Fundamentals of Diffusion and Spread in the Natural Sciences and beyond
Basic Principles of Diffusion and Dispersal
Gero Vogl, Fak. f. Physik d. Universität Wien
The physical and mathematical basis of all dispersal (spread) processes is Fick’s diffusion equation, a differential equation which relates the change in the concentration of particles with time to its spatial gradient (more exactly its second derivative). Fick’s diffusion equation is only valid for simple physical diffusion processes, there its solution is a Gaussian bell-shaped curve. For dispersal in the biosphere, however, birth and death of the “particles” has to be additionally considered. The solutions are temporal and spatial distributions which become even more complex when the “particles” interact, as is the case for dispersal of men (often conflict-ridden), of diseases and also of ideas. It becomes even more complex and untreatable with analytical methods, if the matrix (e.g. the landscape) on which dispersal occurs is structured. Today therefore dispersal processes are usually handled by computer simulations. I will explain the various phenomena by examples trying to avoid mathematics.
Lessons learnt from the spread of invasive alien plants: the interplay of habitat, spread potential and introduction history
Essl F1, Smolik MG2, Dullinger S3, Kleinbauer I3, Leitner M2, Peterseil J1, Stadler L-M2,4 & Vogl G2
1 Essl F, Peterseil J, Federal Environment Agency, Austria
2 Smolik MG, Leitner M, Stadler L-M, Vogl G, University of Vienna, Austria
3 Dullinger S, Kleinbauer I, VINCA, Austria
4 HASYLAB at DESY, Notkestraße 85, 22603 Hamburg, Germany
Understanding and forecasting the spread of alien species is considered an essential tool for proactive management of alien species. Empirical studies usually demonstrate that introduction history, habitat templates and dispersal processes interact in determining the spatial pattern and rate of invasive spread. However, most studies either disregard dispersal or take insufficient account of spatial variation in habitat suitability, and they usually neglect invasion history.
In our talk, we will present the results and methodological achievements of ongoing research using the invasion of the alien annual plant ragweed (Ambrosia artemisiifolia L.) in Austria as case study. We show the results of our reconstruction of the invasion history of this species in Austria. Then, we demonstrate how to integrate two widely used modelling tools – species distribution models delivering habitat-based information on potential distributions and interacting particle systems which simulate spatio-temporal range dynamics as dependent on neighbourhood configurations – into a common framework.
Finally, we will present the implications of our approach, both for improved management of invasive alien species, and more generally, for diffusion processes in general.
References:
Dullinger, D., Kleinbauer, I., Peterseil, J., Smolik, M & Essl, F. (2009): Niche based distribution modelling of an invasive alien plant: effects of population status, propagule pressure and invasion history. Biological Invasions DOI: 10.1007/s10530-009-9424-5.
Essl, F., Dullinger, S. & Kleinbauer, I. (2009): Changes in the spatio-temporal patterns and habitat preferences of Ambrosia artemisiifolia during its invasion of Austria. Preslia 81: 119-133.
Smolik M.G., S. Dullinger I, F. Essl, I. Kleinbauer, M. Leitner, J. Peterseil, L.-M. Stadler & G. Vogl (2010): Integrating habitat distribution models and interacting particle systems to predict the spread of an invasive alien plant. Journal of Biogeography
Equilibrium dynamics
Lorenz-Mathias Stadler
University of Vienna, Austria
Systems in equilibrium are stable on a macroscopic scale. On the microscopic scale, however, random dynamical processes are ubiquitous. In case of concentration gradients, these processes lead to what is commonly denoted as “diffusion”, i.e. to a spreading out, which is observed macroscopically. In crystalline solids, for example, such equilibrium dynamics manifests in the hopping of atoms, which can be followed by means of coherent – or “laser-like” – X-rays, generated at large-scale research facilities, so-called synchrotrons [1]. Apart from this rather abstract example from the sub-nanoworld, equilibrium dynamics forms also the basis for migration of people and neobiota, as will be illustrated in this talk.
[1] Leitner, M., Sepiol, B., Stadler, L.-M., Pfau, B. & Vogl, G. (2009): Atomic diffusion studied with coherent X-rays. Nature Materials 8: 717-720.