  A fundamental feature of collective cell migration is phenotypic
heterogeneity which, for example, influences tumour progression and relapse.
While current mathematical models often consider discrete phenotypic
structuring of the cell population, in-line with the `go-or-grow' hypothesis
\cite{hatzikirou2012go, stepien2018traveling}, they regularly overlook the role
that the environment may play in determining the cells' phenotype during
migration. Comparing a previously studied volume-filling model for a
homogeneous population of generalist cells that can proliferate, move and
degrade extracellular matrix (ECM) \cite{crossley2023travelling} to a novel
model for a heterogeneous population comprising two distinct sub-populations of
specialist cells that can either move and degrade ECM or proliferate, this
study explores how different hypothetical phenotypic switching mechanisms
affect the speed and structure of the invading cell populations. Through a
continuum model derived from its individual-based counterpart, insights into
the influence of the ECM and the impact of phenotypic switching on migrating
cell populations emerge. Notably, specialist cell populations that cannot
switch phenotype show reduced invasiveness compared to generalist cell
populations, while implementing different forms of switching significantly
alters the structure of migrating cell fronts. This key result suggests that
the structure of an invading cell population could be used to infer the
underlying mechanisms governing phenotypic switching.
