Journal
MATHEMATICAL BIOSCIENCES
Volume 171, Issue 1, Pages 83-97Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/S0025-5564(01)00048-7
Keywords
reaction-diffusion equation; traveling waves; strong Allee effects; weak Allee effects; linearization
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We study an invasion model based on a reaction-diffusion equation with an Allee effect. We use a special, piecewise-linear, population growth rate. This function allows us to obtain traveling wave solutions and to compute wave speeds for a full range of Allee effects, including weak Allee effects. Some investigators claim that linearization fails to give the correct speed of invasion if there is an Allee effect. We show that the minimum speed for a sufficiently weak Allee may, in fact, be the same as that derived by means of linearization. (C) 2001 Elsevier Science Inc. All rights reserved.
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