  When employing mechanistic models to study biological phenomena, practical
parameter identifiability is important for making accurate predictions across
wide range of unseen scenarios, as well as for understanding the underlying
mechanisms. In this work we use a profile likelihood approach to investigate
parameter identifiability for four extensions of the Fisher--KPP model, given
experimental data from a cell invasion assay. We show that more complicated
models tend to be less identifiable, with parameter estimates being more
sensitive to subtle differences in experimental procedures, and that they
require more data to be practically identifiable. As a result, we suggest that
parameter identifiability should be considered alongside goodness-of-fit and
model complexity as criteria for model selection.
