Classes of treebased networks

Fischer, Mareike; Galla, Michelle; Herbst, Lina; Long, Yangjing; Wicke, Kristina

doi:10.48550/arxiv.1810.06844

Cited by 2 publications

(8 citation statements)

References 16 publications

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“…We do not restrict the degree of the non-leaf vertices, so we deal with the general "non-binary" case (internal vertices of binary networks have degree exactly 3). 1 The special case of an acyclic phylogenetic network is called a phylogenetic tree.…”

Section: Definitions and Backgroundmentioning

confidence: 99%

“…Moreover, we will refer to the leaf cut graph LCUT (N ) of a proper network N ∈ PN (X), with |V (N )| ≥ 3, which is the graph G obtained from N by deleting all leaves and their incident edges [1]. Note that this may result in some vertices of degree 2 and -e.g.…”

Section: Definitions and Backgroundmentioning

confidence: 99%

“…This family of networks has received quite a bit of theoretical development over the last few years, including extensions to the non-binary case [10,14], and the unrooted setting [3,7,2]. Numerous characterizations of rooted tree-based networks have been published, many using interesting combinatorial constructions such as graph matchings [6,10,14,5,1].…”

Section: Introductionmentioning

confidence: 99%

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How tree-based is my network? Proximity measures for unrooted phylogenetic networks

Fischer

Francis

2020

Discrete Applied Mathematics

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Evolutionary events like hybridization and horizontal gene transfer cannot be represented by a tree but require a phylogenetic network instead. Nonetheless, it has been argued that evolution is fundamentally tree-like, in the sense that it can be modeled by a tree with additional arcs. Phylogenetic networks with this property are called tree-based, and this concept has recently attracted significant attention in evolutionary research. But classifying networks into treebased and non-tree-based ones is usually not sufficient for biological purposes, because sometimes tree-basedness is missed merely due to incomplete sampling. Therefore, measures are needed to quantify how close a non-tree-based network is to being tree-based. Such measures naturally also lead to characterizations of tree-based networks, and some measures for this purpose have recently been introduced both for binary and non-binary rooted phylogenetic networks. In the present manuscript, we generalize all these measures to unrooted networks, for which tree-basedness is mathematically more involved, and also present some new measures. This leads to new characterizations of unrooted tree-based networks. We analyze the relationships of the new proximity measures to one another to demonstrate their common properties as well as their respective differences.

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Section: Definitions and Backgroundmentioning

confidence: 99%

Section: Definitions and Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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How tree-based is my network? Proximity measures for unrooted phylogenetic networks

Fischer

Francis

2020

Discrete Applied Mathematics

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“…Another concept that we need in the following, recently introduced in [3], is the leaf cut graph LCUT (N ) of a proper network N ∈ N (n, k), with |V (N )| ≥ 3, which is the graph G obtained from N by deleting all leaves and their incident edges. Note that this may result in some vertices of degree 2 and -e.g.…”

Section: Definitions and Backgroundmentioning

confidence: 99%

“…For instance, a tree-based network that is pseudo-Hamiltonian (in the sense of [6]: a network whose LCUT (N ) graph [2] has a Hamiltonian cycle, cf. also [3]) will be lineal if there are two vertices that are connected to leaves, and that are adjacent on the Hamiltonian cycle.…”

Section: Definitions and Backgroundmentioning

confidence: 99%

The space of tree-based phylogenetic networks

Fischer¹,

Francis²

2019

Preprint

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Phylogenetic networks are generalizations of phylogenetic trees that allow the representation of reticulation events such as horizontal gene transfer or hybridization, and can also represent uncertainty in inference. A subclass of these, tree-based phylogenetic networks, have been introduced to capture the extent to which reticulate evolution nevertheless broadly follows tree-like patterns. Several important operations that change a general phylogenetic network have been developed in recent years, and are important for allowing algorithms to move around spaces of networks; a vital ingredient in finding an optimal network given some biological data. A key such operation is the Nearest Neighbor Interchange, or NNI. While it is already known that the space of unrooted phylogenetic networks is connected under NNI, it has been unclear whether this also holds for the subspace of tree-based networks. In this paper we show that the space of unrooted tree-based phylogenetic networks is indeed connected under the NNI operation. We do so by explicitly showing how to get from one such network to another one without losing tree-basedness along the way. Moreover, we introduce some new concepts, for instance "shoat networks", and derive some interesting aspects concerning tree-basedness. Last, we use our results to derive an upper bound on the size of the space of tree-based networks.

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Classes of treebased networks

Cited by 2 publications

References 16 publications

How tree-based is my network? Proximity measures for unrooted phylogenetic networks

How tree-based is my network? Proximity measures for unrooted phylogenetic networks

The space of tree-based phylogenetic networks

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