verlag Berlin Heidelberg 2010." 104 Yufeng Wu. Close Lower and Upper Bounds for the Minimum Reticulate Network of Multiple Phylogenetic Trees. In ISMB10, Vol. 26(12):i140-i148 of BIO, 2010.   Keywords: explicit network, from rooted trees, hybridization, minimum number, phylogenetic network, phylogeny, Program PIRN, software. Note: http://dx.doi.org/10.1093/bioinformatics/btq198.         Toggle abstract "Motivation: Reticulate network is a model for displaying and quantifying the effects of complex reticulate processes on the evolutionary history of species undergoing reticulate evolution. A central computational problem on reticulate networks is: given a set of phylogenetic trees (each for some region of the genomes), reconstruct the most parsimonious reticulate network (called the minimum reticulate network) that combines the topological information contained in the given trees. This problem is well-known to be NP-hard. Thus, existing approaches for this problem either work with only two input trees or make simplifying topological assumptions. Results: We present novel results on the minimum reticulate network problem. Unlike existing approaches, we address the fully general problem: there is no restriction on the number of trees that are input, and there is no restriction on the form of the allowed reticulate network. We present lower and upper bounds on the minimum number of reticulation events in the minimum reticulate network (and infer an approximately parsimonious reticulate network). A program called PIRN implements these methods, which also outputs a graphical representation of the inferred network. Empirical results on simulated and biological data show that our methods are practical for a wide range of data. More importantly, the lower and upper bounds match for many datasets (especially when the number of trees is small or reticulation level is low), and this allows us to solve the minimum reticulate network problem exactly for these datasets. Availability: A software tool, PIRN, is available for download from the web page: http://www.engr.uconn.edu/ywu. Contact: ywu@engr.uconn.edu. Supplementary information: Supplementary data is available at Bioinformatics online. © The Author(s) 2010. Published by Oxford University Press." 105 Yufeng Wu and Jiayin Wang. Fast Computation of the Exact Hybridization Number of Two Phylogenetic Trees. In ISBRA10, Vol. 6053:203-214 of LNCS, springer, 2010.   Keywords: agreement forest, explicit network, from rooted trees, hybridization, integer linear programming, minimum number, phylogenetic network, phylogeny, Program HybridNumber, Program SPRDist, SPR distance. Note: http://www.engr.uconn.edu/~ywu/Papers/ISBRA10WuWang.pdf.         Toggle abstract "Hybridization is a reticulate evolutionary process. An established problem on hybridization is computing the minimum number of hybridization events, called the hybridization number, needed in the evolutionary history of two phylogenetic trees. This problem is known to be NP-hard. In this paper, we present a new practical method to compute the exact hybridization number. Our approach is based on an integer linear programming formulation. Simulation results on biological and simulated datasets show that our method (as implemented in program SPRDist) is more efficient and robust than an existing method. © 2010 Springer-Verlag Berlin Heidelberg." 106 Hyun Jung Park, Guohua Jin and Luay Nakhleh. Algorithmic strategies for estimating the amount of reticulation from a collection of gene trees. In CSB10, 2010.   Keywords: bound, from rooted trees, heuristic, phylogenetic network, phylogeny, reconstruction, SPR distance. Note: http://www.cs.rice.edu/~nakhleh/Papers/ParkEtAl-CSB2010.pdf.         107 Gabriel Cardona, Mercè Llabrés and Francesc Rosselló. A metric for galled networks. 2010.   Keywords: distance between networks, explicit network, from network, galled network, phylogenetic network, phylogeny. Note: http://arxiv4.library.cornell.edu/abs/1009.0652.         108 Chris Whidden, Robert G. Beiko and Norbert Zeh. Fast FPT Algorithms for Computing Rooted Agreement Forests: Theory and Experiments. In Proceedings of the ninth International Symposium on Experimental Algorithms (SEA'10), Vol. 6049:141-153 of LNCS, springer, 2010.   Keywords: agreement forest, explicit network, FPT, from rooted trees, hybridization, minimum number, phylogenetic network, phylogeny, Program HybridInterleave, reconstruction, SPR distance. Note: https://www.cs.dal.ca/sites/default/files/technical_reports/CS-2010-03.pdf.         Toggle abstract "We improve on earlier FPT algorithms for computing a rooted maximum agreement forest (MAF) or a maximum acyclic agreement forest (MAAF) of a pair of phylogenetic trees. Their sizes give the subtree-prune-and-regraft (SPR) distance and the hybridization number of the trees, respectively. We introduce new branching rules that reduce the running time of the algorithms from O(3 kn) and O(3 kn log n) to O(2.42 kn) and O(2.42 kn log n), respectively. In practice, the speed up may be much more than predicted by the worst-case analysis.We confirm this intuition experimentally by computing MAFs for simulated trees and trees inferred from protein sequence data. We show that our algorithm is orders of magnitude faster and can handle much larger trees and SPR distances than the best previous methods, treeSAT and sprdist. © Springer-Verlag Berlin Heidelberg 2010." 109 Gabriel Cardona, Mercè Llabrés and Francesc Rosselló. Two Results on Distances for Phylogenetic Networks. In Advances in Intelligent and Soft Computing, Vol. 74:93-100, 2010.   Keywords: distance between networks, explicit network, phylogenetic network, phylogeny, tree sibling network. Note: http://www.merilibrary.com/books/bioinformatics/advances%20in%20bioinformatics.pdf#page=103.         110 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.         Toggle abstract "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." 111 Ulrik Brandes and Sabine Cornelsen. Phylogenetic Graph Models Beyond Trees. In DAM, Vol. 157(10):2361-2369, 2009.   Keywords: abstract network, cactus graph, from splits, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://www.inf.uni-konstanz.de/~cornelse/Papers/bc-pgmbt-07.pdf.         Toggle abstract "A graph model for a set S of splits of a set X consists of a graph and a map from X to the vertices of the graph such that the inclusion-minimal cuts of the graph represent S. Phylogenetic trees are graph models in which the graph is a tree. We show that the model can be generalized to a cactus (i.e. a tree of edges and cycles) without losing computational efficiency. A cactus can represent a quadratic rather than linear number of splits in linear space. We show how to decide in linear time in the size of a succinct representation of S whether a set of splits has a cactus model, and if so construct it within the same time bounds. As a byproduct, we show how to construct the subset of all compatible splits and a maximal compatible set of splits in linear time. Note that it is N P-complete to find a compatible subset of maximum size. Finally, we briefly discuss further generalizations of tree models. © 2008 Elsevier B.V. All rights reserved." 112 Leo van Iersel, Steven Kelk and Matthias Mnich. Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks. In JBCB, Vol. 7(4):597-623, 2009.   Keywords: explicit network, from triplets, galled tree, level k phylogenetic network, NP complete, phylogenetic network, phylogeny, reconstruction, uniqueness. Note: http://arxiv.org/pdf/0712.2932v2.         113 Daniel H. Huson. Drawing Rooted Phylogenetic Networks. In TCBB, Vol. 6(1):103-109, 2009.   Keywords: explicit network, phylogenetic network, phylogeny, Program Dendroscope, Program SplitsTree, visualization. Note: http://dx.doi.org/10.1109/TCBB.2008.58.         Toggle abstract "The evolutionary history of a collection of species is usually represented by a phylogenetic tree. Sometimes, phylogenetic networks are used as a means of representing reticulate evolution or of showing uncertainty and incompatibilities in evolutionary datasets. This is often done using unrooted phylogenetic networks such as split networks, due in part, to the availability of software (SplitsTree) for their computation and visualization. In this paper we discuss the problem of drawing rooted phylogenetic networks as cladograms or phylograms in a number of different views that are commonly used for rooted trees. Implementations of the algorithms are available in new releases of the Dendroscope and SplitsTree programs. © 2006 IEEE." 114 Simone Linz and Charles Semple. Hybridization in non-binary trees. In TCBB, Vol. 6(1):30-45, 2009.   