TY - JOUR
T1 - Approximating the ideal free distribution via reaction-diffusion-advection equations
AU - Cantrell, Robert Stephen
AU - Cosner, Chris
AU - Lou, Yuan
PY - 2008/12/15
Y1 - 2008/12/15
N2 - We consider reaction-diffusion-advection models for spatially distributed populations that have a tendency to disperse up the gradient of fitness, where fitness is defined as a logistic local population growth rate. We show that in temporally constant but spatially varying environments such populations have equilibrium distributions that can approximate those that would be predicted by a version of the ideal free distribution incorporating population dynamics. The modeling approach shows that a dispersal mechanism based on local information about the environment and population density can approximate the ideal free distribution. The analysis suggests that such a dispersal mechanism may sometimes be advantageous because it allows populations to approximately track resource availability. The models are quasilinear parabolic equations with nonlinear boundary conditions.
AB - We consider reaction-diffusion-advection models for spatially distributed populations that have a tendency to disperse up the gradient of fitness, where fitness is defined as a logistic local population growth rate. We show that in temporally constant but spatially varying environments such populations have equilibrium distributions that can approximate those that would be predicted by a version of the ideal free distribution incorporating population dynamics. The modeling approach shows that a dispersal mechanism based on local information about the environment and population density can approximate the ideal free distribution. The analysis suggests that such a dispersal mechanism may sometimes be advantageous because it allows populations to approximately track resource availability. The models are quasilinear parabolic equations with nonlinear boundary conditions.
KW - Ideal free distribution
KW - Reaction-diffusion-advection
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U2 - 10.1016/j.jde.2008.07.024
DO - 10.1016/j.jde.2008.07.024
M3 - Article
AN - SCOPUS:54149117995
VL - 245
SP - 3687
EP - 3703
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 12
ER -