
Sarah Bastkowski,
Daniel Mapleson,
Andreas Spillner,
Taoyang Wu,
Monika Balvociute and
Vincent Moulton. SPECTRE: a Suite of PhylogEnetiC Tools for Reticulate Evolution. In BIO, Vol. 34(6):10571058, 2018. Keywords: abstract network, NeighborNet, phylogenetic network, phylogeny, Program FlatNJ, Program QNet, Program SplitsTree, reconstruction, software, split network. Note: https://doi.org/10.1101/169177.





Guillaume Scholz. New algorithms and mathematical tools for phylogenetics beyond trees. PhD thesis, University of East Anglia, 2018. Keywords: circular split system, explicit network, explicit network, from splits, galled tree, phylogenetic network, phylogeny, polynomial, reconstruction, split network, uniqueness. Note: https://ueaeprints.uea.ac.uk/id/eprint/66952.



Andreas Gunawan,
Bhaskar DasGupta and
Louxin Zhang. A decomposition theorem and two algorithms for reticulationvisible networks. In Information and Computation, Vol. 252:161175, 2017. Keywords: cluster containment, explicit network, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, reticulationvisible network, tree containment. Note: https://www.cs.uic.edu/~dasgupta/resume/publ/papers/Infor_Comput_IC4848_final.pdf.



Philippe Gambette,
Leo van Iersel,
Mark Jones,
Manuel Lafond,
Fabio Pardi and
Celine Scornavacca. Rearrangement Moves on Rooted Phylogenetic Networks. In PLoS Computational Biology, Vol. 13(8):e1005611.121, 2017. Keywords: distance between networks, explicit network, from network, NNI distance, phylogenetic network, phylogeny, SPR distance. Note: https://halupecupem.archivesouvertes.fr/hal01572624/en/.





Monika Balvociute. Flat Embeddings of Genetic and Distance Data. PhD thesis, University of Otago, 2016. Keywords: abstract network, flat, phylogenetic network, phylogeny, planar, Program FlatNJ, Program SplitsTree, split, split network. Note: http://hdl.handle.net/10523/6286.



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):102111, 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.









Leo van Iersel,
Steven Kelk,
Nela Lekic and
Leen Stougie. Approximation algorithms for nonbinary agreement forests. In SIDMA, Vol. 28(1):4966, 2014. Keywords: agreement forest, approximation, from rooted trees, hybridization, minimum number, phylogenetic network, phylogeny, reconstruction. Note: http://arxiv.org/abs/1210.3211.
Toggle abstract
"Given two rooted phylogenetic trees on the same set of taxa X, the Maximum Agreement Forest (maf) problem asks to find a forest that is, in a certain sense, common to both trees and has a minimum number of components. The Maximum Acyclic Agreement Forest (maaf) problem has the additional restriction that the components of the forest cannot have conflicting ancestral relations in the input trees. There has been considerable interest in the special cases of these problems in which the input trees are required to be binary. However, in practice, phylogenetic trees are rarely binary, due to uncertainty about the precise order of speciation events. Here, we show that the general, nonbinary version of maf has a polynomialtime 4approximation and a fixedparameter tractable (exact) algorithm that runs in O(4opoly(n)) time, where n = X and k is the number of components of the agreement forest minus one. Moreover, we show that a capproximation algorithm for nonbinary maf and a dapproximation algorithm for the classical problem Directed Feedback Vertex Set (dfvs) can be combined to yield a d(c+3)approximation for nonbinary maaf. The algorithms for maf have been implemented and made publicly available. © 2014 Society for Industrial and Applied Mathematics."



Jesper Jansson and
Andrzej Lingas. Computing the rooted triplet distance between galled trees by counting triangles. In Journal of Discrete Algorithms, Vol. 25:6678, 2014. Keywords: distance between networks, explicit network, from network, galled network, phylogenetic network, phylogeny, polynomial, triplet distance.
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 socalled galled tree with n leaves then the rooted triplet distance can be computed in o(n2.687) time. Our upper bound is obtained by reducing the problem of computing the rooted triplet distance between two galled trees to that of counting monochromatic and almostmonochromatic triangles in an undirected, edgecolored 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 algorithmic results that may be of independent interest: (i) the number of triangles in a connected, undirected, uncolored graph with m edges can be computed in o(m1.408) time; (ii) if G is a connected, undirected, edgecolored graph with n vertices and C is a subset of the set of edge colors then the number of monochromatic triangles of G with colors in C can be computed in o(n2.687) time; and (iii) if G is a connected, undirected, edgecolored graph with n vertices and R is a binary relation on the colors that is computable in O(1) time then the number of Rchromatic triangles in G can be computed in o(n2.687) time. © 2013 Elsevier B.V. All rights reserved."





Juan Wang. A new algorithm to construct phylogenetic networks from trees. In Genetics and Molecular Research, Vol. 13(1):14561464, 2014. Keywords: explicit network, from clusters, heuristic, phylogenetic network, Program LNetwork, Program QuickCass, reconstruction. Note: http://dx.doi.org/10.4238/2014.March.6.4.
Toggle abstract
"Developing appropriate methods for constructing phylogenetic networks from tree sets is an important problem, and much research is currently being undertaken in this area. BIMLR is an algorithm that constructs phylogenetic networks from tree sets. The algorithm can construct a much simpler network than other available methods. Here, we introduce an improved version of the BIMLR algorithm, QuickCass. QuickCass changes the selection strategy of the labels of leaves below the reticulate nodes, i.e., the nodes with an indegree of at least 2 in BIMLR. We show that QuickCass can construct simpler phylogenetic networks than BIMLR. Furthermore, we show that QuickCass is a polynomialtime algorithm when the output network that is constructed by QuickCass is binary. © FUNPECRP."





Chris Whidden,
Robert G. Beiko and
Norbert Zeh. FixedParameter Algorithms for Maximum Agreement Forests. In SICOMP, Vol. 42(4):14311466, 2013. Keywords: agreement forest, explicit network, FPT, from rooted trees, hybridization, minimum number, phylogenetic network, phylogeny, Program HybridInterleave, reconstruction, SPR distance. Note: http://arxiv.org/abs/1108.2664, slides.
Toggle abstract
"We present new and improved fixedparameter algorithms for computing maximum agreement forests of pairs of rooted binary phylogenetic trees. The size of such a forest for two trees corresponds to their subtree pruneandregraft distance and, if the agreement forest is acyclic, to their hybridization number. These distance measures are essential tools for understanding reticulate evolution. Our algorithm for computing maximum acyclic agreement forests is the first depthbounded search algorithm for this problem. Our algorithms substantially outperform the best previous algorithms for these problems. © 2013 Society for Industrial and Applied Mathematics."



