Mathematical analysis on fish shoaling by a density-dependent diffusion model

Shoaling by juveniles of a cichlid fish Lepidiolamprologus elongatus in Lake Tanganyika, central Africa, is considered by means of a mathematical model with a density-dependent diffusion equation. The spatial size of shoaling is assumed to be determined by the balance between two counteracting forces: aggregation and dispersion. The data on the spatial size of shoaling and the group size are analyzed by the model. Then those tendencies of aggregation and dispersion are quantified. The result gives qualitative information to understand shoaling.