Clusters, Trees, and Phylogenetic Network Classes

Zhang, Louxin

doi:10.1007/978-3-030-10837-3_12

Cited by 24 publications

(25 citation statements)

References 37 publications

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“…Each of these connected components is a tree-component of N . This is a useful concept for characterizing the topological structures of phylogenetic networks [22,14].…”

Section: Phylogenetic Networkmentioning

confidence: 99%

On The Exact Counting of Tree-Child Networks

Pons

Batle

2021

Preprint

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The combinatorial study of phylogenetic networks has attracted much attention in recent times. In particular, one class of them, the so-called tree-child networks, are becoming the most prominent ones. However, their combinatorial properties are largely unknown. In this paper we address the problem of exactly counting them. We conjecture a bijection with a certain class of words, and from this assumption a simple recurrence formula arises. It is able to determine the number of all subclasses, as well as a direct formula, a simple enumeration procedure and precise asympotics. Our results coincide with all currently proved formulas for particular subclasses of tree-child networks, as well as with numerical results obtained for small networks. Since, as we will show, working with words greatly simplies the problem, we expect to contribute to further combinatoric characterizations of this class of networks.

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“…Each of these connected components is a tree-component of N . This is a useful concept for characterizing the topological structures of phylogenetic networks [22,14].…”

Section: Phylogenetic Networkmentioning

confidence: 99%

On The Exact Counting of Tree-Child Networks

Pons

Batle

2021

Preprint

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“…The subnetwork N − (R(N ) ∪ L(N )) is a forest for which each connected component consists of tree nodes. Each connected component is called a tree-component of N [11,25]. Note that each tree-component does not contain any leaves.…”

Section: Decomposition Of Galled Network Into Tree-componentsmentioning

confidence: 99%

Counting and enumerating galled networks

Gunawan

Rathin

Zhang

2020

Discrete Applied Mathematics

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Galled trees are widely studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into galled networks by relaxing a structural condition. In this work, a linear recurrence formula is given for counting 1galled networks, which are galled networks satisfying the condition that each reticulate node has only one leaf descendant. Since every galled network consists of a set of 1-galled networks stacked one on top of the other, a method is also presented to count and enumerate galled networks.

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“…Second, to develop efficient algorithms for NPcomplete problems on RPNs, simple classes of RPNs have been introduced, including galled trees [17,18], tree-child networks (TCNs) [19], normal networks [20], reticulation-visible networks [4] and tree-based networks [21,22] (see also [5,23]). For instance, a RPN is a TCN if every non-leaf node has a child that is a tree node or a leaf.…”

Section: Introductionmentioning

confidence: 99%

Generating normal networks via leaf insertion and nearest neighbor interchange

Zhang

2019

BMC Bioinformatics

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BackgroundGalled trees are studied as a recombination model in theoretical population genetics. This class of phylogenetic networks has been generalized to tree-child networks and other network classes by relaxing a structural condition imposed on galled trees. Although these networks are simple, their topological structures have yet to be fully understood.ResultsIt is well-known that all phylogenetic trees on n taxa can be generated by the insertion of the n-th taxa to each edge of all the phylogenetic trees on n−1 taxa. We prove that all tree-child (resp. normal) networks with k reticulate nodes on n taxa can be uniquely generated via three operations from all the tree-child (resp. normal) networks with k−1 or k reticulate nodes on n−1 taxa. Applying this result to counting rooted phylogenetic networks, we show that there are exactly binary phylogenetic networks with one reticulate node on n taxa.ConclusionsThe work makes two contributions to understand normal networks. One is a generalization of an enumeration procedure for phylogenetic trees into one for normal networks. Another is simple formulas for counting normal networks and phylogenetic networks that have only one reticulate node.

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Clusters, Trees, and Phylogenetic Network Classes

Cited by 24 publications

References 37 publications

On The Exact Counting of Tree-Child Networks

On The Exact Counting of Tree-Child Networks

Counting and enumerating galled networks

Generating normal networks via leaf insertion and nearest neighbor interchange

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