Stefan Grünewald,
Andreas Spillner,
Sarah Bastkowski,
Anja Bögershausen and
Vincent Moulton. SuperQ: Computing Supernetworks from Quartets. In TCBB, Vol. 10(1):151160, 2013. Keywords: abstract network, circular split system, from quartets, heuristic, phylogenetic network, phylogeny, Program QNet, Program SplitsTree, Program SuperQ, software, split network.
Toggle abstract
"Supertrees are a commonly used tool in phylogenetics to summarize collections of partial phylogenetic trees. As a generalization of supertrees, phylogenetic supernetworks allow, in addition, the visual representation of conflict between the trees that is not possible to observe with a single tree. Here, we introduce SuperQ, a new method for constructing such supernetworks (SuperQ is freely available at >www.uea.ac.uk/computing/superq.). It works by first breaking the input trees into quartet trees, and then stitching these together to form a special kind of phylogenetic network, called a split network. This stitching process is performed using an adaptation of the QNet method for split network reconstruction employing a novel approach to use the branch lengths from the input trees to estimate the branch lengths in the resulting network. Compared with previous supernetwork methods, SuperQ has the advantage of producing a planar network. We compare the performance of SuperQ to the Zclosure and Qimputation supernetwork methods, and also present an analysis of some published data sets as an illustration of its applicability. © 20042012 IEEE."



Yun Yu,
R. Matthew Barnett and
Luay Nakhleh. Parsimonious Inference of Hybridization in the Presence of Incomplete Lineage Sorting. In Systematic Biology, Vol. 62(5):738751, 2013. Keywords: from network, from rooted trees, hybridization, lineage sorting, parsimony, phylogenetic network, phylogeny, Program PhyloNet, reconstruction.
Toggle abstract
"Hybridization plays an important evolutionary role in several groups of organisms. A phylogenetic approach to detect hybridization entails sequencing multiple loci across the genomes of a group of species of interest, reconstructing their gene trees, and taking their differences as indicators of hybridization. However, methods that follow this approach mostly ignore population effects, such as incomplete lineage sorting (ILS). Given that hybridization occurs between closely related organisms, ILS may very well be at play and, hence, must be accounted for in the analysis framework. To address this issue, we present a parsimony criterion for reconciling gene trees within the branches of a phylogenetic network, and a local search heuristic for inferring phylogenetic networks from collections of genetree topologies under this criterion. This framework enables phylogenetic analyses while accounting for both hybridization and ILS. Further, we propose two techniques for incorporating information about uncertainty in genetree estimates. Our simulation studies demonstrate the good performance of our framework in terms of identifying the location of hybridization events, as well as estimating the proportions of genes that underwent hybridization. Also, our framework shows good performance in terms of efficiency on handling large data sets in our experiments. Further, in analysing a yeast data set, we demonstrate issues that arise when analysing real data sets. Although a probabilistic approach was recently introduced for this problem, and although parsimonious reconciliations have accuracy issues under certain settings, our parsimony framework provides a much more computationally efficient technique for this type of analysis. Our framework now allows for genomewide scans for hybridization, while also accounting for ILS. [Phylogenetic networks; hybridization; incomplete lineage sorting; coalescent; multilabeled trees.] © 2013 The Author(s). All rights reserved."



Alexey A. Morozov,
Yuri P. Galachyants and
Yelena V. Likhoshway. Inferring Phylogenetic Networks from Gene Order Data. In BMRI, Vol. 2013(503193):17, 2013. Keywords: abstract network, from distances, from gene order, NeighborNet, phylogenetic network, phylogeny, Program SplitsTree, reconstruction, split decomposition, split network.
Toggle abstract
"Existing algorithms allow us to infer phylogenetic networks from sequences (DNA, protein or binary), sets of trees, and distance matrices, but there are no methods to build them using the gene order data as an input. Here we describe several methods to build split networks from the gene order data, perform simulation studies, and use our methods for analyzing and interpreting different real gene order datasets. All proposed methods are based on intermediate data, which can be generated from genome structures under study and used as an input for network construction algorithms. Three intermediates are used: set of jackknife trees, distance matrix, and binary encoding. According to simulations and case studies, the best intermediates are jackknife trees and distance matrix (when used with NeighborNet algorithm). Binary encoding can also be useful, but only when the methods mentioned above cannot be used. © 2013 Alexey Anatolievich Morozov et al."







Gergely J. Szöllösi,
Eric Tannier,
Nicolas Lartillot and
Vincent Daubin. Lateral Gene Transfer from the Dead. In Systematic Biology, Vol. 62(3):386397, 2013. Keywords: duplication, lateral gene transfer, likelihood, loss, phylogeny, Program TERA, reconstruction. Note: http://dx.doi.org/10.1093/sysbio/syt003.
Toggle abstract
"In phylogenetic studies, the evolution of molecular sequences is assumed to have taken place along the phylogeny traced by the ancestors of extant species. In the presence of lateral gene transfer, however, this may not be the case, because the species lineage from which a gene was transferred may have gone extinct or not have been sampled. Because it is not feasible to specify or reconstruct the complete phylogeny of all species, we must describe the evolution of genes outside the represented phylogeny by modeling the speciation dynamics that gave rise to the complete phylogeny. We demonstrate that if the number of sampled species is small compared with the total number of existing species, the overwhelming majority of gene transfers involve speciation to and evolution along extinct or unsampled lineages. We show that the evolution of genes along extinct or unsampled lineages can to good approximation be treated as those of independently evolving lineages described by a few global parameters. Using this result, we derive an algorithm to calculate the probability of a gene tree and recover the maximumlikelihood reconciliation given the phylogeny of the sampled species. Examining 473 nearuniversal gene families from 36 cyanobacteria, we find that nearly a third of transfer events (28%) appear to have topological signatures of evolution along extinct species, but only approximately 6% of transfers trace their ancestry to before the common ancestor of the sampled cyanobacteria. © 2013 The Author(s)."



Sarah Bastkowski. From Trees to Networks and Back. PhD thesis, University of East Anglia, 2013. Keywords: abstract network, NeighborNet, phylogenetic network, phylogeny, Program FlatNJ, Program QNet, Program SplitsTree, reconstruction, software, split network. Note: http://spectresuiteofphylogenetictoolsforreticulateevolution.readthedocs.io/en/latest/_downloads/spectre_bastkowskis_thesis.pdf.





