Modelling fish population movements: from an individual-based representation to an advection-diffusion equation

Blaise Faugeras (1) , Olivier Maury (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 UMR EME - Ecosystèmes Marins Exploités

In this paper we address the problem of modelling fish population movements. We first consider a description of movements at the level of individuals. An individual-based model is formulated as a biased random walk model in which the velocity of each fish has both a deterministic and a stochastic component. These components are function of a habitat suitability index, $h$, and its spatial gradient $\gh$. We derive an advection-diffusion partial differential equation which approximates this individual-based model. The approximation process enables us to obtain a mechanistic representation of the advection and diffusion coefficients which improves the heuristic approaches of former studies. Advection and diffusion are linked and exhibit antagonistic behaviors: strong advection goes with weak diffusion leading to a directed movement of fish. On the contrary weak advection goes with strong diffusion corresponding to a searching behavior. Simulations are conducted for both models which are compared by computing spatial statistics. It is shown that the partial differential equation model is a good approximation to the individual-based model.

Domaines: Modélisation et simulation; Sciences de l'environnement

Blaise Faugeras, Olivier Maury. Modelling fish population movements: from an individual-based representation to an advection-diffusion equation. Journal of Theoretical Biology, 2007, 247, pp.837-848. ⟨hal-00496618⟩