  As an alternative to parsimony analyses, stochastic models have been proposed
(Lewis, 2001), (Nylander, et al., 2004) for morphological characters, so that
maximum likelihood or Bayesian analyses may be used for phylogenetic inference.
A key feature of these models is that they account for ascertainment bias, in
that only varying, or parsimony-informative characters are observed. However,
statistical consistency of such model-based inference requires that the model
parameters be identifiable from the joint distribution they entail, and this
issue has not been addressed.
  Here we prove that parameters for several such models, with finite state
spaces of arbitrary size, are identifiable, provided the tree has at least 8
leaves. If the tree topology is already known, then 7 leaves suffice for
identifiability of the numerical parameters. The method of proof involves first
inferring a full distribution of both parsimony-informative and non-informative
pattern joint probabilities from the parsimony-informative ones, using
phylogenetic invariants. The failure of identifiability of the tree parameter
for 4-taxon trees is also investigated.
