Classes of tree-based networks

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

doi:10.1186/s42492-020-00043-z

Cited by 8 publications

(9 citation statements)

References 20 publications

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“… 2015 ; Fischer et al. 2020 ). Temporal and tree-child networks are especially interesting because of their computation benefits and nice mathematical properties.…”

Section: Introductionmentioning

confidence: 99%

Orchard Networks are Trees with Additional Horizontal Arcs

et al. 2022

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Phylogenetic networks are used in biology to represent evolutionary histories. The class of orchard phylogenetic networks was recently introduced for their computational benefits, without any biological justification. Here, we show that orchard networks can be interpreted as trees with additional horizontal arcs. Therefore, they are closely related to tree-based networks, where the difference is that in tree-based networks the additional arcs do not need to be horizontal. Then, we use this new characterization to show that the space of orchard networks on n leaves with k reticulations is connected under the rNNI rearrangement move with diameter $$O(kn+n\log (n))$$ O ( k n + n log ( n ) ) .

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“… 2015 ; Fischer et al. 2020 ). Temporal and tree-child networks are especially interesting because of their computation benefits and nice mathematical properties.…”

Section: Introductionmentioning

confidence: 99%

Orchard Networks are Trees with Additional Horizontal Arcs

et al. 2022

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“…Such concepts include, but are not limited to, level-1 networks (also known as galled trees) [6,18,23], tree-child networks [5], and tree-based networks [15,16]. Particularly the latter have gained significant interest in recent literature [11,12,17,20,24]. remains connected if any of its vertices is removed.…”

Section: Introductionmentioning

confidence: 99%

“…Edge-based phylogenetic networks and (generalized) series-parallel graphs. We now recall the so-called leaf-shrinking procedure from [11,13]. Let G = (V, E) be a connected graph with at least two vertices, i.e., |V (G)| ≥ 2.…”

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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“…Following publication of the original article [ 1 ], in the description of the leaf shrinking procedure as well as in Algorithm 1 and the definition of edge-based graphs in [ 1 ], the condition that G contains at least two leaves (i.e., the condition | V L ( G )| ≥ 2) needs to be omitted. Moreover, in line 2 of Algorithm 1 it should read .…”

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confidence: 99%