Andreas Spillner and
Vincent Moulton. Optimal algorithms for computing edge weights in planar splitnetworks. In Journal of Applied Mathematics and Computing, Vol. 39(12):113, 2012. Keywords: abstract network, from distances, phylogenetic network, phylogeny, reconstruction, split, split network. Note: http://dx.doi.org/10.1007/s121900110506z.
Toggle abstract
"In phylogenetics, biologists commonly compute split networks when trying to better understand evolutionary data. These graphtheoretical structures represent collections of weighted bipartitions or splits of a finite set, and provide a means to display conflicting evolutionary signals. The weights associated to the splits are used to scale the edges in the network and are often computed using some distance matrix associated with the data. In this paper we present optimal polynomial time algorithms for three basic problems that arise in this context when computing split weights for planar splitnetworks. These generalize algorithms that have been developed for special classes of split networks (namely, trees and outerlabeled planar networks). As part of our analysis, we also derive a Crofton formula for full flat split systems, structures that naturally arise when constructing planar splitnetworks. © 2011 Korean Society for Computational and Applied Mathematics."



ZhiZhong Chen and
Lusheng Wang. Algorithms for Reticulate Networks of Multiple Phylogenetic Trees. In TCBB, Vol. 9(2):372384, 2012. Keywords: explicit network, from rooted trees, minimum number, phylogenetic network, phylogeny, Program CMPT, Program MaafB, reconstruction, software. Note: http://rnc.r.dendai.ac.jp/~chen/papers/rMaaf.pdf.
Toggle abstract
"A reticulate network N of multiple phylogenetic trees may have nodes with two or more parents (called reticulation nodes). There are two ways to define the reticulation number of N. One way is to define it as the number of reticulation nodes in N in this case, a reticulate network with the smallest reticulation number is called an optimal typeI reticulate network of the trees. The better way is to define it as the total number of parents of reticulation nodes in N minus the number of reticulation nodes in N ; in this case, a reticulate network with the smallest reticulation number is called an optimal typeII reticulate network of the trees. In this paper, we first present a fast fixedparameter algorithm for constructing one or all optimal typeI reticulate networks of multiple phylogenetic trees. We then use the algorithm together with other ideas to obtain an algorithm for estimating a lower bound on the reticulation number of an optimal typeII reticulate network of the input trees. To our knowledge, these are the first fixedparameter algorithms for the problems. We have implemented the algorithms in ANSI C, obtaining programs CMPT and MaafB. Our experimental data show that CMPT can construct optimal typeI reticulate networks rapidly and MaafB can compute better lower bounds for optimal typeII reticulate networks within shorter time than the previously best program PIRN designed by Wu. © 2006 IEEE."



Changiz Eslahchi,
Reza Hassanzadeh,
Ehsan Mottaghi,
Mahnaz Habibi,
Hamid Pezeshk and
Mehdi Sadeghi. Constructing circular phylogenetic networks from weighted quartets using simulated annealing. In MBIO, Vol. 235(2):123127, 2012. Keywords: abstract network, from quartets, heuristic, phylogenetic network, phylogeny, Program SAQNet, Program SplitsTree, reconstruction, simulated annealing, software, split network. Note: http://dx.doi.org/10.1016/j.mbs.2011.11.003.
Toggle abstract
"In this paper, we present a heuristic algorithm based on the simulated annealing, SAQNet, as a method for constructing phylogenetic networks from weighted quartets. Similar to QNet algorithm, SAQNet constructs a collection of circular weighted splits of the taxa set. This collection is represented by a split network. In order to show that SAQNet performs better than QNet, we apply these algorithm to both the simulated and actual data sets containing salmonella, Bees, Primates and Rubber data sets. Then we draw phylogenetic networks corresponding to outputs of these algorithms using SplitsTree4 and compare the results. We find that SAQNet produces a better circular ordering and phylogenetic networks than QNet in most cases. SAQNet has been implemented in Matlab and is available for download at http://bioinf.cs.ipm.ac.ir/softwares/saq.net. © 2011 Elsevier Inc."



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):i283i291 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 RANGERDTL, 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 duplicationtransferloss (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 distancedependent 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 000fold speedup 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 reconciliationbased gene and species tree reconstruction methods. © The Author(s) 2012. Published by Oxford University Press."



Daniel H. Huson and
Celine Scornavacca. Dendroscope 3: An Interactive Tool for Rooted Phylogenetic Trees and Networks. In Systematic Biology, Vol. 61(6):10611067, 2012. Keywords: from rooted trees, from triplets, phylogenetic network, phylogeny, Program Dendroscope, reconstruction, software, visualization.
Toggle abstract
"Dendroscope 3 is a new program for working with rooted phylogenetic trees and networks. It provides a number of methods for drawing and comparing rooted phylogenetic networks, and for computing them from rooted trees. The program can be used interactively or in commandline mode. The program is written in Java, use of the software is free, and installers for all 3 major operating systems can be downloaded from www.dendroscope.org. [Phylogenetic trees; phylogenetic networks; software.] © 2012 The Author(s)."





Adrià Alcalà Mena. Trivalent Graph isomorphism in polynomial time. Master's thesis, Universidad de Cantabria, Spain, 2012. Keywords: distance between networks, explicit network, from network, isomorphism, phylogenetic network, phylogeny, polynomial, Program SAGE. Note: http://arxiv.org/abs/1209.1040.



Daniel H. Huson and
Celine Scornavacca. A survey of combinatorial methods for phylogenetic networks. In Genome Biology and Evolution, Vol. 3:2335, 2011. Keywords: phylogenetic network, survey. Note: http://dx.doi.org/10.1093/gbe/evq077.
Toggle abstract
"The evolutionary history of a set of species is usually described by a rooted phylogenetic tree. Although it is generally undisputed that bifurcating speciation events and descent with modifications are major forces of evolution, there is a growing belief that reticulate events also have a role to play. Phylogenetic networks provide an alternative to phylogenetic trees and may be more suitable for data sets where evolution involves significant amounts of reticulate events, such as hybridization, horizontal gene transfer, or recombination. In this article, we give an introduction to the topic of phylogenetic networks, very briefly describing the fundamental concepts and summarizing some of the most important combinatorial methods that are available for their computation. © 2010 The Author(s)."





