




Leo van Iersel,
Steven Kelk,
Nela Lekic,
Chris Whidden and
Norbert Zeh. Hybridization Number on Three Rooted Binary Trees is EPT. In SIDMA, Vol. 30(3):16071631, 2016. Keywords: agreement forest, explicit network, FPT, from rooted trees, hybridization, minimum number, phylogenetic network, phylogeny, reconstruction. Note: http://arxiv.org/abs/1402.2136.



Steven Kelk,
Leo van Iersel,
Celine Scornavacca and
Mathias Weller. Phylogenetic incongruence through the lens of Monadic Second Order logic. In JGAA, Vol. 20(2):189215, 2016. Keywords: agreement forest, explicit network, FPT, from rooted trees, hybridization, minimum number, MSOL, phylogenetic network, phylogeny, reconstruction. Note: http://jgaa.info/accepted/2016/KelkIerselScornavaccaWeller2016.20.2.pdf.



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. 9538:197208 of LNCS, springer, 2016. Keywords: explicit network, from network, from rooted trees, genetically stable network, phylogenetic network, phylogeny, polynomial, tree containment. Note: https://halupecupem.archivesouvertes.fr/hal01226035 .



Philippe Gambette,
Leo van Iersel,
Steven Kelk,
Fabio Pardi and
Celine Scornavacca. Do branch lengths help to locate a tree in a phylogenetic network? In BMB, Vol. 78(9):17731795, 2016. Keywords: branch length, explicit network, FPT, from network, from rooted trees, NP complete, phylogenetic network, phylogeny, pseudopolynomial, time consistent network, tree containment, tree sibling network. Note: http://arxiv.org/abs/1607.06285.









James Oldman,
Taoyang Wu,
Leo van Iersel and
Vincent Moulton. TriLoNet: Piecing together small networks to reconstruct reticulate evolutionary histories. In MBE, Vol. 33(8):21512162, 2016. Keywords: explicit network, from trinets, galled tree, phylogenetic network, phylogeny, Program LEV1ATHAN, Program TriLoNet, reconstruction.





Sha Zhu and
James H. Degnan. Displayed Trees Do Not Determine Distinguishability Under the Network Multispecies Coalescent. In SB, 2016. Keywords: branch length, coalescent, explicit network, from network, likelihood, phylogenetic network, phylogeny, Program Hybridcoal, Program HybridLambda, Program PhyloNet, software, uniqueness. Note: to appear, presentation available at https://www.youtube.com/watch?v=JLYGTfEZG7g.



Mareike Fischer,
Leo van Iersel,
Steven Kelk and
Celine Scornavacca. On Computing The Maximum Parsimony Score Of A Phylogenetic Network. In SIDMA, Vol. 29(1):559585, 2015. Keywords: APX hard, cluster containment, explicit network, FPT, from network, from sequences, integer linear programming, level k phylogenetic network, NP complete, parsimony, phylogenetic network, phylogeny, polynomial, Program MPNet, reconstruction, software. Note: http://arxiv.org/abs/1302.2430.



Philippe Gambette,
Andreas Gunawan,
Anthony Labarre,
Stéphane Vialette and
Louxin Zhang. Locating a Tree in A Phylogenetic Network in Quadratic Time. In RECOMB15, Vol. 9029:96107 of LNCS, Springer, 2015. Keywords: evaluation, explicit network, from network, from rooted trees, genetically stable network, nearlystable network, phylogenetic network, phylogeny, polynomial, tree containment. Note: https://hal.archivesouvertes.fr/hal01116231/en.



Marc Thuillard and
Didier FraixBurnet. Phylogenetic Trees and Networks Reduce to Phylogenies on Binary States: Does It Furnish an Explanation to the Robustness of Phylogenetic Trees against Lateral Transfers? In Evolutionary Bioinformatics, Vol. 11:213221, 2015. [Abstract] Keywords: circular split system, explicit network, from multistate characters, outerplanar, perfect, phylogenetic network, phylogeny, planar, polynomial, reconstruction, split. Note: http://dx.doi.org/10.4137%2FEBO.S28158.



Philippe Gambette,
Katharina Huber and
Guillaume Scholz. Bridging the gap between rooted and unrooted phylogenetic networks. 2015. Keywords: circular split system, explicit network, from splits, galled tree, phylogenetic network, phylogeny, polynomial, reconstruction, split network, uniqueness. Note: http://arxiv.org/abs/1511.08387.



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."



Hadi Poormohammadi,
Changiz Eslahchi and
Ruzbeh Tusserkani. TripNet: A Method for Constructing Rooted Phylogenetic Networks from Rooted Triplets. In PLoS ONE, Vol. 9(9):e106531, 2014. Keywords: explicit network, from triplets, heuristic, level k phylogenetic network, phylogenetic network, phylogeny, Program TripNet, reconstruction, software. Note: http://arxiv.org/abs/1201.3722.
Toggle abstract
"The problem of constructing an optimal rooted phylogenetic network from an arbitrary set of rooted triplets is an NPhard problem. In this paper, we present a heuristic algorithm called TripNet, which tries to construct a rooted phylogenetic network with the minimum number of reticulation nodes from an arbitrary set of rooted triplets. Despite of current methods that work for dense set of rooted triplets, a key innovation is the applicability of TripNet to nondense set of rooted triplets. We prove some theorems to clarify the performance of the algorithm. To demonstrate the efficiency of TripNet, we compared TripNet with SIMPLISTIC. It is the only available software which has the ability to return some rooted phylogenetic network consistent with a given dense set of rooted triplets. But the results show that for complex networks with high levels, the SIMPLISTIC running time increased abruptly. However in all cases TripNet outputs an appropriate rooted phylogenetic network in an acceptable time. Also we tetsed TripNet on the Yeast data. The results show that Both TripNet and optimal networks have the same clustering and TripNet produced a level3 network which contains only one more reticulation node than the optimal network."



Leo van Iersel and
Steven Kelk. Kernelizations for the hybridization number problem on multiple nonbinary trees. In WG14, Vol. 8747:299311 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.



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."



Leo van Iersel,
Steven Kelk,
Nela Lekic and
Celine Scornavacca. A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees. In BMCB, Vol. 15(127):112, 2014. Keywords: agreement forest, approximation, explicit network, from rooted trees, phylogenetic network, phylogeny, Program CycleKiller, Program TerminusEst, reconstruction. Note: http://dx.doi.org/10.1186/1471210515127.





Zhijiang Li. FixedParameter Algorithm for Hybridization Number of Two Multifurcating Trees. Master's thesis, Dalhousie University, Canada, 2014. Keywords: agreement forest, explicit network, FPT, from rooted trees, minimum number, phylogenetic network, phylogeny, reconstruction. Note: http://hdl.handle.net/10222/53976.





Leo van Iersel and
Simone Linz. A quadratic kernel for computing the hybridization number of multiple trees. In IPL, Vol. 113:318323, 2013. Keywords: explicit network, FPT, from rooted trees, kernelization, minimum number, phylogenetic network, phylogeny, Program Clustistic, Program MaafB, Program PIRN, reconstruction. Note: http://arxiv.org/abs/1203.4067, poster.
Toggle abstract
"It has recently been shown that the NPhard problem of calculating the minimum number of hybridization events that is needed to explain a set of rooted binary phylogenetic trees by means of a hybridization network is fixedparameter tractable if an instance of the problem consists of precisely two such trees. In this paper, we show that this problem remains fixedparameter tractable for an arbitrarily large set of rooted binary phylogenetic trees. In particular, we present a quadratic kernel. © 2013 Elsevier B.V."



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."



