Combinatorics of linked systems of quartet trees

Moan, Emili; Rusinko, Joseph

doi:10.2140/involve.2016.9.171

Cited by 2 publications

(6 citation statements)

References 9 publications

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“…The computational constraints involved in computing all ( n 4 ) quarnets suggest the need for adaptations of these algorithms which require only a subset of the complete quarnet set. Those interested in such advances might first examine similar improvements to quartet based tree reconstruction such as those found in [12,4,9,10,15] among others.…”

Section: Discussionmentioning

confidence: 99%

Constructing Semi-Directed Level-1 Phylogenetic Networks from Quarnets

Huebler¹,

Morris²,

Rusinko³

et al. 2019

Preprint

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We introduce two algorithms for reconstructing semi-directed level-1 phylogenetic networks from their complete set of 4-leaf subnetworks, known as quarnets. The first algorithm, the sequential method, begins with a single quarnet and adds on one leaf at a time until all leaves have been placed. The second algorithm, the cherry-blob method, functions similarly to cherry-picking algorithms for phylogenetic trees by identifying exterior network structures from the quarnets.

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Section: Discussionmentioning

confidence: 99%

Constructing Semi-Directed Level-1 Phylogenetic Networks from Quarnets

Huebler¹,

Morris²,

Rusinko³

et al. 2019

Preprint

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“…Small definitive systems of quartets are strong candidates for supertree inputs as they retain all of the combinatorial information from the input trees. One example of a family of small definitive systems of quartets is known as linked systems, introduced in [27]. Definition 5 ( [27]).…”

Section: Lemma Ii2 In a Tree T With N Taxa And Any Eqs Represen-mentioning

confidence: 99%

“…One example of a family of small definitive systems of quartets is known as linked systems, introduced in [27]. Definition 5 ( [27]). Given a subset of quartets L ⊂ Q(T ) of n − 3 quartet trees, define the associated graph G T (L) with vertex set V and edge set E as follows:…”

Section: Lemma Ii2 In a Tree T With N Taxa And Any Eqs Represen-mentioning

confidence: 99%

“…Thus L(T ) is a linked system of quartets. It follows from Theorem 3.1 in [27] that L(T ) is a definitive set of quartets. Since each quartet in E(T ) is displayed by a tree, then T must be the unique tree that displays the quartets in L(T ).…”

Section: Proposition Ii3 An Eqs Is a Definitive Set Of Quartetsmentioning

confidence: 99%

“…An EQS is definitive and thus captures all of the phylogenetic signal contained in the input trees. Since QMC is a heuristic algorithm with no theoretical guarantees it does not always return the correct tree even when the input quartets are definitive (see [27] for a six-taxon example). However, we demonstrate that QMC returns the correct simulated model tree given an EQS as input with extremely high probability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Quartet Representations of Trees and Applications to Supertree and Summary Methods

Davidson

Lawhorn

Rusinko

et al. 2018

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

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Abstract-Quartet trees displayed by larger phylogenetic trees have long been used as inputs for species tree and supertree reconstruction. Computational constraints prevent the use of all displayed quartets in many practical problems with large numbers of taxa. We introduce the notion of an Efficient Quartet System (EQS) to represent a phylogenetic tree with a subset of the quartets displayed by the tree. We show mathematically that the set of quartets obtained from a tree via an EQS contains all of the combinatorial information of the tree itself. Using performance tests on simulated datasets, we also demonstrate that using an EQS to reduce the number of quartets in both summary method pipelines for species tree inference as well as methods for supertree inference results in only small reductions in accuracy.

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Combinatorics of linked systems of quartet trees

Cited by 2 publications

References 9 publications

Constructing Semi-Directed Level-1 Phylogenetic Networks from Quarnets

Constructing Semi-Directed Level-1 Phylogenetic Networks from Quarnets

Efficient Quartet Representations of Trees and Applications to Supertree and Summary Methods

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