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Entanglement invariants and phylogenetic branching

Citation

Sumner, JG and Jarvis, PD, Entanglement invariants and phylogenetic branching, Journal of Mathematical Biology, 51, (1) pp. 18-36. ISSN 0303-6812 (2005) [Refereed Article]

DOI: doi:10.1007/s00285-004-0309-z

Abstract

It is possible to consider stochastic models of sequence evolution in phylogenetics in the context of a dynamical tensor description inspired from physics. Approaching the problem in this framework allows for the well developed methods of mathematical physics to be exploited in the biological arena. We present the tensor description of the homogeneous continuous time Markov chain model of phylogenetics with branching events generated by dynamical operations. Standard results from phylogenetics are shown to be derivable from the tensor framework. We summarize a powerful approach to entanglement measures in quantum physics and present its relevance to phylogenetic analysis. Entanglement measures are found to give distance measures that are equivalent to, and expand upon, those already known in phylogenetics. In particular we make the connection between the group invariant functions of phylogenetic data and phylogenetic distance functions. We introduce a new distance measure valid for three taxa based on the group invariant function known in physics as the "tangle". All work is presented for the homogeneous continuous time Markov chain model with arbitrary rate matrices. © Springer-Verlag 2005.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Other Physical Sciences
Research Field:Physical Sciences not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Physical Sciences
Author:Sumner, JG (Dr Jeremy Sumner)
Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:36012
Year Published:2005
Funding Support:Australian Research Council (DP0344996)
Web of Science® Times Cited:7
Deposited By:Physics
Deposited On:2005-08-01
Last Modified:2006-03-29
Downloads:0

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