Specialization at an expanding front

TL;DR

This paper models how populations expanding into new territories can develop specialized subgroups at the frontier, with simulations showing how mutations and competition influence sector formation and growth dynamics.

Contribution

Introduces a model for specialization at an expanding front, analyzing how mutations and competition lead to sector formation and different scaling behaviors.

Findings

Specialists form sectors that expand and dominate the population.

Scaling of fixation time varies with fitness gains, showing superdiffusive and diffusive behaviors.

Different universality classes emerge based on fitness gain limits.

Abstract

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.