DOI: 10.5061/dryad.15dv41p4h
title: Pigeons use tree structures as the leadership structure for flocking

description: 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.
description: <strong>Participants </strong><strong>and
 experimental protocols: </strong>Twenty-four graduate students
 participated in the experiments. They were randomly divided equally into
 three groups of eight, i.e., G<sup>1</sup>,
 G<sup>2</sup>, and G<sup>3</sup>, and three
 repeated experiments
 (G<em><sup>i</sup></em>, G<em><sup>i</sup></em>, G<em><sup>i</sup></em>, <em>i</em> = 1, 2, 3) were performed for each group. For example, G<sup>1</sup><sup> </sup>represents the second experiment with the group G<sup>1</sup>. 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. <strong>Device and data handling: </strong>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<em><sub>i</sub></em>, y<em><sub>i</sub></em>; t<em><sub>i</sub></em>), where (x<em><sub>i</sub></em>, y<em><sub>i</sub></em>) represents the position vector of the individuals at time t<em><sub>i</sub></em><em> </em>with the time interval of ∆t = 1/20 s.
description: # Pigeons use tree structures as the leadership structure for flocking
 [https://doi.org/10.5061/dryad.15dv41p4h](https://doi.org/10.5061/dryad.15dv41p4h) ## PigeonFight\_Data The file named DATA_G^i_j (i,j=1,2,3) represents the trajectory data of all individuals in the experiment ![](file:///C:\Users\42284\AppData\Local\Temp\ksohtml49640\wps1.jpg)C^i_j. Each data file DATA_G^i_j contains 16 columns of data. These 16 columns of data are divided into 8 pairs in chronological order, which are the coordinates of A, B, C, D, E, F, G, and H, respectively. Specifically, the two columns in each pair of data record the horizontal and vertical coordinates of an individual's movement process, respectively. The time interval between adjacent data is 1/20s. The files named tau*-G^i_j and C*-G^i_j respectively record \tau*![](file:///C:\Users\42284\AppData\Local\Temp\ksohtml49640\wps2.jpg) and ![](file:///C:\Users\42284\AppData\Local\Temp\ksohtml49640\wps3.jpg)C* in the experiment ![](file:///C:\Users\42284\AppData\Local\Temp\ksohtml49640\wps4.jpg)C^i_j. The order of the data is consistent with the data order in Table 1 of the main text.