Revealing the existence of the ontological commitment in fish schools

The heap paradox is an enduring problem in complex systems, and it has many variations. One variation of the heap paradox considers how many parts of a whole are required to generate group behaviour. The initial heap paradox indicates that the recursive adding grain process finally makes a heap at a certain point. In this study, we point out the hidden assumption of this paradox, which a recursive operation involves ontological commitment (i.e. anticipation for the forthcoming heap from non-heap in every procedure). The aim of this study is to show the existence of the ontological commitment in a real fish school via IIT 3.0. We analysed the behaviour of Plecoglossus altivelis with group sizes ranging from 2 to 5 fish. Consequently, the subschool embedded in the whole group has a qualitatively different causal structure compared with a whole group of the same size. That is, 2-fish subschools lose the chasing property, but gain the leadership property, which has never been observed in a 2-fish whole school. Accordingly, 3- and 4-fish subschools also show a completely different property from the same sized whole school. Our results suggest that a real fish school contains the ontological commitment to maintain their group behaviour.