Diffusion during collective turns in bird flocks under predation

Moving in groups offers animals protection against predation. When under attack, grouped individuals often turn collectively to evade a predator, which sometimes makes them rapidly change their relative positions in the group. In bird flocks in particular, the quick reshuffling of flock members confuses the predator, challenging its targeting of a single individual. This confusion is considered to be greater when the internal structure of the group changes faster (i.e. the 'diffusion' of the group is higher). Diffusion may increase when individual birds turn collectively with equal radii (same angular velocity) but not when individuals keep their paths parallel (by adjusting their speed). However, how diffusion depends on individual behaviour is not well known. When under attack, grouping individuals change the way they interact with each other, referred to as 'alarmed coordination' (e.g., increase their reaction frequency or their cohesion tendency), but the effect of such changes on collective turning is unknown. Here, we aimed to gain an understanding of the dynamics of collective turning in bird flocks. First, to investigate the relation between alarmed coordination and flock diffusion, we developed an agent-based model of bird flocks. Second, to test how diffusion relates to collective turns with equal-radii and parallel-paths, we developed a metric of the deviation from these two types. Third, we studied collective turning under predation empirically, by analysing the GPS trajectories of pigeons in small flocks pursued by a RobotFalcon. As a measure of diffusion, we used the instability of neighbours: the rate with which the closest neighbours of a flock member are changing. In our simulations, we showed that this instability increases with group size, reaction frequency, topological range, and cohesion tendency and that the relation between instability of neighbours and the deviation from the two turning types depends in often counter-intuitive ways on these coordination specifics. Empirically, we showed that pigeons turn collectively with less diffusion than starlings and that their collective turns are in between those with equal-radii and parallel-paths. Overall, our work provides a framework for studying collective turning across species.