Speckle statistics as a tool to distinguish collective behaviors of Zebrafish shoals

Zebrafish have become an important model animal for studying the emergence of collective behavior in nature. Here, we show how to properly analyze the polarization statistics to distinguish shoal regimes. In analogy with the statistical properties of optical speckles, we show that exponential and Rayleigh distributions emerge in shoals with many fish with uncorrelated velocity directions. In the opposite limit of just two fish, the polarization distribution peaks at high polarity, with the average value being a decreasing function of the shoal's size, even in the absence of correlations. We also perform a set of experiments unveiling two shoaling regimes. Large shoals behave as small domains with strong intra-domain and weak inter-domain correlations. A strongly correlated regime develops for small shoals. The reported polarization statistical features shall guide future automated neuroscience, pharmacological, toxicological, and embryogenesis-motivated experiments aiming to explore the collective behavior of fish shoals.