Dominating lengthscales of zebrafish collective behaviour

Collective behaviour in living systems is observed across many scales, from bacteria to insects, to fish shoals. Zebrafish have emerged as a model system amenable to laboratory study. Here we report a three-dimensional study of the collective dynamics of fifty zebrafish. We observed the emergence of collective behaviour changing between ordered to randomised, upon adaptation to new environmental conditions. We quantify the spatial and temporal correlation functions of the fish and identify two length scales, the persistence length and the nearest neighbour distance, that capture the essence of the behavioural changes. The ratio of the two length scales correlates robustly with the polarisation of collective motion that we explain with a reductionist model of self–propelled particles with alignment interactions.
Author summary Groups of animals can display complex collective motion, which emerges from physical and social interactions amongst the individuals. A quantitative analysis of emergent collective behaviour in animals is often challenging, as it requires describing the movement of many individual animals. With an innovative 3D tracking system, we comprehensively characterized the motion of large groups of zebrafish (Danio rerio), a freshwater fish commonly used as a vertebrate model organism. We find that the different collective behaviours are captured by two physical scales: the length of persistent motion in a given direction and the typical nearest neighbour distance. Their ratio allows us to interpret the experimental results, in the light of a statistical mechanics model for swarming with persistent motion and local neighbourhood alignment.