Keywords: agreement forest, FPT, from rooted trees, hybridization, phylogenetic network, phylogeny, reconstruction. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/LS08.pdf, slides available at http://www.newton.cam.ac.uk/webseminars/pg+ws/2007/plg/plgw03/1220/linz/.         115 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.         116 Gabriel Cardona, Mercè Llabrés, Francesc Rosselló and Gabriel Valiente. Metrics for phylogenetic networks I: Generalizations of the Robinson-Foulds metric. In TCBB, Vol. 6(1):46-61, 2009.   Keywords: distance between networks, explicit network, phylogenetic network, phylogeny, time consistent network, tree-child network, tripartition distance. Note: http://dx.doi.org/10.1109/TCBB.2008.70.         Toggle abstract "The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the first in a series of papers devoted to the analysis and comparison of metrics for tree-child time consistent phylogenetic networks on the same set of taxa. In this paper, we study three metrics that have already been introduced in the literature: the Robinson-Foulds distance, the tripartitions distance and the $mu$-distance. They generalize to networks the classical Robinson-Foulds or partition distance for phylogenetic trees. We analyze the behavior of these metrics by studying their least and largest values and when they achieve them. As a by-product of this study, we obtain tight bounds on the size of a tree-child time consistent phylogenetic network. © 2006 IEEE." 117 Gabriel Cardona, Mercè Llabrés, Francesc Rosselló and Gabriel Valiente. Metrics for phylogenetic networks II: Nodal and triplets metrics. In TCBB, Vol. 6(3):454-469, 2009.   Keywords: distance between networks, phylogenetic network, phylogeny. Note: http://dx.doi.org/10.1109/TCBB.2008.127.         Toggle abstract "The assessment of phylogenetic network reconstruction methods requires the ability to compare phylogenetic networks. This is the second in a series of papers devoted to the analysis and comparison of metrics for tree-child time consistent phylogenetic networks on the same set of taxa. In this paper, we generalize to phylogenetic networks two metrics that have already been introduced in the literature for phylogenetic trees: the nodal distance and the triplets distance. We prove that they are metrics on any class of tree- child time consistent phylogenetic networks on the same set of taxa, as well as some basic properties for them. To prove these results, we introduce a reduction/expansion procedure that can be used not only to establish properties of tree-child time consistent phylogenetic networks by induction, but also to generate all tree-child time consistent phylogenetic networks with a given number of leaves. © 2009 IEEE." 118 Gabriel Cardona, Mercè Llabrés, Francesc Rosselló and Gabriel Valiente. On Nakhleh's metric for reduced phylogenetic networks. In TCBB, Vol. 6(4):629-638, 2009.   Keywords: distance between networks, phylogenetic network, phylogeny. Note: Preliminary versions: http://arxiv.org/abs/0809.0110 and http://arxiv.org/abs/0801.2354v1.         Toggle abstract "We prove that Nakhleh's metric for reduced phylogenetic networks is also a metric on the classes of tree-child phylogenetic networks, semibinary tree-sibling time consistent phylogenetic networks, and multilabeled phylogenetic trees. We also prove that it separates distinguishable phylogenetic networks. In this way, it becomes the strongest dissimilarity measure for phylogenetic networks available so far. Furthermore, we propose a generalization of that metric that separates arbitrary phylogenetic networks. © 2009 IEEE." 119 Guohua Jin, Luay Nakhleh, Sagi Snir and Tamir Tuller. Parsimony Score of Phylogenetic Networks: Hardness Results and a Linear-time Heuristic. In TCBB, Vol. 6(3):495-505, 2009.   Keywords: explicit network, heuristic, parsimony, phylogenetic network, phylogeny, reconstruction. Note: http://www.cs.rice.edu/~nakhleh/Papers/tcbb-MP.pdf.         120 Ran Libeskind-Hadas and Michael A. Charleston. On the Computational Complexity of the Reticulate Cophylogeny Reconstruction Problem. In JCB, Vol. 16(1):105-117, 2009.   Keywords: cophylogeny, heuristic, NP complete, parsimony, phylogenetic network, reconstruction. Note: http://dx.doi.org/10.1089/cmb.2008.0084.         Toggle abstract "The cophylogeny reconstruction problem is that of finding minimal cost explanations of differences between evolutionary histories of ecologically linked groups of biological organisms. We present a proof that shows that the general problem of reconciling evolutionary histories is NP-complete and provide a sharp boundary where this intractability begins. We also show that a related problem, that of finding Pareto optimal solutions, is NP-hard. As a byproduct of our results, we give a framework by which meta-heuristics can be applied to find good solutions to this problem. © Mary Ann Liebert, Inc. 2009." 121 Thu-Hien To and Michel Habib. Level-k Phylogenetic Networks Are Constructable from a Dense Triplet Set in Polynomial Time. In CPM09, (5577):275-288, springer, 2009.   Keywords: explicit network, from triplets, level k phylogenetic network, minimum number, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://arxiv.org/abs/0901.1657.         Toggle abstract "For a given dense triplet set Τ there exist two natural questions [7]: Does there exist any phylogenetic network consistent with Τ? In case such networks exist, can we find an effective algorithm to construct one? For cases of networks of levels k = 0, 1 or 2, these questions were answered in [1,6,7,8,10] with effective polynomial algorithms. For higher levels k, partial answers were recently obtained in [11] with an O(/Τ/k+1)time algorithm for simple networks. In this paper, we give a complete answer to the general case, solving a problem proposed in [7]. The main idea of our proof is to use a special property of SN-sets in a level-k network. As a consequence, for any fixed k, we can also find a level-k network with the minimum number of reticulations, if one exists, in polynomial time. © 2009 Springer Berlin Heidelberg." 122 Philippe Gambette, Vincent Berry and Christophe Paul. The structure of level-k phylogenetic networks. In CPM09, Vol. 5577:289-300 of LNCS, springer, 2009.   Keywords: coalescent, explicit network, galled tree, level k phylogenetic network, phylogenetic network, Program Recodon. Note: http://hal-lirmm.ccsd.cnrs.fr/lirmm-00371485/en/.         Toggle abstract "Evolution is usually described as a phylogenetic tree, but due to some exchange of genetic material, it can be represented as a phylogenetic network which has an underlying tree structure. The notion of level was recently introduced as a parameter on realistic kinds of phylogenetic networks to express their complexity and tree-likeness. We study the structure of level-k networks, and how they can be decomposed into level-k generators. We also provide a polynomial time algorithm which takes as input the set of level-k generators and builds the set of level-(k + 1) generators. Finally, with a simulation study, we evaluate the proportion of level-k phylogenetic networks among networks generated according to the coalescent model with recombination. © 2009 Springer Berlin Heidelberg." 123 Daniel H. Huson, Regula Rupp, Vincent Berry, Philippe Gambette and Christophe Paul. Computing Galled Networks from Real Data. In ISMBECCB09, Vol. 25(12):i85-i93 of BIO, 2009.   Keywords: abstract network, cluster containment, explicit network, FPT, from clusters, from rooted trees, galled network, NP complete, phylogenetic network, phylogeny, polynomial, Program Dendroscope, reconstruction. Note: http://hal-lirmm.ccsd.cnrs.fr/lirmm-00368545/en/.         