%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Faugeras, Blaise
%A Maury, Olivier
%T Modeling fish population movements : From an individual-based representation to an advection-diffusion equation
%D 2007
%L fdi:010040753
%G ENG
%J Journal of Theoretical Biology
%@ 0022-5193
%K population dynamics ; biased random walk ; individual based model ; partial differential equation
%M CC:0002489907-0023
%N 4
%P 837-848
%R 10.1016/j.jtbi.2007.04.012
%U https://www.documentation.ird.fr/hor/fdi:010040753
%> https://www.documentation.ird.fr/intranet/publi/2007/10/010040753.pdf
%V 247
%W Horizon (IRD)
%X 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.
%$ 036 ; 020