Markov invariants and the isotropy subgroup of a quartet tree

Details Markov invariants and the isotropy subgroup of a quartet tree Markov invariants and the isotropy subgroup of a quartet tree

2008-09-18

arxiv.org/abs/0809.3070v2

J. Theor. Biol., 258:302--310, 2009

Biology

Quantitative Biology

Quantitative Methods

18 pages, sequel to "Markov invariants, plethysms and phylogenetics" (arXiv:0711.3503v3) v2: In press for Journal of Theoretic

Scientific paper

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.

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