Mathematical modeling of fish schooling of Japanese Medaka using basic behavioral patterns

A mathematical model was proposed to describe the behavior of fish schooling in a water tank without the presence of flow. First, video images of schooling Japanese Medaka fish (Japanese killifish, Oryzias latipes) in the water tank were analyzed to determine the interactions between individuals: the spacing between individuals, the spatial distribution of individuals and the communication processes. The behavioral pattern model was then applied to the investigation to simulate the schooling phenomenon. In the behavioral pattern model, the behavior of a single fish was based on four patterns: the repulsion, the parallel orientation, the attraction and the searching. The influence of neighbors was averaged by an arithmetic mean. The optimal model structure was searched by a simple genetic algorithm using the experimental data. The results of the simulations agreed with the experimental data in many regards, including the polarization, the nearest neighbor distance, the expanse and the fractal dimension.