Teresa Piovesan and
Steven Kelk. A simple fixed parameter tractable algorithm for computing the hybridization number of two (not necessarily binary) trees. In TCBB, Vol. 10(1):1825, 2013. Keywords: FPT, from rooted trees, phylogenetic network, phylogeny, Program TerminusEst, reconstruction. Note: http://arxiv.org/abs/1207.6090.
Toggle abstract
"Here, we present a new fixed parameter tractable algorithm to compute the hybridization number (r) of two rooted, not necessarily binary phylogenetic trees on taxon set (X) in time ((6r r) · poly(n)), where (n= X). The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on (X), and several insights from the softwired clusters literature. This yields a surprisingly simple and practical boundedsearch algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem. © 20042012 IEEE."



Peter J. Humphries,
Simone Linz and
Charles Semple. On the complexity of computing the temporal hybridization number for two phylogenies. In DAM, Vol. 161:871880, 2013. Keywords: agreement forest, APX hard, characterization, from rooted trees, hybridization, NP complete, phylogenetic network, phylogeny, reconstruction, time consistent network. Note: http://ab.inf.unituebingen.de/people/linz/publications/TAFapx.pdf.
Toggle abstract
"Phylogenetic networks are now frequently used to explain the evolutionary history of a set of species for which a collection of gene trees, reconstructed from genetic material of different parts of the species' genomes, reveal inconsistencies. However, in the context of hybridization, the reconstructed networks are often not temporal. If a hybridization network is temporal, then it satisfies the time constraint of instantaneously occurring hybridization events; i.e. all species that are involved in such an event coexist in time. Furthermore, although a collection of phylogenetic trees can often be merged into a hybridization network that is temporal, many algorithms do not necessarily find such a network since their primary optimization objective is to minimize the number of hybridization events. In this paper, we present a characterization for when two rooted binary phylogenetic trees admit a temporal hybridization network. Furthermore, we show that the underlying optimization problem is APXhard and, therefore, NPhard. Thus, unless P=NP, it is unlikely that there are efficient algorithms for either computing an exact solution or approximating it within a ratio arbitrarily close to one. © 2012 Elsevier B.V. All rights reserved."



Jialiang Yang,
Stefan Grünewald and
XiuFeng Wan. QuartetNet: A Quartet Based Method to Reconstruct Phylogenetic Networks. In MBE, Vol. 30(5):12061217, 2013. Keywords: from quartets, phylogenetic network, phylogeny, Program QuartetNet, reconstruction.
Toggle abstract
"Phylogenetic networks can model reticulate evolutionary events such as hybridization, recombination, and horizontal gene transfer. However, reconstructing such networks is not trivial. Popular characterbased methods are computationally inefficient, whereas distancebased methods cannot guarantee reconstruction accuracy because pairwise genetic distances only reflect partial information about a reticulate phylogeny. To balance accuracy and computational efficiency, here we introduce a quartetbased method to construct a phylogenetic network from a multiple sequence alignment. Unlike distances that only reflect the relationship between a pair of taxa, quartets contain information on the relationships among four taxa; these quartets provide adequate capacity to infer a more accurate phylogenetic network. In applications to simulated and biological data sets, we demonstrate that this novel method is robust and effective in reconstructing reticulate evolutionary events and it has the potential to infer more accurate phylogenetic distances than other conventional phylogenetic network construction methods such as NeighborJoining, NeighborNet, and Split Decomposition. This method can be used in constructing phylogenetic networks from simple evolutionary events involving a few reticulate events to complex evolutionary histories involving a large number of reticulate events. A software called QuartetNet is implemented and available at http://sysbio.cvm.msstate.edu/QuartetNet/. © 2013 The Author."



Hoa Vu,
Francis Chin,
WingKai Hon,
Henry Leung,
Kunihiko Sadakane,
WingKin Sung and
SiuMing Yiu. Reconstructing kReticulated Phylogenetic Network from a Set of Gene Trees. In ISBRA13, Vol. 7875:112124 of LNCS, springer, 2013. Keywords: from rooted trees, kreticulated, 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 levelx phylogenetic network increases exponentially in x. In this paper, we propose a new classification of phylogenetic networks called kreticulated network. A kreticulated network can model all levelk networks and some levelx networks with x > k. We design algorithms for reconstructing kreticulated 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 levelx 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 2reticulated 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 2reticulated network. © 2013 SpringerVerlag."



Mukul S. Bansal,
Guy Banay,
Timothy J. Harlow,
J. Peter Gogarten and
Ron Shamir. Systematic inference of highways of horizontal gene transfer in prokaryotes. In BIO, Vol. 29(5):571579, 2013. Keywords: duplication, explicit network, from species tree, from unrooted trees, lateral gene transfer, phylogenetic network, phylogeny, Program HiDe, Program RANGERDTL, reconstruction. Note: http://people.csail.mit.edu/mukul/Bansal_Highways_Bioinformatics_2013.pdf.



Peter J. Humphries,
Simone Linz and
Charles Semple. Cherry picking: a characterization of the temporal hybridization number for a set of phylogenies. In BMB, Vol. 75(10):18791890, 2013. Keywords: characterization, from rooted trees, hybridization, NP complete, phylogenetic network, phylogeny, reconstruction, time consistent network. Note: http://ab.inf.unituebingen.de/people/linz/publications/CPSpaper.pdf.
Toggle abstract
"Recently, we have shown that calculating the minimumtemporalhybridization number for a set P of rooted binary phylogenetic trees is NPhard and have characterized this minimum number when P consists of exactly two trees. In this paper, we give the first characterization of the problem for P being arbitrarily large. The characterization is in terms of cherries and the existence of a particular type of sequence. Furthermore, in an online appendix to the paper, we show that this new characterization can be used to show that computing the minimumtemporal hybridization number for two trees is fixedparameter tractable. © 2013 Society for Mathematical Biology."





Chris Whidden. Efficient Computation and Application of Maximum Agreement Forests. PhD thesis, Dalhousie University, Canada, 2013. Keywords: agreement forest, explicit network, FPT, from rooted trees, minimum number, phylogenetic network, phylogeny, reconstruction. Note: http://hdl.handle.net/10222/35349.



Philippe Gambette and
Katharina Huber. On Encodings of Phylogenetic Networks of Bounded Level. In JOMB, Vol. 65(1):157180, 2012. Keywords: characterization, explicit network, from clusters, from rooted trees, from triplets, galled tree, identifiability, level k phylogenetic network, phylogenetic network, uniqueness, weak hierarchy. Note: http://hal.archivesouvertes.fr/hal00609130/en/.
Toggle abstract
"Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the wellstudied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i. e. uniquely describe) the network that induces it? For the large class of level1 (phylogenetic) networks we characterize those level1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. In addition, we show that three known distance measures for comparing phylogenetic networks are in fact metrics on the resulting subclass and give the diameter for two of them. Finally, we investigate the related concept of indistinguishability and also show that many properties enjoyed by level1 networks are not satisfied by networks of higher level. © 2011 SpringerVerlag."



Steven Kelk,
Celine Scornavacca and
Leo van Iersel. On the elusiveness of clusters. In TCBB, Vol. 9(2):517534, 2012. Keywords: explicit network, from clusters, from rooted trees, from triplets, level k phylogenetic network, phylogenetic network, phylogeny, Program Clustistic, reconstruction, software. Note: http://arxiv.org/abs/1103.1834.





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."



Benjamin Albrecht,
Celine Scornavacca,
Alberto Cenci and
Daniel H. Huson. Fast computation of minimum hybridization networks. In BIO, Vol. 28(2):191197, 2012. Keywords: explicit network, from rooted trees, minimum number, phylogenetic network, phylogeny, Program Dendroscope, Program Hybroscale, reconstruction. Note: http://dx.doi.org/10.1093/bioinformatics/btr618.
Toggle abstract
"Motivation: Hybridization events in evolution may lead to incongruent gene trees. One approach to determining possible interspecific hybridization events is to compute a hybridization network that attempts to reconcile incongruent gene trees using a minimum number of hybridization events. Results: We describe how to compute a representative set of minimum hybridization networks for two given bifurcating input trees, using a parallel algorithm and provide a userfriendly implementation. A simulation study suggests that our program performs significantly better than existing software on biologically relevant data. Finally, we demonstrate the application of such methods in the context of the evolution of the Aegilops/Triticum genera. Availability and implementation: The algorithm is implemented in the program Dendroscope 3, which is freely available from www.dendroscope.org and runs on all three major operating systems. © The Author 2011. Published by Oxford University Press. All rights reserved."



