  The continuous-space symbiotic branching model describes the evolution of two
interacting populations that can reproduce locally only in the simultaneous
presence of each other. If started with complementary Heaviside initial
conditions, the interface where both populations coexist remains compact.
Together with a diffusive scaling property, this suggests the presence of an
interesting scaling limit. Indeed, in the present paper, we show weak
convergence of the diffusively rescaled populations as measure-valued processes
in the Skorokhod, respectively the Meyer-Zheng, topology (for suitable
parameter ranges). The limit can be characterized as the unique solution to a
martingale problem and satisfies a "separation of types" property. This
provides an important step toward an understanding of the scaling limit for the
interface. As a corollary, we obtain an estimate on the moments of the width of
an approximate interface.
