Modeling three-dimensional bait ball collective motion

Collective motion of animal groups such as fish schools and bird flocks in three-dimensional (3D) space are modeled by considering a topological (Voronoi) neighborhood. The tridimensionality of the group is quantified. Apart from the patterns of swarming, schooling, and milling, we identify a 3D bait ball around the phase transition boundary. More significantly, we find that by considering a blind angle in this topology based model, an individual interacts statistically with six to seven neighbors, consistent precisely with the previous field observations of the starling flocks. This model could be expected to enable more insightful investigation on realistic collective motion of shoals or flocks.