





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.
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"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."





Sajad Mirzaei and
Yufeng Wu. Fast Construction of Near Parsimonious Hybridization Networks for Multiple Phylogenetic Trees. In TCBB, Vol. 13(3):565570, 2016. Keywords: bound, explicit network, from rooted trees, heuristic, phylogenetic network, phylogeny, Program PIRN, reconstruction, software. Note: http://www.engr.uconn.edu/~ywu/Papers/PIRNspreprint.pdf.



Benjamin Albrecht. Computing all hybridization networks for multiple binary phylogenetic input trees. In BMCB, Vol. 16(236):115, 2015. Keywords: agreement forest, explicit network, exponential algorithm, FPT, from rooted trees, phylogenetic network, phylogeny, Program Hybroscale, Program PIRN, reconstruction. Note: http://dx.doi.org/10.1186/s1285901506607.






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.
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"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. An Algorithm for Constructing Parsimonious Hybridization Networks with Multiple Phylogenetic Trees. In RECOMB13, Vol. 7821:291303 of LNCS, springer, 2013. Keywords: explicit network, exponential algorithm, from rooted trees, phylogenetic network, phylogeny, Program PIRN, reconstruction. Note: http://www.engr.uconn.edu/~ywu/Papers/ExactNetRecomb2013.pdf.
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"Phylogenetic network is a model for reticulate evolution. Hybridization network is one type of phylogenetic network for a set of discordant gene trees, and "displays" each gene tree. A central computational problem on hybridization networks is: given a set of gene trees, reconstruct the minimum (i.e. most parsimonious) hybridization network that displays each given gene tree. This problem is known to be NPhard, and existing approaches for this problem are either heuristics or make simplifying assumptions (e.g. work with only two input trees or assume some topological properties). In this paper, we develop an exact algorithm (called PIRNC ) for inferring the minimum hybridization networks from multiple gene trees. The PIRNC algorithm does not rely on structural assumptions. To the best of our knowledge, PIRN C is the first exact algorithm for this formulation. When the number of reticulation events is relatively small (say four or fewer), PIRNC runs reasonably efficient even for moderately large datasets. For building more complex networks, we also develop a heuristic version of PIRNC called PIRNCH. Simulation shows that PIRNCH usually produces networks with fewer reticulation events than those by an existing method. © 2013 SpringerVerlag."








R. A. Leo Elworth,
Huw A. Ogilvie,
Jiafan Zhu and
Luay Nakhleh. Advances in Computational Methods for Phylogenetic Networks in the Presence of Hybridization. In
Tandy Warnow editor, Bioinformatics and Phylogenetics. Seminal Contributions of Bernard Moret, Vol. 29 of Computational Biology, Springer, 2019. Keywords: explicit network, phylogenetic network, phylogeny, Program Dendroscope, Program PhyloNet, Program PhyloNetworks SNaQ, Program PIRN, Program SplitsTree, reconstruction, survey. Note: https://bioinfocs.rice.edu/sites/g/files/bxs266/f/ElworthZhuOgilvieNakhleh.pdf





