From individual-based models to partial differential equations

The aim of this paper is to introduce a method of verification of individual-based modeling through a relevant example. We build two individual-based models for the movement of elvers in the French river 'Adour'. We rigorously obtain a set of stochastic differential equations and a partial differential equation for the elvers' density, both of which describe the same phenomenon. We solve the partial differential equation numerically and compare statistically the results of both methods, concluding that they are equivalent. This approach constitutes a verification and a protocol of analysis of our individual-based models.