Complex patterns of collective behaviour may emerge through self-organization, from local interactions among individuals in a group. To understand what behavioural rules underlie these patterns, computational models are often necessary. These rules have not yet been systematically studied for bird flocks under predation. Here, we study airborne flocks of homing pigeons attacked by a robotic-falcon, combining empirical data with a species-specific computational model of collective escape. By analysing GPS trajectories of flocking individuals, we identify two new patterns of collective escape: early splits and collective turns, occurring even at large distances from the predator. To examine their formation, we extend an agent-based model of pigeons with a ‘discrete’ escape manoeuvre by a single initiator, namely a sudden turn interrupting the continuous coordinated motion of the group. Both splits and collective turns emerge from this rule. Their relative frequency depends on the angular velocity and position of the initiator in the flock: sharp turns by individuals at the periphery lead to more splits than collective turns. We confirm this association in the empirical data. Our study highlights the importance of discrete and uncoordinated manoeuvres in the collective escape of bird flocks and advocates the systematic study of their patterns across species.

• The pre-processed empirical data were provided by:

Sankey DWE, Storms RF, Musters RJ, Russell TW, Hemelrijk CK, Portugal SJ. 2021 Absence of “selfish herd” dynamics in bird flocks under threat. Curr Biol., 1–7. (doi:10.1016/j.cub.2021.05.009)

During the field experiments, a remotely controlled robotic falcon (‘RobotFalcon’) was used to attack flocks of homing pigeons (Columba livia) just after they have been released at a new location. Both prey and predator were equipped with GPS devices.

• Processed data and code used for the figures and statistics of the manuscript are stored in the Zenodo repository: DOI: 10.5281/zenodo.5889098 (the archived version of the GitHub repository PigeonsCollectiveEscape)
• The simulated data are generated by an extension of the computational model HoPE (Homing Pigeons Escape): a species-specific agent-based model, adjusted to empirical data of pigeon flocks. The model is available at the Zenodo repository: DOI: 10.5281/zenodo.5889123. The original HoPE model is first published in:

Papadopoulou M, Hildenbrandt H, Sankey DWE, Portugal SJ, Hemelrijk CK. 2022 Self-organization of collective escape in pigeon flocks. PLoS Comput Biol., 1–25. (doi:10.1371/journal.pcbi.1009772/journal.pcbi.1009772)

Simulations include one predator-agent and flocks of 8 to 34 individual pigeon-agents that demonstrate escape behavior. 'Catches' of prey by the predator are not modeled.

Please refer to the README files of our dataset and software.