  Cellular populations such as avascular tumors and microbial biofilms may
"invade" or grow into surrounding populations. The invading population is often
comprised of a heterogeneous mixture of cells with varying growth rates. The
population may also exhibit mutational instabilities, such as a heavy
deleterious mutation load in a cancerous growth. We study the dynamics of a
heterogeneous, mutating population competing with a surrounding homogeneous
population, as one might find in a cancerous invasion of healthy tissue. We
find that the shape of the population interface serves as an indicator for the
evolutionary dynamics within the heterogeneous population. In particular,
invasion front undulations become enhanced when the invading population is near
a mutational meltdown transition or when the surrounding "bystander" population
is barely able to reinvade the mutating population. We characterize these
interface undulations and the effective fitness of the heterogeneous population
in one- and two-dimensional systems.
