  As a population grows, spreading to new environments may favor
specialization. In this paper, we introduce and explore a model for
specialization at the front of a colony expanding synchronously into new
territory. We show through numerical simulations that, by gaining fitness
through accumulating mutations, progeny of the initial seed population can
differentiate into distinct specialists. With competition and selection limited
to the growth front, the emerging specialists first segregate into sectors,
which then expand to dominate the entire population. We quantify the scaling of
the fixation time with the size of the population and observe different
behaviors corresponding to distinct universality classes: unbounded and bounded
gains in fitness lead to superdiffusive ($z=3/2$) and diffusive ($z=2$)
stochastic wanderings of the sector boundaries, respectively.
