Collective behaviors leading to various fascinating movement patterns are believed to be the product of complex interplay among individuals. Previous studies have identified two types of leadership structures in pigeon flocks, i.e., hierarchical networks and reciprocal relationships. However, both of these leadership structures are predicated based on data analysis and lack substantial empirical evidence. Additionally, it is difficult to delineate a direct correspondence between leadership structures and trajectory data for pigeon flocks because birds cannot report their leadership structure. Herein, we demonstrated that pigeons adopt leadership relationships that can be characterized as tree structures. In a tree structure, each follower follows its only leader during collective flights, and the single top leader determines the entire flock's flight direction. In the present study, we performed experiments using student volunteers who could report leadership relationships. We identified a one-to-one correspondence between leadership structures and data characteristics and proposed a method for determining the leadership structure based on trajectory data. This strategy was used to analyze flight trajectory data from a pigeon flock and elucidate the pigeons' leadership relationships. The developed approach could effectively model the collective behavior of pigeon flocks, thus accurately replicating findings from previous experimental studies. The results of this study provide insights regarding the leadership structure in pigeon flocks and have implications for artificial collective systems, e.g., autonomous formation control of multiple unmanned aerial vehicles or unmanned surface vehicles.

Participants and experimental protocols: Twenty-four graduate students participated in the experiments. They were randomly divided equally into three groups of eight, i.e., G¹, G², and G³, and three repeated experiments (Gⁱ, Gⁱ, Gⁱ, i = 1, 2, 3) were performed for each group. For example, G¹ represents the second experiment with the group G¹. Each group of students jogs under the leadership relationship we have set up. The leadership relationship requires each individual, except for the main leader, to choose only one leader to follow, and individuals cannot be leaders of one another. The main leader does not have a leader and serves to lead the movement of the flock. The leadership relationship adopts a tree structure, where each individual can only follow its immediate leader.

Device and data handling: The movements of the crowds/flocks were recorded using an unmanned aerial vehicle (DJI MAVIC 3 PRO) in the air at 60 Hz. On the video recordings, individuals were tracked with a cursor using the free TRACKER software. This established tracks (x_i, y_i; t_i), where (x_i, y_i) represents the position vector of the individuals at time t_i with the time interval of ∆t = 1/20 s.