Collective motions of fish originate from balanced local perceptual interactions and individual stochastics.

The movement of a group of biological individuals, such as fish schools, can evolve from disordered motions to synergistic movements or even ordered patterns. However, the physical origins behind such emergent phenomena of complex systems remain elusive. Here, we established a high-precision protocol for studying the collective behavior of biological groups in quasi-two-dimensional systems. Based on our video recording of ∼600h of fish movements, we extracted a force map of the interactions between fish from their trajectories using the convolution neural network. Presumably, this force implies the fish's perception of the surrounding individuals, the environment, and their response to social information. Interestingly, the fish in our experiments were predominantly in a seemingly disordered swarm state, but their local interactions were clearly specific. Combining such local interactions with the inherent stochasticity of the fish movements, we reproduced the collective motions of the fish through simulations. We demonstrated that a delicate balance between the specific local force and the intrinsic stochasticity is essential for ordered movements. This study presents implications for self-organized systems that use basic physical characterization to produce higher-level sophistication.