Gergely J. Szöllösi and
Vincent Daubin. Modeling Gene Family Evolution and Reconciling Phylogenetic Discord. In Evolutionary Genomics, Statistical and Computational Methods, Volume 2, Methods in Molecular Biology, Vol. 856:2951, Chapter 2, springer, 2011. Keywords: duplication, from multilabeled tree, lateral gene transfer, likelihood, phylogeny, reconstruction, statistical model. Note: ArXiv version entitled The pattern and process of gene family evolution.
Toggle abstract
"Largescale databases are available that contain homologous gene families constructed from hundreds of complete genome sequences from across the three domains of life. Here, we discuss the approaches of increasing complexity aimed at extracting information on the pattern and process of gene family evolution from such datasets. In particular, we consider the models that invoke processes of gene birth (duplication and transfer) and death (loss) to explain the evolution of gene families. First, we review birthanddeath models of family size evolution and their implications in light of the universal features of family size distribution observed across different species and the three domains of life. Subsequently, we proceed to recent developments on models capable of more completely considering information in the sequences of homologous gene families through the probabilistic reconciliation of the phylogenetic histories of individual genes with the phylogenetic history of the genomes in which they have resided. To illustrate the methods and results presented, we use data from the HOGENOM database, demonstrating that the distribution of homologous gene family sizes in the genomes of the eukaryota, archaea, and bacteria exhibits remarkably similar shapes. We show that these distributions are best described by models of gene family size evolution, where for individual genes the death (loss) rate is larger than the birth (duplication and transfer) rate but new families are continually supplied to the genome by a process of origination. Finally, we use probabilistic reconciliation methods to take into consideration additional information from gene phylogenies, and find that, for prokaryotes, the majority of birth events are the result of transfer. © 2012 Springer Science+Business Media, LLC."



JeanPhilippe Doyon,
Vincent Ranwez,
Vincent Daubin and
Vincent Berry. Models, algorithms and programs for phylogeny reconciliation. In Briefings in Bioinformatics, Vol. 12(5):392400, 2011. Keywords: explicit network, lateral gene transfer, phylogenetic network, phylogeny, reconstruction, survey.
Toggle abstract
"Gene sequences contain a goldmine of phylogenetic information. But unfortunately for taxonomists this information does not only tell the story of the species from which it was collected. Genes have their own complex histories which record speciation events, of course, but also many other events. Among them, gene duplications, transfers and losses are especially important to identify. These events are crucial to account for when reconstructing the history of species, and they play a fundamental role in the evolution of genomes, the diversification of organisms and the emergence of new cellular functions.We review reconciliations between gene and species trees, which are rigorous approaches for identifying duplications, transfers and losses that mark the evolution of a gene family. Existing reconciliation models and algorithms are reviewed and difficulties in modeling gene transfers are discussed. We also compare different reconciliation programs along with their advantages and disadvantages. © The Author 2011. Published by Oxford University Press."



Jaroslaw Byrka,
Pawel Gawrychowski,
Katharina Huber and
Steven Kelk. Worstcase optimal approximation algorithms for maximizing triplet consistency within phylogenetic networks. In Journal of Discrete Algorithms, Vol. 8(1):6575, 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) worstcase 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 worstcase optimal result for level1 phylogenetic networks improving considerably upon the 5/12 fraction obtained recently by Jansson, Nguyen and Sung. For level2 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."



Changiz Eslahchi,
Mahnaz Habibi,
Reza Hassanzadeh and
Ehsan Mottaghi. MCNet: a method for the construction of phylogenetic networks based on the MonteCarlo method. In BMCEB, Vol. 10:254, 2010. Keywords: abstract network, circular split system, from distances, heuristic, phylogenetic network, Program MCNet, Program SplitsTree, software, split, split network. Note: http://dx.doi.org/10.1186/1471214810254.
Toggle abstract
"Background. A phylogenetic network is a generalization of phylogenetic trees that allows the representation of conflicting signals or alternative evolutionary histories in a single diagram. There are several methods for constructing these networks. Some of these methods are based on distances among taxa. In practice, the methods which are based on distance perform faster in comparison with other methods. The NeighborNet (NNet) is a distancebased method. The NNet produces a circular ordering from a distance matrix, then constructs a collection of weighted splits using circular ordering. The SplitsTree which is a program using these weighted splits makes a phylogenetic network. In general, finding an optimal circular ordering is an NPhard problem. The NNet is a heuristic algorithm to find the optimal circular ordering which is based on neighborjoining algorithm. Results. In this paper, we present a heuristic algorithm to find an optimal circular ordering based on the MonteCarlo method, called MCNet algorithm. In order to show that MCNet performs better than NNet, we apply both algorithms on different data sets. Then we draw phylogenetic networks corresponding to outputs of these algorithms using SplitsTree and compare the results. Conclusions. We find that the circular ordering produced by the MCNet is closer to optimal circular ordering than the NNet. Furthermore, the networks corresponding to outputs of MCNet made by SplitsTree are simpler than NNet. © 2010 Eslahchi et al; licensee BioMed Central Ltd."





Joel Velasco and
Elliott Sober. Testing for Treeness: Lateral Gene Transfer, Phylogenetic Inference, and Model Selection. In Biology and Philosophy, Vol. 25(4):675687, 2010. Keywords: explicit network, model selection, phylogenetic network, phylogeny, reconstruction, statistical model. Note: http://joelvelasco.net/Papers/velascosobertestingfortreeness.pdf.
Toggle abstract
"A phylogeny that allows for lateral gene transfer (LGT) can be thought of as a strictly branching tree (all of whose branches are vertical) to which lateral branches have been added. Given that the goal of phylogenetics is to depict evolutionary history, we should look for the best supported phylogenetic network and not restrict ourselves to considering trees. However, the obvious extensions of popular treebased methods such as maximum parsimony and maximum likelihood face a serious problemif we judge networks by fit to data alone, networks that have lateral branches will always fit the data at least as well as any network that restricts itself to vertical branches. This is analogous to the wellstudied problem of overfitting data in the curvefitting problem. Analogous problems often have analogous solutions and we propose to treat network inference as a case of model selection and use the Akaike Information Criterion (AIC). Strictly treelike networks are more parsimonious than those that postulate lateral as well as vertical branches. This leads to the conclusion that we should not always infer LGT events whenever it would improve our fittodata, but should do so only when the improved fit is larger than the penalty for adding extra lateral branches. © 2010 Springer Science+Business Media B.V."



