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103
NeighborNet: An agglomerative method for the construction of planar phylogenetic networks
"... We introduce NeighborNet, a network construction and data representation method that combines aspects of the neighbor joining (NJ) and SplitsTree. Like NJ, NeighborNet uses agglomeration: taxa are combined into progressively larger and larger overlapping clusters. Like SplitsTree, NeighborNet constr ..."
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Cited by 155 (8 self)
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We introduce NeighborNet, a network construction and data representation method that combines aspects of the neighbor joining (NJ) and SplitsTree. Like NJ, NeighborNet uses agglomeration: taxa are combined into progressively larger and larger overlapping clusters. Like SplitsTree, NeighborNet constructs networks rather than trees, and so can be used to represent multiple phylogenetic hypotheses simultaneously, or to detect complex evolutionary processes like recombination, lateral transfer and hybridization. NeighborNet tends to produce networks that are substantially more resolved than those made with SplitsTree. The method is e#cient (O(n ) time) and is well suited for the preliminary analyses of complex phylogenetic data. We report results of three case studies: one based on mitochondrial gene order data from early branching eukaryotes, another based on nuclear sequence data from New Zealand alpine buttercups (Ranunculi), and a third on poorly corrected synthetic data.
Constructing a Tree from Homeomorphic Subtrees, with Applications to Computational Evolutionary Biology
"... We are given a set T = fT1 ; T2 ; : : : ; Tkg of rooted binary trees, each T i leaflabeled by a subset L(T i ) ae f1; 2; : : : ; ng. If T is a tree on f1; 2; : : : ; ng, we let TjL denote the minimal subtree of T induced by the nodes of L and all their ancestors. The consensus tree problem asks wh ..."
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Cited by 40 (2 self)
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We are given a set T = fT1 ; T2 ; : : : ; Tkg of rooted binary trees, each T i leaflabeled by a subset L(T i ) ae f1; 2; : : : ; ng. If T is a tree on f1; 2; : : : ; ng, we let TjL denote the minimal subtree of T induced by the nodes of L and all their ancestors. The consensus tree problem asks whether there exists a tree T such that for every i, T jL(T i ) is homeomorphic to T i . We present algorithms which test if a given set of trees has a consensus tree and if so, construct one. The deterministic algorithm takes time minfO(Nn 1=2 ); O(N + n 2 log n)g, where N = P i jT i j, and uses linear space. The randomized algorithm takes time O(N log 3 n) and uses linear space. The previous best for this problem was an 1981 O(Nn) algorithm by Aho et al. Our faster deterministic algorithm uses a new efficient algorithm for the following interesting dynamic graph problem: Given a graph G with n nodes and m edges and a sequence of b batches of one or more edge deletions, then a...
Performance study of phylogenetic methods: (unweighted) quartet methods and neighborjoining
, 2003
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Evolutionary Trees can be Learned in Polynomial Time in the TwoState General Markov Model
 SIAM Journal on Computing
, 1998
"... The jState General Markov Model of evolution (due to Steel) is a stochastic model concerned with the evolution of strings over an alphabet of size j . In particular, the TwoState General Markov Model of evolution generalises the wellknown CavenderFarrisNeyman model of evolution by removing the sy ..."
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Cited by 31 (2 self)
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The jState General Markov Model of evolution (due to Steel) is a stochastic model concerned with the evolution of strings over an alphabet of size j . In particular, the TwoState General Markov Model of evolution generalises the wellknown CavenderFarrisNeyman model of evolution by removing the symmetry restriction (which requires that the probability that a `0' turns into a `1' along an edge is the same as the probability that a `1' turns into a `0' along the edge). Farach and Kannan showed how to PAClearn Markov Evolutionary Trees in the CavenderFarrisNeyman model provided that the target tree satisfies the additional restriction that all pairs of leaves have a sufficiently high probability of being the same. We show how to remove both restrictions and thereby obtain the first polynomialtime PAClearning algorithm (in the sense of Kearns et al.) for the general class of TwoState Markov Evolutionary Trees. Research Report RR347, Department of Computer Science, University of Wa...
Learning Nonsingular Phylogenies and Hidden Markov Models
 Proceedings of the thirtyseventh annual ACM Symposium on Theory of computing, Baltimore (STOC05
, 2005
"... In this paper, we study the problem of learning phylogenies and hidden Markov models. We call the Markov model nonsingular if all transtion matrices have determinants bounded away from 0 (and 1). We highlight the role of the nonsingularity condition for the learning problem. Learning hidden Markov m ..."
