Scale-free correlations in collective motion with position-based interactions

Collective Motion (CM) is observed in a variety of animal groups such as bird flocks and fish schools. In a recent study, Cavagna et al. (2010) found that the correlation lengths of speed and velocity fluctuations in starling flocks are not set by a specific interaction range, but are instead scale-free, proportional to the group size. So far, this observation has been justified by hypothesizing that flocks evolved to follow critical dynamics near a phase transition, where scale-free correlations are known to emerge. Criticality could provide an evolutionary advantage by allowing the flock to optimally respond to an external perturbation such as a predator attack. However, a criticality-based explanation may only be required in cases where interactions are based exclusively on relative orientations, as often assumed in CM models, following the seminal work by Vicsek et al. (1995). In this paper, we show that an alternative, more parsimonious, mechanism can produce scale-free correlations when considering interactions based on relative positions.