David A. Morrison. Using datadisplay networks for exploratory data analysis in phylogenetic studies. In MBE, Vol. 27(5):10441057, 2010. Keywords: abstract network, hybridization, NeighborNet, Program SplitsTree, recombination, split decomposition. Note: http://dx.doi.org/10.1093/molbev/msp309.
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"Exploratory data analysis (EDA) is a frequently undervalued part of data analysis in biology. It involves evaluating the characteristics of the data "before" proceeding to the definitive analysis in relation to the scientific question at hand. For phylogenetic analyses, a useful tool for EDA is a datadisplay network. This type of network is designed to display any character (or tree) conflict in a data set, without prior assumptions about the causes of those conflicts. The conflicts might be caused by 1) methodological issues in data collection or analysis, 2) homoplasy, or 3) horizontal gene flow of some sort. Here, I explore 13 published data sets using splits networks, as examples of using datadisplay networks for EDA. In each case, I performed an original EDA on the data provided, to highlight the aspects of the resulting network that will be important for an interpretation of the phylogeny. In each case, there is at least one important point (possibly missed by the original authors) that might affect the phylogenetic analysis. I conclude that EDA should play a greater role in phylogenetic analyses than it has done. © 2010 The Author. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved."



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. 6049:141153 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/CS201003.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 subtreepruneandregraft (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 worstcase 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. © SpringerVerlag Berlin Heidelberg 2010."



Gabriel Cardona,
Francesc Rosselló and
Gabriel Valiente. Comparison of treechild phylogenetic networks. In TCBB, Vol. 6(4):552569, 2009. Keywords: explicit network, phylogenetic network, phylogeny, Program Bio PhyloNetwork, Program PhyloNetwork, tree child network, tree sibling network. Note: http://arxiv.org/abs/0708.3499.
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"Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of nontreelike evolutionary events, like recombination, hybridization, or lateral gene transfer. While much progress has been made to find practical algorithms for reconstructing a phylogenetic network from a set of sequences, all attempts to endorse a class of phylogenetic networks (strictly extending the class of phylogenetic trees) with a wellfounded distance measure have, to the best of our knowledge and with the only exception of the bipartition distance on regular networks, failed so far. In this paper, we present and study a new meaningful class of phylogenetic networks, called treechild phylogenetic networks, and we provide an injective representation of these networks as multisets of vectors of natural numbers, their path multiplicity vectors. We then use this representation to define a distance on this class that extends the wellknown RobinsonFoulds distance for phylogenetic trees and to give an alignment method for pairs of networks in this class. Simple polynomial algorithms for reconstructing a treechild phylogenetic network from its path multiplicity vectors, for computing the distance between two treechild phylogenetic networks and for aligning a pair of treechild phylogenetic networks, are provided. They have been implemented as a Perl package and a Java applet, which can be found at http://bioinfo.uib.es/~recerca/ phylonetworks/mudistance/. © 2009 IEEE."



Daniel H. Huson. Drawing Rooted Phylogenetic Networks. In TCBB, Vol. 6(1):103109, 2009. Keywords: explicit network, phylogenetic network, phylogeny, Program Dendroscope, Program SplitsTree, visualization. Note: http://dx.doi.org/10.1109/TCBB.2008.58.
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"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."



Robert G. Beiko and
Mark A. Ragan. Untangling Hybrid Phylogenetic Signals: Horizontal Gene Transfer and Artifacts of Phylogenetic Reconstruction. In Horizontal Gene Transfer, Vol. 532:241256 of Methods in Molecular Biology, 2009. Note: http://dx.doi.org/10.1007/9781603278539_14.
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"Phylogenomic methods can be used to investigate the tangled evolutionary relationships among genomes. Building 'all the trees of all the genes' can potentially identify common pathways of horizontal gene transfer (HGT) among taxa at varying levels of phylogenetic depth. Phylogenetic affinities can be aggregated and merged with the information about genetic linkage and biochemical function to examine hypotheses of adaptive evolution via HGT. Additionally, the use of many genetic data sets increases the power of statistical tests for phylogenetic artifacts. However, largescale phylogenetic analyses pose several challenges, including the necessary abandonment of manual validation techniques, the need to translate inferred phylogenetic discordance into inferred HGT events, and the challenges involved in aggregating results from searchbased inference methods. In this chapter we describe a tree search procedure to recover the most parsimonious pathways of HGT, and examine some of the assumptions that are made by this method."



Maria S. Poptsova. Testing Phylogenetic Methods to Identify Horizontal Gene Transfer. In Horizontal Gene Transfer, Pages 227240, 2009. Note: http://dx.doi.org/10.1007/9781603278539_13.
Toggle abstract
"The subject of this chapter is to describe the methodology for assessing the power of phylogenetic HGT detection methods. Detection power is defined in the framework of hypothesis testing. Rates of false positives and false negatives can be estimated by testing HGT detection methods on HGTfree orthologous sets, and on the same sets with in silico simulated HGT events. The whole process can be divided into three steps: obtaining HGTfree orthologous sets, in silico simulation of HGT events in the same set, and submitting both sets for evaluation by any of the tested methods.Phylogenetic methods of HGT detection can be roughly divided into three types: likelihoodbased tests of topologies (KishinoHasegawa (KH), ShimodairaHasegawa (SH), and Approximately Unbiased (AU) tests), tree distance methods (symmetrical difference of Robinson and Foulds (RF), and Subtree Pruning and Regrafting (SPR) distances), and genome spectral approaches (bipartition and quartet decomposition analysis). Restrictions that are inherent to phylogenetic methods of HGT detection in general and the power and precision of each method are discussed and comparative analyses of different approaches are provided, as well as some examples of assessing the power of phylogenetic HGT detection methods from a case study of orthologous sets from gammaproteobacteria (Poptsova and Gogarten, BMC Evol Biol 7, 45, 2007) and cyanobacteria (Zhaxybayeva et al., Genome Res 16, 1099108, 2006)."



Josh Voorkamp né Collins. Rekernelisation Algorithms in Hybrid Phylogenies. Master's thesis, University of Canterbury, New Zealand, 2009. Keywords: agreement forest, explicit network, FPT, from rooted trees, from unrooted trees, hybridization, minimum number, phylogenetic network, phylogeny, Program HybridInterleave, reconstruction, software. Note: http://hdl.handle.net/10092/2852.



