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Quantitative Biology > Populations and Evolution

arXiv:q-bio/0310037 (q-bio)
[Submitted on 31 Oct 2003 (v1), last revised 3 Nov 2003 (this version, v2)]

Title:U(1)xU(1)xU(1) symmetry of the Kimura 3ST model and phylogenetic branching processes

Authors:J. D. Bashford, P. D. Jarvis, J. G. Sumner (U Tasmania), M. A. Steel (U Canterbury)
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Abstract: 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)xU(1)xU(1) phase subgroup of the group GL(4) of 4x4x4 invertible complex matrices acting on a linear space spanned by the 4 nucleic acid base letters. The diagonal `branching operator' representing speciation is defined, and shown to intertwine the U(1)xU(1)xU(1) action. Using the intertwining property, a general formula for the probability density on the leaves of a binary tree under the Kimura model is derived, which is shown to be equivalent to established phylogenetic spectral transform methods.
Comments: 9 pages, LaTeX, uses amsmath
Subjects: Populations and Evolution (q-bio.PE); Statistics Theory (math.ST); Quantitative Methods (q-bio.QM)
Report number: UTAS-PHYS-03-07
Cite as: arXiv:q-bio/0310037 [q-bio.PE]
  (or arXiv:q-bio/0310037v2 [q-bio.PE] for this version)
  https://doi.org/10.48550/arXiv.q-bio/0310037
Related DOI: https://doi.org/10.1088/0305-4470/37/8/L01

Submission history

From: Peter Jarvis [view email]
[v1] Fri, 31 Oct 2003 02:26:00 UTC (11 KB)
[v2] Mon, 3 Nov 2003 00:27:32 UTC (11 KB)
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