title: Finite element approximation of a population spatial adaptation model.
abstract: In [18], Sighesada, Kawasaki and Teramoto presented a system of partial differential equations for modeling spatial segregation of interacting species. Apart from competitive Lotka-Volterra (reaction) and population pressure (cross-diffusion) terms, a convective term modeling the populations attraction to more favorable environmental regions was included. In this article, we study numerically a modification of their convective term to take account for the notion of spatial adaptation of populations. After describing the model, in which a time non-local drift term is considered, we propose a numerical discretization in terms of a mass-preserving time semi-implicit finite element method. Finally, we provied the results of some biologically inspired numerical experiments showing qualitative differences between the original model of [18] and the model proposed in this article.
authors.affiliation: Dpto. de Matematicas, Universidad de Oviedo, c/ Calvo Sotelo, 33007-Oviedo, Spain. galiano@uniovi.es
authors.forename: Gonzalo
authors.initials: G
authors.lastname: Galiano
authors.forename: Julian
authors.initials: J
authors.lastname: Velasco
mesh_terms: D000220:Adaptation, Biological; D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D004777:Environment; D020342:Finite Element Analysis; D006801:Humans; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D049490:Systems Biology