Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 247, Issue 4, Pages 837-848Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2007.04.012
Keywords
population dynamics; biased random walk; individual-based model; partial differential equation
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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. (c) 2007 Elsevier Ltd. All rights reserved.
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