We report on the dynamics of collective alignment in groups of the cichlid fish, Etroplus suratensis. Focusing on small-to-intermediate sized groups (10 N 100), we demonstrate that schooling (highly polarised and coherent motion) is noise-induced, arising from the intrinsic stochasticity associated with finite numbers of interacting fish. The fewer the fish, the greater the (multiplicative) noise and therefore the likelihood of alignment. Such empirical evidence is rare, and tightly constrains the possible underlying interactions between fish: computer simulations indicate that E. suratensis align with each other one at a time, which is at odds with the canonical mechanism of collective alignment, local direction-averaging. More broadly, our results confirm that, rather than simply obscuring otherwise deterministic dynamics, noise is fundamental to the characterisation of emergent collective behaviours, suggesting a need to re-appraise aspects of both collective motion and behavioural inference. arXiv:1903.12132v1 [cond-mat.stat-mech]
Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group-level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real organisms; for example, fish stochastically align towards only one randomly chosen neighbour and yet the schools are highly polarized. Here, we ask—how do organisms maintain group cohesion? Using a spatially explicit model, inspired from empirical investigations, we show that group cohesion can be achieved in finite groups even when organisms randomly choose only one neighbour to interact with. Cohesion is maintained even in the absence of local averaging that requires interactions with many neighbours. Furthermore, we show that choosing a neighbour randomly is a better way to achieve cohesion than interacting with just its closest neighbour. To understand how cohesion emerges from these random pairwise interactions, we turn to a graph-theoretic analysis of the underlying dynamic interaction networks. We find that randomness in choosing a neighbour gives rise to well-connected networks that essentially cause the groups to stay cohesive. We compare our findings with the canonical averaging models (analogous to the Vicsek model). In summary, we argue that randomness in the choice of interacting neighbours plays a crucial role in achieving cohesion.
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