Data-Driven Stochastic Modeling of Schooling Fish: From Collective Dynamics to Individual Fluctuations

TL;DR

Using high-resolution trajectories of schooling fish, a data-driven stochastic framework is inferred that reproduces with remarkable accuracy the behavior of real fish schools and bridges experiment and theory, showing that the collective dynamics of animal groups can be faithfully reconstructed from first principles directly from data.

Abstract

Collective motion in animal groups emerges from the interplay between individual variability and social coordination, yet connecting these scales quantitatively has remained a major challenge.Using high-resolution trajectories of schooling fish, we infer a data-driven stochastic framework that reproduces with remarkable accuracy the behavior of real fish schools. We decompose motion into two coupled components: the dynamics of the school's center of mass (or centroid), modeled as an active Brownian particle confined by the tank, and individual motions relative to that center, described by stochastic equations with data-inferred mean-field potentials and multiplicative noise. Simulations of these equations produce synthetic schools that quantitatively match real ones across multiple observables, including burst-and-coast dynamics, polarization, and spatial cohesion. This minimal, predictive framework bridges experiment and theory, showing that the collective dynamics of animal groups can be faithfully reconstructed from first principles directly from data.

Figures (5)

• Figure 1: Probability density functions (PDFs) of the school centroid (CM) position (a) and velocity (b) from empirical data, aggregated over three experimental realizations ($N=60$). Panels (c) and (d) show the corresponding PDFs obtained from numerical simulations. Results for other group sizes are presented in Supplemental Figure SF1.
• Figure 2: Radial density of fish in the CM frame for (a) experimental data and (b) model simulations (b). Densities are normalized by each realization’s radius of gyration $R_g$ and by $\rho_0$ so curves collapse. Dashed lines mark $r=R_g$. (c) Speed distribution in the CM frame from experimental data. (d) Corresponding speed distribution from the model.
• Figure 3: (a,b) Side-by-side comparison of a real fish trajectory and a simulated trajectory of equal duration (group size $N = 60$). (c,d) Temporal traces of speed for selected individuals from experiments (c) and simulations (d), illustrating synchronized burst‑and‑coast episodes. The same Gaussian smoothing applied to experimental data was also applied to simulation outputs for direct comparison.
• Figure 4: Mean square displacement (MSD) in the laboratory frame for (a) $N=40$, (b) $N=50$, and (c) $N=60$. Gray lines represent individual experimental realizations; colored lines depict the corresponding model predictions. MSD exhibits a short‑time ballistic regime and long‑time saturation due to tank confinement. Small oscillations in the plateau reflect collective circulation of the group's center of mass within the tank.
• Figure 5: (a) PDFs of residence time $\tau_{\mathrm{in}}$ inside $R_g$ and (b) excursion time $\tau_{\mathrm{out}}$ outside $R_g$: experimental data (solid lines) and model simulations (dashed lines). Experimental results are aggregated over three realizations per group size. (c) PDF of peripheral residence time on the convex hull: experimental points and simulation curves. (d) PDF of polarization: experimental points compared with simulation curves.