Parameter Identifiability for a Profile Mixture Model of Protein Evolution

A profile mixture (PM) model is a model of protein evolution, describing sequence data in which sites are assumed to follow many related substitution processes on a single evolutionary tree. The processes depend, in part, on different amino acid distributions, or profiles, varying over sites in aligned sequences. A fundamental question for any stochastic model, which must be answered positively to justify model-based inference, is whether the parameters are identifiable from the probability distribution they determine. Here, using algebraic methods, we show that a PM model has identifiable parameters under circumstances in which it is likely to be used for empirical analyses. In particular, for a tree relating 9 or more taxa, both the tree topology and all numerical parameters are generically identifiable when the number of profiles is less than 74.

Automated summary

The PM model for protein evolution describes sequence data with sites following multiple related substitution processes depending on different amino acid distributions. Using algebraic methods, parameters in the PM model are shown to be identifiable for empirical analyses, particularly when the tree relates 9 or more taxa and the number of profiles is less than 74.