The study of languages to determine when they diverged from being the same language.
Note 9: The evidence supporting the continued value of glottochronology is most convincingly seen when again and again there are correlations found between archaeology and linguistic based conclusions.
It is important to recognize, however, that many linguists do not agree on the validity and accuracy of glottochronology and lexicostatistics in determining linguistic diffusion.
The reason for the criticism appears to stem largely from a mix-up about what the tool of glottochronology claims to do.
Historical linguistics, in particular, has provided a method for measuring change in language, called glottochronology.
As to the fact that the Ute and the Aztec spoke languages derived from the same root-language, you might want to introduce your readers to glottochronology, the science of dating origins by language attrition.
The word 'glottochronology' comes from Greek roots meaning 'tongue', 'time', and 'study'.