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.

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• Fluctuations & noise
• Organismal, population, evolutionary & ecological systems
• Lattice models in statistical physics
• Finite-size scaling