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Abstract

We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is k, the resulting model is a continuous-time Markov chain on k-states and, as a consequence of the product rule in the semigroup, satisfies the property of multiplicative closure. This means that the product of any two probability substitution matrices taken from the model produces another substitution matrix also in the model. We show that our construction is a natural generalization of the concept of group-based models.

Item Type:	Article
Authors/Creators:	Sumner, JG and Woodhams, MD
Keywords:	Lie algebras, continuous-time Markov chains, group-based models, phylogenetics
Journal or Publication Title:	Bulletin of Mathematical Biology
Publisher:	Academic Press Ltd Elsevier Science Ltd
ISSN:	0092-8240
DOI / ID Number:	https://doi.org/10.1007/s11538-018-0455-x
Copyright Information:	Copyright 2018 Society for Mathematical Biology
Related URLs:	Google Scholar: Sumner, JG UTAS Profile: Sumner, JG Google Scholar: Woodhams, MD UTAS Profile: Woodhams, MD
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