On a possible origin of the fat-tailed dispersal in population dynamics

Populations do not remain fixed in space. Their distribution changes continuously due to the impact of environmental factors, such as wind, and/or due to self-motion of individuals. A cornerstone for understanding mechanisms of dispersal is identification of factors affecting the dispersal curve, in particular, its rate of decay at large distance. The standard random walk approach resulting in a dispersal curve with a ‘thin’ Gaussian tail was eventually opposed by the theory of Lévy flights, which predicts a more realistic ‘fat’ tail with a lower rate of decay. However, here we argue that the Gaussian large-distance asymptotics is more an artefact of an oversimplified description of the dispersing population rather than an immanent property of the random walk diffusion. Specifically, we show that, when some inherent population structure is taken into account, diffusion results in a dispersal curve with either exponential or power law rate of decay. Our theoretical results appear to be in a very good agreement with some available data.