Properties of Normal Phylogenetic Networks

Willson, Stephen J.

doi:10.1007/s11538-009-9449-z

Cited by 47 publications

(56 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, it may be seen that in a normal network v = O(n 2 ) and a = O(n 2 ), see [26]. Hence given D satisfying the hypotheses of Theorem 4.3 and with a members, it follows that N can be reconstructed in time O(n 2 n 2 (n 2 ) 2 ) = O(n 8 ).…”

Section: Algorithm Maximal Childmentioning

confidence: 97%

Regular Networks Can be Uniquely Constructed from Their Trees

Willson

2011

IEEE/ACM Trans. Comput. Biol. and Bioinf.

View full text Add to dashboard Cite

Abstract-A rooted acyclic digraph N with labelled leaves displays a tree T when there exists a way to select a unique parent of each hybrid vertex resulting in the tree T . Let T r(N ) denote the set of all trees displayed by the network N . In general, there may be many other networks M such that T r(M ) = T r(N ). A network is regular if it is isomorphic with its cover digraph. If N is regular and D is a collection of trees displayed by N , this paper studies some procedures to try to reconstruct N given D. If the input is D = T r(N ), one procedure is described which will reconstruct N . Hence if N and M are regular networks and T r(N ) = T r(M ), it follows that N = M , proving that a regular network is uniquely determined by its displayed trees. If D is a (usually very much smaller) collection of displayed trees that satisfies certain hypotheses, modifications of the procedure will still reconstruct N given D.

show abstract

Section: Algorithm Maximal Childmentioning

confidence: 97%

Regular Networks Can be Uniquely Constructed from Their Trees

Willson

2011

IEEE/ACM Trans. Comput. Biol. and Bioinf.

View full text Add to dashboard Cite

show abstract

“…Although we do not use the result, in a normal network, distinct vertices have distinct sets of leaf descendants [15]. Now consider a tree-child network, and suppose that there is a nontrivial automorphism f which fixes each leaf.…”

Section: Leaf-labelled Tree-child and Normal Networkmentioning

confidence: 99%

Counting Phylogenetic Networks

2015

View full text Add to dashboard Cite

Abstract. We give approximate counting formulae for the numbers of labelled general, tree-child, and normal (binary) phylogenetic networks on n vertices. These formulae are of the form 2 γn log n+O(n) , where the constant γ is 3 2 for general networks, and 5 4 for tree-child and normal networks. We also show that the number of leaf-labelled tree-child and normal networks with leaves are both 2 2 log +O( ) . Further we determine the typical numbers of leaves, tree vertices, and reticulation vertices for each of these classes of networks.

show abstract

“…Willson as the class of networks where to look for meaningful phylogenies [47], and polynomial time algorithms are known for reconstructing a normal network from distances [45], [46], [48], but for the moment no reconstruction algorithm for arbitrary tree-child phylogenetic networks has been developed. Therefore, it remains an interesting open question to characterize the sets of sequences whose evolution can be explained by means of a tree-child network and to provide an algorithm to reconstruct this network, as well as to characterize the computational complexity of these problems.…”

Section: Remarkmentioning

confidence: 99%

“…This is a slightly more restricted class of phylogenetic networks than the treesibling ones (see Section 2.3), where one of the versions of the error metric was defined. Tree-child phylogenetic networks include galled trees [12], [13] as a particular case, and they have been recently proposed as the class where meaningful phylogenetic networks should be searched [47].…”

mentioning

confidence: 99%

Comparison of Tree-Child Phylogenetic Networks

Cardona

Rosselló

Valiente

2009

IEEE/ACM Trans. Comput. Biol. and Bioinf.

171

224

View full text Add to dashboard Cite

Abstract-Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of nontreelike evolutionary events, like recombination, hybridization, or lateral gene transfer. While much progress has been made to find practical algorithms for reconstructing a phylogenetic network from a set of sequences, all attempts to endorse a class of phylogenetic networks (strictly extending the class of phylogenetic trees) with a well-founded distance measure have, to the best of our knowledge and with the only exception of the bipartition distance on regular networks, failed so far. In this paper, we present and study a new meaningful class of phylogenetic networks, called tree-child phylogenetic networks, and we provide an injective representation of these networks as multisets of vectors of natural numbers, their path multiplicity vectors. We then use this representation to define a distance on this class that extends the well-known Robinson-Foulds distance for phylogenetic trees and to give an alignment method for pairs of networks in this class. Simple polynomial algorithms for reconstructing a tree-child phylogenetic network from its path multiplicity vectors, for computing the distance between two tree-child phylogenetic networks and for aligning a pair of tree-child phylogenetic networks, are provided. They have been implemented as a Perl package and a Java applet, which can be found at

show abstract

Properties of Normal Phylogenetic Networks

Cited by 47 publications

References 24 publications

Regular Networks Can be Uniquely Constructed from Their Trees

Regular Networks Can be Uniquely Constructed from Their Trees

Counting Phylogenetic Networks

Comparison of Tree-Child Phylogenetic Networks

Contact Info

Product

Resources

About