Information structure of heterogeneous criticality in a fish school.

Integrated information theory (IIT) assesses the degree of consciousness in living organisms from an information-theoretic perspective. This theory can be generalised to other systems, including those exhibiting criticality. In this study, we applied IIT to the collective behaviour of Plecoglossus altivelis and observed that the group integrity (Φ) was maximised at the critical state. Multiple levels of criticality were identified within the group, existing as distinct subgroups. Moreover, these fragmented critical subgroups coexisted alongside the overall criticality of the group. The distribution of high-criticality subgroups was heterogeneous across both time and space. Notably, core fish in the high-criticality subgroups were less affected by internal and external stimuli compared to those in low-criticality subgroups. These findings are consistent with previous interpretations of critical phenomena and offer a new perspective on the dynamics of an empirical critical state.