






Sarah Bastkowski,
Andreas Spillner and
Vincent Moulton. Fishing for minimum evolution trees with NeighborNets. In IPL, Vol. 114(12):318, 2014. Keywords: circular split system, from distances, NeighborNet, phylogeny, polynomial.
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"In evolutionary biology, biologists commonly use a phylogenetic tree to represent the evolutionary history of some set of species. A common approach taken to construct such a tree is to search through the space of all possible phylogenetic trees on the set so as to find one that optimizes some score function, such as the minimum evolution criterion. However, this is hampered by the fact that the space of phylogenetic trees is extremely large in general. Interestingly, an alternative approach, which has received somewhat less attention in the literature, is to instead search for trees within some set of bipartitions or splits of the set of species in question. Here we consider the problem of searching through a set of splits that is circular. Such sets can, for example, be generated by the NeighborNet algorithm for constructing phylogenetic networks. More specifically, we present an O(n4) time algorithm for finding an optimal minimum evolution tree in a circular set of splits on a set of species of size n. In addition, using simulations, we compare the performance of this algorithm when applied to NeighborNet output with that of FastME, a leading method for searching for minimum evolution trees in tree space. We find that, even though a circular set of splits represents just a tiny fraction of the total number of possible splits of a set, the trees obtained from circular sets compare quite favorably with those obtained with FastME, suggesting that the approach could warrant further investigation. © 2013 Elsevier B.V."



Monika Balvociute,
Andreas Spillner and
Vincent Moulton. FlatNJ: A Novel NetworkBased Approach to Visualize Evolutionary and Biogeographical Relationships. In Systematic Biology, Vol. 63(3):383396, 2014. Keywords: abstract network, flat, phylogenetic network, phylogeny, Program FlatNJ, Program SplitsTree, split network. Note: http://dx.doi.org/10.1093/sysbio/syu001.
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"Split networks are a type of phylogenetic network that allow visualization of conflict in evolutionary data. We present a new method for constructing such networks called FlatNetJoining (FlatNJ). A key feature of FlatNJ is that it produces networks that can be drawn in the plane in which labels may appear inside of the network. For complex data sets that involve, for example, nonneutral molecular markers, this can allow additional detail to be visualized as compared to previous methods such as split decomposition and NeighborNet. We illustrate the application of FlatNJ by applying it to whole HIV genome sequences, where recombination has taken place, fluorescent proteins in corals, where ancestral sequences are present, and mitochondrial DNA sequences from gall wasps, where biogeographical relationships are of interest. We find that the networks generated by FlatNJ can facilitate the study of genetic variation in the underlying molecular sequence data and, in particular, may help to investigate processes such as intralocus recombination. FlatNJ has been implemented in Java and is freely available at www.uea.ac.uk/computing/software/ flatnj. [flat split system; NeighborNet; Phylogenetic network; QNet; split; split network.] © The Author(s) 2014."






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








Andreas Spillner,
Binh T. Nguyen and
Vincent Moulton. Constructing and Drawing Regular Planar Split Networks. In TCBB, Vol. 9(2):395407, 2012. Keywords: abstract network, from splits, phylogenetic network, phylogeny, reconstruction, visualization. Note: slides and presentation available at http://www.newton.ac.uk/programmes/PLG/seminars/062111501.html.
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"Split networks are commonly used to visualize collections of bipartitions, also called splits, of a finite set. Such collections arise, for example, in evolutionary studies. Split networks can be viewed as a generalization of phylogenetic trees and may be generated using the SplitsTree package. Recently, the NeighborNet method for generating split networks has become rather popular, in part because it is guaranteed to always generate a circular split system, which can always be displayed by a planar split network. Even so, labels must be placed on the "outside" of the network, which might be problematic in some applications. To help circumvent this problem, it can be helpful to consider socalled flat split systems, which can be displayed by planar split networks where labels are allowed on the inside of the network too. Here, we present a new algorithm that is guaranteed to compute a minimal planar split network displaying a flat split system in polynomial time, provided the split system is given in a certain format. We will also briefly discuss two heuristics that could be useful for analyzing phylogeographic data and that allow the computation of flat split systems in this format in polynomial time. © 2006 IEEE."



