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

Branching Brownian Motion, mean curvature flow and the motion of hybrid zones