Toggle abstract "Motivation: Developing methods for computing phylogenetic networks from biological data is an important problem posed by molecular evolution and much work is currently being undertaken in this area. Although promising approaches exist, there are no tools available that biologists could easily and routinely use to compute rooted phylogenetic networks on real datasets containing tens or hundreds of taxa. Biologists are interested in clades, i.e. groups of monophyletic taxa, and these are usually represented by clusters in a rooted phylogenetic tree. The problem of computing an optimal rooted phylogenetic network from a set of clusters, is hard, in general. Indeed, even the problem of just determining whether a given network contains a given cluster is hard. Hence, some researchers have focused on topologically restricted classes of networks, such as galled trees and level-k networks, that are more tractable, but have the practical draw-back that a given set of clusters will usually not possess such a representation. Results: In this article, we argue that galled networks (a generalization of galled trees) provide a good trade-off between level of generality and tractability. Any set of clusters can be represented by some galled network and the question whether a cluster is contained in such a network is easy to solve. Although the computation of an optimal galled network involves successively solving instances of two different NP-complete problems, in practice our algorithm solves this problem exactly on large datasets containing hundreds of taxa and many reticulations in seconds, as illustrated by a dataset containing 279 prokaryotes. © 2009 The Author(s)." 124 Peter J. Humphries and Charles Semple. Note on the hybridization number and subtree distance in phylogenetics. In Applied Mathematics Letters, Vol. 22(4):611-615, 2009.   Keywords: explicit network, minimum number, phylogenetic network, phylogeny, SPR distance. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/HS08.pdf.         125 Laura S. Kubatko. Identifying Hybridization Events in the Presence of Coalescence via Model Selection. In Systematic Biology, Vol. 58(5):478-488, 2009.   Keywords: AIC, BIC, branch length, coalescent, explicit network, from rooted trees, from species tree, hybridization, lineage sorting, model selection, phylogenetic network, phylogeny, statistical model. Note: http://dx.doi.org/10.1093/sysbio/syp055.         126 Chen Meng and Laura S. Kubatko. Detecting hybrid speciation in the presence of incomplete lineage sorting using gene tree incongruence: A model. In Theoretical Population Biology, Vol. 75(1):35-45, 2009.   Keywords: bayesian, coalescent, from network, from rooted trees, hybridization, likelihood, lineage sorting, phylogenetic network, phylogeny, statistical model. Note: http://dx.doi.org/10.1016/j.tpb.2008.10.004.         Toggle abstract "The application of phylogenetic inference methods, to data for a set of independent genes sampled randomly throughout the genome, often results in substantial incongruence in the single-gene phylogenetic estimates. Among the processes known to produce discord between single-gene phylogenies, two of the best studied in a phylogenetic context are hybridization and incomplete lineage sorting. Much recent attention has focused on the development of methods for estimating species phylogenies in the presence of incomplete lineage sorting, but phylogenetic models that allow for hybridization have been more limited. Here we propose a model that allows incongruence in single-gene phylogenies to be due to both hybridization and incomplete lineage sorting, with the goal of determining the contribution of hybridization to observed gene tree incongruence in the presence of incomplete lineage sorting. Using our model, we propose methods for estimating the extent of the role of hybridization in both a likelihood and a Bayesian framework. The performance of our methods is examined using both simulated and empirical data. © 2008 Elsevier Inc. All rights reserved." 127 Poornima Venugopal and Sergey Bereg. Layout of Phylogenetic Networks and Multi-Labeled Trees. In BIOT'09, Pages 91, 2009.   Keywords: explicit network, phylogenetic network, phylogeny, Program PADRE, visualization. Note: http://www.biotconf.org/PDFs/1456.pdf.         128 Chris Whidden and Norbert Zeh. A Unifying View on Approximation and FPT of Agreement Forests. In WABI09, Vol. 5724:390-402 of LNCS, Springer, 2009.   Keywords: agreement forest, approximation, explicit network, FPT, minimum number, phylogenetic network, phylogeny, reconstruction. Note: https://www.cs.dal.ca/sites/default/files/technical_reports/CS-2009-02.pdf.         Toggle abstract "We provide a unifying view on the structure of maximum (acyclic) agreement forests of rooted and unrooted phylogenies. This enables us to obtain linear- or O(n log n)-time 3-approximation and improved fixed-parameter algorithms for the subtree prune and regraft distance between two rooted phylogenies, the tree bisection and reconnection distance between two unrooted phylogenies, and the hybridization number of two rooted phylogenies. © 2009 Springer Berlin Heidelberg." 129 Gabriel Cardona, Francesc Rosselló and Gabriel Valiente. Tripartitions do not always discriminate phylogenetic networks. In MBIO, Vol. 211(2):356-370, 2008.   Keywords: distance between networks, phylogenetic network, phylogeny, Program Bio PhyloNetwork, tree-child network, tripartition distance. Note: http://arxiv.org/abs/0707.2376, slides available at http://www.newton.cam.ac.uk/webseminars/pg+ws/2007/plg/plgw01/0904/valiente/.         Toggle abstract "Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In a recent series of papers devoted to the study of reconstructibility of phylogenetic networks, Moret, Nakhleh, Warnow and collaborators introduced the so-called tripartition metric for phylogenetic networks. In this paper we show that, in fact, this tripartition metric does not satisfy the separation axiom of distances (zero distance means isomorphism, or, in a more relaxed version, zero distance means indistinguishability in some specific sense) in any of the subclasses of phylogenetic networks where it is claimed to do so. We also present a subclass of phylogenetic networks whose members can be singled out by means of their sets of tripartitions (or even clusters), and hence where the latter can be used to define a meaningful metric. © 2007 Elsevier Inc. All rights reserved." 130 Philippe Gambette and Daniel H. Huson. Improved Layout of Phylogenetic Networks. In TCBB, Vol. 5(3):472-479, 2008.   Keywords: abstract network, heuristic, phylogenetic network, phylogeny, Program SplitsTree, software, split network, visualization. Note: http://hal-lirmm.ccsd.cnrs.fr/lirmm-00309694/en/.         Toggle abstract "Split networks are increasingly being used in phylogenetic analysis. Usually, a simple equal-angle algorithm is used to draw such networks, producing layouts that leave much room for improvement. Addressing the problem of producing better layouts of split networks, this paper presents an algorithm for maximizing the area covered by the network, describes an extension of the equal-daylight algorithm to networks, looks into using a spring embedder, and discusses how to construct rooted split networks. © 2008 IEEE." 131 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/.         Toggle abstract "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." 132 Iyad A. Kanj, Luay Nakhleh and Ge Xia. The Compatibility of Binary Characters on Phylogenetic Networks: Complexity and Parameterized Algorithms. In ALG, Vol. 51(2):99-128, 2008.   Keywords: perfect, phylogenetic network, phylogeny. Note: http://www.cs.rice.edu/~nakhleh/Papers/algorithmica.pdf.         133 Gabriel Cardona, Francesc Rosselló and Gabriel Valiente. A Perl Package and an Alignment Tool for Phylogenetic Networks. In BMCB, Vol. 9:175, 2008.   Keywords: distance between networks, phylogenetic network, phylogeny, Program Bio PhyloNetwork, tree sibling network, tree-child network. Note: http://dx.doi.org/10.1186/1471-2105-9-175.         Toggle abstract "Background: Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of evolutionary events acting at the population level, like recombination between genes, hybridization between lineages, and lateral gene transfer. While most phylogenetics tools implement a wide range of algorithms on phylogenetic trees, there exist only a few applications to work with phylogenetic networks, none of which are open-source libraries, and they do not allow for the comparative analysis of phylogenetic networks by computing distances between them or aligning them. Results: In order to improve this situation, we have developed a Perl package that relies on the BioPerl bundle and implements many algorithms on phylogenetic networks. We have also developed a Java applet that makes use of the aforementioned Perl package and allows the user to make simple experiments with phylogenetic networks without having to develop a program or Perl script by him or herself. Conclusion: The Perl package is available as part of the BioPerl bundle, and can also be downloaded. A web-based application is also available (see availability and requirements). The Perl package includes full documentation of all its features. © 2008 Cardona et al; licensee BioMed Central Ltd." 134 Stephen J. Willson. Reconstruction of certain phylogenetic networks from the genomes at their leaves. In JTB, Vol. 252(2):185-376, 2008.   