New sector morphologies emerge from anisotropic colony growth

TL;DR

This paper models anisotropic colony growth using coupled surface growth and competition equations, revealing how anisotropy influences spatial invasion patterns and velocities, leading to distinct morphologies like shock-wave-like structures.

Contribution

It introduces a generalized anisotropic growth model that relaxes previous parameter constraints and characterizes resulting spatial patterns and invasion velocities.

Findings

Strong anisotropy causes kinked invasion morphologies.

Anisotropic growth leads to shock-wave-like spatial patterns.

Model completely characterizes invasion velocities and patterns.

Abstract

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.