Topological interactions account for border dynamics of murmurations and transit flocks.

Murmurations are one of nature's most striking examples of collective behaviour. Despite extensive research the dynamics of individuals at the borders of these flocks remain poorly understood. These dynamics result in two unexplained phenomena: the tendency of birds to remain longer at the border than the way internal birds keep their position inside the flock; and the hardness (sharpness) of the borders. It has been suggested that the border dynamics can be attributed to selection pressures for advantageous behaviours such as prey evasion. Here with the aid of stochastic models we show that the observed border dynamics are an accidental but potentially advantageous by-product of topological interactions (when birds interact with a fixed number of neighbours) and that they do not arise with metric interactions (when birds coordinate with neighbours based on spatial distance). I find support for these predictions in an analysis of pre-existing telemetry data for flocks of jackdaws (Corvus monedula).