KPZ and Fisher equations describe competition in microbial colonies

In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. I will discuss a theory that integrates both aspects fitness via a coupling between two classic reaction-diffusion equations: the KPZ equation, which describes surface growth, and the Fisher equation, which describes the spatial spread of a beneficial allele. The coupled equations exhibit distinct dynamical regimes and colony morphologies depending on whether the Fisher equation admits pulled (linear) or pushed (nonlinear) solutions. This theory explains recent experimental observation of slow expanders taking over the expansion front and makes intriguing predictions about the role of chirality in spatial growth.