Non-local interactions in collective motion

The collective motion of animal groups often exhibits velocity-velocity correlations between nearest neighbours, with the strongest velocity correlations observed at the shortest inter-animal spacings. This may have been a motivational factor in the development of models based  primarily on short-ranged interactions. Here we ask whether such observations necessarily mean that the interactions are short-ranged. We develop a minimal model of collective motion capable of supporting interactions of arbitrary range and show that it represents a counter-example: the strongest velocity correlations emerge at the shortest distances, even when the interactions are explicitly non-local.