Brauer and partition diagram models for phylogenetic trees and forests

Francis, Andrew R.; Jarvis, Peter

doi:10.1098/rspa.2022.0044

Cited by 6 publications

(26 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, there may be connections to algebraic structures to explore. In the case of trees and forests, which correspond to partitions of finite sets, there is a corresponding set of partition diagrams that can be acted on by elements of the symmetric group or Brauer monoid [10]. What, if any, are the corresponding algebraic structures that correspond to covers, and can these be used to move around network space?…”

Section: Discussionmentioning

confidence: 99%

“…Note that this order reduces to the order used for labelling internal vertices in phylogenetic forests (in Algorithm 1 of [10]).…”

Section: Labellable Networkmentioning

confidence: 99%

“…The labelling algorithm for binary trees given by [6] and [4], and extended to non-binary trees and forests in [10], takes a tree or forest with leaves labelled by [n], and progressively labels internal vertices in sequence, until all except the root are labelled. At each step the algorithm chooses a new vertex to label from those whose children are all labelled, by choosing the one whose children have the lowest label.…”

Section: Labellable Networkmentioning

confidence: 99%

“…In this paper we will show that a large class of rooted phylogenetic networks is encoded by certain covers of finite sets. This specifically generalises encodings for phylogenetic trees and forests that were given for binary trees by Diaconis and Holmes in 1998 [4], and for general phylogenetic forests more recently [10].…”

Section: Introductionmentioning

confidence: 99%

“…In the case of binary trees (those whose internal vertices have out-degree 2), there are a total of 2 n – 2 labels, and a correspondence with perfect matchings follows by forming pairs of labels of sibling vertices (sibling vertices are those that share a parent) [4]. In the case of non-binary trees and phylogenetic forests, the same process of forming sets of sibling vertices gives a correspondence between the set of phylogenetic forests and all partitions of finite sets [10] (see Fig. 1).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Labellable Phylogenetic Networks

Francis

Steel

2023

Preprint

Self Cite

View full text Add to dashboard Cite

Phylogenetic networks are mathematical representations of evolutionary history that are able to capture both tree-like evolutionary processes (speciations), and non-tree-like ``reticulate'' processes such as hybridization or horizontal gene transfer. The additional complexity that comes with this capacity, however, makes networks harder to infer from data, and more complicated to work with as mathematical objects. In this paper we define a new, large class of phylogenetic networks, that we call labellable, and show that they are in bijection with the set of ''expanding covers'' of finite sets. This correspondence is a generalisation of the encoding of phylogenetic forests by partitions of finite sets. Labellable networks can be characterised by a simple combinatorial condition, and we describe the relationship between this large class and other commonly studied classes. Furthermore, we show that all phylogenetic networks have a quotient network that is labellable.

show abstract

Section: Discussionmentioning

confidence: 99%

“…Note that this order reduces to the order used for labelling internal vertices in phylogenetic forests (in Algorithm 1 of [10]).…”

Section: Labellable Networkmentioning

confidence: 99%

Section: Labellable Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Labellable Phylogenetic Networks

Francis

Steel

2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Phylogenetic network classes through the lens of expanding covers

Francis,

Marchei,

Steel

2024

J. Math. Biol.

Self Cite

View full text Add to dashboard Cite

It was recently shown that a large class of phylogenetic networks, the ‘labellable’ networks, is in bijection with the set of ‘expanding’ covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks can be characterised purely in terms of properties of their associated covers. These classes include the tree-based, tree-child, orchard, tree-sibling, and normal networks. In the opposite direction, we give an example of how a restriction on the set of expanding covers can define a new class of networks, which we call ‘spinal’ phylogenetic networks.

show abstract

Labellable Phylogenetic Networks

Francis

Steel

2023

Bull Math Biol

Self Cite

View full text Add to dashboard Cite

Phylogenetic networks are mathematical representations of evolutionary history that are able to capture both tree-like evolutionary processes (speciations) and non-tree-like ‘reticulate’ processes such as hybridization or horizontal gene transfer. The additional complexity that comes with this capacity, however, makes networks harder to infer from data, and more complicated to work with as mathematical objects. In this paper, we define a new, large class of phylogenetic networks, that we call labellable, and show that they are in bijection with the set of ‘expanding covers’ of finite sets. This correspondence is a generalisation of the encoding of phylogenetic forests by partitions of finite sets. Labellable networks can be characterised by a simple combinatorial condition, and we describe the relationship between this large class and other commonly studied classes. Furthermore, we show that all phylogenetic networks have a quotient network that is labellable.

show abstract

Brauer and partition diagram models for phylogenetic trees and forests

Cited by 6 publications

References 27 publications

Labellable Phylogenetic Networks

Labellable Phylogenetic Networks

Phylogenetic network classes through the lens of expanding covers

Labellable Phylogenetic Networks

Contact Info

Product

Resources

About