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

  title={Efficient Quartet Representations of Trees and Applications to Supertree and Summary Methods},
  author={Ruth Davidson and MaLyn Lawhorn and Joseph P. Rusinko and Noah Weber},
  journal={IEEE/ACM Transactions on Computational Biology and Bioinformatics},
  • Ruth Davidson, MaLyn Lawhorn, +1 author Noah Weber
  • Published 16 December 2015
  • Mathematics, Computer Science, Biology, Medicine
  • IEEE/ACM Transactions on Computational Biology and Bioinformatics
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… 
Quartet-based computations of internode certainty provide robust measures of phylogenetic incongruence.
Three new Internode Certainty measures based on the frequencies of quartets are developed, which naturally apply to both complete and partial trees and are more robust to the absence of phylogenetic signal and errors in phylogenetic inference than bipartition-based measures.
Constructing Semi-Directed Level-1 Phylogenetic Networks from Quarnets
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
Assessing the fit of the multi-species network coalescent to multi-locus data
A goodness-of-fit test is proposed to quantify the fit between data observed from genome-wide multi-locus data, and patterns expected under the multi-species coalescent model on a candidate phylogenetic network, to provide one of the first rigorous tools for model selection.
Algebraic Statistics in Practice: Applications to Networks
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems


Accurate Phylogenetic Tree Reconstruction from Quartets: A Heuristic Approach
This paper presents a novel and highly accurate quartet-based phylogenetic tree reconstruction method, and performs an extensive experimental study to evaluate the accuracy and scalability of the approach on both simulated and biological datasets.
Quartets MaxCut: A Divide and Conquer Quartets Algorithm
  • S. Snir, Satish Rao
  • Mathematics, Medicine
    IEEE/ACM Transactions on Computational Biology and Bioinformatics
  • 2010
This paper describes an algorithm for constructing a tree from a set of input quartet trees even with a significant fraction of errors and shows empirically that conflicts in the inputs are handled satisfactorily and that it significantly outperforms and outraces the Matrix Representation with Parsimony (MRP) methods that have previously been most successful in dealing with supertrees.
Weighted quartets phylogenetics.
A scheme to assign weights to quartets coming from weighted trees and devise a tree similarity measure for weighted trees based on weighted quartets are proposed and extended.
Quartet MaxCut: a fast algorithm for amalgamating quartet trees.
An extremely fast algorithm for quartet amalgamation is devised and implemented in a very efficient code that can handle over a hundred millions of quartet trees over several hundreds of taxa with very high accuracy.
An experimental study of Quartets MaxCut and other supertree methods
The results show that supertree methods that improve upon MRP are possible, and that an effort should be made to produce scalable and robust implementations of the most accuratesupertree methods.
Quartet Puzzling: A Quartet Maximum-Likelihood Method for Reconstructing Tree Topologies
A versatile method, quartet puzzling, is introduced to reconstruct the topology (branching pattern) of a phylogenetic tree based on DNA or amino acid sequence data and outperforms neighbor joining in some cases with high transition/transversion bias.
Short Quartet Puzzling: A New Quartet-Based Phylogeny Reconstruction Algorithm
This study presents Short Quartet Puzzling, a new quartet-based phylogeny reconstruction algorithm, and demonstrates the improved topological accuracy of the new method over maximum parsimony and neighbor joining, disproving the conjecture of Ranwez and Gascuel.
Quartet decomposition server: a platform for analyzing phylogenetic trees
A web server that takes a collection of gene phylogenies, decomposes them into quartets, generates a Quartet Spectrum, and draws a split network is presented and will empower users to find statistically supported phylogenetic conflicts.
A simulation study comparing supertree and combined analysis methods using SMIDGen
This study demonstrates that MRP and weighted MRP produce distinctly less accurate trees than combined analyses for a given base method (maximum parsimony or maximum likelihood), indicating a clear need for better supertree methods.
Quartet Inference from SNP Data Under the Coalescent Model
A method to infer relationships among quartets of taxa under the coalescent model using techniques from algebraic statistics is developed, and uncertainty in the estimated relationships is quantified using the nonparametric bootstrap.