  We consider a minimal go-or-grow model of cell invasion, whereby cells can
either proliferate, following logistic growth, or move, via linear diffusion,
and phenotypic switching between these two states is density-dependent. Formal
analysis in the fast switching regime shows that the total cell density in the
two-population go-or-grow model can be described in terms of a single
reaction-diffusion equation with density-dependent diffusion and proliferation.
Using the connection to single-population models, we study travelling wave
solutions, showing that the wave speed in the go-or-grow model is always
bounded by the wave speed corresponding to the well-known Fisher-KPP equation.
