Identifiability of the GTR+Γmodel of molecular evolution

Inference of evolutionary trees and rates from biological sequences is commonly performed using models of character change that incorporate rate variation across sites. Though an incorrect proof of the identifiability of the GTR+$\Gamma$+I model has been published, very little has been rigorously established concerning the identifiability of the models currently in common use in data analysis. Here we prove that the GTR+$\Gamma$ model is identifiable for generic parameters, and for all parameter choices in the case of 4-state (DNA) models. This is the first proof of identifiability of a phylogenetic model with a continuous distribution of rate classes.