Mathematical model of fish schooling behaviour in a set-net

Abstract

Abstract We investigated the validity of a mathematical model to describe fish schooling behaviour towards a simple set-net model. We apply a model considered to be “an autonomous decentralized system” and based on Newton's equation of motion. It includes the parameter M, which indicates “the quantity of information exchange” (i.e. the number of neighbours that affect an individual's behaviour) and strongly affects fish school size and schooling behaviour in an enclosed space. To evaluate the model, simulations of fish schooling behaviour in a set-net model consisting of a leading fence and a box-shaped trap similar to a primitive type of set-net were compared with experimentally observed behaviour of bitterling and mackerel, with a focus on M. A small M induces improper behaviour because there is low cooperation among fish in a school. On the other hand, if M is too large, improper simulation results of individuals in deadlock states in the trap are obtained as a result of excessive information exchange among the fish. The results suggest that the mathematical model can describe the behaviour in a set-net model adequately when M is greater than 2 and less than 10.