Information structure of heterogeneous criticality in a fish school

The integrated information theory (IIT) measures the degree of consciousness in living organisms from an information-theoretic perspective. This theory can be extended to general systems such as those measuring criticality. Herein, we applied the IIT to actual collective behaviour ( Plecoglossus altivelis ). We found that the group integrity (i.e., Φ) could be maximised in the critical state and that several levels of criticalities existed in a group as subgroups. Furthermore, these fragmented critical groups coexisted with traditional criticality as a whole. The distribution of high-criticality subgroups was heterogeneous in terms of time and space. In particular, the core fish in the high-criticality group tended to be unaffected by internal and external stimulation, in contrast to those in the low-criticality group. The results of this study are consistent with previous interpretations of critical phenomena and provide a new interpretation of the detailed dynamics of an empirical critical state. ### Competing Interest Statement The authors have declared no competing interest.