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Markov invariants and the isotropy subgroup of a quartet tree


Sumner, JG and Jarvis, PD, Markov invariants and the isotropy subgroup of a quartet tree, Journal of Theoretical Biology, 258, (2) pp. 302-310. ISSN 0022-5193 (2009) [Refereed Article]

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DOI: doi:10.1016/j.jtbi.2009.01.021


The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we give an explicit construction of the full set of representations and describe their properties. We apply these results directly to Markov invariants, thereby extending previous theoretical results by systematically identifying linear combinations that vanish for a given quartet. We also note that the theory is fully generalizable to arbitrary trees and is equally applicable to the related case of phylogenetic invariants. All results follow from elementary consideration of the representation theory of finite groups.

Item Details

Item Type:Refereed Article
Research Division:Physical Sciences
Research Group:Medical and biological physics
Research Field:Biological physics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the physical sciences
UTAS Author:Sumner, JG (Dr Jeremy Sumner)
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:60709
Year Published:2009
Web of Science® Times Cited:13
Deposited By:Physics
Deposited On:2010-02-16
Last Modified:2015-01-27

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