Performance of a new invariants method on homogeneous and nonhomogeneous quartet trees.

An attempt to use phylogenetic invariants for tree reconstruction was made at the end of the 80s and the beginning of the 90s by several researchers (the initial idea due to Lake [1987] and Cavender and Felsenstein [1987]). However, the efficiency of methods based on invariants is still in doubt (Huelsenbeck 1995; Jin and Nei 1990). Probably because these methods only used few generators of the set of phylogenetic invariants. The method studied in this paper was first introduced in Casanellas et al. (2005) and it is the first method based on invariants that uses the "whole" set of generators for DNA data. The simulation studies performed in this paper prove that it is a very competitive and highly efficient phylogenetic reconstruction method, especially for nonhomogeneous models on phylogenetic trees.

[1]  Seth Sullivant,et al.  Toric Ideals of Phylogenetic Invariants , 2004, J. Comput. Biol..

[2]  L. Pachter,et al.  Algebraic Statistics for Computational Biology: Preface , 2005 .

[3]  Elizabeth S. Allman,et al.  Phylogenetic ideals and varieties for the general Markov model , 2004, Adv. Appl. Math..

[4]  E. Allman,et al.  Phylogenetic invariants for the general Markov model of sequence mutation. , 2003, Mathematical biosciences.

[5]  L F Landweber,et al.  Phylogenetic invariants and geometry. , 2000, Journal of theoretical biology.

[6]  Editors , 1986, Brain Research Bulletin.

[7]  Seth Sullivant,et al.  Algebraic Statistics for Computational Biology: The Strand Symmetric Model , 2005 .

[8]  Elizabeth S. Allman,et al.  The Identifiability of Tree Topology for Phylogenetic Models, Including Covarion and Mixture Models , 2005, J. Comput. Biol..

[9]  Seth Sullivant,et al.  Algebraic Statistics for Computational Biology: Catalog of Small Trees , 2005 .

[10]  L. Jin,et al.  Limitations of the evolutionary parsimony method of phylogenetic analysis. , 1990, Molecular biology and evolution.

[11]  J. Felsenstein,et al.  Invariants of phylogenies in a simple case with discrete states , 1987 .

[12]  Terence P. Speed,et al.  Invariants of Some Probability Models Used in Phylogenetic Inference , 1993 .

[13]  Ina Ruck,et al.  USA , 1969, The Lancet.

[14]  Andrew Rambaut,et al.  Seq-Gen: an application for the Monte Carlo simulation of DNA sequence evolution along phylogenetic trees , 1997, Comput. Appl. Biosci..

[15]  Korbinian Strimmer,et al.  APE: Analyses of Phylogenetics and Evolution in R language , 2004, Bioinform..

[16]  Ziheng Yang,et al.  Estimation of the Transition/Transversion Rate Bias and Species Sampling , 1999, Journal of Molecular Evolution.

[17]  N. Saitou,et al.  The neighbor-joining method: a new method for reconstructing phylogenetic trees. , 1987, Molecular biology and evolution.

[18]  E. Allman,et al.  Quartets and Parameter Recovery for the General Markov Model of Sequence Mutation , 2004 .

[19]  Ziheng Yang,et al.  PAML: a program package for phylogenetic analysis by maximum likelihood , 1997, Comput. Appl. Biosci..

[20]  J A Lake,et al.  A rate-independent technique for analysis of nucleic acid sequences: evolutionary parsimony. , 1987, Molecular biology and evolution.

[21]  M. Gouy,et al.  Inferring pattern and process: maximum-likelihood implementation of a nonhomogeneous model of DNA sequence evolution for phylogenetic analysis. , 1998, Molecular biology and evolution.

[22]  Z. Yang,et al.  On the use of nucleic acid sequences to infer early branchings in the tree of life. , 1995, Molecular biology and evolution.

[23]  M. Kimura.  A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences , 1980, Journal of Molecular Evolution.

[24]  M. Kimura.  Estimation of evolutionary distances between homologous nucleotide sequences. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[25]  J. Felsenstein.  Evolutionary trees from DNA sequences: A maximum likelihood approach , 2005, Journal of Molecular Evolution.

[26]  David Sankoff,et al.  Phylogenetic Invariants for Genome Rearrangements , 1999, J. Comput. Biol..

[27]  V. F.,et al.  Phylogenetic Invariants for More General Evolutionary Models , 2022 .

[28]  N. Eriksson.  Algebraic Statistics for Computational Biology: Tree Construction using Singular Value Decomposition , 2005 .

[29]  Seong-Hun Paeng,et al.  Phylogenetic tree constructing algorithms fit for grid computing with SVD , 2006, q-bio/0611015.

[30]  László A. Székely,et al.  A complete family of phylogenetic invariants for any number of taxa under Kimura's 3ST model , 1993 .

[31]  J. Huelsenbeck.  Performance of Phylogenetic Methods in Simulation , 1995 .