Steven Kelk,
Leo van Iersel,
Nela Lekic,
Simone Linz,
Celine Scornavacca and
Leen Stougie. Cycle killer... qu'estce que c'est? On the comparative approximability of hybridization number and directed feedback vertex set. In SIDMA, Vol. 26(4):16351656, 2012. Keywords: agreement forest, approximation, explicit network, from rooted trees, minimum number, phylogenetic network, phylogeny, Program CycleKiller, reconstruction. Note: http://arxiv.org/abs/1112.5359, about the title.
Toggle abstract
"We show that the problem of computing the hybridization number of two rooted binary phylogenetic trees on the same set of taxa X has a constant factor polynomialtime approximation if and only if the problem of computing a minimumsize feedback vertex set in a directed graph (DFVS) has a constant factor polynomialtime approximation. The latter problem, which asks for a minimum number of vertices to be removed from a directed graph to transform it into a directed acyclic graph, is one of the problems in Karp's seminal 1972 list of 21 NPcomplete problems. Despite considerable attention from the combinatorial optimization community, it remains to this day unknown whether a constant factor polynomialtime approximation exists for DFVS. Our result thus places the (in)approximability of hybridization number in a much broader complexity context, and as a consequence we obtain that it inherits inapproximability results from the problem Vertex Cover. On the positive side, we use results from the DFVS literature to give an O(log r log log r) approximation for the hybridization number where r is the correct value. Copyright © by SIAM."



Philippe Gambette,
Vincent Berry and
Christophe Paul. Quartets and Unrooted Phylogenetic Networks. In JBCB, Vol. 10(4):1250004, 2012. Keywords: abstract network, circular split system, explicit network, from quartets, level k phylogenetic network, phylogenetic network, phylogeny, polynomial, reconstruction, split, split network. Note: http://hal.archivesouvertes.fr/hal00678046/en/.
Toggle abstract
"Phylogenetic networks were introduced to describe evolution in the presence of exchanges of genetic material between coexisting species or individuals. Split networks in particular were introduced as a special kind of abstract network to visualize conflicts between phylogenetic trees which may correspond to such exchanges. More recently, methods were designed to reconstruct explicit phylogenetic networks (whose vertices can be interpreted as biological events) from triplet data. In this article, we link abstract and explicit networks through their combinatorial properties, by introducing the unrooted analog of levelk networks. In particular, we give an equivalence theorem between circular split systems and unrooted level1 networks. We also show how to adapt to quartets some existing results on triplets, in order to reconstruct unrooted levelk phylogenetic networks. These results give an interesting perspective on the combinatorics of phylogenetic networks and also raise algorithmic and combinatorial questions. © 2012 Imperial College Press."



AnChiang Chu,
Jesper Jansson,
Richard Lemence,
Alban Mancheron and
KunMao Chao. Asymptotic Limits of a New Type of Maximization Recurrence with an Application to Bioinformatics. In TAMC12, Vol. 7287:177188 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)/1x 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(ni)(ni1)/2} and S′ n = max 0≤i<n{S′ i + ( 3 ni) + 2i( 2 ni) + (ni)( 2 i)}. We prove that lim n→∞ S′n/3( 3 n) = 2(√31)/3 ≈ 0.488033..., resolving an open problem from Bioinformatics about rooted triplets consistency in phylogenetic networks. © 2012 SpringerVerlag."



Reza Hassanzadeh,
Changiz Eslahchi and
WingKin Sung. Constructing phylogenetic supernetworks based on simulated annealing. In MPE, Vol. 63(3):738744, 2012. Keywords: abstract network, from unrooted trees, heuristic, phylogenetic network, phylogeny, Program SNSA, reconstruction, simulated annealing, software, split network. Note: http://dx.doi.org/10.1016/j.ympev.2012.02.009.
Toggle abstract
Different partial phylogenetic trees can be derived from different sources of evidence and different methods. One important problem is to summarize these partial phylogenetic trees using a supernetwork. We propose a novel simulated annealing based method called SNSA which uses an optimization function to produce a simple network that still retains a great deal of phylogenetic information. We report the performance of this new method on real and simulated datasets. © 2012 Elsevier Inc.



Jesper Jansson and
Andrzej Lingas. Computing the rooted triplet distance between galled trees by counting triangles. In CPM12, Vol. 7354:385398 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 socalled 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, 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 related results that may be of independent interest. © 2012 SpringerVerlag."



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(430440) 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 exponentialtime 2approximation (or 4approximation 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 SpringerVerlag."



Devin Robert Bickner. On normal networks. PhD thesis, Iowa State University, U.S.A., 2012. Keywords: distance between networks, explicit network, from network, from trees, normal network, phylogenetic network, phylogeny, polynomial, reconstruction, SPR distance. Note: http://gradworks.umi.com/3511361.pdf.



Donovan H. Parks and
Robert G. Beiko. Measuring Community Similarity with Phylogenetic Networks. In MBE, Vol. 29(12):39473958, 2012. Keywords: abstract network, diversity, phylogenetic network, phylogeny, split network. Note: poster available at http://dparks.wdfiles.com/localfiles/publications/SMBE_BetaDiversity_2011.pdf.
Toggle abstract
"Environmental drivers of biodiversity can be identified by relating patterns of community similarity to ecological factors. Community variation has traditionally been assessed by considering changes in species composition and more recently by incorporating phylogenetic information to account for the relative similarity of taxa. Here, we describe how an important class of measures including BrayCurtis, Canberra, and UniFrac can be extended to allow community variation to be computed on a phylogenetic network. We focus on phylogenetic split systems, networks that are produced by the widely used median network and neighbornet methods, which can represent incongruence in the evolutionary history of a set of taxa. Calculating β diversity over a split system provides a measure of community similarity averaged over uncertainty or conflict in the available phylogenetic signal. Our freely available software, Network Diversity, provides 11 qualitative (presenceabsence, unweighted) and 14 quantitative (weighted) networkbased measures of community similarity that model different aspects of community richness and evenness. We demonstrate the broad applicability of networkbased diversity approaches by applying them to three distinct data sets: pneumococcal isolates from distinct geographic regions, human mitochondrial DNA data from the Indonesian island of Nias, and proteorhodopsin sequences from the Sargasso and Mediterranean Seas. Our results show that major expected patterns of variation for these data sets are recovered using networkbased measures, which indicates that these patterns are robust to phylogenetic uncertainty and conflict. Nonetheless, networkbased measures of community similarity can differ substantially from measures ignoring phylogenetic relationships or from treebased measures when incongruent signals are present in the underlying data. Networkbased measures provide a methodology for assessing the robustness of βdiversity results in light of incongruent phylogenetic signal and allow β diversity to be calculated over widely used network structures such as median networks. © 2012 The Author 2012."



Josh Voorkamp né Collins,
Simone Linz and
Charles Semple. Quantifying hybridization in realistic time. In JCB, Vol. 18(10):13051318, 2011. Keywords: explicit network, FPT, from rooted trees, hybridization, minimum number, phylogenetic network, phylogeny, Program HybridInterleave, reconstruction, software. Note: http://wwwcsif.cs.ucdavis.edu/~linzs/CLS10_interleave.pdf, software available at http://www.math.canterbury.ac.nz/~c.semple/software.shtml.
Toggle abstract
"Recently, numerous practical and theoretical studies in evolutionary biology aim at calculating the extent to which reticulationfor example, horizontal gene transfer, hybridization, or recombinationhas influenced the evolution for a set of presentday species. It has been shown that inferring the minimum number of hybridization events that is needed to simultaneously explain the evolutionary history for a set of trees is an NPhard and also fixedparameter tractable problem. In this article, we give a new fixedparameter algorithm for computing the minimum number of hybridization events for when two rooted binary phylogenetic trees are given. This newly developed algorithm is based on interleavinga technique using repeated kernelization steps that are applied throughout the exhaustive search part of a fixedparameter algorithm. To show that our algorithm runs efficiently to be applicable to a wide range of practical problem instances, we apply it to a grass data set and highlight the significant improvements in terms of running times in comparison to an algorithm that has previously been implemented. © 2011, Mary Ann Liebert, Inc."



