  Phylogenetic mixture models are statistical models of character evolution
allowing for heterogeneity. Each of the classes in some unknown partition of
the characters may evolve by different processes, or even along different
trees. The fundamental question of whether parameters of such a model are
identifiable is difficult to address, due to the complexity of the
parameterization. We analyze mixture models on large trees, with many mixture
components, showing that both numerical and tree parameters are indeed
identifiable in these models when all trees are the same. We also explore the
extent to which our algebraic techniques can be employed to extend the result
to mixtures on different trees.
