Faugeras Blaise, Maury Olivier. (2007). Modeling fish population movements : From an individual-based representation to an advection-diffusion equation. Journal of Theoretical Biology, 247 (4), p. 837-848. ISSN 0022-5193.
Titre du document
Modeling fish population movements : From an individual-based representation to an advection-diffusion equation
Journal of Theoretical Biology, 2007,
247 (4), p. 837-848 ISSN 0022-5193
In this paper, we address the problem of modeling 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 Vh. We derive an advection-diffusion partial differential equation (PDE) which approximates this individual- based model (IBM). 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 PDE model is a good approximation to the IBM.
Plan de classement
Sciences fondamentales / Techniques d'analyse et de recherche [020]
;
Ecologie, systèmes aquatiques [036]
