Four-Types of IIT-Induced Group Integrity of Plecoglossus altivelis.

Integrated information theory (IIT) was initially proposed to describe human consciousness in terms of intrinsic-causal brain network structures. Particularly, IIT 3.0 targets the system's cause-effect structure from spatio-temporal grain and reveals the system's irreducibility. In a previous study, we tried to apply IIT 3.0 to an actual collective behaviour in Plecoglossus altivelis. We found that IIT 3.0 exhibits qualitative discontinuity between three and four schools of fish in terms of Φ value distributions. Other measures did not show similar characteristics. In this study, we followed up on our previous findings and introduced two new factors. First, we defined the global parameter settings to determine a different kind of group integrity. Second, we set several timescales (from Δ t = 5 / 120 to Δ t = 120 / 120 s). The results showed that we succeeded in classifying fish schools according to their group sizes and the degree of group integrity around the reaction time scale of the fish, despite the small group sizes. Compared with the short time scale, the interaction heterogeneity observed in the long time scale seems to diminish. Finally, we discuss one of the longstanding paradoxes in collective behaviour, known as the heap paradox, for which two tentative answers could be provided through our IIT 3.0 analysis.

Finding continuity and discontinuity in fish schools via integrated information theory.

Collective behaviours are known to be the result of diverse dynamics and are sometimes likened to living systems. Although many studies have revealed the dynamics of various collective behaviours, their main focus has been on the information processing performed by the collective, not on interactions within the collective. For example, the qualitative difference between three and four elements in a system has rarely been investigated. Tononi et al. proposed integrated information theory (IIT) to measure the degree of consciousness Φ. IIT postulates that the amount of information loss caused by the minimum information partition is equivalent to the degree of information integration in the system. This measure is not only useful for estimating the degree of consciousness but can also be applied to more general network systems. Here, we obtained two main results from the application of IIT (in particular, IIT 3.0) to the analysis of real fish schools (Plecoglossus altivelis). First, we observed that the discontinuity on 〈Φ(N)〉 distributions emerges for a school of four or more fish. This transition was not observed by measuring the mutual information or the sum of the transfer entropy. We also analysed the IIT on Boids simulations with respect to different coupling strengths; however, the results of the Boids model were found to be quite different from those of real fish. Second, we found a correlation between this discontinuity and the emergence of leadership. We discriminate leadership in this paper from its traditional meaning (e.g. defined by transfer entropy) because IIT-induced leadership refers not to group behaviour, as in other methods, but the degree of autonomy (i.e. group integrity). These results suggest that integrated information Φ can reveal the emergence of a new type of leadership which cannot be observed using other measures.