Corrected Parsimony, Minimum Evolution, and Hadamard Conjugations

Phylogenetic spectral analysis based on Hadamard transforms is an interesting new development for the inference of evo? lutionary trees and for understanding the interrelationships of existing methods (Hendy and Penny, 1989, 1993; Steel et al., 1993a; Hendy et al., 1994; Lento et al., 1994). We use it to interconvert between an underlying evolutionary model and the ex? pected frequencies of patterns observed in sequences. Because the Hadamard is a dis? crete Fourier transform on a finite group (Diaconis, 1988), we call this approach spectral analysis. It gives a mathematical description of an invertible relationship be? tween data and model: the expected fre? quencies of patterns in the data can be cal? culated from the model, and the model can be recovered consistently from the fre? quencies of patterns in the data. Recently, Takezaki and Nei (1994) que? ried four aspects of the utility of spectral analysis: the use of the parsimony criterion after correcting for multiple changes (cor? rected parsimony), the current limitation of spectral analysis on nucleotide sequenc? es to the Kimura 3-ST mechanism of evo? lution, the relationship between a Hada? mard transform and the minimum

[1]  M Steel,et al.  Links between maximum likelihood and maximum parsimony under a simple model of site substitution. , 1997, Bulletin of mathematical biology.

[2]  D Penny,et al.  Evolution of chlorophyll and bacteriochlorophyll: the problem of invariant sites in sequence analysis. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Michael D. Hendy,et al.  Complete Families of Linear Invariants for Some Stochastic Models of Sequence Evolution, with and without Molecular Clock Assumption , 1996, J. Comput. Biol..

[4]  D. Penny,et al.  Use of spectral analysis to test hypotheses on the origin of pinnipeds. , 1995, Molecular biology and evolution.

[5]  Mike A. Steel,et al.  Classifying and Counting Linear Phylogenetic Invariants for the Jukes-Cantor Model , 1995, J. Comput. Biol..

[6]  Michael D. Hendy,et al.  The sampling distributions and covariance matrix of phylogenetic spectra , 1994 .

[7]  M. Steel,et al.  Recovering evolutionary trees under a more realistic model of sequence evolution. , 1994, Molecular biology and evolution.

[8]  J. Huelsenbeck,et al.  Application and accuracy of molecular phylogenies. , 1994, Science.

[9]  D Penny,et al.  A discrete Fourier analysis for evolutionary trees. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[10]  J. Lake,et al.  Reconstructing evolutionary trees from DNA and protein sequences: paralinear distances. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[11]  MICHAEL A. CHARLESTON,et al.  The Effects of Sequence Length, Tree Topology, and Number of Taxa on the Performance of Phylogenetic Methods , 1994, J. Comput. Biol..

[12]  László A. Székely,et al.  Reconstructing Trees When Sequence Sites Evolve at Variable Rates , 1994, J. Comput. Biol..

[13]  Michael D. Hendy,et al.  Parsimony Can Be Consistent , 1993 .

[14]  Z. Yang,et al.  Maximum-likelihood estimation of phylogeny from DNA sequences when substitution rates differ over sites. , 1993, Molecular biology and evolution.

[15]  M. Nei,et al.  Theoretical foundation of the minimum-evolution method of phylogenetic inference. , 1993, Molecular biology and evolution.

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

[17]  D. Penny,et al.  Some recent progress with methods for evolutionary trees , 1993 .

[18]  D. Penny,et al.  Spectral analysis of phylogenetic data , 1993 .

[19]  László A. Székely,et al.  Fourier Calculus on Evolutionary Trees , 1993 .

[20]  László A. Székely,et al.  SPECTRAL ANALYSIS AND A CLOSEST TREE METHOD FOR GENETIC SEQUENCES , 1992 .

[21]  M. Nei,et al.  A Simple Method for Estimating and Testing Minimum-Evolution Trees , 1992 .

[22]  G A Churchill,et al.  Sample size for a phylogenetic inference. , 1992, Molecular biology and evolution.

[23]  Joseph T. Chang,et al.  Reconstruction of Evolutionary Trees from Pairwise Distributions on Current Species , 1992 .

[24]  Nick Goldman,et al.  MAXIMUM LIKELIHOOD INFERENCE OF PHYLOGENETIC TREES, WITH SPECIAL REFERENCE TO A POISSON PROCESS MODEL OF DNA SUBSTITUTION AND TO PARSIMONY ANALYSES , 1990 .

[25]  D Penny,et al.  Trees from sequences: panacea or Pandora's box. , 1990 .

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

[27]  Michael D. Hendy,et al.  A Framework for the Quantitative Study of Evolutionary Trees , 1989 .

[28]  M. Hendy.  The Relationship Between Simple Evolutionary Tree Models and Observable Sequence Data , 1989 .

[29]  M. A. STEEL,et al.  Loss of information in genetic distances , 1988, Nature.

[30]  P. Diaconis.  Group representations in probability and statistics , 1988 .

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

[32]  Joseph Felsenstein,et al.  Parsimony and likelihood: an exchange , 1986 .

[33]  D Penny,et al.  Estimating the reliability of evolutionary trees. , 1986, Molecular biology and evolution.

[34]  J. Felsenstein.  Cases in which Parsimony or Compatibility Methods will be Positively Misleading , 1978 .

[35]  Walter M. Fitch,et al.  On the Problem of Discovering the Most Parsimonious Tree , 1977, The American Naturalist.

[36]  J. Farris.  A Successive Approximations Approach to Character Weighting , 1969 .