The model-specific Markov embedding problem for symmetric group-based models.
Embedding problem
Evolutionary models
Group-based models
Markov generator
Markov matrix
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
09 09 2021
09 09 2021
Historique:
received:
15
06
2020
accepted:
17
08
2021
revised:
04
08
2021
entrez:
9
9
2021
pubmed:
10
9
2021
medline:
21
10
2021
Statut:
epublish
Résumé
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.
Identifiants
pubmed: 34499233
doi: 10.1007/s00285-021-01656-5
pii: 10.1007/s00285-021-01656-5
pmc: PMC8429190
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
33Informations de copyright
© 2021. The Author(s).
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