Distinguishing level-1 phylogenetic networks on the basis of data generated by Markov processes

Gross, Elizabeth; Iersel, Leo van; Janssen, Remie; Jones, Mark; Long, Colby; Murakami, Yukihiro

doi:10.48550/arxiv.2007.08782

Cited by 3 publications

(7 citation statements)

References 33 publications

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“…Together with earlier results in [24,25], the following table summarizes the relationships between varieties associated with a tree, level-1 and simple nice level-2 networks with four leaves under the JC, K2P, or K3P models. The non-containment of varieties associated with type 4 and the other types of networks is only valid under the JC model.…”

Section: Distinguishing 4-leaf Nice Level-2 Networkmentioning

confidence: 92%

“…We now introduce a Markov model on phylogenetic networks, which were previously studied in [24,25]. For k ≥ 1, let N be an n-leaf level-k semi-directed network on X.…”

Section: Markov Model On Networkmentioning

confidence: 99%

“…Another main tool to obtain the results is some earlier results stating that two of large cycle networks are distinguishable, which are provided in [24] under the JC model and in [28] under the K2P and K3P models. Additionally, the result for general triangle-free level-1 networks is provided in [25]. Results provided in this paper are obtained under the JC, K2P or K3P model unless specifically stated otherwise.…”

Section: Now Suppose That Smentioning

confidence: 99%

“…For these algebraic models, we will study the generic identifiability of the model, which is a slightly weaker notion than the (global) identifiability. In the network setting, recent works in [24,25] provide generic identifiability results for level-1 triangle-free networks. These results are obtained by first checking that the two given networks are distinguishable.…”

Section: Introductionmentioning

confidence: 99%

“…The second statement of Lemma 3.8 allows us to apply the Fourier transformation method to simplify the joint probability distributions for level-1 semi-directed network as presented in [24] and [25]. This would not be the case for level-2 networks.…”

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confidence: 99%

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Distinguishing Level-2 Phylogenetic Networks Using Phylogenetic Invariants

Ardiyansyah¹

2021

Preprint

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In phylogenetics, it is important for the phylogenetic network model parameters to be identifiable so that the evolutionary histories of a group of species can be consistently inferred. However, as the complexity of the phylogenetic network models grows, the identifiability of network models becomes increasingly difficult to analyze. As an attempt to analyze the identifiability of network models, we check whether two networks are distinguishable. In this paper, we specifically study the distinguishability of phylogenetic network models associated with level-2 networks. Using an algebraic approach, namely using discrete Fourier transformation, we present some results on the distinguishability of some level-2 networks, which generalize earlier work on the distinguishability of level-1 networks. In particular, we study simple and semisimple level-2 networks. Simple and semisimple level-2 networks can be thought as generalizations of level-1 sunlet and cycle networks, respectively. Moreover, we also compare the varieties associated with semisimple level-2 and cycle networks.

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Section: Distinguishing 4-leaf Nice Level-2 Networkmentioning

confidence: 92%

“…We now introduce a Markov model on phylogenetic networks, which were previously studied in [24,25]. For k ≥ 1, let N be an n-leaf level-k semi-directed network on X.…”

Section: Markov Model On Networkmentioning

confidence: 99%

Section: Now Suppose That Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Distinguishing Level-2 Phylogenetic Networks Using Phylogenetic Invariants

Ardiyansyah¹

2021

Preprint

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Classes of Explicit Phylogenetic Networks and their Biological and Mathematical Significance

Kong¹,

Pons²,

Kubatko³

et al. 2021

Preprint

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The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately represented by a phylogenetic tree, and rooted phylogenetic networks have been introduced as a generalization of rooted phylogenetic trees. In fact, estimating rooted phylogenetic networks from genomic sequence data and analyzing their structural properties is one of the most important tasks in contemporary phylogenetics. Over the last two decades, several subclasses of rooted phylogenetic networks (characterized by certain structural constraints) have been introduced in the literature, either to model specific biological phenomena or to enable tractable mathematical and computational analyses. In the present manuscript, we provide a thorough review of these network classes, as well as provide a biological interpretation of the structural constraints underlying these networks where possible. In addition, we discuss how imposing structural constraints on the network topology can be used to address the scalability and identifiability challenges faced in the estimation of pyhlogenetic networks from empirical data.

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Identifiability of local and global features of phylogenetic networks from average distances

Xu¹,

Ané²

2021

Preprint

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Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with likelihood-based methods limits the size of networks that can be handled. Methods based on pairwise distances could offer faster alternatives. We study here the information that average pairwise distances contain on the underlying phylogenetic network, by characterizing local and global features that can or cannot be identified. For general networks, we clarify that the root and edge lengths adjacent to reticulations are not identifiable, and then focus on the class of zipped-up semidirected networks. We provide a criterion to swap subgraphs locally, such as 3-cycles, resulting in undistinguishable networks. We propose the "distance split tree", which can be constructed from pairwise distances, and prove that it is a refinement of the network's blob tree, capturing the tree-like features of the network. For level-1 networks, this distance split tree is equal to the blob tree refined to separate polytomies from blobs, and we prove that the mixed representation of the network is identifiable. The information loss is localized around 4cycles, for which the placement of the reticulation is unidentifiable. The mixed representation combines split edges for 4-cycles, with regular tree and hybrid edges from the semidirected network, with edge parameters that encode all information identifiable from average pairwise distances.

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Distinguishing level-1 phylogenetic networks on the basis of data generated by Markov processes

Cited by 3 publications

References 33 publications

Distinguishing Level-2 Phylogenetic Networks Using Phylogenetic Invariants

Distinguishing Level-2 Phylogenetic Networks Using Phylogenetic Invariants

Classes of Explicit Phylogenetic Networks and their Biological and Mathematical Significance

Identifiability of local and global features of phylogenetic networks from average distances

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