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We propose here a motivation for a mixed local/nonlocal problem with a newtype of Neumann condition.  Our description is based on formal expansions and approximations. In anutshell, a biological species is supposed to diffuse either by a random walkor by a jump process, according to prescribed probabilities. If the processmakes an individual exit the niche, it must come to the niche right away, byselecting the return point according to the underlying stochastic process. Moreprecisely, if the random particle exits the domain, it is forced to immediatelyreenter the domain, and the new point in the domain is chosen randomly byfollowing a bouncing process with the same distribution as the original one.  By a suitable definition outside the niche, the density of the populationends up solving a mixed local/nonlocal equation, in which the dispersion isgiven by the superposition of the classical and the fractional Laplacian. Thisdensity function satisfies two types of Neumann conditions, namely theclassical Neumann condition on the boundary of the niche, and a nonlocalNeumann condition in the exterior of the niche.

Description of an ecological niche for a mixed local/nonlocal dispersal:  an evolution equation and a new Neumann condition arising from the  superposition of Brownian and L\'evy processes