Leo van Iersel and
Steven Kelk. Constructing the Simplest Possible Phylogenetic Network from Triplets. In ALG, Vol. 60(2):207235, 2011. Keywords: explicit network, from triplets, galled tree, level k phylogenetic network, minimum number, phylogenetic network, phylogeny, polynomial, Program Marlon, Program Simplistic. Note: http://dx.doi.org/10.1007/s0045300993330.
Toggle abstract
"A phylogenetic network is a directed acyclic graph that visualizes an evolutionary history containing socalled reticulations such as recombinations, hybridizations or lateral gene transfers. Here we consider the construction of a simplest possible phylogenetic network consistent with an input set T, where T contains at least one phylogenetic tree on three leaves (a triplet) for each combination of three taxa. To quantify the complexity of a network we consider both the total number of reticulations and the number of reticulations per biconnected component, called the level of the network. We give polynomialtime algorithms for constructing a level1 respectively a level2 network that contains a minimum number of reticulations and is consistent with T (if such a network exists). In addition, we show that if T is precisely equal to the set of triplets consistent with some network, then we can construct such a network with smallest possible level in time O(T k+1), if k is a fixed upper bound on the level of the network. © 2009 The Author(s)."



Leo van Iersel and
Steven Kelk. When two trees go to war. In JTB, Vol. 269(1):245255, 2011. Keywords: APX hard, explicit network, from clusters, from rooted trees, from sequences, from triplets, level k phylogenetic network, minimum number, NP complete, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://arxiv.org/abs/1004.5332.
Toggle abstract
"Rooted phylogenetic networks are used to model nontreelike evolutionary histories. Such networks are often constructed by combining trees, clusters, triplets or characters into a single network that in some welldefined sense simultaneously represents them all. We review these four models and investigate how they are related. Motivated by the parsimony principle, one often aims to construct a network that contains as few reticulations (nontreelike evolutionary events) as possible. In general, the model chosen influences the minimum number of reticulation events required. However, when one obtains the input data from two binary (i.e. fully resolved) trees, we show that the minimum number of reticulations is independent of the model. The number of reticulations necessary to represent the trees, triplets, clusters (in the softwired sense) and characters (with unrestricted multiple crossover recombination) are all equal. Furthermore, we show that these results also hold when not the number of reticulations but the level of the constructed network is minimised. We use these unification results to settle several computational complexity questions that have been open in the field for some time. We also give explicit examples to show that already for data obtained from three binary trees the models begin to diverge. © 2010 Elsevier Ltd."





Lavanya Kannan,
Hua Li and
Arcady Mushegian. A PolynomialTime Algorithm Computing Lower and Upper Bounds of the Rooted Subtree Prune and Regraft Distance. In JCB, Vol. 18(5):743757, 2011. Keywords: bound, minimum number, polynomial, SPR distance. Note: http://dx.doi.org/10.1089/cmb.2010.0045.
Toggle abstract
"Rooted, leaflabeled trees are used in biology to represent hierarchical relationships of various entities, most notably the evolutionary history of molecules and organisms. Rooted Subtree Prune and Regraft (rSPR) operation is a tree rearrangement operation that is used to transform a tree into another tree that has the same set of leaf labels. The minimum number of rSPR operations that transform one tree into another is denoted by drSPR and gives a measure of dissimilarity between the trees, which can be used to compare trees obtained by different approaches, or, in the context of phylogenetic analysis, to detect horizontal gene transfer events by finding incongruences between trees of different evolving characters. The problem of computing the exact d rSPR measure is NPhard, and most algorithms resort to finding sequences of rSPR operations that are sufficient for transforming one tree into another, thereby giving upper bound heuristics for the distance. In this article, we present an O(n4) recursive algorithm DClust that gives both lower bound and upper bound heuristics for the distance between trees with n shared leaves and also gives a sequence of operations that transforms one tree into another. Our experiments on simulated pairs of trees containing up to 100 leaves showed that the two bounds are almost equal for small distances, thereby giving the nearlyprecise actual value, and that the upper bound tends to be close to the upper bounds given by other approaches for all pairs of trees. © Copyright 2011, Mary Ann Liebert, Inc. 2011."



Yun Yu,
Cuong Than,
James H. Degnan and
Luay Nakhleh. Coalescent Histories on Phylogenetic Networks and Detection of Hybridization Despite Incomplete Lineage Sorting. In Systematic Biology, Vol. 60(2):138149, 2011. Keywords: coalescent, hybridization, lineage sorting, reconstruction, statistical model. Note: http://www.cs.rice.edu/~nakhleh/Papers/YuEtAlSB11.pdf.
Toggle abstract
"Analyses of the increasingly available genomic data continue to reveal the extent of hybridization and its role in the evolutionary diversification of various groups of species. We show, through extensive coalescentbased simulations of multilocus data sets on phylogenetic networks, how divergence times before and after hybridization events can result in incomplete lineage sorting with gene tree incongruence signatures identical to those exhibited by hybridization. Evolutionary analysis of such data under the assumption of a species tree model can miss all hybridization events, whereas analysis under the assumption of a species network model would grossly overestimate hybridization events. These issues necessitate a paradigm shift in evolutionary analysis under these scenarios, from a model that assumes a priori a single source of gene tree incongruence to one that integrates multiple sources in a unifying framework. We propose a framework of coalescence within the branches of a phylogenetic network and show how this framework can be used to detect hybridization despite incomplete lineage sorting. We apply the model to simulated data and show that the signature of hybridization can be revealed as long as the interval between the divergence times of the species involved in hybridization is not too small. We reanalyze a data set of 106 loci from 7 ingroup Saccharomyces species for which a species tree with no hybridization has been reported in the literature. Our analysis supports the hypothesis that hybridization occurred during the evolution of this group, explaining a large amount of the incongruence in the data. Our findings show that an integrative approach to gene tree incongruence and its reconciliation is needed. Our framework will help in systematically analyzing genomic data for the occurrence of hybridization and elucidating its evolutionary role. [Coalescent history; incomplete lineage sorting; hybridization; phylogenetic network.]. © 2011 The Author(s)."



Lawrence A. David and
Eric J. Alm. Rapid evolutionary innovation during an Archaean genetic expansion. In Nature, Vol. 469:9396, 2011. Keywords: duplication, dynamic programming, from multilabeled tree, from rooted trees, from species tree, parsimony, phylogenetic network, phylogeny, Program Angst. Note: http://dx.doi.org/10.1038/nature09649, Program Angst described here.





Mukul S. Bansal,
Guy Banay,
J. Peter Gogarten and
Ron Shamir. Detecting Highways of Horizontal Gene Transfer. In JCB, Vol. 18(9):10871114, 2011. Keywords: explicit network, from rooted trees, from species tree, lateral gene transfer, phylogenetic network, phylogeny, polynomial, reconstruction. Note: http://people.csail.mit.edu/mukul/HighwayFull_preprint.pdf.
Toggle abstract
"In a horizontal gene transfer (HGT) event, a gene is transferred between two species that do not have an ancestordescendant 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 and m input quartet trees, we give an efficient O(m+n 2)time algorithm for detecting highways, 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. © 2011, Mary Ann Liebert, Inc."



