When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends of the reproductive advantage (fitness), as well as ability to colonize new domains. Based on symmetry considerations, we present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations on growth morphology are explored, providing a framework to study spatial competition, fixation, and differentiation, In particular, we find that ability to expand in space may overcome reproductive advantage in colonizing new territory.
