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We consider a generalisation of the well-studied N-BBM process which is a simple model for survival-of-the-fittest in a population of fixed size. We will explore it’s properties and show that the hydrodynamic limit of the system is the solution of an F-KPP type equation. One the one hand, this connection allows us to understand many reaction-diffusion equations as modelling simply described population dynamics, and on the other hand, properties of the PDE (convergence, travelling waves, etc.) can tell us about the properties of the particle system.