Changiz Eslahchi and
Reza Hassanzadeh. New Algorithm for Constructing Supernetworks from Partial Trees. In MCCMB11, Pages 106107, 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.





ZhiZhong Chen and
Lusheng Wang. HybridNET: a tool for constructing hybridization networks. In BIO, Vol. 26(22):29122913, 2010. Keywords: agreement forest, FPT, from rooted trees, hybridization, phylogenetic network, phylogeny, Program HybridNET, software. Note: http://rnc.r.dendai.ac.jp/~chen/papers/note2.pdf.
Toggle abstract
"Motivations: When reticulation events occur, the evolutionary history of a set of existing species can be represented by a hybridization network instead of an evolutionary tree. When studying the evolutionary history of a set of existing species, one can obtain a phylogenetic tree of the set of species with high confidence by looking at a segment of sequences or a set of genes. When looking at another segment of sequences, a different phylogenetic tree can be obtained with high confidence too. This indicates that reticulation events may occur. Thus, we have the following problem: given two rooted phylogenetic trees on a set of species that correctly represent the treelike evolution of different parts of their genomes, what is the hybridization network with the smallest number of reticulation events to explain the evolution of the set of species under consideration? Results: We develop a program, named HybridNet, for constructing a hybridization network with the minimum number of reticulate vertices from two input trees. We first implement the O(3dn)time algorithm by Whidden et al. for computing a maximum (acyclic) agreement forest. Our program can output all the maximum (acyclic) agreement forests. We then augment the program so that it can construct an optimal hybridization network for each given maximum acyclic agreement forest. To our knowledge, this is the first time that optimal hybridization networks can be rapidly constructed. © The Author 2010. Published by Oxford University Press. All rights reserved."



Philippe Gambette. Méthodes combinatoires de reconstruction de réseaux phylogénétiques. PhD thesis, Université Montpellier 2, France, 2010. Keywords: abstract network, characterization, circular split system, explicit network, FPT, from clusters, from triplets, integer linear programming, level k phylogenetic network, NP complete, phylogenetic network, phylogeny, Program Dendroscope, pyramid, reconstruction, split network, weak hierarchy. Note: http://tel.archivesouvertes.fr/tel00608342/en/.



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."



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):i124i131 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."





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.
Toggle abstract
"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."



Yufeng Wu. Close Lower and Upper Bounds for the Minimum Reticulate Network of Multiple Phylogenetic Trees. In ISMB10, Vol. 26(12):i140i148 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 wellknown to be NPhard. 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."



Yufeng Wu and
Jiayin Wang. Fast Computation of the Exact Hybridization Number of Two Phylogenetic Trees. In ISBRA10, Vol. 6053:203214 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 NPhard. 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 SpringerVerlag Berlin Heidelberg."



Sophie Abby,
Eric Tannier,
Manolo Gouy and
Vincent Daubin. Detecting lateral gene transfers by statistical reconciliation of phylogenetic forests. In BMCB, Vol. 11:324, 2010. Keywords: explicit network, from rooted trees, from species tree, heuristic, lateral gene transfer, phylogenetic network, phylogeny, Program EEEP, Program PhyloNet, Program Prunier, reconstruction, software. Note: http://www.biomedcentral.com/14712105/11/324.
Toggle abstract
"Background: To understand the evolutionary role of Lateral Gene Transfer (LGT), accurate methods are needed to identify transferred genes and infer their timing of acquisition. Phylogenetic methods are particularly promising for this purpose, but the reconciliation of a gene tree with a reference (species) tree is computationally hard. In addition, the application of these methods to real data raises the problem of sorting out real and artifactual phylogenetic conflict.Results: We present Prunier, a new method for phylogenetic detection of LGT based on the search for a maximum statistical agreement forest (MSAF) between a gene tree and a reference tree. The program is flexible as it can use any definition of "agreement" among trees. We evaluate the performance of Prunier and two other programs (EEEP and RIATAHGT) for their ability to detect transferred genes in realistic simulations where gene trees are reconstructed from sequences. Prunier proposes a single scenario that compares to the other methods in terms of sensitivity, but shows higher specificity. We show that LGT scenarios carry a strong signal about the position of the root of the species tree and could be used to identify the direction of evolutionary time on the species tree. We use Prunier on a biological dataset of 23 universal proteins and discuss their suitability for inferring the tree of life.Conclusions: The ability of Prunier to take into account branch support in the process of reconciliation allows a gain in complexity, in comparison to EEEP, and in accuracy in comparison to RIATAHGT. Prunier's greedy algorithm proposes a single scenario of LGT for a gene family, but its quality always compares to the best solutions provided by the other algorithms. When the root position is uncertain in the species tree, Prunier is able to infer a scenario per root at a limited additional computational cost and can easily run on large datasets.Prunier is implemented in C++, using the Bio++ library and the phylogeny program Treefinder. It is available at: http://pbil.univlyon1.fr/software/prunier. © 2010 Abby et al; licensee BioMed Central Ltd."





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."



Luay Nakhleh,
Derek Ruths and
Hideki Innan. Gene Trees, Species Trees, and Species Networks. In
R. Guerra,
D. B. Allison and
D. Goldstein editors, Metaanalysis 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.



Leo van Iersel. Algorithms, Haplotypes and Phylogenetic Networks. PhD thesis, Eindhoven University of Technology, The Netherlands, 2009. Keywords: evaluation, explicit network, exponential algorithm, FPT, from triplets, galled tree, level k phylogenetic network, mu distance, phylogenetic network, phylogeny, polynomial, Program Level2, Program Marlon, Program Simplistic, Program T REX, reconstruction. Note: http://www.win.tue.nl/~liersel/thesis_vaniersel_viewing.pdf.



ThuHien To and
Michel Habib. Levelk Phylogenetic Networks Are Constructable from a Dense Triplet Set in Polynomial Time. In CPM09, (5577):275288, 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 SNsets in a levelk network. As a consequence, for any fixed k, we can also find a levelk network with the minimum number of reticulations, if one exists, in polynomial time. © 2009 Springer Berlin Heidelberg."



Philippe Gambette,
Vincent Berry and
Christophe Paul. The structure of levelk phylogenetic networks. In CPM09, Vol. 5577:289300 of LNCS, springer, 2009. Keywords: coalescent, explicit network, galled tree, level k phylogenetic network, phylogenetic network, Program Recodon. Note: http://hallirmm.ccsd.cnrs.fr/lirmm00371485/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 treelikeness. We study the structure of levelk networks, and how they can be decomposed into levelk generators. We also provide a polynomial time algorithm which takes as input the set of levelk generators and builds the set of level(k + 1) generators. Finally, with a simulation study, we evaluate the proportion of levelk phylogenetic networks among networks generated according to the coalescent model with recombination. © 2009 Springer Berlin Heidelberg."



Daniel H. Huson,
Regula Rupp,
Vincent Berry,
Philippe Gambette and
Christophe Paul. Computing Galled Networks from Real Data. In ISMBECCB09, Vol. 25(12):i85i93 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://hallirmm.ccsd.cnrs.fr/lirmm00368545/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 levelk networks, that are more tractable, but have the practical drawback 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 tradeoff 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 NPcomplete 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)."





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."



Ali Tofigh. Using Trees to Capture Reticulate Evolution, Lateral Gene Transfers and Cancer Progression. PhD thesis, KTH Royal Institute of Technology, Sweden, 2009. Keywords: duplication, dynamic programming, from multilabeled tree, from rooted trees, from species tree, lateral gene transfer, loss, NP complete, phylogenetic network, phylogeny, reconstruction. Note: http://kth.divaportal.org/smash/record.jsf?pid=diva2:220830&searchId=1.



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.



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):3545, 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 singlegene phylogenetic estimates. Among the processes known to produce discord between singlegene 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 singlegene 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."