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



Katharina Huber,
Vincent Moulton,
Andreas Spillner,
Sabine Storandt and
Radoslaw Suchecki. Computing a consensus of multilabeled trees. In ALENEX12, Pages 8492, 2012. Keywords: duplication, explicit network, exponential algorithm, phylogenetic network, phylogeny. Note: http://siam.omnibooksonline.com/2012ALENEX/data/papers/020.pdf.
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In this paper we consider two challenging problems that arise in the context of computing a consensus of a collection of multilabeled trees, namely (1) selecting a compatible collection of clusters on a multiset from an ordered list of such clusters and (2) optimally refining high degree vertices in a multilabeled tree. Forming such a consensus is part of an approach to reconstruct the evolutionary history of a set of species for which events such as genome duplication and hybridization have occurred in the past. We present exact algorithms for solving (1) and (2) that have an exponential runtime in the worst case. To give some impression of their performance in practice, we apply them to simulated input and to a real biological data set highlighting the impact of several structural properties of the input on the performance.






Stefan Grünewald,
Vincent Moulton and
Andreas Spillner. Consistency of the QNet algorithm for generating planar split networks from weighted quartets. In DAM, Vol. 157(10):23252334, 2009. Keywords: abstract network, consistency, from quartets, phylogenetic network, phylogeny, Program QNet, reconstruction, software. Note: http://dx.doi.org/10.1016/j.dam.2008.06.038.
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"Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that allow the representation of conflicting signals or alternative evolutionary histories in a single diagram. Recently the QuartetNet or "QNet" method was introduced, a method for computing a special kind of phylogenetic network called a split network from a collection of weighted quartet trees (i.e. phylogenetic trees with 4 leaves). This can be viewed as a quartet analogue of the distancebased NeighborNet (NNet) method for constructing outerlabeled planar split networks. In this paper, we prove that QNet is a consistent method, that is, we prove that if QNet is applied to a collection of weighted quartets arising from a circular split weight function, then it will return precisely this function. This key property of QNet not only ensures that it is guaranteed to produce a tree if the input corresponds to a tree, and an outerlabeled planar split network if the input corresponds to such a network, but also provides the main guiding principle for the design of the method. © 2008 Elsevier B.V. All rights reserved."



Stefan Grünewald,
Katharina Huber,
Vincent Moulton,
Charles Semple and
Andreas Spillner. Characterizing weak compatibility in terms of weighted quartets. In Advances in Applied Mathematics, Vol. 42(3):329341, 2009. Keywords: abstract network, characterization, from quartets, split network, weak hierarchy. Note: http://www.math.canterbury.ac.nz/~c.semple/papers/GHMSS08.pdf, slides at http://www.lirmm.fr/miep08/slides/12_02_huber.pdf.



Martin Lott,
Andreas Spillner,
Katharina Huber and
Vincent Moulton. PADRE: A Package for Analyzing and Displaying Reticulate Evolution. In BIO, Vol. 25(9):11991200, 2009. Keywords: duplication, explicit network, from multilabeled tree, phylogenetic network, phylogeny, Program PADRE, reconstruction, software. Note: http://dx.doi.org/10.1093/bioinformatics/btp133.
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"Recent advances in gene sequencing for polyploid species, coupled with standard phylogenetic tree reconstruction, leads to gene trees in which the same species can label several leaves. Such multilabeled trees are then used to reconstruct the evolutionary history of the polyploid species in question. However, this reconstruction process requires new techniques that are not available in current phylogenetic software packages. Here, we describe the software package PADRE (Package for Analyzing and Displaying Reticulate Evolution) that implements such techniques, allowing the reconstruction of complex evolutionary histories for polyploids in the form of phylogenetic networks. © The Author 2009. Published by Oxford University Press. All rights reserved."



