  A Profile Mixture 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 we show
that a Profile Mixture 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.
