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Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels

journal contribution
posted on 2023-05-17, 12:00 authored by Peter JarvisPeter Jarvis, Jeremy SumnerJeremy Sumner
We consider novel phylogenetic models with rate matrices that arise via the embedding of a progenitor model on a small number of character states, into a target model on a larger number of character states. Adapting representation-theoretic results from recent investigations of Markov invariants for the general rate matrix model, we give a prescription for identifying and counting Markov invariants for such "symmetric embedded" models, and we provide enumerations of these for the first few cases with a small number of character states. The simplest example is a target model on three states, constructed from a general 2 state model; the "2 ↪ 3" embedding. We show that for 2 taxa, there exist two invariants of quadratic degree that can be used to directly infer pairwise distances from observed sequences under this model. A simple simulation study verifies their theoretical expected values, and suggests that, given the appropriateness of the model class, they have superior statistical properties than the standard (log) Det invariant (which is of cubic degree for this case).


Australian Research Council


Publication title

IEEE/ACM Transactions on Computational Biology and Bioinformatics








School of Natural Sciences


Association for Computing Machinery, Inc.

Place of publication

United States

Rights statement

Copyright 2012 IEEE

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  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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