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U(1)xU(1)xU(1) symmetry of the Kimura 3ST model and phylogenetic branching processes | | J. D. Bashford
; P. D. Jarvis
; J. G. Sumner
; M. A. Steel
; | | Date: |
31 Oct 2003 | | Subject: | Populations and Evolution; Quantitative Methods | q-bio.PE q-bio.QM | | Affiliation: | U Tasmania), and M. A. Steel (U Canterbury | | 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. | | Source: | arXiv, q-bio.PE/0310037 | | Services: | Forum | Review | PDF | Favorites | |
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