From Lévy walks to Brownian motion in schools of zebrafish (Danio rerio).

Authors

Andreza M da Silva, Francisco C B Leal, Pabyton G Cadena, Viviane M de Oliveira, Adauto J F de Souza, Antonio R de C Romaguera, Anderson L R Barbosa

Published in

The European physical journal. E, Soft matter. Volume 49. Issue 8. Jul 21, 2026. Epub Jul 21, 2026.

Abstract

Population density strongly affects the internal organization and movement dynamics of fish schools. Here, we investigate density-dependent collective motion in zebrafish (Danio rerio) schools with group sizes ranging from 2 to 30 individuals. Using trajectories measured relative to the school center of mass, we show that individual motion is superdiffusive at low densities and progressively approaches Brownian-like behavior as density increases. Step-length distributions are well described by truncated power laws: for $N\le 15$ , the fitted exponents are compatible with a Lévy-walk regime, whereas larger groups show a transition toward Brownian motion. In parallel, q-Gaussian fits of the signed radial displacement increments reveal heavy-tailed, non-Gaussian fluctuations at low densities and a gradual convergence toward Gaussian-like behavior at high densities. These results support a density-driven transition from a polarized, strongly correlated schooling state to a more disordered shoaling state, suggesting that increased density reorganizes local interactions within the group.

PMID:
42479287
Bibliographic data and abstract were imported from PubMed on 21 Jul 2026.

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