Diffusion models in anisotropic media applied to South American paleo-indean dispersals

MARTINO, LUIS; OSELLA, ANA; DORSO, CLAUDIO; LANATA, JOSÉ LUIS

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

American Physical Society

Año: 2007 vol. 76 p. 1 - 10

1063-651X

Fisher equation is commonly used to model population dynamics. This equation allows describ- ing reaction-di®usion processes, considering both population growth and di®usion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic di®usion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habi- tats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of popula- tions. Solutions to Fisher equation are di±cult to obtain for complex geometries, moreover when anisotropy has to be considered and so few studies have been conducted in this direction, With this scope in mind, we present in this paper a solution for Fisher equation, introducing anisotropy. We apply a ¯nite di®erence method using Crank Nicholsons approximation, and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal. PACS numbers: 87.23.-n 83.23.Cc