Finding Continuity and Discontinuity in Fish Schools via Integrated Information Theory

Integrated Information Theory (IIT), originally developed to measure consciousness, can reveal emergent properties in fish schools that other measures miss. Applying IIT 3.0 to real ayu fish (Plecoglossus altivelis) schools, the authors found that leadership behavior emerges only when school size reaches four or more individuals, not at sizes of three or fewer. This discontinuous transition was not detected by mutual information or in a simple Boids model. The results suggest that integrated information Φ captures inherent collective properties invisible to other metrics, and that figure-ground perception in fish may relate to optimal paths for the functional evolution of collective behavior.

Study at a glance

Abstract

Collective behaviour is known to be the result of diverse dynamics and is sometimes likened to a living system. Although many studies have revealed the dynamics of various collective behaviours, their main focus was on the information process inside the collective, not on the whole system itself. For example, the qualitative difference between two elements and three elements as a system has rarely been investigated. Tononi et al. have proposed Integrated Information Theory (IIT) to measure the degree of consciousness $Φ$. IIT postulates that the amount of information loss caused by certain partitions 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 applied IIT (in particular, IIT 3.0 using PyPhi) to analyse real fish schools ({\it Plecoglossus altivelis}). Our hypothesis in this study is a very simple one: a living system evolves to raise its $Φ$ value. If we accept this hypothesis, IIT reveals the existence of continuous and discontinuous properties as group size varies. For example, leadership in the fish school emerged for a school size of four or above; but not below three. Furthermore, this transition was not observed by measuring mutual information or in a simple Boids model. This result suggests that integrated information $Φ$ can reveal some inherent properties which cannot be observed using other measures. We also discuss how the fish recognition of the figure-ground relation, that is, what determines the relevant ON and OFF states, may reveal various optimal paths for obtaining the functional evolution of collective behaviour.