  We provide a probabilistic proof of a well known connection between a special
case of the Allen-Cahn equation and mean curvature flow. We then prove a
corresponding result for scaling limits of the spatial $\Lambda$-Fleming-Viot
process with selection, in which the selection mechanism is chosen to model
what are known in population genetics as hybrid zones. Our proofs will exploit
a duality with a system of branching (and coalescing) random walkers which is
of some interest in its own right.
