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Speciation at an expanding front

As a population grows, expansion into new geographical terrains often induces speciation. We introduce and explore a model for speciation at the front of a colony expanding synchronously into new territory. Gaining ﬁtness by accumulating mutations, progeny of the initial seed population can evolve into distinct species specializing in speciﬁc traits. With competition and selection limited to the growth front, the emerging species ﬁrst segregate into sectors and then expand to take over 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. In particular, we ﬁnd that bounded and unbounded gains in ﬁtness lead to diﬀusive ( z = 2) and superdiﬀusive ( z = 3 / 2) stochastic wanderings of the sector boundaries, respectively.