Self-organized shape and frontal density of fish schools

Models of swarming (based on avoidance, alignment and attraction) produce patterns of behaviour also seen in schools of fish. However, the significance of such similarities has been questioned, because some model assumptions are unrealistic [e.g. speed in most models is constant with random error, the perception is global and the size of the schools that have been studied is small (up to 128 individuals)]. This criticism also applies to our former model, in which we demonstrated the emergence of two patterns of spatial organization, i.e. oblong school form and high frontal density, which are supposed to function as protection against predators. In our new model we respond to this criticism by making the following improvements: individuals have a preferred 'cruise speed' from which they can deviate in order to avoid others or to catch up with them. Their range of perception is inversely related to density, with which we take into account that high density limits the perception of others that are further away. Swarm sizes range from 10 to 2000 individuals. The model is three-dimensional. Further, we show that the two spatial patterns (oblong shape and high frontal density) emerge by self-organization as a side-effect of coordination at two speeds (of two or four body lengths per second) for schools of sizes above 20. Our analysis of the model leads to the development of a new set of hypotheses. If empirical data confirm these hypotheses, then in a school of real fish these patterns may arise as a side-effect of their coordination in the same way as in the model.