Keywords: labeling, polynomial. Note: http://www.public.iastate.edu/~swillson/ReconstructNormalHomopap6.pdf.         Toggle abstract "A network N is a rooted acyclic digraph. A base-set X for N is a subset of vertices including the root (or outgroup), all leaves, and all vertices of outdegree 1. A simple model of evolution is considered in which all characters are binary and in which back-mutations occur only at hybrid vertices. It is assumed that the genome is known for each member of the base-set X. If the network is known and is assumed to be "normal," then it is proved that the genome of every vertex is uniquely determined and can be explicitly reconstructed. Under additional hypotheses involving time-consistency and separation of the hybrid vertices, the network itself can also be reconstructed from the genomes of all members of X. An explicit polynomial-time procedure is described for performing the reconstruction. © 2008 Elsevier Ltd. All rights reserved." 135 Andreas W. M. Dress, Katharina Huber, Jacobus Koolen and Vincent Moulton. Compatible decompositions and block realizations of finite metrics. In EJC, Vol. 29(7):1617-1633, 2008.   Keywords: abstract network, block realization, from distances, phylogenetic network, phylogeny, realization, reconstruction. Note: http://www.ims.nus.edu.sg/preprints/2007-21.pdf.         Toggle abstract "Given a metric D defined on a finite set X, we define a finite collection D of metrics on X to be a compatible decomposition of D if any two distinct metrics in D are linearly independent (considered as vectors in RX × X), D = ∑d ∈ D d holds, and there exist points x, x′ ∈ X for any two distinct metrics d, d′ in D such that d (x, y) d′ (x′, y) = 0 holds for every y ∈ X. In this paper, we show that such decompositions are in one-to-one correspondence with (isomorphism classes of) block realizations of D, that is, graph realizations G of D for which G is a block graph and for which every vertex in G not labelled by X has degree at least 3 and is a cut point of G. This generalizes a fundamental result in phylogenetic combinatorics that states that a metric D defined on X can be realized by a tree if and only if there exists a compatible decomposition D of D such that all metrics d ∈ D are split metrics, and lays the foundation for a more general theory of metric decompositions that will be explored in future papers. © 2007 Elsevier Ltd. All rights reserved." 136 Tobias Kloepper and Daniel H. Huson. Drawing explicit phylogenetic networks and their integration into SplitsTree. In BMCEB, Vol. 8(22), 2008.   Keywords: explicit network, phylogenetic network, phylogeny, Program SplitsTree, software, split network, visualization. Note: http://dx.doi.org/10.1186/1471-2148-8-22.         Toggle abstract "Background. SplitsTree provides a framework for the calculation of phylogenetic trees and networks. It contains a wide variety of methods for the import/export, calculation and visualization of phylogenetic information. The software is developed in Java and implements a command line tool as well as a graphical user interface. Results. In this article, we present solutions to two important problems in the field of phylogenetic networks. The first problem is the visualization of explicit phylogenetic networks. To solve this, we present a modified version of the equal angle algorithm that naturally integrates reticulations into the layout process and thus leads to an appealing visualization of these networks. The second problem is the availability of explicit phylogenetic network methods for the general user. To advance the usage of explicit phylogenetic networks by biologists further, we present an extension to the SplitsTree framework that integrates these networks. By addressing these two problems, SplitsTree is among the first programs that incorporates implicit and explicit network methods together with standard phylogenetic tree methods in a graphical user interface environment. Conclusion. In this article, we presented an extension of SplitsTree 4 that incorporates explicit phylogenetic networks. The extension provides a set of core classes to handle explicit phylogenetic networks and a visualization of these networks. © 2008 Kloepper and Huson; licensee BioMed Central Ltd." 137 Paola Bonizzoni, Gianluca Della Vedova, Riccardo Dondi and Giancarlo Mauri. The Comparison of Phylogenetic Networks: Algorithms and Complexity. In Ion Mandoiu and Alexander Zelikovsky editors, Bioinformatics Algorithms, John Wiley and Sons Ltd, 2008.   Keywords: phylogenetic network, phylogeny. Note: http://www.amazon.com/gp/reader/0470097736/.         138 Gabriel Cardona, Mercè Llabrés, Francesc Rosselló and Gabriel Valiente. A Distance Metric for a Class of Tree-Sibling Phylogenetic Networks. In BIO, Vol. 24(13):1481-1488, 2008.   Keywords: distance between networks, phylogenetic network, phylogeny, polynomial, tree sibling network. Note: http://dx.doi.org/10.1093/bioinformatics/btn231.         Toggle abstract "Motivation: The presence of reticulate evolutionary events in phylogenies turn phylogenetic trees into phylogenetic networks. These events imply in particular that there may exist multiple evolutionary paths from a non-extant species to an extant one, and this multiplicity makes the comparison of phylogenetic networks much more difficult than the comparison of phylogenetic trees. In fact, all attempts to define a sound distance measure on the class of all phylogenetic networks have failed so far. Thus, the only practical solutions have been either the use of rough estimates of similarity (based on comparison of the trees embedded in the networks), or narrowing the class of phylogenetic networks to a certain class where such a distance is known and can be efficiently computed. The first approach has the problem that one may identify two networks as equivalent, when they are not; the second one has the drawback that there may not exist algorithms to reconstruct such networks from biological sequences. Results: We present in this articlea distance measure on the class of semi-binary tree-sibling time consistent phylogenetic networks, which generalize tree-child time consistent phylogenetic networks, and thus also galled-trees. The practical interest of this distance measure is 2-fold: it can be computed in polynomial time by means of simple algorithms, and there also exist polynomial-time algorithms for reconstructing networks of this class from DNA sequence data. © 2008 The Author(s)." 139 James B. Whitfield, Sydney A. Cameron, Daniel H. Huson and Mike Steel. Filtered Z-Closure Supernetworks for Extracting and Visualizing Recurrent Signal from Incongruent Gene Trees. In Systematic Biology, Vol. 57(6):939-947, 2008.   Keywords: abstract network, from unrooted trees, phylogenetic network, phylogeny, Program SplitsTree, split, split network, supernetwork. Note: http://www.life.uiuc.edu/scameron/pdfs/Filtered%20Z-closure%20SystBiol.pdf.         140 Simone Linz. Reticulation in evolution. PhD thesis, Heinrich-Heine-University, Düsseldorf, Germany, 2008.   Keywords: agreement forest, FPT, from rooted trees, lateral gene transfer, phylogenetic network, phylogeny, SPR distance, statistical model. Note: http://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=8505.         141 Jesper Jansson and Wing-Kin Sung. The Maximum Agreement of Two Nested Phylogenetic Networks. In Oleg N. Terikhovsky and William N. Burton editors, New Topics in Theoretical Computer Science, Pages 119-141, Nova Publishers, 2008.   Keywords: dynamic programming, MASN, nested network, phylogenetic network, phylogeny, polynomial. Note: http://www.df.lth.se/~jj/Publications/nested12_NTTCS2008_corrected.pdf.         142 Tobias Kloepper. Algorithms for the Calculation and Visualisation of Phylogenetic Networks. PhD thesis, Eberhard-Karls-Universität Tübingen, Germany, 2008.   Keywords: from rooted trees, from sequences, from unrooted trees, galled network, phylogenetic network, phylogeny, Program SplitsTree, reconstruction, split network, visualization. Note: https://publikationen.uni-tuebingen.de/xmlui/handle/10900/49159.         143 Cuong Than, Derek Ruths and Luay Nakhleh. PhyloNet: A Software Package for Analyzing and Reconstructing Reticulate Evolutionary Relationships. In BMCB, Vol. 9(322), 2008.   Keywords: Program PhyloNet, software. Note: http://dx.doi.org/10.1186/1471-2105-9-322.         