Embeddability of Kimura 3ST Markov matrices
Abstract
In this note, we characterize the embeddability of generic Kimura 3ST Markov matrices in terms of their eigenvalues. As a consequence, we are able to compute the volume of such matrices relative to the volume of all Markov matrices within the model. We also provide examples showing that, in general, mutation rates are not identifiable from substitution probabilities. These examples also illustrate that symmetries between mutation probabilities do not necessarily arise from symmetries between the corresponding mutation rates.
 Publication:

Journal of Theoretical Biology
 Pub Date:
 May 2018
 DOI:
 10.1016/j.jtbi.2018.02.005
 arXiv:
 arXiv:1703.02263
 Bibcode:
 2018JThBi.445..128R
 Keywords:

 Markov matrix;
 Markov generator;
 Eigenvalues;
 Evolutionary model;
 Embeddability;
 Quantitative Biology  Populations and Evolution;
 Mathematics  Probability;
 60J27;
 60J22;
 92D15
 EPrint:
 7 pages