Information structure of heterogeneous criticality in 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., {Phi}) 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.