CSD Homomorphisms between Phylogenetic Networks

Willson, Stephen J.

doi:10.1109/tcbb.2012.52

Cited by 6 publications

(20 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let N = (V , A, ρ, φ) and N = (V , A , ρ , φ ) be X -directed graphs. A connected surjective digraph (CSD) map (Willson 2012)…”

Section: Basic Notionsmentioning

confidence: 99%

“…This paper relies on results from Willson ( 2012 ). This earlier paper focused on networks that were not necessarily acyclic.…”

Section: Introductionmentioning

confidence: 99%

“…If N and M are X -networks, a connected surjective digraph map (CSD map) is a surjective map with various properties. (See Willson 2012 and Sect. 2 of this paper.)…”

Section: Introductionmentioning

confidence: 99%

“…The merging procedure in this paper always yields a CSD map . Results in Willson ( 2012 ) show that there is then a “wired lift” of into N , from which properties of can be visualized in N . The wired lift is not a subnetwork of N in the usual sense.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Merging Arcs to Produce Acyclic Phylogenetic Networks and Normal Networks

Willson

2022

Bull Math Biol

View full text Add to dashboard Cite

As phylogenetic networks grow increasingly complicated, systematic methods for simplifying them to reveal properties will become more useful. This paper considers how to modify acyclic phylogenetic networks into other acyclic networks by contracting specific arcs that include a set D. The networks need not be binary, so vertices in the networks may have more than two parents and/or more than two children. In general, in order to make the resulting network acyclic, additional arcs not in D must also be contracted. This paper shows how to choose D so that the resulting acyclic network is “pre-normal”. As a result, removal of all redundant arcs yields a normal network. The set D can be selected based only on the geometry of the network, giving a well-defined normal phylogenetic network depending only on the given network. There are CSD maps relating most of the networks. The resulting network can be visualized as a “wired lift” in the original network, which appears as the original network with each arc drawn in one of three ways.

show abstract

“…Let N = (V , A, ρ, φ) and N = (V , A , ρ , φ ) be X -directed graphs. A connected surjective digraph (CSD) map (Willson 2012)…”

Section: Basic Notionsmentioning

confidence: 99%

“…This paper relies on results from Willson ( 2012 ). This earlier paper focused on networks that were not necessarily acyclic.…”

Section: Introductionmentioning

confidence: 99%

“…If N and M are X -networks, a connected surjective digraph map (CSD map) is a surjective map with various properties. (See Willson 2012 and Sect. 2 of this paper.)…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Merging Arcs to Produce Acyclic Phylogenetic Networks and Normal Networks

Willson

2022

Bull Math Biol

View full text Add to dashboard Cite

show abstract

“…This allows us to provide an alternative characterisation for stable networks (Corollary 3 ). It is worth noting that an alternative framework for considering maps between phylogenetic networks is developed in Willson ( 2012 ).…”

Section: Introductionmentioning

confidence: 99%

Folding and unfolding phylogenetic trees and networks

et al. 2016

View full text Add to dashboard Cite

Phylogenetic networks are rooted, labelled directed acyclic graphswhich are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any phylogenetic network N can be “unfolded” to obtain a MUL-tree U(N) and, conversely, a MUL-tree T can in certain circumstances be “folded” to obtain aphylogenetic network F(T) that exhibits T. In this paper, we study properties of the operations U and F in more detail. In particular, we introduce the class of stable networks, phylogenetic networks N for which F(U(N)) is isomorphic to N, characterise such networks, and show that they are related to the well-known class of tree-sibling networks. We also explore how the concept of displaying a tree in a network N can be related to displaying the tree in the MUL-tree U(N). To do this, we develop aphylogenetic analogue of graph fibrations. This allows us to view U(N) as the analogue of the universal cover of a digraph, and to establish a close connection between displaying trees in U(N) and reconciling phylogenetic trees with networks.

show abstract

Distinct-Cluster Tree-Child Phylogenetic Networks and Possible Uses to Study Polyploidy

Willson

2022

Bull Math Biol

View full text Add to dashboard Cite

As phylogenetic networks become more widely studied and the networks grow larger, it may be useful to “simplify” such networks into especially tractable networks. Recent results have found methods to simplify networks into normal networks. By definition, normal networks contain no redundant arcs. Nevertheless, there may be redundant arcs in networks where speciation events involving allopolyploidy occur. It is therefore desirable to find a different tractable class of networks that may contain redundant arcs. This paper proposes distinct-cluster tree-child networks as such a class, here abbreviated as DCTC networks. They are shown to have a number of useful properties, such as quadratic growth of the number of vertices with the number of leaves. A DCTC network is shown to be essentially a normal network to which some redundant arcs may have been added without losing the tree-child property. Every phylogenetic network can be simplified into a DCTC network depending only on the structure of the original network. There is always a CSD map from the original network to the resulting DCTC network. As a result, the simplified network can readily be interpreted via a “wired lift” in which the original network is redrawn with each arc represented in one of two ways.

show abstract

CSD Homomorphisms between Phylogenetic Networks

Cited by 6 publications

References 17 publications

Merging Arcs to Produce Acyclic Phylogenetic Networks and Normal Networks

Merging Arcs to Produce Acyclic Phylogenetic Networks and Normal Networks

Folding and unfolding phylogenetic trees and networks

Distinct-Cluster Tree-Child Phylogenetic Networks and Possible Uses to Study Polyploidy

Contact Info

Product

Resources

About