LETTER TO THE EDITOR: U(1) × U(1) × U(1) symmetry of the Kimura 3ST model and phylogenetic branching processes

@article{Bashford2003LETTERTT,
  title={LETTER TO THE EDITOR: U(1) × U(1) × U(1) symmetry of the Kimura 3ST model and phylogenetic branching processes},
  author={J. Bashford and P. Jarvis and J. Sumner and M. Steel},
  journal={Journal of Physics A},
  year={2003}
}
  • J. Bashford, P. Jarvis, +1 author M. Steel
  • Published 2003
  • Mathematics, Physics, Biology
  • Journal of Physics A
  • An analysis of the Kimura 3ST model of DNA sequence evolution is given on the basis of its continuous Lie symmetries. The rate matrix commutes with a U(1) × U(1) × U(1) phase subgroup of the group GL(4) of 4 × 4 invertible complex matrices acting on a linear space spanned by the four nucleic acid base letters. The diagonal 'branching operator' representing speciation is defined, and shown to intertwine the U(1) × U(1) × U(1) action. Using the intertwining property, a general formula for the… CONTINUE READING
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    References

    SHOWING 1-10 OF 15 REFERENCES
    Reconstructing Phylogenies From Nucleotide Pattern Probabilities: A Survey and some New Results
    • 44
    A discrete Fourier analysis for evolutionary trees.
    • M. Hendy, D. Penny, M. Steel
    • Biology, Medicine
    • Proceedings of the National Academy of Sciences of the United States of America
    • 1994
    • 94
    • PDF
    Estimation of evolutionary distances between homologous nucleotide sequences.
    • M. Kimura
    • Biology, Medicine
    • Proceedings of the National Academy of Sciences of the United States of America
    • 1981
    • 937
    • PDF
    Quantum field theory and phylogenetic branching
    • 8
    • PDF
    Taxonomy with confidence
    • 195
    The general stochastic model of nucleotide substitution.
    • 2,258
    Fourier Calculus on Evolutionary Trees
    • 66
    • PDF
    Discrete Fourier analysis for evolutionary trees Proc. Natl Acad. Sci. USA 91
    • Discrete Fourier analysis for evolutionary trees Proc. Natl Acad. Sci. USA 91
    • 1994