Decoding social integration in schooling fish using closed-loop real-virtual interactions

Collective motion in fish schools emerges from local attraction, alignment, and repulsion rules whose strengths vary with behavioural and biomechanical context. Although swimming speed is known to shape turning capacity, spatial positioning, and information flow, its causal influence on social interaction strength remains poorly quantified. Using an open-loop immersive virtual-reality system, we expose freely swimming Hemigrammus rhodostomus to a virtual conspecific moving along circular trajectories at six controlled speeds. This approach isolates the effect of neighbour speed on attraction, alignment, vertical positioning, and wall avoidance. Across all speeds, real fish reliably track the virtual fish and adjust their own speed toward that of the partner. Behavioural distributions reveal systematic changes in spatial positioning and perception angles, with fish shifting from leader-like to follower-like configurations as virtual-fish speed increases. A data-driven 3D self-propelled particle model, in which only the amplitudes of interaction functions are modulated, quantitatively reproduces these patterns. Model-based reconstructions shows that higher partner speed weakens both horizontal and vertical attraction, strengthens alignment, and increases wall repulsion. These results demonstrate that fish tune their social-interaction rules in a speed-dependent manner, revealing swimming speed as a key control parameter shaping coordination in minimal groups and, potentially, in larger schools.