Martin Lott,
Andreas Spillner,
Katharina Huber,
Anna Petri,
Bengt Oxelman and
Vincent Moulton. Inferring polyploid phylogenies from multiplylabeled gene trees. In BMCEB, Vol. 9:216, 2009. Keywords: duplication, explicit network, from multilabeled tree, phylogenetic network, phylogeny, Program PADRE, reconstruction. Note: http://dx.doi.org/10.1186/147121489216.
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"Background : Gene trees that arise in the context of reconstructing the evolutionary history of polyploid species are often multiplylabeled, that is, the same leaf label can occur several times in a single tree. This property considerably complicates the task of forming a consensus of a collection of such trees compared to usual phylogenetic trees. Results. We present a method for computing a consensus tree of multiplylabeled trees. As with the wellknown greedy consensus tree approach for phylogenetic trees, our method first breaks the given collection of gene trees into a set of clusters. It then aims to insert these clusters one at a time into a tree, starting with the clusters that are supported by most of the gene trees. As the problem to decide whether a cluster can be inserted into a multiplylabeled tree is computationally hard, we have developed a heuristic method for solving this problem. Conclusion. We illustrate the applicability of our method using two collections of trees for plants of the genus Silene, that involve several allopolyploids at different levels. © 2009 Lott et al; licensee BioMed Central Ltd."






Andreas Spillner,
Binh T. Nguyen and
Vincent Moulton. Computing phylogenetic diversity for split systems. In TCBB, Vol. 5(2):235244, 2008. Keywords: abstract network, diversity, phylogenetic network, phylogeny, split. Note: http://dx.doi.org/10.1109/TCBB.2007.70260, slides available at http://www.newton.cam.ac.uk/webseminars/pg+ws/2007/plg/plgw01/0906/spillner/.
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"In conservation biology it is a central problem to measure, predict, and preserve biodiversity as species face extinction. In 1992 Faith proposed measuring the diversity of a collection of species in terms of their relationships on a phylogenetic tree, and to use this information to identify collections of species with high diversity. Here we are interested in some variants of the resulting optimization problem that arise when considering species whose evolution is better represented by a network rather than a tree. More specifically, we consider the problem of computing phylogenetic diversity relative to a split system on a collection of species of size $n$. We show that for general split systems this problem is NPhard. In addition we provide some efficient algorithms for some special classes of split systems, in particular presenting an optimal $O(n)$ time algorithm for phylogenetic trees and an $O(nlog n + n k)$ time algorithm for choosing an optimal subset of size $k$ relative to a circular split system. © 2006 IEEE."



Stefan Grünewald,
Andreas Spillner,
Kristoffer Forslund and
Vincent Moulton. Constructing Phylogenetic Supernetworks from Quartets. In WABI08, Vol. 5251:284295 of LNCS, springer, 2008. Keywords: abstract network, from quartets, from unrooted trees, phylogenetic network, phylogeny, Program QNet, Program SplitsTree, reconstruction, split network. Note: http://dx.doi.org/10.1007/9783540873617_24.
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"In phylogenetics it is common practice to summarize collections of partial phylogenetic trees in the form of supertrees. Recently it has been proposed to construct phylogenetic supernetworks as an alternative to supertrees as these allow the representation of conflicting information in the trees, information that may not be representable in a single tree. Here we introduce SuperQ, a new method for constructing such supernetworks. It works by breaking the input trees into quartet trees, and stitching together the resulting set to form a network. The stitching process is performed using an adaptation of the QNet method for phylogenetic network reconstruction. In addition to presenting the new method, we illustrate the applicability of SuperQ to three data sets and discuss future directions for testing and development. © 2008 SpringerVerlag Berlin Heidelberg."






David Bryant,
Vincent Moulton and
Andreas Spillner. Consistency of the NeighborNet Algorithm. In AMB, Vol. 2(8), 2007. Keywords: abstract network, consistency, from distances, NeighborNet. Note: http://dx.doi.org/10.1186/1748718828.
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"Background: NeighborNet is a novel method for phylogenetic analysis that is currently being widely used in areas such as virology, bacteriology, and plant evolution. Given an input distance matrix, NeighborNet produces a phylogenetic network, a generalization of an evolutionary or phylogenetic tree which allows the graphical representation of conflicting phylogenetic signals. Results: In general, any network construction method should not depict more conflict than is found in the data, and, when the data is fitted well by a tree, the method should return a network that is close to this tree. In this paper we provide a formal proof that NeighborNet satisfies both of these requirements so that, in particular, NeighborNet is statistically consistent on circular distances. © 2007 Bryant et al; licensee BioMed Central Ltd."



