The model-specific Markov embedding problem for symmetric group-based models

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Abstract

We study model embeddability, which is a variation of the famous embedding problem in probability theory, when apart from the requirement that the Markov matrix is the matrix exponential of a rate matrix, we additionally ask that the rate matrix follows the model structure. We provide a characterisation of model embeddable Markov matrices corresponding to symmetric group-based phylogenetic models. In particular, we provide necessary and sufficient conditions in terms of the eigenvalues of symmetric group-based matrices. To showcase our main result on model embeddability, we provide an application to hachimoji models, which are eight-state models for synthetic DNA. Moreover, our main result on model embeddability enables us to compute the volume of the set of model embeddable Markov matrices relative to the volume of other relevant sets of Markov matrices within the model.
Original languageEnglish
Article number33
Number of pages26
JournalJournal of Mathematical Biology
Volume83
Issue number3
DOIs
Publication statusPublished - 9 Sep 2021
MoE publication typeA1 Journal article-refereed

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