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.