eCite Digital Repository

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


Bashford, JD and Jarvis, PD and Sumner, JG and Steel, MA, U(1) U(1) U(1) symmetry of the Kimura 3ST model and phylogenetic branching processes, Journal of Physics A-Mathematical and General, 37, (8) pp. L81-L89. ISSN 0305-4470 (2004) [Refereed Article]

DOI: doi:10.1088/0305-4470/37/8/L01


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 G L (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 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.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other physical sciences
Research Field:Other physical sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Bashford, JD (Dr James Bashford)
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
UTAS Author:Sumner, JG (Associate Professor Jeremy Sumner)
ID Code:30825
Year Published:2004
Web of Science® Times Cited:3
Deposited By:Physics
Deposited On:2004-08-01
Last Modified:2010-06-10

Repository Staff Only: item control page