Lagrangian modelling of plankton motion: From deceptively simple random walks to Fokker-Planck and back again

The movement of plankton, either by turbulent mixing or their own inherent motility, can be simulated in a Lagrangian framework as a random walk. Validation of random walk simulations is essential. There is a continuum of mathematically valid stochastic integration schemes upon which random walk simulations depend, each of which lead to radically different macro-scale dynamics as expressed in their corresponding Fokker-Planck equations. In addition, diffusivity is not a unique parameter describing a random walk and its corresponding Fokker-Planck equation. Spatially varying translation speed and turn frequency have different effects on population distributions. Validation requires extra information either in the form of the well-mixed condition for physical diffusion, or in detailed information on the sensing ability, internal state modulation and swimming response for plankton motility. (C) 2007 Elsevier B.V. All rights reserved.