Chris Whidden. A Unifying View on Approximation and FPT of Agreement Forests. Master's thesis, Dalhousie University, Canada, 2009. Keywords: agreement forest, approximation, explicit network, FPT, from rooted trees, hybridization, phylogenetic network, phylogeny, reconstruction, SPR distance. Note: http://web.cs.dal.ca/~whidden/MCSThesis09.pdf.



Chris Whidden and
Norbert Zeh. A Unifying View on Approximation and FPT of Agreement Forests. In WABI09, Vol. 5724:390402 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/CS200902.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 3approximation and improved fixedparameter 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."



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."



Rune Lyngsø,
Yun S. Song and
Jotun Hein. Accurate Computation of Likelihoods in the Coalescent with Recombination via Parsimony. In RECOMB08, Vol. 4955:463477 of LNCS, springer, 2008. Keywords: coalescent, likelihood, phylogenetic network, phylogeny, recombination, statistical model. Note: http://dx.doi.org/10.1007/9783540788393_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 widelyused 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 twolocus 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, parsimonybased method of accurately computing the likelihood for multilocus 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 algorithmbased method described here opens up a new window of opportunities for testing and finetuning statistical methods for computing likelihoods. © 2008 SpringerVerlag Berlin Heidelberg."



Steven M. Woolley,
David Posada and
Keith A. Crandall. A Comparison of Phylogenetic Network Methods Using Computer Simulation. In PLoSONE, 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, neighbornet, simulated history recombination upper bound, medianjoining, reduced median joining and minimum spanning network) compared to standard tree approaches (neighborjoining 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."



Simone Linz. Reticulation in evolution. PhD thesis, HeinrichHeineUniversity, Düsseldorf, Germany, 2008. Keywords: agreement forest, FPT, from rooted trees, lateral gene transfer, phylogenetic network, phylogeny, SPR distance, statistical model. Note: http://docserv.uniduesseldorf.de/servlets/DocumentServlet?id=8505.



Leo van Iersel and
Steven Kelk. Constructing the Simplest Possible Phylogenetic Network from Triplets. In ISAAC08, Vol. 5369:472483 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.



Cuong Than and
Luay Nakhleh. SPRbased Tree Reconciliation: Nonbinary Trees and Multiple Solutions. In APBC08, Pages 251260, 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.



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.



Miguel Arenas,
Gabriel Valiente and
David Posada. Characterization of reticulate networks based on the coalescent with recombination. In MBE, Vol. 25(12):25172520, 2008. Keywords: coalescent, evaluation, explicit network, galled tree, phylogenetic network, phylogeny, Program Recodon, regular network, simulation, tree child network, tree sibling 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."



Supriya Munshaw and
Thomas B. Kepler. An InformationTheoretic Method for the Treatment of Plural Ancestry in Phylogenetics. In MBE, Vol. 25(6):11991208, 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."



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/10.1186/147121058458.
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 timereversible model of nucleotide substitution with a proportion of invariable sites and amongsite rate variation. In addition, the program implements nonreversible 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."



Magnus Bordewich,
Simone Linz,
Katherine St. John and
Charles Semple. A reduction algorithm for computing the hybridization number of two trees. In EBIO, Vol. 3:8698, 2007. Keywords: agreement forest, FPT, from rooted trees, hybridization, phylogenetic network, phylogeny, Program HybridNumber. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/BLSS07.pdf.



Magnus Bordewich and
Charles Semple. Computing the minimum number of hybridization events for a consistent evolutionary history. In DAM, Vol. 155:914918, 2007. Keywords: agreement forest, approximation, APX hard, explicit network, from rooted trees, hybridization, inapproximability, NP complete, phylogenetic network, phylogeny, SPR distance. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/BS06a.pdf.





Stefan Grünewald,
Kristoffer Forslund,
Andreas W. M. Dress and
Vincent Moulton. QNet: An agglomerative method for the construction of phylogenetic networks from weighted quartets. In MBE, Vol. 24(2):532538, 2007. Keywords: abstract network, circular split system, from quartets, phylogenetic network, phylogeny, Program QNet, reconstruction, software. Note: http://mbe.oxfordjournals.org/cgi/content/abstract/24/2/532.
Toggle abstract
"We present QNet, a method for constructing split networks from weighted quartet trees. QNet can be viewed as a quartet analogue of the distancebased NeighborNet (NNet) method for network construction. Just as NNet, QNet works by agglomeratively computing a collection of circular weighted splits of the taxa set which is subsequently represented by a planar split network. To illustrate the applicability of QNet, we apply it to a previously published Salmonella data set. We conclude that QNet can provide a useful alternative to NNet if distance data are not available or a characterbased approach is preferred. Moreover, it can be used as an aid for determining when a quartetbased treebuilding method may or may not be appropriate for a given data set. QNet is freely available for download. © The Author 2006. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved."



Dan Gusfield,
Dean Hickerson and
Satish Eddhu. An efficiently computed lower bound on the number of recombinations in phylogenetic networks: Theory and empirical study. In DAM, Vol. 155(67):806830, 2007. Note: http://wwwcsif.cs.ucdavis.edu/~gusfield/cclowerbound.pdf.
Toggle abstract
"Phylogenetic networks are models of sequence evolution that go beyond trees, allowing biological operations that are not treelike. One of the most important biological operations is recombination between two sequences. An established problem [J. Hein, Reconstructing evolution of sequences subject to recombination using parsimony, Math. Biosci. 98 (1990) 185200; J. Hein, A heuristic method to reconstruct the history of sequences subject to recombination, J. Molecular Evoluation 36 (1993) 396405; Y. Song, J. Hein, Parsimonious reconstruction of sequence evolution and haplotype blocks: finding the minimum number of recombination events, in: Proceedings of 2003 Workshop on Algorithms in Bioinformatics, Berlin, Germany, 2003, Lecture Notes in Computer Science, Springer, Berlin; Y. Song, J. Hein, On the minimum number of recombination events in the evolutionary history of DNA sequences, J. Math. Biol. 48 (2003) 160186; L. Wang, K. Zhang, L. Zhang, Perfect phylogenetic networks with recombination, J. Comput. Biol. 8 (2001) 6978; S.R. Myers, R.C. Griffiths, Bounds on the minimum number of recombination events in a sample history, Genetics 163 (2003) 375394; V. Bafna, V. Bansal, Improved recombination lower bounds for haplotype data, in: Proceedings of RECOMB, 2005; Y. Song, Y. Wu, D. Gusfield, Efficient computation of close lower and upper bounds on the minimum number of needed recombinations in the evolution of biological sequences, Bioinformatics 21 (2005) i413i422. Bioinformatics (Suppl. 1), Proceedings of ISMB, 2005, D. Gusfield, S. Eddhu, C. Langley, Optimal, efficient reconstruction of phylogenetic networks with constrained recombination, J. Bioinform. Comput. Biol. 2(1) (2004) 173213; D. Gusfield, Optimal, efficient reconstruction of rootunknown phylogenetic networks with constrained and structured recombination, J. Comput. Systems Sci. 70 (2005) 381398] is to find a phylogenetic network that derives an input set of sequences, minimizing the number of recombinations used. No efficient, general algorithm is known for this problem. Several papers consider the problem of computing a lower bound on the number of recombinations needed. In this paper we establish a new, efficiently computed lower bound. This result is useful in methods to estimate the number of needed recombinations, and also to prove the optimality of algorithms for constructing phylogenetic networks under certain conditions [D. Gusfield, S. Eddhu, C. Langley, Optimal, efficient reconstruction of phylogenetic networks with constrained recombination, J. Bioinform. Comput. Biol. 2(1) (2004) 173213; D. Gusfield, Optimal, efficient reconstruction of rootunknown phylogenetic networks with constrained and structured recombination, J. Comput. Systems Sci. 70 (2005) 381398; D. Gusfield, Optimal, efficient reconstruction of rootunknown phylogenetic networks with constrained recombination, Technical Report, Department of Computer Science, University of California, Davis, CA, 2004]. The lower bound is based on a structural, combinatorial insight, using only the site conflicts and incompatibilities, and hence it is fundamental and applicable to many biological phenomena other than recombination, for example, when gene conversions or recurrent or back mutations or crossspecies hybridizations cause the phylogenetic history to deviate from a tree structure. In addition to establishing the bound, we examine its use in more complex lower bound methods, and compare the bounds obtained to those obtained by other established lower bound methods. © 2006 Elsevier B.V. All rights reserved."



