Shape fluctuations reveal the hydrodynamics of wild fish schools
Abhijeet Melkani (ENS Lyon)
The shape of an animal group, such as a school of fish or a herd of buffalos, continuously fluctuates even in the absence of external perturbations. Although these shape fluctuations are among the most accessible observables of large living collectives, the physical principles governing them remain unknown.
Using aerial recordings of wild fish, we show that the fluctuating boundaries of milling schools exhibit power-law spectra and propagating shape waves. These scaling laws are shared across three species, contrasting ecosystems, and multiple years. By simulating and coarse-graining a minimal agent-based model, we identify milling schools as droplets of polar active fluids and derive a boundary law analogous to Laplace’s law in passive fluids.
The resulting hydrodynamic theory, which models an animal group as a droplet of active matter, accounts for all our measurements. Our results establish shape fluctuations as a quantitative probe of the physical laws governing collective animal motion, while opening new avenues for understanding how animal groups respond to their environment and interact with other groups and predators.