Hierarchies from Lowest Stable Ancestors in Nonbinary Phylogenetic Networks

Huber, Katharina T.; Moulton, Vincent; Wu, Taoyang

doi:10.1007/s00357-018-9279-5

Cited by 4 publications

(4 citation statements)

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“…Following Huber et al. ( 2019a ), we call a vertex v that is -minimal in a block B a terminal vertex (of B ). Note that every terminal vertex v of a non-trivial block B must always have indegree at least 2 since, by Corollary 1 , v lies on some undirected cycle in B and, by -minimality of v in B , its two incident vertices on this cycle must both be in-neighbors.…”

Section: Preliminariesmentioning

confidence: 99%

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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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Section: Preliminariesmentioning

confidence: 99%

“…In many applications, vertex- or arc-labeled networks are considered as a scaffold to explain genomic sequence data (Huber and Moulton 2006 ; Huber et al. 2019a ; Huber and Scholz 2018 ; Hellmuth et al. 2015 ; Hellmuth and Wieseke 2016 ; Hellmuth and Scholz 2021 ; Hellmuth et al.…”

Section: Level-1 Networkmentioning

confidence: 99%

Clustering systems of phylogenetic networks

Hellmuth,

Schaller,

Stadler

2023

Theory Biosci.

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“…Moreover, if (u, v) ∈ E, we say that u is a parent of v, u ∈ par G (v), and v is a child of u, v ∈ child G (u). Following [32], we call a vertex v that is G -minimal in a block B a terminal vertex (of B). Note that every terminal vertex v of a non-trivial block B must always have indegree at least 2 since, by Cor.…”

Section: Directed Acyclic Graphsmentioning

confidence: 99%

“…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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