@article{fdi:010040753,
  title = {{M}odeling fish population movements : {F}rom an individual-based representation to an advection-diffusion equation},
  author = {{F}augeras, {B}laise and {M}aury, {O}livier},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this paper, we address the problem of modeling fish population movements. {W}e first consider a description of movements at the level of individuals. {A}n 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. {T}hese components are function of a habitat suitability index, h, and its spatial gradient {V}h. {W}e derive an advection-diffusion partial differential equation ({PDE}) which approximates this individual- based model ({IBM}). {T}he approximation process enables us to obtain a mechanistic representation of the advection and diffusion coefficients which improves the heuristic approaches of former studies. {A}dvection and diffusion are linked and exhibit antagonistic behaviors: strong advection goes with weak diffusion leading to a directed movement of fish. {O}n the contrary weak advection goes with strong diffusion corresponding to a searching behavior. {S}imulations are conducted for both models which are compared by computing spatial statistics. {I}t is shown that the {PDE} model is a good approximation to the {IBM}.},
  keywords = {population dynamics ; biased random walk ; individual based model ; partial differential equation},
  booktitle = {},
  journal = {{J}ournal of {T}heoretical {B}iology},
  volume = {247},
  numero = {4},
  pages = {837--848},
  ISSN = {0022-5193},
  year = {2007},
  DOI = {10.1016/j.jtbi.2007.04.012},
  URL = {https://www.documentation.ird.fr/hor/fdi:010040753},
}