Collective turns in jackdaw flocks: kinematics and information transfer

Abstract

The rapid, cohesive turns of bird flocks are one of the most vivid examples of collective behaviour in nature, and have attracted much research. Three-dimensional imaging techniques now allow us to characterize the kinematics of turning and their group-level consequences in precise detail. We measured the kinematics of flocks of wild jackdaws executing collective turns in two contexts: during transit to roosts and anti-predator mobbing. All flocks reduced their speed during turns, probably because of constraints on individual flight capability. Turn rates increased with the angle of the turn so that the time to complete turns remained constant. We also find that context may alter where turns are initiated in the flocks: for transit flocks in the absence of predators, initiators were located throughout the flocks, but for mobbing flocks with a fixed ground-based predator, they were always located at the front. Moreover, in some transit flocks, initiators were far apart from each other, potentially because of the existence of subgroups and variation in individual interaction ranges. Finally, we find that as the group size increased the information transfer speed initially increased, but rapidly saturated to a constant value. Our results highlight previously unrecognized complexity in turning kinematics and information transfer in social animals.

Keywords: bird flocks; collective behaviour; collective turns; flight kinematics; information transfer; three-dimensional imaging.

Figure 1.

(a) Snapshots of positions (dots) and velocities (arrows) of individual birds in three-dimensional space during a collective turn made by flock M05. Birds are coloured by the turning delay t_i. (b,c) Sample bird trajectories (b) and flight speeds |u| (c) for birds with turning rank r_j = 1, N/2 and N taken from flock M05 (dots are the ends of the trajectories). (d) Relation between τ_ij and τ_ik + τ_kj showing that τ_ij ≈ τ_ik + τ_kj, indicating that the calculation of τ_ij is biologically meaningful. More examples of collective turns are shown in electronic supplementary material, figures S1–S3 and movies S1–S3. (Online version in colour.)

Figure 2.

(a,c,e,g,i) Temporal variations of (a) group turn rate w_g, (c) group flight speed U_g, (e) group turn radius R_g, (g) group radial acceleration a_ng, and (i) group polarization ϕ during collective turns for flocks T06 and T12 (data for other flocks are shown in electronic supplementary material, figures S4 and S5). (b,d,f,h,j,k,l) Effects of the magnitude of the change of travelling direction θ_g on (b) maximum group turn rate $w_g^{max}$, (d) minimum group flight speed $U_g^{min}$, (f) minimum group turn radius $R_g^{min}$, (h) peak group radial acceleration $a_{ng}^{max}$, (j) minimum group polarization ϕ^min, (k) maximum group angular momentum m^max, and (l) the time for flocks to complete turns t_g. Here, t_m is defined as the time when w_g reaches $w_g^{max}$. (Online version in colour.)

Figure 3.

(a–c) Snapshots of positions (dots) and velocities (arrows) of individual birds projected onto a horizontal plane at t = t_s (the time when a turn starts). Triangles are birds with r_i < 0.2N and squares are birds with r_i > 0.8N. Data for other flocks are shown in electronic supplementary material, figures S6 and S7. (d) Distributions of θ_s and V_top for 13 transit and eight mobbing flocks. (e,f) Probability density functions of (e) θ_s and (f) V_top. θ_s = 0 means that information propagates from front to back, θ_s = 90° means that it propagates from side to side and θ_s = 180° means that it propagates from back to front. Larger V_top means that the first birds that start to turn are further apart. (Online version in colour.)

Figure 4.

(a) Snapshots of positions (dots) and velocities (arrows) of individual birds projected onto a horizontal plane for flock M05 at t = t_s (data for other flocks are shown in electronic supplementary material, figure S9). Birds are coloured by t_i. (b) Information propagation distance d_i as a function of t_i for flock M05 (data for other flocks are shown in electronic supplementary material, figure S10). The information propagation speed c_s is obtained by fitting the linear region of the curve. (c,d) Relation between (c) N and c_s and (d) time-averaged group polarization〈ϕ〉_t and c_s for the eight mobbing flocks. Errors in c_s are due to the uncertainty when fitting d_i(t_i). (Online version in colour.)