The goal in this project was to develop a mathematical model that can be used to simulate the behaviors of a school of fish, and thereby increase the general understanding of the behavior patterns of migrating schools.

Using what is known about how fish sense changes in their environment and use information to navigate (see the work of Czirok & Vicsek (1999), and Partridge (1980, 1982)), we can use mathematics in a computer program to mimic certain known collective behaviors of a school of fish. The unpredictability of living organisms can be simulated with random numbers in the program. If these behaviors can be modeled in such a way as to leave room for data-driven parameters such as ocean currents, temperature data, food availability, etc. to be input, fisheries resource managers and scientists can better predict the size and directions of migrating or stationary schools of fish. This model uses discrete equations to give solutions for localized behaviors. Similar models using continuous equations can be used to study global behaviors, and three-dimensional adaptations are possible. The model may also be applicable to other organisms, and even robotics and computer animation technologies.