title: Front dynamics in a two-species competition model driven by Lévy flights.
abstract: A number of recent studies suggest that many biological species follow a Lévy random walk in their search for food. Such a strategy has been shown to be more efficient than classical Brownian motion when resources are scarce. However, current diffusion-reaction models used to describe many ecological systems do not account for the superdiffusive spread of populations due to Lévy flights. We have developed a model to simulate the spatial spread of two species competing for the same resources and driven by Lévy flights. The model is based on the Lotka-Volterra equations and has been obtained by replacing the second-order diffusion operator by a fractional-order one. Consistent with previous known results, theoretical developments and numerical simulations show that fractional-order diffusion leads to an exponential acceleration of the population fronts and a power-law decay of the fronts' leading tail. Depending on the skewness of the fractional derivative, we derive catch-up conditions for different types of fronts. Our results indicate that second-order diffusion-reaction models are not well-suited to simulate the spatial spread of biological species that follow a Lévy random walk as they are inclined to underestimate the speed at which these species propagate.
authors.affiliation: Université Catholique de Louvain, Earth and Life Institute, Environmental Sciences, Croix du Sud 2 Bte L7.05.16, B-1348 Louvain-la-Neuve, Belgium. emmanuel.hanert@uclouvain.be
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Hanert
mesh_terms: D000818:Animals; D003163:Competitive Behavior / Q000502:physiology*; D005247:Feeding Behavior / Q000502:physiology*; D008954:Models, Biological; D009068:Movement / Q000502:physiology*; D011157:Population Dynamics