Closed-loop real-virtual interactions validate 3D model of social coordination in fish

Collective motion in animal groups arises from social interactions rules, yet uncovering these rules requires quantitative models grounded in real behavior. We developed a fully three-dimensional, data-driven model of pairwise interactions in the schooling fish Hemigrammus rhodostomus, reconstructing attraction, alignment from experiments with two real fish swimming freely in a hemispherical bowl. Simulations of this model quantitatively reproduced empirical distributions of speed, distance, and orientation. We then embedded the model into a closed-loop virtual reality system, allowing a real fish to interact in real time with a virtual conspecific whose movements were governed by the same interaction rules. This biohybrid setup revealed that the model captures key social interactions underlying coordinated swimming. Our results establish a robust validation framework linking data, models, and behavior, paving the way for hybrid biological-digital collectives.