Katharina Huber,
Bengt Oxelman,
Martin Lott and
Vincent Moulton. Reconstructing the Evolutionary History of Polyploids from Multilabeled Trees. In MBE, Vol. 23(9):17841791, 2007. Keywords: duplication, explicit network, from multilabeled tree, from trees, phylogenetic network, phylogeny, Program PADRE, reconstruction, software. Note: http://mbe.oxfordjournals.org/cgi/content/full/23/9/1784.
Toggle abstract
"In recent studies, phylogenetic networks have been derived from socalled multilabeled trees in order to understand the origins of certain polyploids. Although the trees used in these studies were constructed using sophisticated techniques in phylogenetic analysis, the presented networks were inferred using ad hoc arguments that cannot be easily extended to larger, more complicated examples. In this paper, we present a general method for constructing such networks, which takes as input a multilabeled phylogenetic tree and outputs a phylogenetic network with certain desirable properties. To illustrate the applicability of our method, we discuss its use in reconstructing the evolutionary history of plant allopolyploids. We conclude with a discussion concerning possible future directions. The network construction method has been implemented and is freely available for use from http://www.uea.ac.uk/ ∼a043878/padre.html. © The Author 2006. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved."



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.





Maria S. Poptsova and
J. Peter Gogarten. The power of phylogenetic approaches to detect horizontally transferred genes. In BMCEB, Vol. 7(45), 2007. Keywords: evaluation, from rooted trees, lateral gene transfer, Program EEEP. Note: http://dx.doi.org/10.1186/14712148745.
Toggle abstract
"Background. Horizontal gene transfer plays an important role in evolution because it sometimes allows recipient lineages to adapt to new ecological niches. High genes transfer frequencies were inferred for prokaryotic and early eukaryotic evolution. Does horizontal gene transfer also impact phylogenetic reconstruction of the evolutionary history of genomes and organisms? The answer to this question depends at least in part on the actual gene transfer frequencies and on the ability to weed out transferred genes from further analyses. Are the detected transfers mainly false positives, or are they the tip of an iceberg of many transfer events most of which go undetected by current methods? Results. Phylogenetic detection methods appear to be the method of choice to infer gene transfers, especially for ancient transfers and those followed by orthologous replacement. Here we explore how well some of these methods perform using in silico transfers between the terminal branches of a gamma proteobacterial, genome based phylogeny. For the experiments performed here on average the AU test at a 5% significance level detects 90.3% of the transfers and 91% of the exchanges as significant. Using the RobinsonFoulds distance only 57.7% of the exchanges and 60% of the donations were identified as significant. Analyses using bipartition spectra appeared most successful in our test case. The power of detection was on average 97% using a 70% cutoff and 94.2% with 90% cutoff for identifying conflicting bipartitions, while the rate of false positives was below 4.2% and 2.1% for the two cutoffs, respectively. For all methods the detection rates improved when more intervening branches separated donor and recipient. Conclusion. Rates of detected transfers should not be mistaken for the actual transfer rates; most analyses of gene transfers remain anecdotal. The method and significance level to identify potential gene transfer events represent a tradeoff between the frequency of erroneous identification (false positives) and the power to detect actual transfer events. © 2007 Poptsova and Gogarten; licensee BioMed Central Ltd."



Dan Gusfield,
Vikas Bansal,
Vineet Bafna and
Yun S. Song. A Decomposition Theory for Phylogenetic Networks and Incompatible Characters. In JCB, Vol. 14(10):12471272, 2007. Keywords: explicit network, from sequences, galled tree, phylogenetic network, phylogeny, Program Beagle, Program GalledTree, recombination, reconstruction, software. Note: http://www.eecs.berkeley.edu/~yss/Pub/decomposition.pdf.



Joanna L. Davies,
Frantisek Simancík,
Rune Lyngsø,
Thomas Mailund and
Jotun Hein. On RecombinationInduced Multiple and Simultaneous Coalescent Events. In GEN, Vol. 177:21512160, 2007. Keywords: coalescent, phylogenetic network, phylogeny, recombination, statistical model. Note: http://dx.doi.org/10.1534/genetics.107.071126.
Toggle abstract
"Coalescent theory deals with the dynamics of how sampled genetic material has spread through a population from a single ancestor over many generations and is ubiquitous in contemporary molecular population genetics. Inherent in most applications is a continuoustime approximation that is derived under the assumption that sample size is small relative to the actual population size. In effect, this precludes multiple and simultaneous coalescent events that take place in the history of large samples. If sequences do not recombine, the number of sequences ancestral to a large sample is reduced sufficiently after relatively few generations such that use of the continuoustime approximation is justified. However, in tracing the history of large chromosomal segments, a large recombination rate per generation will consistently maintain a large number of ancestors. This can create a major disparity between discretetime and continuoustime models and we analyze its importance, illustrated with model parameters typical of the human genome. The presence of gene conversion exacerbates the disparity and could seriously undermine applications of coalescent theory to complete genomes. However, we show that multiple and simultaneous coalescent events influence global quantities, such as total number of ancestors, but have negligible effect on local quantities, such as linkage disequilibrium. Reassuringly, most applications of the coalescent model with recombination (including association mapping) focus on local quantities. Copyright © 2007 by the Genetics Society of America."





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."



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.



Robert G. Beiko and
Nicholas Hamilton. Phylogenetic identification of lateral genetic transfer events. In BMCEB, Vol. 6(15), 2006. Keywords: evaluation, from rooted trees, from unrooted trees, lateral gene transfer, Program EEEP, Program HorizStory, Program LatTrans, reconstruction, software, SPR distance. Note: http://dx.doi.org/10.1186/14712148615.
Toggle abstract
"Background: Lateral genetic transfer can lead to disagreements among phylogenetic trees comprising sequences from the same set of taxa. Where topological discordance is thought to have arisen through genetic transfer events, tree comparisons can be used to identify the lineages that may have shared genetic information. An 'edit path' of one or more transfer events can be represented with a series of subtree prune and regraft (SPR) operations, but finding the optimal such set of operations is NPhard for comparisons between rooted trees, and may be so for unrooted trees as well. Results: Efficient Evaluation of Edit Paths (EEEP) is a new tree comparison algorithm that uses evolutionarily reasonable constraints to identify and eliminate many unproductive search avenues, reducing the time required to solve many edit path problems. The performance of EEEP compares favourably to that of other algorithms when applied to strictly bifurcating trees with specified numbers of SPR operations. We also used EEEP to recover edit paths from over 19 000 unrooted, incompletely resolved protein trees containing up to 144 taxa as part of a large phylogenomic study. While inferred protein trees were far more similar to a reference supertree than random trees were to each other, the phylogenetic distance spanned by random versus inferred transfer events was similar, suggesting that real transfer events occur most frequently between closely related organisms, but can span large phylogenetic distances as well. While most of the protein trees examined here were very similar to the reference supertree, requiring zero or one edit operations for reconciliation, some trees implied up to 40 transfer events within a single orthologous set of proteins. Conclusion: Since sequence trees typically have no implied root and may contain unresolved or multifurcating nodes, the strategy implemented in EEEP is the most appropriate for phylogenomic analyses. The high degree of consistency among inferred protein trees shows that vertical inheritance is the dominant pattern of evolution, at least for the set of organisms considered here. However, the edit paths inferred using EEEP suggest an important role for genetic transfer in the evolution of microbial genomes as well. © 2006Beiko and Hamilton; licensee BioMed Central Ltd."







