A model of the formation of fish schools and migrations of fish

We consider an individual based, discrete and stochastic model for the collective motion of fish. The fish are regarded as self-propelled interacting particles, such that the motion of individual fish is governed by two “forces”: a tendency to imitate the motion of other fish in a local neighbourhood and an external vector field, such as a temperature gradient or food density gradient. In addition, there is a stochastic component, which can be defined in such a way that the entire group will tend to move in the direction towards a specified region, taken to be the spawning grounds. The model includes boundaries representing for example isotherms or depth contours where specific behaviour of individual fish can be defined. We then present simulations of a hypothetical fish stock migrating between feeding grounds and spawning grounds.