Dispersal in a statistically structured population: fat tails revisited

Dispersal has long been recognized as a crucial factor affecting population dynamics. Several studies on long-distance dispersal revealed a peculiarity now widely known as a problem of "fat tail": instead of the rate of decay in the population density over large distances being described by a normal distribution, which is apparently predicted by the standard diffusion approach, field data often show much lower rates such as exponential or power law. The question as to what are the processes and mechanisms resulting in the fat tail is still largely open. In this note, by introducing the concept of a statistically structured population, we show that a fat-tailed long-distance dispersal is a consequence of the fundamental observation that individuals of the same species are not identical. Fat-tailed dispersal thus appears to be an inherent property of any real population. We show that our theoretical predictions are in good agreement with available data.