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Markov invariants, plethysms, and phylogenetics
journal contribution
posted on 2023-05-16, 22:58 authored by Jeremy SumnerJeremy Sumner, Charleston, MA, Jermiin, LS, Peter JarvisPeter JarvisWe explore model-based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, lthough we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log–Det distance measure. We take as our primary tool group representation theory, and show that it provides a general framework for analyzing Markov processes on trees. From this algebraic perspective, the inherent symmetries of these processes become apparent, and focusing on plethysms, we are able to define Markov invariants and give existence proofs. We give an explicit technique for constructing the invariants, valid for any number of character states and taxa. For phylogenetic trees with three and four leaves, we demonstrate that the corresponding Markov invariants can be fruitfully exploited in applied phylogenetic studies.
Funding
Australian Research Council
History
Publication title
Journal of Theoretical BiologyVolume
253Pagination
601-615ISSN
0022-5193Department/School
School of Natural SciencesPublisher
Academic Press Ltd Elsevier Science LTdPlace of publication
LondonRights statement
The definitive version is available at http://www.sciencedirect.comRepository Status
- Restricted