Competition during range expansions is of great interest from both practical and theoretical viewpoints. 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. The anisotropy is encoded in how strongly genetic boundaries between strains are moved as a result of the expansion front morphology. 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 outcompeted strain is similar to a shock wave and serves as a signature of anisotropic growth. We confirm these predictions with a commonly employed reaction-diffusion model of anisotropic growth.

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• Evolutionary & population dynamics
• Growth processes
• Cellular automata
• Coarse graining
• Kardar–Parisi–Zhang equation