Behavioural plasticity and the transition to order in jackdaw flocks

Abstract

Collective behaviour is typically thought to arise from individuals following fixed interaction rules. The possibility that interaction rules may change under different circumstances has thus only rarely been investigated. Here we show that local interactions in flocks of wild jackdaws (Corvus monedula) vary drastically in different contexts, leading to distinct group-level properties. Jackdaws interact with a fixed number of neighbours (topological interactions) when traveling to roosts, but coordinate with neighbours based on spatial distance (metric interactions) during collective anti-predator mobbing events. Consequently, mobbing flocks exhibit a dramatic transition from disordered aggregations to ordered motion as group density increases, unlike transit flocks where order is independent of density. The relationship between group density and group order during this transition agrees well with a generic self-propelled particle model. Our results demonstrate plasticity in local interaction rules and have implications for both natural and artificial collective systems.

Fig. 1

Metric interactions in transit flocks and topological interactions in mobbing flocks. a Jackdaw trajectories in a sample transit flock. b Jackdaw trajectories in a sample mobbing flock. c Alignment angle between a focal bird and its neighbours. d, e Anisotropy factor γ for the distributions of neighbours relative to a focal bird for d mobbing and e transit flocks. r is the distance between the focal bird and its neighbour, and n is the topological rank. In a, b coloured lines show the jackdaws’ three-dimensional (3D) trajectories, and the black dots show their positions in flocks at the final time step. The grey planes are arbitrary horizontal planes (that is, perpendicular to the direction of gravity). Data in c, d are calculated from 10 mobbing flocks and 6 transit flocks. Standard errors are smaller than the symbol size

Fig. 2

Three representative mobbing flocks showing increasing group order with group density. a Flock at low density (ρ = 0.002 m⁻³). b Flock at moderate density (ρ = 0.008 m⁻³). c Flock at high density (ρ = 0.014 m⁻³). d Instantaneous group order ϕ_t for the flocks shown in (a–c). For a, c the meanings of the coloured lines, black dots, and grey planes are same as those shown Fig. 1

Fig. 3

Relationship between group density and group order. For the mobbing flocks, results are calculated by averaging the results from 154 groups of jackdaws over a total of 36,960 time frames. Error bars represent standard errors. Distributions of group density ρ and group order ϕ for the 154 groups can be found in Supplementary Fig. 6. For the transit flocks, results are calculated by averaging 30,498 samples, where each sample represents a local subgroup of one focal bird and four nearest neighbours embedded in a larger flock. Data for subgroups with sizes of 10 and 20 for transit flocks are shown in Supplementary Fig. 6

Fig. 4

Self-propelled particle model captures the phase transition in mobbing jackdaw flocks. a A sample modelling result at low density. b A sample modelling result at high density. c Time variation of the instantaneous group order ϕ_t for the cases shown in (a, b). d Group order ϕ as a function of group size N at three different noise levels. e ϕ as a function of N−N_c. f N_c as a function of noise. Here, N_c denotes the critical group size for the ordering transition. For a, b the meanings of the coloured lines, black dots, and grey planes are the same as those shown Fig. 1