  In growing populations, the fate of mutations depends on their competitive
ability against the ancestor and their ability to colonize new territory. Here
we present a theory that integrates both aspects of mutant fitness by coupling
the classic description of one-dimensional competition (Fisher equation) to the
minimal model of front shape (KPZ equation). We solved these equations and
found three regimes, which are controlled solely by the expansion rates, solely
by the competitive abilities, or by both. Collectively, our results provide a
simple framework to study spatial competition.
