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.

Supplementary Fig. 1 | Flock morphology and evidence of pairing for flocks #2 to #6. a1-a5, Spatial distributions and velocities of birds in three-dimensional space. Paired birds are colored in red. b1-b5, Radial distribution functions G(r). c1-c5, Joint PDFs of D i, n=1 and D i, n=2 . Supplementary Fig. 2 | Pairing causes variations in local interaction for flocks #2 to #6. a1-a5, Change of distance between a bird and its nearest neighbour at time 0. Flock #6 shows a somewhat different trend from the other flocks for unpaired birds, which may be due to the relatively large value of in this flock. b1-b5, Acceleration in the direction away from the nearest neighbour; positive values are repulsive and negative values are attractive. Flock #5 shows a somewhat different trend from the other flocks for paired birds, which may be due to a tendency in this flock for paired birds to be located in front of or in back of each other. c1-c5, Alignment angle between a focal bird and its n th neighbour. Error bars show the standard error and are smaller than the symbols in most figures. Supplementary Fig. 3 | Wingbeat frequency as a function of flight speed during cruising flight for flocks #2 to #6. Paired birds typically have lower wingbeat frequency than unpaired birds at same flight speed. Error bars show the standard error. The magnitudes of |u| represent ground speeds.

Digital holographic microscopy is used for characterizing the profiles of mean velocity, viscous and Reynolds shear stresses, as well as turbulence level in the inner part of turbulent boundary layers over several super-hydrophobic surfaces (SHSs) with varying roughness/texture characteristics. The friction Reynolds numbers vary from 693 to 4496, and the normalized root mean square values of roughness $(k_{rms}^{+})$ vary from 0.43 to 3.28. The wall shear stress is estimated from the sum of the viscous and Reynolds shear stress at the top of roughness elements and the slip velocity is obtained from the mean profile at the same elevation. For flow over SHSs with $k_{rms}^{+}<1$, drag reduction and an upward shift of the mean velocity profile occur, along with a mild increase in turbulence in the inner part of the boundary layer. As the roughness increases above $k_{rms}^{+}\sim 1$, the flow over the SHSs transitions from drag reduction, where the viscous stress dominates, to drag increase where the Reynolds shear stress becomes the primary contributor. For the present maximum value of $k_{rms}^{+}=3.28$, the inner region exhibits the characteristics of a rough wall boundary layer, including elevated wall friction and turbulence as well as a downward shift in the mean velocity profile. Increasing the pressure in the test facility to a level that compresses the air layer on the SHSs and exposes the protruding roughness elements reduces the extent of drag reduction. Aligning the roughness elements in the streamwise direction increases the drag reduction. For SHSs where the roughness effect is not dominant ($k_{rms}^{+}<1$), the present measurements confirm previous theoretical predictions of the relationships between drag reduction and slip velocity, allowing for both spanwise and streamwise slip contributions.

As one of nature's most striking examples of collective behaviour, bird flocks have attracted extensive research. However, we still lack an understanding of the attractive and repulsive forces that govern interactions between individuals within flocks and how these forces influence neighbours' relative positions and ultimately determine the shape of flocks. We address these issues by analysing the three-dimensional movements of wild jackdaws ( Corvus monedula ) in flocks containing 2–338 individuals. We quantify the social interaction forces in large, airborne flocks and find that these forces are highly anisotropic. The long-range attraction in the direction perpendicular to the movement direction is stronger than that along it, and the short-range repulsion is generated mainly by turning rather than changing speed. We explain this phenomenon by considering wingbeat frequency and the change in kinetic and gravitational potential energy during flight, and find that changing the direction of movement is less energetically costly than adjusting speed for birds. Furthermore, our data show that collision avoidance by turning can alter local neighbour distributions and ultimately change the group shape. Our results illustrate the macroscopic consequences of anisotropic interaction forces in bird flocks, and help to draw links between group structure, local interactions and the biophysics of animal locomotion.

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.

Tracking the movements of birds in three dimensions is integral to a wide range of problems in animal ecology, behaviour and cognition. Multicamera stereo-imaging has been used to track the three-dimensional (3D) motion of birds in dense flocks, but precise localization of birds remains a challenge due to imaging resolution in the depth direction and optical occlusion. This paper introduces a portable stereo-imaging system with improved accuracy and a simple stereo-matching algorithm that can resolve optical occlusion. This system allows us to decouple body and wing motion, and thus measure not only velocities and accelerations but also wingbeat frequencies along the 3D trajectories of birds. We demonstrate these new methods by analysing six flocking events consisting of 50 to 360 jackdaws (Corvus monedula) and rooks (Corvus frugilegus) as well as 32 jackdaws and 6 rooks flying in isolated pairs or alone. Our method allows us to (i) measure flight speed and wingbeat frequency in different flying modes; (ii) characterize the U-shaped flight performance curve of birds in the wild, showing that wingbeat frequency reaches its minimum at moderate flight speeds; (iii) examine group effects on individual flight performance, showing that birds have a higher wingbeat frequency when flying in a group than when flying alone and when flying in dense regions than when flying in sparse regions; and (iv) provide a potential avenue for automated discrimination of bird species. We argue that the experimental method developed in this paper opens new opportunities for understanding flight kinematics and collective behaviour in natural environments.

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This paper deals with two issues affecting the application of digital holographic microscopy (DHM) for measuring the spatial distribution of particles in a dense suspension, namely discriminating between real and virtual images and accurate detection of the particle center. Previous methods to separate real and virtual fields have involved applications of multiple phase-shifted holograms, combining reconstructed fields of multiple axially displaced holograms, and analysis of intensity distributions of weakly scattering objects. Here, we introduce a simple approach based on simultaneously recording two in-line holograms, whose planes are separated by a short distance from each other. This distance is chosen to be longer than the elongated trace of the particle. During reconstruction, the real images overlap, whereas the virtual images are displaced by twice the distance between hologram planes. Data analysis is based on correlating the spatial intensity distributions of the two reconstructed fields to measure displacement between traces. This method has been implemented for both synthetic particles and a dense suspension of 2 μm particles. The correlation analysis readily discriminates between real and virtual images of a sample containing more than 1300 particles. Consequently, we can now implement DHM for three-dimensional tracking of particles when the hologram plane is located inside the sample volume. Spatial correlations within the same reconstructed field are also used to improve the detection of the axial location of the particle center, extending previously introduced procedures to suspensions of microscopic particles. For each cross section within a particle trace, we sum the correlations among intensity distributions in all planes located symmetrically on both sides of the section. This cumulative correlation has a sharp peak at the particle center. Using both synthetic and recorded particle fields, we show that the uncertainty in localizing the axial location of the center is reduced to about one particle's diameter.