skyline plots and nucleotide substitution model

[Jacob Christensen]

I've recently read about reviewers having problems with people using jModelTest and other ML programs to find the best nucleotide substitution model for use in Bayesian phylogenetics. I have no problem using bModelTest for phylogenies, but how would it affect a skyline plot? Might it be better to use a singular model for demographic histories that rely on specific data such as mutation rate?