A discrete and stochastic simulation model for migration of fish with application to capelin in the seas around Iceland

An individual based, discrete and stochastic model for the collective motion of fish presented in Hubbard et al. (2004) is applied to the task of simulating migrations of capelin in the seas around Iceland. In this application the individual particles may be viewed as small schools of fish that are self-propelled and interacting in such a way that the motion is governed on one hand by a tendency to imitate the motion of other particles in a local neighbourhood and on the other hand by external environmental vector fields for temperature, food density and oceanic currents, as well as a force field generated by an attracting spawning region. In addition there is a stochastic component. The implementation of this model is based on a triangularization of the region under consideration which is shown to be advantageous both in terms of computational efficiency and access to external data. Results of simulations are presented showing the migration pattern of capelin that is situated northwest off Iceland at the beginning October and migrates to spawning grounds south off Iceland by the end of March the following year.