Rooted NNI moves and distance-1 tail moves on tree-based phylogenetic networks

Erdős, Péter L.; Francis, Andrew R.; Mezei, Tamás Róbert

doi:10.1016/j.dam.2021.02.016

Cited by 4 publications

(8 citation statements)

References 14 publications

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“…The bound is, in any case, close to the bound for tree-based networks ( Erdős et al. 2021 ). It is clear the asymptotic bound cannot get smaller than , as this is tight for trees, but it may be possible to remove or reduce the kn part.…”

Section: Discussionsupporting

confidence: 76%

“…This confirms the speculation that was mentioned in the concluding remarks of Erdős et al. ( 2021 ). Connectedness of search spaces under rearrangement moves, such as the rNNI move, is important because of their use in local search heuristics and Bayesian methods in phylogenetics (e.g., Markin et al.…”

Section: Introductionsupporting

confidence: 91%

“…Note that our results are only given for rNNI moves, and not for local tail or local head moves separately, as is done for tree-based networks in Erdős et al. ( 2021 ). It might be true that the space of orchard networks is also connected under distance-1 tail moves, or distance-2 head moves, but our proof does not imply this, as we have used a mix of distance-1 tail moves and distance-1 head moves.…”

Section: Discussionmentioning

confidence: 99%

“…We prove that the space of binary orchard networks is connected using a strategy that is reminiscent of the proofs of connectedness in Janssen ( 2021 ) for local head moves and in Erdős et al. ( 2021 ) for tree-based networks. We first move all reticulations to the top of the network and then change the pendant trees below these reticulations.…”

Section: Orchard Network Spacementioning

confidence: 97%

“… 2017 ; Klawitter 2020 ; Erdős et al. 2021 ), the connectedness of the space of orchard networks has not been investigated yet.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionsupporting

confidence: 76%

Section: Introductionsupporting

confidence: 91%

Section: Discussionmentioning

confidence: 99%

Section: Orchard Network Spacementioning

confidence: 97%

“… 2017 ; Klawitter 2020 ; Erdős et al. 2021 ), the connectedness of the space of orchard networks has not been investigated yet.…”

Section: Introductionmentioning

confidence: 99%

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Orchard Networks are Trees with Additional Horizontal Arcs

et al. 2022

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Exploring spaces of semi-directed level-1 networks

Linz,

Wicke

2023

J. Math. Biol.

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Semi-directed phylogenetic networks have recently emerged as a class of phylogenetic networks sitting between rooted (directed) and unrooted (undirected) phylogenetic networks as they contain both directed as well as undirected edges. While various spaces of rooted phylogenetic networks and unrooted phylogenetic networks have been analyzed in recent years and several rearrangement moves to traverse these spaces have been introduced, little is known about spaces of semi-directed phylogenetic networks. Here, we propose a simple rearrangement move for semi-directed phylogenetic networks, called cut edge transfer (CET), and show that the space of semi-directed level-1 networks with precisely k reticulations is connected under CET. This level-1 space is currently the predominantly used search space for most algorithms that reconstruct semi-directed phylogenetic networks. Our results imply that every semi-directed level-1 network with a fixed number of reticulations and leaf set can be reached from any other such network by a sequence of CETs. By introducing two additional moves, R$$^+$$ + and R$$^-$$ - , that allow for the addition and deletion, respectively, of a reticulation, we then establish connectedness for the space of all semi-directed level-1 networks on a fixed leaf set. As a byproduct of our results for semi-directed phylogenetic networks, we also show that the space of rooted level-1 networks with a fixed number of reticulations and leaf set is connected under CET, when translated into the rooted setting.

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Autopolyploidy, Allopolyploidy, and Phylogenetic Networks with Horizontal Arcs

Huber¹,

Maher²

2023

Bull Math Biol

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Polyploidization is an evolutionary process by which a species acquires multiple copies of its complete set of chromosomes. The reticulate nature of the signal left behind by it means that phylogenetic networks offer themselves as a framework to reconstruct the evolutionary past of species affected by it. The main strategy for doing this is to first construct a so-called multiple-labelled tree and to then somehow derive such a network from it. The following question therefore arises: How much can be said about that past if such a tree is not readily available? By viewing a polyploid dataset as a certain vector which we call a ploidy (level) profile, we show that among other results, there always exists a phylogenetic network in the form of a beaded phylogenetic tree with additional arcs that realizes a given ploidy profile. Intriguingly, the two end vertices of almost all of these additional arcs can be interpreted as having co-existed in time thereby adding biological realism to our network, a feature that is, in general, not enjoyed by phylogenetic networks. In addition, we show that our network may be viewed as a generator of ploidy profile space, a novel concept similar to phylogenetic tree space that we introduce to be able to compare phylogenetic networks that realize one and the same ploidy profile. We illustrate our findings in terms of a publicly available Viola dataset.

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Rooted NNI moves and distance-1 tail moves on tree-based phylogenetic networks

Cited by 4 publications

References 14 publications

Orchard Networks are Trees with Additional Horizontal Arcs

Orchard Networks are Trees with Additional Horizontal Arcs

Exploring spaces of semi-directed level-1 networks

Autopolyploidy, Allopolyploidy, and Phylogenetic Networks with Horizontal Arcs

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