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Volume 15,     Number 2,     Summer 2007

 

CROSS DIFFUSION AND COEXISTENCE OF
TWO SPECIES ON A GRADIENT
K. P. HADELER

Abstract. Starting from observations on an apparent replacement process between two closely related bird species, the problem of joint diffusion of two species is studied in terms of a cross diffusion model, without any competitive interaction. It is assumed that each species observes (or reacts to) the joint gradient and that the joint population follows the linear diffusion equation. Under this realistic hypothesis the density of each individual species is governed by a highly non-linear diffusion equation, and this dynamics favors the species which is less evenly distributed. In particular, in regions where the domains of both species overlap, i.e., where reservoirs stabilize clines, the species with the steeper gradient has an advantage. This effect is studied in greater detail.

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© 2006, Canadian Applied Mathematics Quarterly (CAMQ)