Inference of evolutionary trees and rates from biological
sequences is commonly performed using continuous-time Markov
models of character change. The Markov process evolves along an
unknown tree while observations arise only from the tips of the
tree. Rate heterogeneity is present in most real data sets and is
accounted for by the use of flexible mixture models where each
site is allowed its own rate. Very little has been rigorously
established concerning the identifiability of the models currently
in common use in data analysis, although nonidentifiability was
proven for a semiparametric model and an incorrect proof of
identifiability was published for a general parametric model
(GTR + Γ + I). Here we prove that one of the most widely
used models (GTR + Γ) is identifiable for generic
parameters, and for all parameter choices in the case of
four-state (DNA) models. This is the first proof of
identifiability of a phylogenetic model with a continuous
distribution of rates.
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