Mihaela Baroni,
Stefan Grünewald,
Vincent Moulton and
Charles Semple. Bounding the number of hybridization events for a consistent evolutionary history. In JOMB, Vol. 51(2):171182, 2005. Keywords: agreement forest, bound, explicit network, from rooted trees, hybridization, minimum number, phylogenetic network, phylogeny, reconstruction, SPR distance. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/BGMS05.pdf.
Toggle abstract
"Evolutionary processes such as hybridisation, lateral gene transfer, and recombination are all key factors in shaping the structure of genes and genomes. However, since such processes are not always best represented by trees, there is now considerable interest in using more general networks instead. For example, in recent studies it has been shown that networks can be used to provide lower bounds on the number of recombination events and also for the number of lateral gene transfers that took place in the evolutionary history of a set of molecular sequences. In this paper we describe the theoretical performance of some related bounds that result when merging pairs of trees into networks. © SpringerVerlag 2005."



Magnus Bordewich and
Charles Semple. On the computational complexity of the rooted subtree prune and regraft distance. In ACOM, Vol. 8:409423, 2005. Keywords: agreement forest, from rooted trees, NP complete, SPR distance. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/BS04.pdf.
Toggle abstract
"The graphtheoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NPhard. This resolves a longstanding open problem. Furthermore, we show that this distance is fixed parameter tractable when parameterised by the distance between the two trees."



Trinh N. D. Huynh,
Jesper Jansson,
Nguyen Bao Nguyen and
WingKin Sung. Constructing a Smallest Refining Galled Phylogenetic Network. In RECOMB05, Vol. 3500:265280 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.



Rune Lyngsø,
Yun S. Song and
Jotun Hein. Minimum Recombination Histories by Branch and Bound. In WABI05, Vol. 3692:239250 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/WABI05239.pdf.



Luay Nakhleh,
Tandy Warnow,
C. Randal Linder and
Katherine St. John. Reconstructing reticulate evolution in species  theory and practice. In JCB, Vol. 12(6):796811, 2005. Keywords: from rooted trees, galled tree, phylogenetic network, phylogeny, polynomial, Program SPNet, reconstruction, software. Note: http://www.cs.rice.edu/~nakhleh/Papers/NWLSjcb.pdf.





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:i413i422 of BIO, 2005. Keywords: 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 NPhard, 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."



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):363372, 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.



Vineet Bafna and
Vikas Bansal. The Number of Recombination Events in a Sample History: Conflict Graph and Lower Bounds. In TCBB, Vol. 1(2):7890, 2004. Keywords: ARG, bound, minimum number, phylogeny, recombination. Note: http://wwwcse.ucsd.edu/users/vbafna/pub/tcbb04.pdf.
Toggle abstract
"We consider the following problem: Given a set of binary sequences, determine lower bounds on the minimum number of recombinations required to explain the history of the sample, under the infinitesites model of mutation. The problem has implications for finding recombination hotspots and for the Ancestral Recombination Graph reconstruction problem. Hudson and Kaplan gave a lower bound based on the fourgamete test. In practice, their bound R m often greatly underestimates the minimum number of recombinations. The problem was recently revisited by Myers and Griffiths, who introduced two new lower bounds R h and R s which are provably better, and also yield good bounds in practice. However, the worstcase complexities of their procedures for computing R h and R s are exponential and superexponential, respectively. In this paper, we show that the number of nontrivial connected components, Rc, in the conflict graph for a given set of sequences, computable in time O(nm 2), is also a lower bound on the minimum number of recombination events. We show that in many cases, R c is a better bound than R h. The conflict graph was used by Gusfield et al. to obtain a polynomial time algorithm for the galled tree problem, which is a special case of the Ancestral Recombination Graph (ARG) reconstruction problem. Our results also offer some insight into the structural properties of this graph and are of interest for the general Ancestral Recombination Graph reconstruction problem."



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."



Mihaela Baroni,
Charles Semple and
Mike Steel. A framework for representing reticulate evolution. In ACOM, Vol. 8:398401, 2004. Keywords: explicit network, from clusters, hybridization, minimum number, phylogenetic network, phylogeny, reconstruction, regular network, SPR distance. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/BSS04.pdf.
Toggle abstract
"Acyclic directed graphs (ADGs) are increasingly being viewed as more appropriate for representing certain evolutionary relationships, particularly in biology, than rooted trees. In this paper, we develop a framework for the analysis of these graphs which we call hybrid phylogenies. We are particularly interested in the problem whereby one is given a set of phylogenetic trees and wishes to determine a hybrid phylogeny that 'embeds' each of these trees and which requires the smallest number of hybridisation events. We show that this quantity can be greatly reduced if additional species are involved, and investigate other combinatorial aspects of this and related questions."



Dan Gusfield and
Dean Hickerson. A Fundamental, EfficientlyComputed Lower Bound on the Number of Recombinations Needed in Phylogenetic Networks. 2004. Note: UC Davis Computer Science Technical Report.





Luay Nakhleh. Phylogenetic Networks. PhD thesis, University of Texas at Austin, U.S.A., 2004. Keywords: distance between networks, evaluation, generation, phylogenetic network, phylogeny, Program SPNet, reconstruction, split, statistical model, tree sibling network. Note: http://www.library.utexas.edu/etd/d/2004/nakhlehl042/nakhlehl042.pdf.



Luay Nakhleh,
Tandy Warnow and
C. Randal Linder. Reconstructing reticulate evolution in species  theory and practice. In RECOMB04, Pages 337346, 2004. Keywords: from rooted trees, galled tree, phylogenetic network, phylogeny, polynomial, Program SPNet, reconstruction, software. Note: http://www.cs.rice.edu/~nakhleh/Papers/144nakhleh.pdf.



Yun S. Song and
Jotun Hein. On the Minimum Number of Recombination Events in the Evolutionary History of DNA Sequences. In JOMB, Vol. 48(2):160186, 2004. Keywords: minimum number, recombination. Note: http://dx.doi.org/10.1007/s0028500302275.
Toggle abstract
"In representing the evolutionary history of a set of binary DNA sequences by a connected graph, a set theoretical approach is introduced for studying recombination events. We show that set theoretical constraints have direct implications on the number of recombination events. We define a new lower bound on the number of recombination events and demonstrate the usefulness of our new approach through several explicit examples. © SpringerVerlag 2003."





Mihaela Baroni. Hybrid phylogenies : a graphbased approach to represent reticulate evolution. PhD thesis, University of Canterbury, New Zealand, 2004. Keywords: explicit network, from rooted trees, galled tree, hybridization, minimum number, phylogenetic network, phylogeny, reconstruction, regular network. Note: http://ir.canterbury.ac.nz/bitstream/10092/4803/1/baroni_thesis.pdf.







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.



















Richard R. Hudson. Properties of the neutral allele model with intragenic recombination. In TPP, Vol. 23:183201, 1983. Keywords: coalescent. Note: http://dx.doi.org/10.1016/00405809(83)900138, see also http://www.brics.dk/~compbio/coalescent/hudson_animator.html.
Toggle abstract
"An infinitesite neutral allele model with crossingover possible at any of an infinite number of sites is studied. A formula for the variance of the number of segregating sites in a sample of gametes is obtained. An approximate expression for the expected homozygosity is also derived. Simulation results are presented to indicate the accuracy of the approximations. The results concerning the number of segregating sites and the expected homozygosity indicate that a twolocus model and the infinitesite model behave similarly for 4Nu ≤ 2 and r ≤ 5u, where N is the population size, u is the neutral mutation rate, and r is the recombination rate. Simulations of a twolocus model and a fourlocus model were also carried out to determine the effect of intragenic recombination on the homozygosity test ofWatterson (Genetics 85, 789814; 88, 405417) and on the number of unique alleles in a sample. The results indicate that for 4Nu ≤ 2 and r ≤ 10u, the effect of recombination is quite small. © 1983."


