In this paper we consider a stepping-stone model on a circle with circular
Brownian migration. We first point out a connection between Arratia flow and
the marginal distribution of this model. We then give a new representation for
the stepping-stone model using Arratia flow and circular coalescing Brownian
motion. Such a representation enables us to carry out some explicit
computation. In particular, we find the Laplace transform for the time when
there is only a single type left across the circle.Comment: 12 page
