Density induced transition in a school of fish

Collective behaviour has been studied in various fields of science. As an example, we may consider the patterns observed in living systems, whose aggregates form organized groups such as flocks of birds, herds of mammals and schools of fish. These aggregates may be formed as a consequence of an external stimulus or due to the local interaction among nearby specimens. As an example of the latter case one may think about a school of fish, where each individual bases its behaviour on its perception of the position and velocity of its nearest neighbours. As a result of these interactions, global collective behaviour may emerge, originating and maintaining the cohesion of the aggregate. In this work, we model the collective movement of a school of fish using an agent-based model which follows biologically motivated behavioural rules previously proposed. The distributions of nearest neighbour distance and relative orientations between neighbouring fishes are measured and the results are found to be in good agreement with previous experimental measurements.