Fickian transport

The classic paradigm of simple diffusion is used to describe a wide range of phenomena, ranging from how the original humans migrated and dispersed out of Africa to the spread of pollen. Until the twentieth century, Fick's laws were thought to be universally valid for describing diffusion. The physiologist Adolf Fick introduced the idea that diffusion is proportional to the gradient of concentration. For practical as well as for historical reasons, normal diffusion is commonly assumed for transport processes. For example, Fourier's law for heat flow is analogous to Fick's laws of diffusion, with temperature gradients playing the role of concentration gradients.

Like Gaussian statistics, normal diffusion is ubiquitous because of the wide applicability of the central limit theorem. Standard methods in spatial ecology traditionally have tended to assume Brownian motion and Fickian diffusion as two basic properties of animal movement in the long time limit, i.e., at large spatial scales and long temporal scales. We refer the reader to the seminal book by Berg [35] on random walks in biology.

Fickian or normal diffusion assumes that animal movements can be modeled, in the long-term limit, as uncorrelated random walks [21, 35, 265]. In many cases, normal diffusion describes experimentally observed phenomena. The classic study by Skellam [349] of the colonization of Europe by muskrats assumed normal diffusion, for example (Figure 5.1).