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Cited by 27 (6 self)
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In this paper, we study the problem of learning phylogenies and hidden Markov models. We call the Markov model nonsingular if all transtion matrices have determinants bounded away from 0 (and 1). We highlight the role of the nonsingularity condition for the learning problem. Learning hidden Markov models without the nonsingularity condition is at least as hard as learning parity with noise. On the other hand, we give a polynomialtime algorithm for learning nonsingular phylogenies and hidden Markov models.
Phase transitions in phylogeny
 Trans. Amer. Math. Soc
, 2003
"... Abstract. We apply the theory of Markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the CavenderFarrisNeyman model of evolution on trees, where all the inner nodes have degree at least 3, and the net transitio ..."
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Cited by 23 (8 self)
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Abstract. We apply the theory of Markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the CavenderFarrisNeyman model of evolution on trees, where all the inner nodes have degree at least 3, and the net transition on each edge is bounded by ɛ. Motivated by a conjecture by M. Steel, we show that if 2(1 − 2ɛ) 2> 1, then for balanced trees, the topology of the underlying tree, having n leaves, can be reconstructed from O(log n) samples (characters) at the leaves. On the other hand, we show that if 2(1 − 2ɛ) 2 < 1, then there exist topologies which require at least n Ω(1) samples for reconstruction. Our results are the first rigorous results to establish the role of phase transitions for Markov random fields on trees, as studied in probability, statistical physics and information theory, for the study of phylogenies in mathematical biology. 1.
On the impossibility of reconstructing ancestral data and phylogenies
 J. Comput. Biol
, 2003
"... We prove that it is impossible to reconstruct ancestral data at the root of “deep ” phylogenetic trees with high mutation rates. Moreover, we prove that it is impossible to reconstruct the topology of “deep ” trees with high mutation rates from a number of characters smaller than a lowdegree polyno ..."
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Cited by 21 (9 self)
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We prove that it is impossible to reconstruct ancestral data at the root of “deep ” phylogenetic trees with high mutation rates. Moreover, we prove that it is impossible to reconstruct the topology of “deep ” trees with high mutation rates from a number of characters smaller than a lowdegree polynomial in the number of leaves. Our impossibility results hold for all reconstruction methods. The proofs apply tools from information theory and percolation theory. Key words: phylogeny, phase transitions, trees, ancestral data. 1.
Fast Recovery of Evolutionary Trees with Thousands of Nodes
 RECOMB
, 2001
"... We present a novel distancebased algorithm for evolutionary tree reconstruction. Our algorithm reconstructs the topology of a tree with n leaves in O(n 2 ) time using O(n) working space. In the general Markov model of evolution, the algorithm recovers the topology successfully with (1o(1)) probabi ..."
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Cited by 21 (0 self)
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We present a novel distancebased algorithm for evolutionary tree reconstruction. Our algorithm reconstructs the topology of a tree with n leaves in O(n 2 ) time using O(n) working space. In the general Markov model of evolution, the algorithm recovers the topology successfully with (1o(1)) probability from sequences with polynomial length in n. Moreover, for almost all trees, our algorithm achieves the same success probability on polylogarithmic sample sizes. The theoretical results are supported by simulation experiments involving trees with 500, 1895, and 3135 leaves. The topologies of the trees are recovered with high success from 2000 bp DNA sequences.
A Phase Transition for a Random Cluster Model on Phylogenetic Trees
, 2004
"... We investigate a simple model that generates random partitions of the leaf set of a tree. Of particular interest is the reconstruction question: what number k of independent samples (partitions) are required to correctly reconstruct the underlying tree (with high probability)? We demonstrate a phase ..."
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Cited by 20 (13 self)
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We investigate a simple model that generates random partitions of the leaf set of a tree. Of particular interest is the reconstruction question: what number k of independent samples (partitions) are required to correctly reconstruct the underlying tree (with high probability)? We demonstrate a phase transition for k as a function of the mutation rate, from logarithmic to polynomial dependence on the size of the tree. We also describe a simple polynomialtime tree reconstruction algorithm that applies in the logarithmic region. This model and the associated reconstruction questions are motivated by a Markov model for genomic evolution in molecular biology.