  Competition during range expansions is of great interest from both practical
and theoretical view points. Experimentally, range expansions are often studied
in homogeneous Petri dishes, which lack spatial anisotropy that might be
present in realistic populations. Here, we analyze a model of anisotropic
growth, based on coupled Kardar-Parisi-Zhang and
Fisher-Kolmogorov-Petrovsky-Piskunov equations that describe surface growth and
lateral competition. Compared to a previous study of isotropic growth,
anisotropy relaxes a constraint between parameters of the model. We completely
characterize spatial patterns and invasion velocities in this generalized
model. In particular, we find that strong anisotropy results in a distinct
morphology of spatial invasion with a kink in the displaced strain ahead of the
boundary between the strains. This morphology of the out-competed strain is
similar to a shock wave and serves as a signature of anisotropic growth.
