A motivation to study grouping behavior of planktonic organisms will be presented, first. I will review two individual based models for planktonic organism aggregation; one makes use of non-parametric density estimation technique in one-dimensional space (Yamazaki & Haury, 1993) and the other utilizes the second order autoregressive equation in two-dimensional space (Yamazaki & Okubo, 1995). Both models are related to random walks, so I will revisit Okubo (1986) in order to relate the random walk problem to the corresponding diffusion equation. A particular attention is paid to a variable diffusivity problem. At the end of my talk, I will introduce marine particle aggregation in a turbulent flow from both Direct Numerical Simulation and field data.
Yamazaki, H. and L.R. Haury (1993) A new Lagrangian model to study animal aggregation. Ecol. Model, 69, 99-111.
Yamazaki, H. and A. Okubo (1995) A simulation of grouping: aggregating random walk. Ecol. Model, 79, 159-165.
Okubo, A. (1986) Dynamical aspects of animal grouping: swarms, schools, flocks and herds. Adv. Biophys., 22, 1-94.