Fish shoals resemble a stochastic excitable system driven by environmental perturbations

Abstract

Groups of animals can perform highly coordinated collective behaviours that confer benefits to the participating individuals by facilitating social information exchange and protection from predators1. Some of these characteristics could arise when groups operate at critical points between two structurally and functionally different states, leading to maximal responsiveness to external stimuli and effective propagation of information2,3. It has been proposed that animal groups constitute examples of self-organized systems at criticality2,3; however, direct empirical evidence of this hypothesis—in particular in the wild—is mostly absent. Here we show that highly conspicuous, repetitive and rhythmic collective dive cascades produced by many thousands of freshwater fish under high predation risk resemble a stochastic excitable system driven by environmental perturbations. Together with the results of an agent-based model of the system, this suggests that these fish shoals might operate at a critical point between a state of high individual diving activity and low overall diving activity. We show that the best fitting model, which is located at a critical point, allows information about external perturbations—such as predator attacks—to propagate most effectively through the shoal. Our results suggest that criticality might be a plausible principle of distributed information processing in large animal collectives.

Burstiness and information spreading in active particle systems

“…The minimum values of ht N i around the phase transition points are consistent with the recent idea that animal groups stay around the phase transition points to make the information spreading between individuals most efficiently. [38][39][40] Although we have observed some deep connection between the temporal heterogeneities and the phase transition in the active particles from the nonmonotonic behavior of the burstiness parameter (Fig. 3(c)) and the full prevalence time (Fig.…”

“…The minimum values of 〈 t N 〉 around the phase transition points are consistent with the recent idea that animal groups stay around the phase transition points to make the information spreading between individuals most efficiently. 38–40…”

The role of hydrodynamics in collective motions of fish schools and bioinspired underwater robots

“…Using a towed net, a recent comparative study examined the swarming patterns of California market squid (Doryteuthis opalescens) and Pacific sardine (Sardinops sagax), which have distinct propulsive mechanisms [160]. Using rectified videos, another team of researchers measured the duration and size of fish shoal disturbances [161]. Adaptive resolution imaging sonar (ARIS) [162,163] and drone footage [164][165][166][167] have also emerged as powerful tools in identifying schooling structures in the field.…”

Exploring the criticality hypothesis using programmable swarm robots with Vicsek-like interactions

“…the 'criticality hypothesis') [1][2][3][4]. The related biological systems include the brain and cortex [5][6][7], retinal neurons [8], gene regulation networks [9], bacterial clusters [10], social amoebas [11], ant colonies [12,13], midge swarms [14], sheep herds [15], bird flocks [16][17][18] and fish schools [19][20][21]. In principle, criticality is essential to biological systems, and it provides a delicate balance between two unrealistic tendencies [22,23]: if a system is too random, it will not be able to transfer information and reproduce stability; if it is too ordered, it will not be able to adapt to perturbations quickly.…”

“…Here, we focus on the criticality hypothesis presented in coordinated collective motion of animals [16][17][18][19][20][21]. Most claims on the benefits of criticality in these self-organized systems are speculative [19,25,44] and have not been validated with rigorous testing [28].…”