Collective predator evasion: Putting the criticality hypothesis to the test

Abstract

According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different dynamical regimes. Critical systems exhibit unique properties, which may benefit collective information processing such as maximal responsiveness to external stimuli. Besides neuronal and gene-regulatory networks, recent empirical data suggests that also animal collectives may be examples of self-organized critical systems. However, open questions about self-organization mechanisms in animal groups remain: Evolutionary adaptation towards a group-level optimum (group-level selection), implicitly assumed in the “criticality hypothesis”, appears in general not reasonable for fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important self-organization and spatial sorting effects. Using a generic, spatially-explicit model of schooling prey being attacked by a predator, we show first that schools operating at criticality perform best. However, this is not due to optimal response of the prey to the predator, as suggested by the “criticality hypothesis”, but rather due to the spatial structure of the prey school at criticality. Secondly, by investigating individual-level evolution, we show that strong spatial self-sorting effects at the critical point lead to strong selection gradients, and make it an evolutionary unstable state. Our results demonstrate the decisive role of spatio-temporal phenomena in collective behavior, and that individual-level selection is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality.

Impact of Variable Speed on Collective Movement of Animal Groups

“…We also found that a minimum in cohesion at the transition exists for fixed-speed models, but weakens or even vanishes with increasing speed variability. This has important implications for studies that investigate collective behavior at criticality [19]. For example, a weak cohesion is associated with a high probability of group splits (smaller group size) and lower densities.…”

“…Additionally, the interaction between fish is modelled by using the continuous version (i.e. overlapping instead of discrete zones) of a well established three-zone model that traditionally uses fixed speed [19]. The force acting on an individual i has a selfpropulsion term (including noise) and a social term.…”

“…At the transition the directional correlation of the agents is maximal (i.e. susceptibility peaks, Figure 4A inset) and the directional fluctuations cause subgroups of the collective to head in different directions, leading to an expansion of the collective [19]. This expansion weakens with increasing speed variability because the distance regulating force can now lower the speed from a subgroup if it moves away from the shoal, effectively inhibiting expansion.…”

“…In addition to empirical observations, mathematical models are an important tool for studying self-organization and collective behavior, and have been instrumental in uncovering general principles of how robust, large-scale coordination can emerge from simple, local interactions between self-propelled agents [10,18,19].…”

Modeling the influence of noise and interaction strength on the collective motion of interactive particles

“…In addition, they found that phase transition is realized even without noise. One popular interesting outcome of these kinds of studies, which helps us to find similar behavior in collective motions of living systems, is the criticality hypothesis in living systems [14][15][16]. According to this hypothesis, collective motions in bio-systems can be observed in the special conditions where the macroscopic dynamics of the systems are improved, and long-range correlation is observed in the group motion to find the optimal living activities [16,17].…”