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While a rich variety of self-propelled particle models propose to explain thecollective motion of fish and other animals, rigorous statistical comparisonbetween models and data remains a challenge. Plausible models should beflexible enough to capture changes in the collective behaviour of animal groupsat their different developmental stages and group sizes. Here we analyse thestatistical properties of schooling fish (Pseudomugil signifer) through acombination of experiments and simulations. We make novel use of a Boltzmanninversion method, usually applied in molecular dynamics, to identify theeffective potential of the mean force of fish interactions. Specifically, weshow that larger fish have a larger repulsion zone, but stronger attraction,resulting in greater alignment in their collective motion. We model thecollective dynamics of schools using a self-propelled particle model, modifiedto include varying particle speed and a local repulsion rule. We demonstratethat the statistical properties of the fish schools are reproduced by ourmodel, thereby capturing a number of features of the behaviour and developmentof schooling fish.

Body size affects the strength of social interactions and spatial organisation of a schooling fish (Pseudomugil signifer)