Duration-aware unsupervised segmentation reveals collective movement modes in homing flights of pigeon flocks

Homing flights of pigeon flocks require rapid adjustments in individual behaviour while maintaining group cohesion. However, how heading adjustments and coordinated movement changes are temporally organised during continuous flight, and whether they form repeatable collective movement modes, remain poorly characterised.

During homing flights of domestic pigeon (Columba livia) flocks, we synchronously recorded individual GPS trajectories and inertial measurement data. After standardised preprocessing, candidate flock-level kinematic features were constructed to characterise flock movement changes across six aspects: flock-level turning intensity, acceleration intensity, turning consistency, acceleration consistency, turning directionality and acceleration directionality. After comparing candidate input schemes, four flock-level kinematic indicators were selected as model inputs. A hidden semi-Markov model with an explicit duration structure was then used to perform unsupervised segmentation of continuous homing flights.

We identified five collective movement modes that were comparable across flight trials. In addition to steady cruising, coordinated counterclockwise turning and coordinated clockwise turning, two modes were identified that were difficult to distinguish from flock trajectory geometry alone. The first was rapid collective reorientation, which showed the highest flock-level turning intensity, acceleration intensity and turning consistency, but whose turning directionality was not fixed to a single clockwise or counterclockwise direction. The second was a transition mode that connected different movement modes during mode switching. All five modes recurred during homing flights, with overall occupancies of 10.5%-26.7%, median durations of 0.60-1.03 s, and approximately 90% of mode segments ending within 2 s. Transitions among modes were concentrated in a small number of source-mode-specific high-probability pathways, indicating a non-uniform transition structure during homing flights.

Homing flights of pigeon flocks contain a recurrent set of second-scale collective movement modes rather than a simple "straight flight-turning" dichotomy. An unsupervised segmentation framework based on flock-level kinematic indicators and explicit duration modelling can identify these short-timescale modes at the level of flock kinematics and characterise their transition structure, providing a comparable temporal reference for future analyses of spatial organisation, information transfer and leader-follower relationships across different modes.