Mark A. Ragan. Trees and networks before and after Darwin. In Biology Direct, Vol. 4(43), 2009. Keywords: abstract network, explicit network, phylogenetic network, phylogeny, survey, visualization. Note: http://dx.doi.org/10.1186/17456150443.
Toggle abstract
"It is wellknown that Charles Darwin sketched abstract trees of relationship in his 1837 notebook, and depicted a tree in the Origin of Species (1859). Here I attempt to place Darwin's trees in historical context. By the midEighteenth century the Great Chain of Being was increasingly seen to be an inadequate description of order in nature, and by about 1780 it had been largely abandoned without a satisfactory alternative having been agreed upon. In 1750 Donati described aquatic and terrestrial organisms as forming a network, and a few years later Buffon depicted a network of genealogical relationships among breeds of dogs. In 1764 Bonnet asked whether the Chain might actually branch at certain points, and in 1766 Pallas proposed that the gradations among organisms resemble a tree with a compound trunk, perhaps not unlike the tree of animal life later depicted by Eichwald. Other trees were presented by Augier in 1801 and by Lamarck in 1809 and 1815, the latter two assuming a transmutation of species over time. Elaborate networks of affinities among plants and among animals were depicted in the late Eighteenth and very early Nineteenth centuries. In the two decades immediately prior to 1837, socalled affinities and/or analogies among organisms were represented by diverse geometric figures. Series of plant and animal fossils in successive geological strata were represented as trees in a popular textbook from 1840, while in 1858 Bronn presented a system of animals, as evidenced by the fossil record, in a form of a tree. Darwin's 1859 tree and its subsequent elaborations by Haeckel came to be accepted in many but not all areas of biological sciences, while network diagrams were used in others. Beginning in the early 1960s trees were inferred from protein and nucleic acid sequences, but networks were reintroduced in the mid1990s to represent lateral genetic transfer, increasingly regarded as a fundamental mode of evolution at least for bacteria and archaea. In historical context, then, the Network of Life preceded the Tree of Life and might again supersede it. Reviewers: This article was reviewed by Eric Bapteste, Patrick Forterre and Dan Graur. © 2009 Ragan; licensee BioMed Central Ltd."



Gabriel Valiente. Combinatorial Pattern Matching Algorithms in Computational Biology Using Perl and R. Pages 184208, Taylor & Francis/CRC Press, 2009. Keywords: counting, distance between networks, galled tree, generation, phylogenetic network, phylogeny, survey, time consistent network, tree child network, tree sibling network. Note: http://books.google.fr/books?id=F4YIIUWb7yMC.



Laura S. Kubatko. Identifying Hybridization Events in the Presence of Coalescence via Model Selection. In Systematic Biology, Vol. 58(5):478488, 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.



Bui Quang Minh,
Steffen Klaere and
Arndt von Haeseler. Taxon Selection under Split Diversity. In Systematic Biology, Vol. 58(6):586594, 2009. Keywords: abstract network, circular split system, diversity, from network, phylogenetic network, split network. Note: http://dx.doi.org/10.1093/sysbio/syp058.
Toggle abstract
"The phylogenetic diversity (PD) measure of biodiversity is evaluated using a phylogenetic tree, usually inferred from morphological or molecular data. Consequently, it is vulnerable to errors in that tree, including those resulting from sampling error, model misspecification, or conflicting signals. To improve the robustness of PD, we can evaluate the measure using either a collection (or distribution) of trees or a phylogenetic network. Recently, it has been shown that these 2 approaches are equivalent but that the problem of maximizing PD in the general concept is NPhard. In this study, we provide an efficient dynamic programming algorithm for maximizing PD when splits in the trees or network form a circular split system. We illustrate our method using a case study of game birds (Galliformes) and discuss the different choices of taxa based on our approach and PD."





Gabriel Cardona,
Francesc Rosselló and
Gabriel Valiente. Tripartitions do not always discriminate phylogenetic networks. In MBIO, Vol. 211(2):356370, 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 nontreelike 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 socalled 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."



Philippe Gambette and
Daniel H. Huson. Improved Layout of Phylogenetic Networks. In TCBB, Vol. 5(3):472479, 2008. Keywords: abstract network, heuristic, phylogenetic network, phylogeny, Program SplitsTree, software, split network, visualization. Note: http://hallirmm.ccsd.cnrs.fr/lirmm00309694/en/.
Toggle abstract
"Split networks are increasingly being used in phylogenetic analysis. Usually, a simple equalangle 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 equaldaylight algorithm to networks, looks into using a spring embedder, and discusses how to construct rooted split networks. © 2008 IEEE."



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 child network, tree sibling network. Note: http://dx.doi.org/10.1186/147121059175.
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 opensource 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 webbased 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."



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/10.1186/14712148822.
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."





Stefan Grünewald,
Andreas Spillner,
Kristoffer Forslund and
Vincent Moulton. Constructing Phylogenetic Supernetworks from Quartets. In WABI08, Vol. 5251:284295 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/10.1007/9783540873617_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 SpringerVerlag Berlin Heidelberg."



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_611.pdf.





Barbara R. Holland,
Glenn Conner,
Katharina Huber and
Vincent Moulton. Imputing Supertrees and Supernetworks from Quartets. In Systematic Biology, Vol. 56(1):5767, 2007. Keywords: abstract network, from unrooted trees, phylogenetic network, phylogeny, Program Quartet, reconstruction, split network, supernetwork. Note: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.99.3215.
Toggle abstract
"Inferring species phylogenies is an important part of understanding molecular evolution. Even so, it is well known that an accurate phylogenetic tree reconstruction for a single gene does not always necessarily correspond to the species phylogeny. One commonly accepted strategy to cope with this problem is to sequence many genes; the way in which to analyze the resulting collection of genes is somewhat more contentious. Supermatrix and supertree methods can be used, although these can suppress conflicts arising from true differences in the gene trees caused by processes such as lineage sorting, horizontal gene transfer, or gene duplication and loss. In 2004, Huson et al. (IEEE/ACM Trans. Comput. Biol. Bioinformatics 1:151158) presented the Zclosure method that can circumvent this problem by generating a supernetwork as opposed to a supertree. Here we present an alternative way for generating supernetworks called Qimputation. In particular, we describe a method that uses quartet information to add missing taxa into gene trees. The resulting trees are subsequently used to generate consensus networks, networks that generalize strict and majorityrule consensus trees. Through simulations and application to real data sets, we compare Qimputation to the matrix representation with parsimony (MRP) supertree method and Zclosure, and demonstrate that it provides a useful complementary tool. Copyright © Society of Systematic Biologists."



Daniel H. Huson. Split networks and Reticulate Networks. In
Olivier Gascuel and
Mike Steel editors, Reconstructing Evolution, New Mathematical and Computational Advances, Pages 247276, Oxford University Press, 2007. Keywords: abstract network, consensus, from rooted trees, from sequences, from splits, from unrooted trees, galled tree, hybridization, phylogenetic network, phylogeny, Program Beagle, Program Spectronet, Program SplitsTree, Program SPNet, recombination, reconstruction, split network, survey. Note: similar to http://wwwab.informatik.unituebingen.de/research/phylonets/GCB2006.pdf.