Toggle abstract "Background: Phylogenies, i.e., the evolutionary histories of groups of taxa, play a major role in representing the interrelationships among biological entities. Many software tools for reconstructing and evaluating such phylogenies have been proposed, almost all of which assume the underlying evolutionary history to be a tree. While trees give a satisfactory first-order approximation for many families of organisms, other families exhibit evolutionary mechanisms that cannot be represented by trees. Processes such as horizontal gene transfer (HGT), hybrid speciation, and interspecific recombination, collectively referred to as reticulate evolutionary events, result in networks, rather than trees, of relationships. Various software tools have been recently developed to analyze reticulate evolutionary relationships, which include SplitsTree4, LatTrans, EEEP, HorizStory, and T-REX. Results: In this paper, we report on the PhyloNet software package, which is a suite of tools for analyzing reticulate evolutionary relationships, or evolutionary networks, which are rooted, directed, acyclic graphs, leaf-labeled by a set of taxa. These tools can be classified into four categories: (1) evolutionary network representation: reading/writing evolutionary networks in a newly devised compact form; (2) evolutionary network characterization: analyzing evolutionary networks in terms of three basic building blocks - trees, clusters, and tripartitions; (3) evolutionary network comparison: comparing two evolutionary networks in terms of topological dissimilarities, as well as fitness to sequence evolution under a maximum parsimony criterion; and (4) evolutionary network reconstruction: reconstructing an evolutionary network from a species tree and a set of gene trees. Conclusion: The software package, PhyloNet, offers an array of utilities to allow for efficient and accurate analysis of evolutionary networks. The software package will help significantly in analyzing large data sets, as well as in studying the performance of evolutionary network reconstruction methods. Further, the software package supports the proposed eNewick format for compact representation of evolutionary networks, a feature that allows for efficient interoperability of evolutionary network software tools. Currently, all utilities in PhyloNet are invoked on the command line. © 2008 Than et al; licensee BioMed Central Ltd." 144 Iyad A. Kanj, Luay Nakhleh, Cuong Than and Ge Xia. Seeing the Trees and Their Branches in the Network is Hard. In TCS, Vol. 401:153-164, 2008.   Keywords: evaluation, from network, from rooted trees, NP complete, phylogenetic network, phylogeny, tree containment. Note: http://www.cs.rice.edu/~nakhleh/Papers/tcs08.pdf.         145 Barbara R. Holland, Steffi Benthin, Peter J. Lockhart, Vincent Moulton and Katharina Huber. Using supernetworks to distinguish hybridization from lineage-sorting. In BMCEB, Vol. 8(202), 2008.   Keywords: explicit network, from unrooted trees, hybridization, lineage sorting, phylogenetic network, phylogeny, reconstruction, supernetwork. Note: http://dx.doi.org/10.1186/1471-2148-8-202.         Toggle abstract "Background. A simple and widely used approach for detecting hybridization in phylogenies is to reconstruct gene trees from independent gene loci, and to look for gene tree incongruence. However, this approach may be confounded by factors such as poor taxon-sampling and/or incomplete lineage-sorting. Results. Using coalescent simulations, we investigated the potential of supernetwork methods to differentiate between gene tree incongruence arising from taxon sampling and incomplete lineage-sorting as opposed to hybridization. For few hybridization events, a large number of independent loci, and well-sampled taxa across these loci, we found that it was possible to distinguish incomplete lineage-sorting from hybridization using the filtered Z-closure and Q-imputation supernetwork methods. Moreover, we found that the choice of supernetwork method was less important than the choice of filtering, and that count-based filtering was the most effective filtering technique. Conclusion. Filtered supernetworks provide a tool for detecting and identifying hybridization events in phylogenies, a tool that should become increasingly useful in light of current genome sequencing initiatives and the ease with which large numbers of independent gene loci can be determined using new generation sequencing technologies. © 2008 Holland et al; licensee BioMed Central Ltd." 146 Wing-Kin Sung. Constructing a Galled Phylogenetic Network. In Ming-Yang Kao editor, Encyclopedia of Algorithms, Springer Reference, 2008.   Keywords: explicit network, from triplets, galled tree, phylogenetic network, phylogeny, reconstruction. Note: http://dx.doi.org/10.1007/978-0-387-30162-4_92.         147 Miguel Arenas, Gabriel Valiente and David Posada. Characterization of reticulate networks based on the coalescent with recombination. In MBE, Vol. 25(12):2517-2520, 2008.   Keywords: coalescent, evaluation, explicit network, galled tree, phylogenetic network, phylogeny, Program Recodon, regular network, simulation, tree sibling network, tree-child network. Note: http://dx.doi.org/10.1093/molbev/msn219.         Toggle abstract "Phylogenetic networks aim to represent the evolutionary history of taxa. Within these, reticulate networks are explicitly able to accommodate evolutionary events like recombination, hybridization, or lateral gene transfer. Although several metrics exist to compare phylogenetic networks, they make several assumptions regarding the nature of the networks that are not likely to be fulfilled by the evolutionary process. In order to characterize the potential disagreement between the algorithms and the biology, we have used the coalescent with recombination to build the type of networks produced by reticulate evolution and classified them as regular, tree sibling, tree child, or galled trees. We show that, as expected, the complexity of these reticulate networks is a function of the population recombination rate. At small recombination rates, most of the networks produced are already more complex than regular or tree sibling networks, whereas with moderate and large recombination rates, no network fit into any of the standard classes. We conclude that new metrics still need to be devised in order to properly compare two phylogenetic networks that have arisen from reticulating evolutionary process. © 2008 The Authors." 148 Gabriel Cardona, Francesc Rosselló and Gabriel Valiente. Extended Newick: It is Time for a Standard Representation. In BMCB, Vol. 9:532, 2008.   Keywords: evaluation, explicit network, phylogenetic network, Program Bio PhyloNetwork, Program Dendroscope, Program NetGen, Program PhyloNet, Program SplitsTree, Program TCS, visualization. Note: http://bioinfo.uib.es/media/uploaded/bmc-2008-enewick-sub.pdf.         149 Miguel Arenas and David Posada. Recodon: Coalescent simulation of coding DNA sequences with recombination, migration and demography. In BMCB, Vol. 8(458), 2008.   Keywords: coalescent, generation, Program Recodon, software. Note: http://dx.doi.org/10.1186/1471-2105-8-458.         Toggle abstract "Background: Coalescent simulations have proven very useful in many population genetics studies. In order to arrive to meaningful conclusions, it is important that these simulations resemble the process of molecular evolution as much as possible. To date, no single coalescent program is able to simulate codon sequences sampled from populations with recombination, migration and growth. Results: We introduce a new coalescent program, called Recodon, which is able to simulate samples of coding DNA sequences under complex scenarios in which several evolutionary forces can interact simultaneously (namely, recombination, migration and demography). The basic codon model implemented is an extension to the general time-reversible model of nucleotide substitution with a proportion of invariable sites and among-site rate variation. In addition, the program implements non-reversible processes and mixtures of different codon models. Conclusion: Recodon is a flexible tool for the simulation of coding DNA sequences under realistic evolutionary models. These simulations can be used to build parameter distributions for testing evolutionary hypotheses using experimental data. Recodon is written in C, can run in parallel, and is freely available from http://darwin.uvigo.es/. © 2007 Arenas and Posada; licensee BioMed Central Ltd." 150 Anthony Labarre. Combinatorial aspects of genome rearrangements and haplotype networks. PhD thesis, Université Libre de Bruxelles, Belgium, 2008.   