Space dimension and scaling in fish school-size distributions

A simple model of aggregation has been used, in its mean-field version, to explain the observed scaling property of tuna fish school-size distributions (Bonabeau E and Dagorn L 1995 Phys. Rev. E 51 5220). This model makes additional predictions when the dimension of the space in which the fish move is taken into account. In this letter, we identify two cases where the mean-field assumption, which was justified for free-swimming tuna fish, is no longer valid. In these two examples, scaling is also observed and the exponent is modified from the mean-field case in a way predicted by the model.