Accumulation Phylogenies

Baroni, Mihaela; Steel, Mike

doi:10.1007/s00026-006-0271-0

Cited by 10 publications

(17 citation statements)

References 10 publications

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“…Baroni et al [3], [4] defined the notion of a regular network. The precise definition is given in Section 2.…”

Section: Introductionmentioning

confidence: 99%

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Regular Networks Can be Uniquely Constructed from Their Trees

Willson

2011

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Abstract-A rooted acyclic digraph N with labelled leaves displays a tree T when there exists a way to select a unique parent of each hybrid vertex resulting in the tree T . Let T r(N ) denote the set of all trees displayed by the network N . In general, there may be many other networks M such that T r(M ) = T r(N ). A network is regular if it is isomorphic with its cover digraph. If N is regular and D is a collection of trees displayed by N , this paper studies some procedures to try to reconstruct N given D. If the input is D = T r(N ), one procedure is described which will reconstruct N . Hence if N and M are regular networks and T r(N ) = T r(M ), it follows that N = M , proving that a regular network is uniquely determined by its displayed trees. If D is a (usually very much smaller) collection of displayed trees that satisfies certain hypotheses, modifications of the procedure will still reconstruct N given D.

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“…Baroni et al [3], [4] defined the notion of a regular network. The precise definition is given in Section 2.…”

Section: Introductionmentioning

confidence: 99%

“…When N is regular, the procedure outputs the network N up to isomorphism. (In fact it outputs the cover digraph of N , see [4].) An example is worked in Section 5, illustrating the procedure.…”

Section: Introductionmentioning

confidence: 99%

Regular Networks Can be Uniquely Constructed from Their Trees

Willson

2011

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…It was shown in [4] that if a phylogenetic network is regular, then the genomes of all vertices under Accumulation Phylogeny are uniquely determined by the genomes at members of X. Here a partial converse Theorem 3.2 is proved.…”

Section: Regular Networkmentioning

confidence: 93%

“…In this section the model of evolution called Accumulation Phylogeny, described by Baroni and Steel [4], is reviewed. It was shown in [4] that if a phylogenetic network is regular, then the genomes of all vertices under Accumulation Phylogeny are uniquely determined by the genomes at members of X.…”

Section: Regular Networkmentioning

confidence: 99%

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Properties of Normal Phylogenetic Networks

Willson

2009

Bull. Math. Biol.

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Abstract.A phylogenetic network is a rooted acyclic digraph with vertices corresponding to taxa. Let X denote a set of vertices containing the root, the leaves, and all vertices of outdegree 1. Regard X as the set of vertices on which measurements such as DNA can be made. A vertex is called normal if it has one parent, and hybrid if it has more than one parent. The network is called normal if it has no redundant arcs and also from every vertex there is a directed path to a member of X such that all vertices after the first are normal. This paper studies properties of normal networks.Under a simple model of inheritance that allows homoplasies only at hybrid vertices, there is essentially unique determination of the genomes at all vertices by the genomes at members of X if and only if the network is normal. This model is a limiting case of more standard models of inheritance when the substitution rate is sufficiently low.Various mathematical properties of normal networks are described. These properties include that the number of vertices grows at most quadratically with the number of leaves and that the number of hybrid vertices grows at most linearly with the number of leaves.

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The hybrid number of a ploidy profile

Huber

Maher

2022

J. Math. Biol.

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Polyploidization, whereby an organism inherits multiple copies of the genome of their parents, is an important evolutionary event that has been observed in plants and animals. One way to study such events is in terms of the ploidy number of the species that make up a dataset of interest. It is therefore natural to ask: How much information about the evolutionary past of the set of species that form a dataset can be gleaned from the ploidy numbers of the species? To help answer this question, we introduce and study the novel concept of a ploidy profile which allows us to formalize it in terms of a multiplicity vector indexed by the species the dataset is comprised of. Using the framework of a phylogenetic network, we present a closed formula for computing the hybrid number (i.e. the minimal number of polyploidization events required to explain a ploidy profile) of a large class of ploidy profiles. This formula relies on the construction of a certain phylogenetic network from the simplification sequence of a ploidy profile and the hybrid number of the ploidy profile with which this construction is initialized. Both of them can be computed easily in case the ploidy numbers that make up the ploidy profile are not too large. To help illustrate the applicability of our approach, we apply it to a simplified version of a publicly available Viola dataset.

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Accumulation Phylogenies

Cited by 10 publications

References 10 publications

Regular Networks Can be Uniquely Constructed from Their Trees

Regular Networks Can be Uniquely Constructed from Their Trees

Properties of Normal Phylogenetic Networks

The hybrid number of a ploidy profile

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