Keywords: abstract network, from unrooted trees, haplotype network, phylogenetic network, phylogeny, reconstruction. Note: http://homepages.ulb.ac.be/~alabarre/publications/phd-thesis.pdf.         151 Jaroslaw Byrka. Randomized Approximation Algorithms: Facility Location, Phylogenetic Networks, Nash Equilibria. PhD thesis, Eindhoven University of Technology, Netherlands, 2008.   Note: http://disopt.epfl.ch/webdav/site/disopt/users/191068/public/phdthesis_byrka.pdf.         152 Tal Dagan, Yael Artzy-Randrup and William Martin. Modular networks and cumulative impact of lateral transfer in prokaryote genome evolution. In PNAS, Vol. 105:10039-10044, 2008.   Keywords: from sequences, from species tree, heuristic, lateral gene transfer, phylogenetic network, phylogeny, reconstruction. Note: http://dx.doi.org/10.1073/pnas.0800679105.         Toggle abstract "Lateral gene transfer is an important mechanism of natural variation among prokaryotes, but the significance of its quantitative contribution to genome evolution is debated. Here, we report networks that capture both vertical and lateral components of evolutionary history among 539,723 genes distributed across 181 sequenced prokaryotic genomes. Partitioning of these networks by an eigenspectrum analysis identifies community structure in prokaryotic gene-sharing networks, the modules of which do not correspond to a strictly hierarchical prokaryotic classification. Our results indicate that, on average, at least 81 ± 15% of the genes in each genome studied were involved in lateral gene transfer at some point in their history, even though they can be vertically inherited after acquisition, uncovering a substantial cumulative effect of lateral gene transfer on longer evolutionary time scales. © 2008 by The National Academy of Sciences of the USA." 153 Olivier Gauthier and François-Joseph Lapointe. Seeing the Trees for the Network: Consensus, Information Content, and Superphylogenies. In Systematic Biology, Vol. 56(2):345-355, 2007.   Keywords: consensus. Note: http://dx.doi.org/10.1080/10635150701286549.         Toggle abstract [No abstract available] 154 Daniel H. Huson and Tobias Kloepper. Beyond Galled Trees - Decomposition and Computation of Galled Networks. In RECOMB07, Vol. 4453:211-225 of LNCS, springer, 2007.   Keywords: FPT, from splits, from trees, galled network, phylogenetic network, phylogeny, Program SplitsTree, reconstruction. Note: http://dx.doi.org/10.1007/978-3-540-71681-5_15, errata..         155 Guohua Jin, Luay Nakhleh, Sagi Snir and Tamir Tuller. Efficient Parsimony-based Methods for Phylogenetic Network Reconstruction. In ECCB06, Vol. 23(2):e123-e128 of BIO, 2007.   Keywords: parsimony, phylogenetic network, phylogeny, Program Nepal, reconstruction. Note: http://www.cs.rice.edu/~nakhleh/Papers/eccb06.pdf.         156 Guohua Jin, Luay Nakhleh, Sagi Snir and Tamir Tuller. A New Linear-time Heuristic Algorithm for Computing the Parsimony Score of Phylogenetic Networks: Theoretical Bounds and Empirical Performance. In ISBRA07, Vol. 4463:61-72 of LNCS, springer, 2007.   Keywords: approximation, heuristic, parsimony, phylogenetic network, phylogeny, Program Nepal. Note: http://www.cs.rice.edu/~nakhleh/Papers/isbra07.pdf.         157 Iyad A. Kanj, Luay Nakhleh, Cuong Than and Ge Xia. Seeing the Trees and Their Branches in the Network is Hard. In Proceedings of the Tenth Italian Conference on Theoretical Computer Science (ICTCS'07), 2007.   Keywords: evaluation, from network, from rooted trees, NP complete, phylogenetic network, phylogeny, tree containment. Note: http://www.cs.rice.edu/~nakhleh/Papers/ictcs07.pdf.         158 Yufeng Wu and Dan Gusfield. A new recombination lower bound and the minimum perfect phylogenetic forest problem. In COCOON07, Vol. 4598:16-26 of LNCS, springer, 2007.   Keywords: perfect, phylogenetic network, phylogeny. Note: http://dx.doi.org/10.1007/978-3-540-73545-8_5.         159 Patricia Buendia and Giri Narasimhan. Searching for Recombinant Donors in a Phylogenetic Network of Serial Samples. In ISBRA07, Vol. 4463:109-120 of LNCS, springer, 2007.   Keywords: evaluation, phylogenetic network, phylogeny, recombination, recombination detection. Note: http://dx.doi.org/10.1007/978-3-540-72031-7_10.         160 D. S. Rao, G. N. Kumar, Dheeresh K. Mallick and Prasanta K. Jana. Parallel Construction of Conflict Graph for Phylogenetic Network Problem. In Pattern Recognition and Machine Intelligence (PReMI'07), Vol. 4815:398-405 of LNCS, springer, 2007.   Note: http://dx.doi.org/10.1007/978-3-540-77046-6_49.         161 Galina Glazko, Vladimir Makarenkov, Jing Liu and Arcady Mushegian. Evolutionary history of bacteriophages with double-stranded DNA genomes. In Biology Direct, Vol. 2(36), 2007.   Keywords: explicit network, from sequences, phylogenetic network, phylogeny, Program T REX. Note: http://dx.doi.org/10.1186/1745-6150-2-36.         Toggle abstract "Background: Reconstruction of evolutionary history of bacteriophages is a difficult problem because of fast sequence drift and lack of omnipresent genes in phage genomes. Moreover, losses and recombinational exchanges of genes are so pervasive in phages that the plausibility of phylogenetic inference in phage kingdom has been questioned. Results: We compiled the profiles of presence and absence of 803 orthologous genes in 158 completely sequenced phages with double-stranded DNA genomes and used these gene content vectors to infer the evolutionary history of phages. There were 18 well-supported clades, mostly corresponding to accepted genera, but in some cases appearing to define new taxonomic groups. Conflicts between this phylogeny and trees constructed from sequence alignments of phage proteins were exploited to infer 294 specific acts of intergenome gene transfer. Conclusion: A notoriously reticulate evolutionary history of fast-evolving phages can be reconstructed in considerable detail by quantitative comparative genomics. © 2007 Glazko et al; licensee BioMed Central Ltd." 162 Cuong Than, Derek Ruths, Hideki Innan and Luay Nakhleh. Confounding Factors in HGT Detection: Statistical Error, Coalescent Effects, and Multiple Solutions. In JCB, Vol. 14(4):517-535, 2007.   Keywords: counting, explicit network, from rooted trees, from species tree, lateral gene transfer, phylogenetic network, phylogeny, Program LatTrans, Program PhyloNet. Note: http://www.cs.rice.edu/~nakhleh/Papers/recombcg06-jcb.pdf.         163 Hadas Birin, Zohar Gal-Or, Isaac Elias and Tamir Tuller. Inferring Models of Rearrangements, Recombinations, and Horizontal Transfers by the Minimum Evolution Criterion. In WABI07, Vol. 4645:111-123 of LNCS, springer, 2007.   Keywords: explicit network, from sequences, phylogenetic network, phylogeny, reconstruction. Note: http://safrabio.cs.tau.ac.il/download/Papers/Birin_et_al.pdf.         164 Barbara R. Holland, Lars S. Jermiin and Vincent Moulton. Improved Consensus Network Techniques for Genome-Scale Phylogeny. In Proceedings of the SMBE Tri-National Young Investigators' Workshop 2005 (SMBE'05), Vol. 23(5):848-855 of MBE, 2006.   Keywords: consensus. Note: http://dx.doi.org/10.1093/molbev/msj061.         165 Daniel H. Huson, Mike Steel and James B. Whitfield. Reducing Distortion in Phylogenetic Networks. In WABI06, Vol. 4175:150-161 of LNCS, springer, 2006.   Keywords: phylogenetic network, reconstruction. Note: http://www.math.canterbury.ac.nz/~m.steel/research/Non_UC/files/distortion.pdf.         166 Jesper Jansson and Wing-Kin Sung. Inferring a level-1 phylogenetic network from a dense set of rooted triplets. In TCS, Vol. 363(1):60-68, 2006. 1 comment   Keywords: explicit network, from triplets, galled tree, level k phylogenetic network, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://www.df.lth.se/~jj/Publications/ipnrt8_TCS2006.pdf.         Toggle abstract "We consider the following problem: Given a set T of rooted triplets with leaf set L, determine whether there exists a phylogenetic network consistent with T, and if so, construct one. We show that if no restrictions are placed on the hybrid nodes in the solution, the problem is trivially solved in polynomial time by a simple sorting network-based construction. For the more interesting (and biologically more motivated) case where the solution is required to be a level-1 phylogenetic network, we present an algorithm solving the problem in O (| T |2) time when T is dense, i.e., when T contains at least one rooted triplet for each cardinality three subset of L. We also give an O (| T |5 / 3)-time algorithm for finding the set of all phylogenetic networks having a single hybrid node attached to exactly one leaf (and having no other hybrid nodes) that are consistent with a given dense set of rooted triplets. © 2006 Elsevier B.V. All rights reserved." 