Daniel H. Huson and
Tobias Kloepper. Beyond Galled Trees  Decomposition and Computation of Galled Networks. In RECOMB07, Vol. 4453:211225 of LNCS, springer, 2007. Keywords: FPT, from splits, from trees, galled network, phylogenetic network, phylogeny, Program SplitsTree, reconstruction. Note: http://dx.doi.org/10.1007/9783540716815_15, errata..



Cam Thach Nguyen,
Nguyen Bao Nguyen and
WingKin Sung. Fast Algorithms for computing the Tripartitionbased Distance between Phylogenetic Networks. In JCO, Vol. 13(3), 2007. Keywords: distance between networks, phylogenetic network, phylogeny, tripartition distance. Note: http://dx.doi.org/10.1007/s1087800690255.
Toggle abstract
"Consider two phylogenetic networks N and N′ of size n. The tripartitionbased distance finds the proportion of tripartitions which are not shared by N and N′. This distance is proposed by Moret et al. (2004) and is a generalization of RobinsonFoulds distance, which is orginally used to compare two phylogenetic trees. This paper gives an O(min {kn log n, n log n + hn} time algorithm to compute this distance, where h is the number of hybrid nodes in N and N′ while k is the maximum number of hybrid nodes among all biconnected components in N and N′. Note that k ≪ h ≪ n in a phylogenetic network. In addition, we propose algorithms for comparing galledtrees, which are an important, biological meaningful special case of phylogenetic network. We give an O(n)time algorithm for comparing two galledtrees. We also give an O(n + kh)time algorithm for comparing a galledtree with another general network, where h and k are the number of hybrid nodes in the latter network and its biggest biconnected component respectively. © Springer Science+Business Media, LLC 2007."





Monique M. Morin. Phylogenetic Networks: Simulation, Characterization, and Reconstruction. PhD thesis, The University of New Mexico, U.S.A., 2007. Keywords: evaluation, explicit network, hybridization, lateral gene transfer, phylogenetic network, phylogeny, Program NetGen, simulation, software. Note: http://www.cs.unm.edu/~morin/morin_phd.pdf.



Bastienne Vriesendorp. Phylogenenetworks, exploring reticulate evolution and its consequences for phylogenetic reconstruction. PhD thesis, Wageningen University, The Netherlands, 2007. Keywords: consensus, distance between networks, evaluation, hybridization, median network, NeighborNet, parsimony, phylogenetic network, phylogeny, Program SplitsTree, split decomposition, survey. Note: http://library.wur.nl/wda/dissertations/dis4239.pdf.



Yuanyi Zhang. Optimization Algorithms for Phylogenetic Networks. PhD thesis, University of Texas at Dallas, U.S.A., 2007. Keywords: abstract network, explicit network, from distances, phylogenetic network, phylogeny, reconstruction, split, split network, visualization. Note: http://proquest.umi.com/pqdlink?did=1421626541&sid=1&Fmt=6&clientId=176295&RQT=309&VName=PQD.



Mihaela Baroni,
Charles Semple and
Mike Steel. Hybrids in Real Time. In Systematic Biology, Vol. 55(1):4656, 2006. Keywords: agreement forest, from rooted trees, phylogenetic network, phylogeny, polynomial, reconstruction, time consistent network. Note: http://www.math.canterbury.ac.nz/~m.steel/Non_UC/files/research/hybrids.pdf.
Toggle abstract
"We describe some new and recent results that allow for the analysis and representation of reticulate evolution by nontree networks. In particular, we (1) present a simple result to show that, despite the presence of reticulation, there is always a welldefined underlying tree that corresponds to those parts of life that do not have a history of reticulation; (2) describe and apply new theory for determining the smallest number of hybridization events required to explain conflicting gene trees; and (3) present a new algorithm to determine whether an arbitrary rooted network can be realized by contemporaneous reticulation events. We illustrate these results with examples. Copyright © Society of Systematic Biologists."



Daniel H. Huson and
David Bryant. Application of Phylogenetic Networks in Evolutionary Studies. In MBE, Vol. 23(2):254267, 2006. Keywords: abstract network, phylogenetic network, phylogeny, Program SplitsTree, software, survey. Note: http://dx.doi.org/10.1093/molbev/msj030, software available from www.splitstree.org.
Toggle abstract
"The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models. Further, even when evolution proceeds in a treelike manner, analysis of the data may not be best served by using methods that enforce a tree structure but rather by a richer visualization of the data to evaluate its properties, at least as an essential first step. Thus, phylogenetic networks should be employed when reticulate events such as hybridization, horizontal gene transfer, recombination, or gene duplication and loss are believed to be involved, and, even in the absence of such events, phylogenetic networks have a useful role to play. This article reviews the terminology used for phylogenetic networks and covers both split networks and reticulate networks, how they are defined, and how they can be interpreted. Additionally, the article outlines the beginnings of a comprehensive statistical framework for applying split network methods. We show how split networks can represent confidence sets of trees and introduce a conservative statistical test for whether the conflicting signal in a network is treelike. Finally, this article describes a new program, SplitsTree4, an interactive and comprehensive tool for inferring different types of phylogenetic networks from sequences, distances, and trees. © The Author 2005. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved."



Jesper Jansson,
Nguyen Bao Nguyen and
WingKin Sung. Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network. In SICOMP, Vol. 35(5):10981121, 2006. 1 comment Keywords: approximation, explicit network, from triplets, galled tree, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://www.df.lth.se/~jj/Publications/triplets_to_gn7_SICOMP2006.pdf.
Toggle abstract
"This paper considers the problem of determining whether a given set Τ of rooted triplets can be merged without conflicts into a galled phylogenetic network and, if so, constructing such a network. When the input Τ is dense, we solve the problem in O(Τ) time, which is optimal since the size of the input is Θ(Τ). In comparison, the previously fastest algorithm for this problem runs in O(Τ2) time. We also develop an optimal O(Τ)time algorithm for enumerating all simple phylogenetic networks leaflabeled by L that are consistent with Τ, where L is the set of leaf labels in Τ, which is used by our main algorithm. Next, we prove that the problem becomes NPhard if extended to nondense inputs, even for the special case of simple phylogenetic networks. We also show that for every positive integer n, there exists some set Τ of rooted triplets on n leaves such that any galled network can be consistent with at most 0.4883 ·Τ of the rooted triplets in Τ. On the other hand, we provide a polynomialtime approximation algorithm that always outputs a galled network consistent with at least a factor of 5/12 (> 0.4166) of the rooted triplets in Τ. © 2006 Society for Industrial and Applied Mathematics."



