Scaling space and time by α and α² carries a random walk toward its continuum limit, a Brownian motion. Our voter model, from the backward perspective, is a system of interacting random walks, so it should approach a continuum limit along the same scaling. Its limit, constructed by Richard Arratia in the late 1970s, is called a Brownian web.

To include mutation in our continuum limit, we need to reduce the mutation rate per generation as we get more generations per unit time. Scaling the mutation rate by α² carries the mutation process on each lineage toward a Poisson process.