167 Vladimir Makarenkov, Dmytro Kevorkov and Pierre Legendre. Phylogenetic Network Construction Approaches. In Applied Mycology and Biotechnology, Vol. 6:61-97, 2006.   Keywords: from distances, hybridization, lateral gene transfer, median network, NeighborNet, netting, Program Arlequin, Program Network, Program Pyramids, Program Reticlad, Program SplitsTree, Program T REX, Program TCS, Program WeakHierarchies, pyramid, reticulogram, split, split decomposition, split network, survey, weak hierarchy. Note: http://www.labunix.uqam.ca/~makarenv/makarenv/MKL_article.pdf.         168 Cuong Than, Derek Ruths, Hideki Innan and Luay Nakhleh. Identifiability Issues in Phylogeny-Based Detection of Horizontal Gene Transfer. In Proceedings of the Fourth RECOMB Comparative Genomics Satellite Workshop (RECOMB-CG'06), Vol. 4205:215-229 of LNCS, springer, 2006. 1 comment   Keywords: explicit network, from rooted trees, from species tree, lateral gene transfer, phylogenetic network, phylogeny, Program LatTrans, Program PhyloNet. Note: http://www.cs.rice.edu/~nakhleh/Papers/recombcg06-final.pdf.         169 Juan Diego Trujillo and Carlos Cotta. An Evolutionary Approach to the Inference of Phylogenetic Networks. In Proceedings of the ninth Conference on Parallel Problem Solving from Nature (PPSN'IX), Vol. 4193:332-341 of LNCS, springer, 2006.   Note: http://www.lcc.uma.es/~ccottap/papers/trujillo06ppsn.pdf.         170 Guillaume Bourque and Louxin Zhang. Models and Methods in Comparative Genomics. In Chau-Wen Tseng editor, Advances in Computers, Special Volume: Computational Biology, Vol. 68, Elsevier, 2006.   Keywords: from distances, from rooted trees, from sequences, galled tree, phylogenetic network, phylogeny, survey. Note: http://www.math.nus.edu.sg/~matzlx/papers/CompGen_ZLX.pdf.         171 Ho-Leung Chan, Jesper Jansson, Tak-Wah Lam and Siu-Ming Yiu. Reconstructing an Ultrametric Galled Phylogenetic Network from a Distance Matrix. In MFCS05, Vol. 3618:224-235 of LNCS, springer, 2005.   Keywords: from distances, galled tree, phylogenetic network, phylogeny, reconstruction. Note: http://dx.doi.org/10.1007/11549345_20.         172 Dan Gusfield and Vikas Bansal. A Fundamental Decomposition Theory for Phylogenetic Networks and Incompatible Characters. In RECOMB05, Vol. 3500:217-232 of LNCS, springer, 2005.   Keywords: explicit network, from sequences, phylogenetic network, phylogeny, polynomial, recombination, reconstruction. Note: http://wwwcsif.cs.ucdavis.edu/~gusfield/gusfieldrecomb.pdf.         173 Trinh N. D. Huynh, Jesper Jansson, Nguyen Bao Nguyen and Wing-Kin Sung. Constructing a Smallest Refining Galled Phylogenetic Network. In RECOMB05, Vol. 3500:265-280 of LNCS, springer, 2005.   Keywords: from rooted trees, galled tree, NP complete, phylogenetic network, phylogeny, polynomial, Program SPNet, reconstruction. Note: http://www.df.lth.se/~jj/Publications/refining_gn3_RECOMB2005.pdf.         174 Daniel H. Huson, Tobias Kloepper, Peter J. Lockhart and Mike Steel. Reconstruction of Reticulate Networks from Gene Trees. In RECOMB05, Vol. 3500:233-249 of LNCS, springer, 2005.   Keywords: from rooted trees, from splits, phylogenetic network, phylogeny, reconstruction, split, split network, visualization. Note: http://dx.doi.org/10.1007/11415770_18.         175 Daniel H. Huson and Tobias Kloepper. Computing recombination networks from binary sequences. In ECCB05, Vol. 21(suppl. 2):ii159-ii165 of BIO, 2005.   Keywords: from sequences, phylogenetic network, phylogeny, recombination. Note: http://dx.doi.org/10.1093/bioinformatics/bti1126.         Toggle abstract "Motivation:Phylogenetic networks are becoming an important tool in molecular evolution, as the evolutionary role of reticulate events, such as hybridization, horizontal gene transfer and recombination, is becoming more evident, and as the available data is dramatically increasing in quantity and quality. Results: This paper addresses the problem of computing a most parsimonious recombination network for an alignment of binary sequences that are assumed to have arisen under the 'infinite sites' model of evolution with recombinations. Using the concept of a splits network as the underlying datastructure, this paper shows how a recent method designed for the computation of hybridization networks can be extended to also compute recombination networks. A robust implementation of the approach is provided and is illustrated using a number of real biological datasets. © The Author 2005. Published by Oxford University Press. All rights reserved." 176 Jesper Jansson and Wing-Kin Sung. The Maximum Agreement of Two Nested Phylogenetic Networks. In ISAAC04, Vol. 3341:581-593 of LNCS, springer, 2005.   Keywords: dynamic programming, MASN, nested network, NP complete, phylogenetic network, phylogeny, polynomial. Note: http://www.df.lth.se/~jj/Publications/nested7_ISAAC2004.pdf.         177 Jesper Jansson, Nguyen Bao Nguyen and Wing-Kin Sung. Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network. In SODA05, Pages 349-358, 2005. 1 comment   Keywords: approximation, explicit network, from triplets, galled tree, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://portal.acm.org/citation.cfm?id=1070481.         178 Rune Lyngsø, Yun S. Song and Jotun Hein. Minimum Recombination Histories by Branch and Bound. In WABI05, Vol. 3692:239-250 of LNCS, springer, 2005.   Keywords: ARG, branch and bound, from sequences, minimum number, Program Beagle, recombination, reconstruction, software. Note: http://www.cs.ucdavis.edu/~yssong/Pub/WABI05-239.pdf.         179 Luay Nakhleh and Li-San Wang. Phylogenetic Networks, Trees, and Clusters. In IWBRA05, Vol. 3515:919-926 of LNCS, springer, 2005.   Keywords: cluster containment, evaluation, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, tree containment, tree-child network. Note: http://www.cs.rice.edu/~nakhleh/Papers/NakhlehWang.pdf.         180 Luay Nakhleh and Li-San Wang. Phylogenetic Networks: Properties and Relationship to Trees and Clusters. In TCSB2, Vol. 3680:82-99 of LNCS, springer, 2005.   Keywords: cluster containment, evaluation, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, tree containment, tree-child network. Note: http://www.cs.rice.edu/~nakhleh/Papers/LNCS_TCSB05.pdf.         181 Luay Nakhleh, Guohua Jin, Fengmei Zhao and John Mellor-Crummey. Reconstructing Phylogenetic Networks Using Maximum Parsimony. In CSB05, Pages 93-102, 2005.   Keywords: parsimony, phylogenetic network, phylogeny, Program Nepal, reconstruction. Note: http://www.cs.rice.edu/~nakhleh/Papers/CSB05.pdf.         182 Cam Thach Nguyen, Nguyen Bao Nguyen and Wing-Kin Sung. Fast Algorithms for computing the Tripartition-based Distance between Phylogenetic Networks. In ISAAC05, Pages 402-411, 2005.   Keywords: distance between networks, phylogenetic network, phylogeny, tripartition distance. Note: http://www.cs.washington.edu/homes/ncthach/Papers/ISAAC2006.pdf.         183 Luay Nakhleh, Derek Ruths and Li-San Wang. RIATA-HGT: A Fast and Accurate Heuristic for Reconstructing Horizontal Gene Transfer. In COCOON05, Vol. 3595:84-93 of LNCS, springer, 2005.   Keywords: from rooted trees, heuristic, lateral gene transfer, phylogenetic network, phylogeny, Program PhyloNet. Note: http://www.cs.rice.edu/~nakhleh/Papers/COCOON05.pdf.         184 Yun S. Song, Yufeng Wu and Dan Gusfield. Efficient computation of close lower and upper bounds on the minimum number of recombinations in biological sequence evolution. In ISMB05, Vol. 21:i413-i422 of BIO, 2005.   Keywords: integer linear programming, minimum number, Program HapBound, Program SHRUB, recombination. Note: http://dx.doi.org/10.1093/bioinformatics/bti1033.         Toggle abstract "Motivation: We are interested in studying the evolution of DNA single nucleotide polymorphism sequences which have undergone (meiotic) recombination. For a given set of sequences, computing the minimum number of recombinations needed to explain the sequences (with one mutation per site) is a standard question of interest, but it has been shown to be NP-hard, and previous algorithms that compute it exactly work either only on very small datasets or on problems with special structure. Results: In this paper, we present efficient, practical methods for computing both upper and lower bounds on the minimum number of needed recombinations, and for constructing evolutionary histories that explain the input sequences. We study in detail the efficiency and accuracy of these algorithms on both simulated and real data sets. The algorithms produce very close upper and lower bounds, which match exactly in a surprisingly wide range of data. Thus, with the use of new, very effective lower bounding methods and an efficient algorithm for computing upper bounds, this approach allows the efficient, exact computation of the minimum number of needed recombinations, with high frequency in a large range of data. When upper and lower bounds match, evolutionary histories found by our algorithm correspond to the most parsimonious histories. © The Author 2005. Published by Oxford University Press. All rights reserved." 