Vladimir Makarenkov,
Dmytro Kevorkov and
Pierre Legendre. Phylogenetic Network Construction Approaches. In Applied Mycology and Biotechnology, Vol. 6:6197, 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.



Monique M. Morin and
Bernard M. E. Moret. NetGen: generating phylogenetic networks with diploid hybrids. In BIO, Vol. 22(15):19211923, 2006. Keywords: generation, hybridization, Program NetGen, software. Note: http://dx.doi.org/10.1093/bioinformatics/btl191.
Toggle abstract
"Summary: NetGen is an eventdriven simulator that creates phylogenetic networks by extending the birthdeath model to include diploid hybridizations. DNA sequences are evolved in conjunction with the topology, enabling hybridization decisions to be based on contemporary evolutionary distances. NetGen supports variable rate lineages, root sequence specification, outgroup generation and many other options. This note describes the NetGen application and proposes an extension of the Newick format to accommodate phylogenetic networks. © 2006 Oxford University Press."





Guillaume Bourque and
Louxin Zhang. Models and Methods in Comparative Genomics. In
ChauWen 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.



Jesper Jansson,
Nguyen Bao Nguyen and
WingKin Sung. Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network. In SODA05, Pages 349358, 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.





Richard C. Winkworth,
David Bryant,
Peter J. Lockhart,
David Havell and
Vincent Moulton. Biogeographic Interpretation of Splits Graphs: Least Squares Optimization of Branch Lengths. In Systematic Biology, Vol. 54(1):5665, 2005. Keywords: abstract network, from distances, from network, phylogenetic network, phylogeny, reconstruction, split, split network. Note: http://www.math.auckland.ac.nz/~bryant/Papers/05Biogeographic.pdf.



David Bryant. Extending tree models to splits networks. In
Lior Pachter and
Bernd Sturmfels editors, Algebraic Statistics for Computational Biology, Pages 322334, 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.







David Bryant and
Vincent Moulton. NeighborNet: An Agglomerative Method for the Construction of Phylogenetic Networks. In MBE, Vol. 21(2):255265, 2004. Keywords: phylogenetic network, phylogeny, Program SplitsTree, reconstruction, split network. Note: http://www.math.auckland.ac.nz/~bryant/Papers/04NeighborNet.pdf.
Toggle abstract
"We present NeighborNet, a distance based method for constructing phylogenetic networks that is based on the NeighborJoining (NJ) algorithm of Saitou and Nei. NeighborNet provides a snapshot of the data that can guide more detailed analysis. Unlike split decomposition, NeighborNet scales well and can quickly produce detailed and informative networks for several hundred taxa. We illustrate the method by reanalyzing three published data sets: a collection of 110 highly recombinant Salmonella multilocus sequence typing sequences, the 135 "African Eve" human mitochondrial sequences published by Vigilant et al., and a collection of 12 Archeal chaperonin sequences demonstrating strong evidence for gene conversion. NeighborNet is available as part of the SplitsTree4 software package."



Andreas W. M. Dress and
Daniel H. Huson. Constructing splits graphs. In TCBB, Vol. 1(3):109115, 2004. Keywords: abstract network, circular split system, from trees, phylogenetic network, phylogeny, Program SplitsTree, reconstruction, split network, visualization. Note: http://scilib.kiev.ua/ieee/tcbb/2004/03/n3/n0109.pdf.
Toggle abstract
"Phylogenetic trees correspond onetoone to compatible systems of splits and so splits play an important role in theoretical and computational aspects of phylogeny. Whereas any tree reconstruction method can be thought of as producing a compatible system of splits, an increasing number of phylogenetlc algorithms are available that compute split systems that are not necessarily compatible and, thus, cannot always be represented by a tree. Such methods include the split decomposition, NeighborNet, consensus networks, and the Zclosure method. A more general split system of this kind can be represented graphically by a socalled splits graph, which generalizes the concept of a phylogenetic tree. This paper addresses the problem of computing a splits graph for a given set of splits. We have implemented all presented algorithms in a new program called SplitsTree4. © 2004 IEEE."



Daniel H. Huson,
Tobias Dezulian,
Tobias Kloepper and
Mike Steel. Phylogenetic SuperNetworks from Partial Trees. In TCBB, Vol. 1(4):151158, 2004. Keywords: abstract network, from unrooted trees, phylogenetic network, phylogeny, Program SplitsTree, reconstruction, supernetwork. Note: http://hdl.handle.net/10092/3177.
Toggle abstract
"In practice, one is often faced with incomplete phylogenetic data, such as a collection of partial trees or partial splits. This paper poses the problem of Inferring a phylogenetic supernetwork from such data and provides an efficient algorithm for doing so, called the Zclosure method. Additionally, the questions of assigning lengths to the edges of the network and how to restrict the "dimensionality" of the network are addressed. Applications to a set of five published partial gene trees relating different fungal species and to six published partial gene trees relating different grasses illustrate the usefulness of the method and an experimental study confirms Its potential. The method Is implemented as a plugin for the program SplitsTree4. © 2004 IEEE."









David Bryant and
Vincent Moulton. NeighborNet: An Agglomerative Method for the Construction of Planar Phylogenetic Networks. In WABI02, Vol. 2452:375391 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/10.1007/3540457844_28.





David Posada and
Keith A. Crandall. Intraspecific gene genealogies: trees grafting into networks. In TEE, Vol. 16(1):3745, 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.



FrançoisJoseph Lapointe. How to account for reticulation events in phylogenetic analysis: A review of distancebased methods. In Journal of Classification, Vol. 17:175184, 2000. Keywords: abstract network, evaluation, from distances, phylogenetic network, Program Pyramids, Program SplitsTree, Program T REX, pyramid, reconstruction, reticulogram, split network, survey, weak hierarchy. Note: http://dx.doi.org/10.1007/s003570000016.





Vincent Berry and
David Bryant. Faster reliable phylogenetic analysis. In RECOMB99, Pages 5968, 1999. Keywords: abstract network, from quartets, phylogenetic network, phylogeny, polynomial, Program SplitsTree, reconstruction, split network, weakly compatible. Note: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.9151.





Andreas W. M. Dress,
Daniel H. Huson and
Vincent Moulton. Analyzing and visualizing distance data using SplitsTree. In DAM, Vol. 71(1):95109, 1996. Keywords: abstract network, from distances, phylogenetic network, phylogeny, Program SplitsTree, software, split network, visualization. Note: http://bibiserv.techfak.unibielefeld.de/splits/splits.pdf.






