From modular decomposition trees to rooted median graphs

Bruckmann, Carmen; Stadler, Peter F.; Hellmuth, Marc

doi:10.1016/j.dam.2021.12.017

Cited by 10 publications

(5 citation statements)

References 35 publications

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“…In [18] pyramid networks were implicitly defined and shown to be planar. An example of such a network also appeared recently in [32,Fig 2. ].…”

Section: Regular Networkmentioning

confidence: 96%

Planar Rooted Phylogenetic Networks

Moulton

2023

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

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A phylogenetic network is a rooted, directed acyclic graph, with a single root, whose sinks correspond to a set of species. Such networks are commonly used to represent the evolution of species that have undergone reticulate evolution. Recently, there has been great interest in developing the theory behind and algorithms for constructing such networks. One issue with phylogenetic networks is that, unlike rooted evolutionary trees, they can be highly non-planar (i.e. it is not possible to draw them in the plane without some arcs crossing). This can make them difficult to visualise and interpret. In this paper we investigate properties of planar phylogenetic networks and algorithms for deciding whether or not phylogenetic networks have certain special planarity properties. In particular, as well as defining some natural subclasses of planar phylogenetic networks and working out their interrelationships, we characterize when the well-known level-k networks are planar as well as showing that planar regular networks are closely related to pyramids. Our results make use of the highly developed field of planar digraphs, and we believe that the link between phylogenetic networks and this field should prove useful in future for developing new approaches to both construct and visualise phylogenetic networks.

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“…In [18] pyramid networks were implicitly defined and shown to be planar. An example of such a network also appeared recently in [32,Fig 2. ].…”

Section: Regular Networkmentioning

confidence: 96%

Planar Rooted Phylogenetic Networks

Moulton

2023

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

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“… 2019 ; Bruckmann et al. 2022 ). In this context, it is of considerable interest to understand the structure of least-resolved networks that still explain the same data and are obtained from the original network by shortcut removal and contraction of arcs (cf.…”

Section: Level-1 Networkmentioning

confidence: 99%

Clustering systems of phylogenetic networks

Hellmuth,

Schaller,

Stadler

2023

Theory Biosci.

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Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set X of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization that cannot be captured by trees. A variety of classes of such networks have been discussed in the literature, including phylogenetic, level-1, tree-child, tree-based, galled tree, regular, or normal networks as models of different types of evolutionary processes. Clusters arise in models of phylogeny as the sets $${{\,\mathrm{\texttt{C}}\,}}(v)$$ C ( v ) of descendant taxa of a vertex v. The clustering system $$\mathscr {C}_N$$ C N comprising the clusters of a network N conveys key information on N itself. In the special case of rooted phylogenetic trees, T is uniquely determined by its clustering system $$\mathscr {C}_T$$ C T . Although this is no longer true for networks in general, it is of interest to relate properties of N and $$\mathscr {C}_N$$ C N . Here, we systematically investigate the relationships of several well-studied classes of networks and their clustering systems. The main results are correspondences of classes of networks and clustering systems of the following form: If N is a network of type $$\mathbb {X}$$ X , then $$\mathscr {C}_N$$ C N satisfies $$\mathbb {Y}$$ Y , and conversely if $$\mathscr {C}$$ C is a clustering system satisfying $$\mathbb {Y},$$ Y , then there is network N of type $$\mathbb {X}$$ X such that $$\mathscr {C}\subseteq \mathscr {C}_N$$ C ⊆ C N .This, in turn, allows us to investigate the mutual dependencies between the distinct types of networks in much detail.

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“…In many applications, vertex-or arc-labeled networks are considered as a scaffold to explain genomic sequence data [14,[27][28][29][30][31][32][33]. In this context, it is of considerable interest to understand the structure of least-resolved networks that still explain the same data and are obtained from the original network by shortcut removal and contraction of arcs (cf.…”

Section: Clusters and Least Common Ancestorsmentioning

confidence: 99%

Clustering Systems of Phylogenetic Networks

Hellmuth¹,

Schaller²,

Stadler³

2022

Preprint

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Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set X of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization, that cannot be captured by trees. A variety of classes of such networks have been discussed in the literature, including phylogenetic, level-1, tree-child, tree-based, galled tree, regular, or normal networks as models of different types of evolutionary processes. Clusters arise in models of phylogeny as the sets C(v) of descendant taxa of a vertex v. The clustering system C N comprising the clusters of a network N conveys key information on N itself. In the special case of rooted phylogenetic trees, T is uniquely determined by its clustering system C T . Although this is no longer true for networks in general, it is of interest to relate properties of N and C N . Here, we systematically investigate the relationships of several well-studied classes of networks and their clustering systems. The main results are correspondences of classes of networks and clustering system of the following form: If N is a network of type X, then C N satisfies Y, and conversely if C is a clustering system satisfying Y then there is network N of type X such that C ⊆ C N .This, in turn, allows us to investigate the mutual dependencies between the distinct types of networks in much detail.

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From modular decomposition trees to rooted median graphs

Cited by 10 publications

References 35 publications

Planar Rooted Phylogenetic Networks

Planar Rooted Phylogenetic Networks

Clustering systems of phylogenetic networks

Clustering Systems of Phylogenetic Networks

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