Regular Networks Can be Uniquely Constructed from Their Trees

Willson, Stephen J.

doi:10.1109/tcbb.2010.69

Cited by 36 publications

(31 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Complementing the insights for when N is a phylogenetic tree alluded to above, answers were recently provided for R (N ) in case N is a very special type of level-k network, k ≥ 2 (van Iersel et al 2009b) and for T (N ) for the special case that N is a regular network (Willson 2011). Undoubtedly these are important first results.…”

Section: Introductionmentioning

confidence: 82%

On encodings of phylogenetic networks of bounded level

Gambette

Huber

2011

J. Math. Biol.

View full text Add to dashboard Cite

Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? For the large class of level-1 (phylogenetic) networks we characterize those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. In addition, we show that three known distance measures for comparing phylogenetic networks are in fact metrics on the resulting subclass and give the diameter for two of them. Finally, we investigate the related concept of indistinguishability and also show that many properties enjoyed by level-1 networks are not satisfied by networks of higher level.

show abstract

Section: Introductionmentioning

confidence: 82%

On encodings of phylogenetic networks of bounded level

Gambette

Huber

2011

J. Math. Biol.

View full text Add to dashboard Cite

show abstract

“…Fig. 1) and, in fact, we do not even know when a phylogenetic network is uniquely determined by all of the trees that it displays [32].…”

Section: Introductionmentioning

confidence: 96%

Encoding and Constructing 1-Nested Phylogenetic Networks with Trinets

Huber

Moulton

2012

Algorithmica

View full text Add to dashboard Cite

Abstract. Phylogenetic networks are a generalization of phylogenetic trees that are used in biology to represent reticulate or non-treelike evolution. Recently, several algorithms have been developed which aim to construct phylogenetic networks from biological data using triplets, i.e. binary phylogenetic trees on 3-element subsets of a given set of species. However, a fundamental problem with this approach is that the triplets displayed by a phylogenetic network do not necessary uniquely determine or encode the network. Here we propose an alternative approach to encoding and constructing phylogenetic networks, which uses phylogenetic networks on 3-element subsets of a set, or trinets, rather than triplets. More specifically, we show that for a special, well-studied type of phylogenetic network called a 1-nested network, the trinets displayed by a 1-nested network always encode the network. We also present an efficient algorithm for deciding whether a dense set of trinets (i.e. one that contains a trinet on every 3-element subset of a set) can be displayed by a 1-nested network or not and, if so, constructs that network. In addition, we discuss some potential new directions that this new approach opens up for constructing and comparing phylogenetic networks.

show abstract

“…Note that this class of networks includes the class of regular networks [1]. Thus it is interesting to note that a regular network is encoded by the set of trees 1 that it contains [28], but that this is not the case for tree-child networks (e.g. all of the networks in Figure 1 contain the same set of trees).…”

Section: Introductionmentioning

confidence: 99%

Trinets encode tree-child and level-2 phylogenetic networks

Iersel

Moulton

2013

J. Math. Biol.

View full text Add to dashboard Cite

Abstract. Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general encode rooted phylogenetic networks, which is a potential issue for any such method. Motivated by this fact, Huber and Moulton recently introduced trinets as a natural extension of rooted triplets to networks. In particular, they showed that level-1 phylogenetic networks are encoded by their trinets, and also conjectured that all "recoverable" rooted phylogenetic networks are encoded by their trinets. Here we prove that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets. To do this we prove two decomposition theorems based on trinets which hold for all recoverable binary rooted phylogenetic networks. Our results provide some additional evidence in support of the conjecture that trinets encode all recoverable rooted phylogenetic networks, and could also lead to new approaches to construct phylogenetic networks from trinets.

show abstract

Regular Networks Can be Uniquely Constructed from Their Trees

Cited by 36 publications

References 28 publications

On encodings of phylogenetic networks of bounded level

On encodings of phylogenetic networks of bounded level

Encoding and Constructing 1-Nested Phylogenetic Networks with Trinets

Trinets encode tree-child and level-2 phylogenetic networks

Contact Info

Product

Resources

About