A generalized stochastic approach to particle dispersal in soils and sediments

We explore a generalized stochastic description for the dispersal of particles in soils and sediments. The model is based on the continuous-time random-walk (CTRW), which enables a very general description of particle mixing due to biological activity. A community of burrowing organisms is characterized by a bioturbation fingerprint that consists of two probability distributions. The jump-length distribution describes the distance a particle travels within a given bioturbation event. The waiting-time distribution describes the time interval a particle waits at a given location in between two bioturbation events. Our stochastic analysis provides insight on the applicability of the widely used biodiffusion model, which forms the asymptotic limit of the CTRW model. This asymptotic behaviour of diffusion is always reached, independent of the shape of bioturbation fingerprint, provided that the waiting-time distribution has a finite mean and the jump-length distribution has a finite variance. The biodiffusion coefficient can be decomposed as the variance of the jump-length distribution over the mean of the waiting-time distribution. Since the variance enables a squared weighing of the jump distance, long-range displacements will contribute more to the mixing intensity D-b than short-range displacements. Therefore, large macrofauna will contribute disproportionately to the mixing intensity relative to their abundance, as they displace particles over longer distances than smaller organisms. Finally, we review the potential for bioturbation of so-called anomalous transport models where either the mean of the waiting-time distribution or the variance of the jump-length distribution becomes infinite. (C) 2008 Elsevier Ltd. All rights reserved.