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125
On the computational complexity of the rooted subtree prune and regraft distance
 ANNALS OF COMBINATORICS
, 2004
"... 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 phylogene ..."
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Cited by 85 (9 self)
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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.
Reconstructing reticulate evolution in species  theory and practice
 In Proc. of 8’th Annual International Conference on Computational Molecular Biology
, 2004
"... We present new methods for reconstructing reticulate evolution of species due to events such as horizontal transfer or hybrid speciation; both methods are based upon extensions of Wayne Maddison’s approach in his seminal 1997 paper. Our first method is a polynomial time algorithm for constructing ph ..."
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Cited by 58 (7 self)
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We present new methods for reconstructing reticulate evolution of species due to events such as horizontal transfer or hybrid speciation; both methods are based upon extensions of Wayne Maddison’s approach in his seminal 1997 paper. Our first method is a polynomial time algorithm for constructing phylogenetic networks from two gene trees contained inside the network. We allow the network to have an arbitrary number of reticulations, but we limit the reticulation in the network so that the cycles in network are nodedisjoint (“galled”). Our second method is a polynomial time algorithm for constructing networks with one reticulation, where we allow for errors in the estimated gene trees. Using simulations, we demonstrate improved performance of this method over both NeighborNet and Maddison’s method. 1
A Framework for Representing Reticulate Evolution
 ANNALS OF COMBINATORICS
, 2004
"... 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 particul ..."
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Cited by 50 (5 self)
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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.
Case Study: Visualizing Sets of Evolutionary Trees
, 2002
"... We describe a visualization tool which allows a biologist to explore a large set of hypothetical evolutionary trees. Interacting with such a dataset allows the biologist to identify distinct hypotheses about how different species or organisms evolved, which would not have been clear from traditional ..."
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Cited by 48 (4 self)
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We describe a visualization tool which allows a biologist to explore a large set of hypothetical evolutionary trees. Interacting with such a dataset allows the biologist to identify distinct hypotheses about how different species or organisms evolved, which would not have been clear from traditional analyses. Our system integrates a pointset visualization of the distribution of hypothetical trees with detail views of an individual tree, or of a consensus tree summarizing a subset of trees. Efficient algorithms were required for the key tasks of computing distances between trees, finding consensus trees, and laying out the pointset visualization. 1
A fast algorithm for computing geodesic distances in Tree Space
 IEEE/ACM Trans. Comput. Biol. Bioinforma
"... Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths is the length of the shortest path between them in the conti ..."
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Cited by 41 (11 self)
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Comparing and computing distances between phylogenetic trees are important biological problems, especially for models where edge lengths play an important role. The geodesic distance measure between two phylogenetic trees with edge lengths is the length of the shortest path between them in the continuous tree space introduced by Billera, Holmes, and Vogtmann. This tree space provides a powerful tool for studying and comparing phylogenetic trees, both in exhibiting a natural distance measure and in providing a Euclideanlike structure for solving optimization problems on trees. An important open problem is to find a polynomial time algorithm for finding geodesics in tree space. This paper gives such an algorithm, which starts with a simple initial path and moves through a series of successively shorter paths until the geodesic is attained. 1
Comparison of treechild phylogenetic networks
 IEEE/ACM Trans. Comput. Biol. Bioinform
, 2009
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Subtree prune and regraft: A reversible realtree valued Markov chain
 Ann. Prob
"... Abstract. We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains that appear in phylogenetic analysis. A key technic ..."
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Cited by 36 (8 self)
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Abstract. We use Dirichlet form methods to construct and analyze a reversible Markov process, the stationary distribution of which is the Brownian continuum random tree. This process is inspired by the subtree prune and regraft (SPR) Markov chains that appear in phylogenetic analysis. A key technical ingredient in this work is the use of a novel Gromov– Hausdorff type distance to metrize the space whose elements are compact real trees equipped with a probability measure. Also, the investigation of the Dirichlet form hinges on a new path decomposition of the Brownian excursion. 1.
Computing the quartet distance between evolutionary trees
 In Proceedings of the 11th Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2000
"... The comparison of evolutionary trees is a fundamental problem in evolutionary biology. Di erent evolutionary hypotheses (or con icting phylogenies) arise ..."
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Cited by 32 (0 self)
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The comparison of evolutionary trees is a fundamental problem in evolutionary biology. Di erent evolutionary hypotheses (or con icting phylogenies) arise
Computing the hybridization number of two phylogenetic trees is fixedparameter tractable
 IEEE/ACM Transactions on Computational Biology and Bioinformatics
"... Abstract—Reticulation processes in evolution mean that the ancestral history of certain groups of presentday species is nontreelike. These processes include hybridization, lateral gene transfer, and recombination. Despite the existence of reticulation, such events are relatively rare and, so, a f ..."
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Cited by 31 (6 self)
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Abstract—Reticulation processes in evolution mean that the ancestral history of certain groups of presentday species is nontreelike. These processes include hybridization, lateral gene transfer, and recombination. Despite the existence of reticulation, such events are relatively rare and, so, a fundamental problem for biologists is the following: Given a collection of rooted binary phylogenetic trees on sets of species that correctly represent the treelike evolution of different parts of their genomes, what is the smallest number of “reticulation ” vertices in any network that explains the evolution of the species under consideration? It has been previously shown that this problem is NPhard even when the collection consists of only two rooted binary phylogenetic trees. However, in this paper, we show that the problem is fixedparameter tractable in the twotree instance when parameterized by this smallest number of reticulation vertices. Index Terms—Rooted phylogenetic tree, reticulate evolution, hybridization network, agreement forest, subtree prune and regraft. Ç 1
J.P.Bowen.Fromprogramstoobjectcodeandbackagainusinglogic programming:Compilationanddecompilation
 Journal of Software Maintenance: Research and Practice,5(4):205{234,December1993
, 2007
"... Summary: TOPD/FMTS has been developed to evaluate similarities and differences between phylogenetic trees. The software implements several new algorithms (including the Disagree method that returns the taxa, that disagree between two trees and the Nodal method that compares two trees using nodal inf ..."
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Cited by 30 (0 self)
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Summary: TOPD/FMTS has been developed to evaluate similarities and differences between phylogenetic trees. The software implements several new algorithms (including the Disagree method that returns the taxa, that disagree between two trees and the Nodal method that compares two trees using nodal information) and several previously described methods (such as the Partition method, Triplets or Quartets) to compare phylogenetic trees. One of the novelties of this software is that the FMTS (From Multiple to Single) program allows the comparison of trees that contain both orthologs and paralogs. Each option is also complemented with a randomization analysis to test the null hypothesis that the similarity between two trees is not better than chance expectation. Availability: The Perl source code of TOPD/FMTS is available at