Compact interface property for symbiotic branching

A process which we call symbiotic branching, is suggested covering three well-known interacting models: mutually catalytic branching, the stepping stone model, and the Anderson model. Basic tools such as self-duality, particle system moment duality, measure case moment duality, and moment equations are still available in this generalized context. As an application, we show that in the setting of the one-dimensional continuum the compact interface property holds: starting from complementary Heaviside states, the interface is finite at all times almost surely