Phylogenetic invariants and geometry.

The method of invariants is an important approach in biology for determining phylogenetic information which avoids the problems involving long branch lengths that plague some other methods. In this paper, we present a geometric framework underlying the method of invariants. This perspective sheds new lights on problems in the field. It has recently enabled the solution of questions on the number and structure of phylogenetic invariants and suggests possible avenues for future empirical and theoretical research.

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

[2]  D Sankoff,et al.  Phylogenetic invariants for more general evolutionary models. , 1995, Journal of theoretical biology.

[3]  J. Huelsenbeck,et al.  SUCCESS OF PHYLOGENETIC METHODS IN THE FOUR-TAXON CASE , 1993 .

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

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

[6]  Michael D. Hendy,et al.  A combinatorial description of the closest tree algorithm for finding evolutionary trees , 1991, Discret. Math..

[7]  J. A. Cavender,et al.  Mechanized derivation of linear invariants. , 1989, Molecular biology and evolution.

[8]  Steven N. Evans,et al.  Constructing and Counting Phylogenetic Invariants , 1998, J. Comput. Biol..

[9]  D Sankoff,et al.  A remarkable nonlinear invariant for evolution with heterogeneous rates. , 1996, Mathematical biosciences.

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

[11]  David A. Cox,et al.  Ideals, Varieties, and Algorithms , 1997 .

[12]  R J Little,et al.  Bayesian hypothesis testing of four-taxon topologies using molecular sequence data. , 1996, Biometrics.

[13]  T. Jukes.  CHAPTER 24 – Evolution of Protein Molecules , 1969 .

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

[15]  J. Felsenstein,et al.  Counting phylogenetic invariants in some simple cases. , 1991, Journal of theoretical biology.

[16]  H. Munro,et al.  Mammalian protein metabolism , 1964 .

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

[18]  R. Little,et al.  Inference for phylogenies under a hybrid parsimony method: evolutionary-symmetric transversion parsimony. , 1997, Biometrics.

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

[20]  Thomas R. Hagedorn,et al.  Determining the Number and Structure of Phylogenetic Invariants , 2000, Adv. Appl. Math..