185 Bhaskar DasGupta, Sergio Ferrarini, Uthra Gopalakrishnan and Nisha Raj Paryani. Inapproximability results for the lateral gene transfer problem. In Proceedings of the Ninth Italian Conference on Theoretical Computer Science (ICTCS'05), Pages 182-195, springer, 2005.   Keywords: approximation, from rooted trees, from species tree, inapproximability, lateral gene transfer, parsimony, phylogenetic network, phylogeny. Note: http://www.cs.uic.edu/~dasgupta/resume/publ/papers/ictcs-final.pdf.         186 Insa Cassens, Patrick Mardulyn and Michel C. Milinkovitch. Evaluating Intraspecific Network Construction Methods Using Simulated Sequence Data: Do Existing Algorithms Outperform the Global Maximum Parsimony Approach? In Systematic Biology, Vol. 54(3):363-372, 2005.   Keywords: abstract network, evaluation, from unrooted trees, haplotype network, parsimony, phylogenetic network, phylogeny, Program Arlequin, Program CombineTrees, Program Network, Program TCS, reconstruction, software. Note: http://www.lanevol.org/LANE/publications_files/Cassens_etal_SystBio_2005.pdf.         187 David Bryant. Extending tree models to splits networks. In Lior Pachter and Bernd Sturmfels editors, Algebraic Statistics for Computational Biology, Pages 322-334, Cambridge University Press, 2005.   Keywords: abstract network, from splits, likelihood, phylogenetic network, phylogeny, split, split network, statistical model. Note: http://www.math.auckland.ac.nz/~bryant/Papers/05ascbChapter.pdf.         188 Wei-Shun Su, Tso-Ching Lee and Yaw-Ling Lin. Efficient Algorithms for Constructing Phylogenetic Networks with Restricted Recombinations. In NCS05, Pages 1-7, 2005.   Keywords: explicit network, from sequences, phylogenetic network, phylogeny, reconstruction. Note: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.168.6735.         189 Charles Choy, Jesper Jansson, Kunihiko Sadakane and Wing-Kin Sung. Computing the maximum agreement of phylogenetic networks. In Proceedings of Computing: the Tenth Australasian Theory Symposium (CATS'04), Vol. 91:134-147 of Electronic Notes in Theoretical Computer Science, 2004.   Keywords: dynamic programming, FPT, level k phylogenetic network, MASN, NP complete, phylogenetic network, phylogeny. Note: http://www.df.lth.se/~jj/Publications/masn6_CATS2004.pdf.         Toggle abstract "We introduce the maximum agreement phylogenetic subnetwork problem (MASN) of finding a branching structure shared by a set of phylogenetic networks. We prove that the problem is NP-hard even if restricted to three phylogenetic networks and give an O(n2)-time algorithm for the special case of two level-1 phylogenetic networks, where n is the number of leaves in the input networks and where N is called a level-f phylogenetic network if every biconnected component in the underlying undirected graph contains at most f nodes having indegree 2 in N. Our algorithm can be extended to yield a polynomial-time algorithm for two level-f phylogenetic networks N 1,N2 for any f which is upper-bounded by a constant; more precisely, its running time is O(|V(N1)|·|V(N 2)|·4f), where V(Ni) denotes the set of nodes of Ni. © 2004 Published by Elsevier B.V." 190 Luay Nakhleh, Tandy Warnow and C. Randal Linder. Reconstructing reticulate evolution in species - theory and practice. In RECOMB04, Pages 337-346, 2004.   Keywords: from rooted trees, galled tree, phylogenetic network, phylogeny, polynomial, Program SPNet, reconstruction, software. Note: http://www.cs.rice.edu/~nakhleh/Papers/144-nakhleh.pdf.         191 Mike Hallett, Jens Lagergren and Ali Tofigh. Simultaneous Identification of Duplications and Lateral Transfers. In RECOMB04, Pages 347-356, 2004.   Keywords: duplication, explicit network, FPT, from rooted trees, from species tree, lateral gene transfer, loss, NP complete, parsimony, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://www.nada.kth.se/~jensl/p164-hallett.pdf.         192 Pawel Górecki. Reconciliation problems for duplication, loss and horizontal gene transfer. In RECOMB04, Pages 316-325, 2004.   Keywords: duplication, explicit network, from rooted trees, from species tree, lateral gene transfer, loss, NP complete, parsimony, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://ai.stanford.edu/~serafim/CS374_2004/Papers/Gorecki_Reconciliation.pdf.         193 Louigi Addario-Berry, Mike Hallett and Jens Lagergren. Towards Identifying Lateral Gene Transfer Events. In PSB03, 2003.   Keywords: evaluation, from rooted trees, from species tree, lateral gene transfer, phylogenetic network, phylogeny, Program LatTrans, reconstruction. Note: http://www.nada.kth.se/~jensl/AHLPsb.pdf.         194 Dan Gusfield, Satish Eddhu and Charles Langley. Efficient reconstruction of phylogenetic networks with constrained recombination. In CSB03, Pages 363-374, 2003.   Keywords: explicit network, from sequences, galled tree, phylogenetic network, phylogeny, recombination, reconstruction. Note: http://wwwcsif.cs.ucdavis.edu/~gusfield/ieeefinal.pdf.         195 Luay Nakhleh, Jerry Sun, Tandy Warnow, C. Randal Linder, Bernard M. E. Moret and Anna Tholse. Towards the Development of Computational Tools for Evaluating Phylogenetic Network Reconstruction Methods. In PSB03, 2003.   Keywords: distance between networks, evaluation, phylogenetic network, phylogeny, polynomial, tripartition distance. Note: http://www.cs.rice.edu/~nakhleh/Papers/psb03.pdf.         196 Yun S. Song and Jotun Hein. Parsimonious reconstruction of sequence evolution and haplotype blocks: Finding the minimum number of recombination events. In WABI03, Vol. 2812:287-302 of LNCS, springer, 2003.   Keywords: minimum number, recombination. Note: http://www.cs.ucdavis.edu/~yssong/Pub/SH-WABI03.pdf.         197 Daniel H. Huson. What If I Don't Have a Tree? Split Decomposition and Related Models. In Current Protocols in Bioinformatics, Vol. Unit 6.7, 2003.   Keywords: abstract network, phylogenetic network, Program SplitsTree, software, split decomposition, split network. Note: http://dx.doi.org/10.1002/0471250953.bi0607s01.         198 David Bryant and Vincent Moulton. Neighbor-Net: An Agglomerative Method for the Construction of Planar Phylogenetic Networks. In WABI02, Vol. 2452:375-391 of LNCS, springer, 2002.   Keywords: abstract network, circular split system, from distances, NeighborNet, phylogenetic network, phylogeny, Program SplitsTree, reconstruction, split network. Note: http://dx.doi.org/10.1007/3-540-45784-4_28.         199 Dan Gusfield. Haplotyping as Perfect Phylogeny: Conceptual Framework and Efficient Solutions. In RECOMB02, 2002.   Keywords: haplotyping, perfect, phylogeny. Note: http://wwwcsif.cs.ucdavis.edu/~gusfield/acmhapre.pdf .         200 Mike Hallett and Jens Lagergren. Efficient algorithms for lateral gene transfers problems. In RECOMB01, Pages 141-148, 2001.   Keywords: from rooted trees, lateral gene transfer, NP complete, phylogeny, polynomial, Program McKiTscH, reconstruction. Note: http://dx.doi.org/10.1145/369133.369188.         201 David Posada and Keith A. Crandall. Intraspecific gene genealogies: trees grafting into networks. In TEE, Vol. 16(1):37-45, 2001.   Keywords: likelihood, median network, netting, parsimony, phylogenetic network, phylogeny, Program Arlequin, Program SplitsTree, Program T REX, Program TCS, pyramid, reticulogram, split decomposition, statistical parsimony, survey. Note: http://darwin.uvigo.es/download/papers/09.networks01.pdf.         202 Lusheng Wang, Kaizhong Zhang and Louxin Zhang. Perfect phylogenetic networks with recombination. In SAC01, Pages 46-50, 2001.   Keywords: from sequences, galled tree, NP complete, perfect, phylogenetic network, phylogeny, polynomial, recombination, reconstruction. Note: http://dx.doi.org/10.1145/372202.372271.         203 Bin Ma, Lusheng Wang and Ming Li. Fixed topology alignment with recombination. In DAM, Vol. 104:281-300, 2000.   Keywords: approximation, explicit network, from network,