Causes of variation of darkness in flocks of starlings, a computational model

The coordinated motion of large flocks of starlings is fascinating for both laymen and scientists. During their aerial displays, the darkness of flocks often changes, for instance dark bands propagate through the flock (so-called agitation waves) and small or large parts of the flock darken. The causes of dark bands in agitation waves have recently been shown to depend on changes in orientation of birds relative to the observer rather than changes in density of the flock, but what causes other changes in darkness need to be studied still and this is the aim of the present investigation. Because we cannot empirically relate changes in darkness in flocks to quantities, such as position and orientation of the flock and of its members relative to the observer, we study this in a computational model. We use StarDisplay, a model of collective motion of starlings, because its flocks resemble empirical data in many properties, such as their three-dimensional shape, their manner of turning, the correlation of heading of its group-members, and its internal structure regarding density and stability of neighbors. We show that the change in darkness in the flocks perceived by an observer on the ground mostly depends on the observer’s distance to the flock and on the degree of exposure of the wing surface of flock members to the observer, and that darkness appears to decrease when birds roll during sharp turns. Remarkably, the darkness of the flock perceived by the observer was neither affected by the orientation of the flock relative to the observer nor by the density of the flock. Further studies are needed to investigate changes in darkness for flocks under predation

What underlies waves of agitation in starling flocks

Fast transfer of information in groups can have survival value. An example is the so-called wave of agitation observed in groups of animals of several taxa under attack. It has been shown to reduce predator success. It usually involves the repetition of a manoeuvre throughout the group, transmitting the information of the attack quickly, faster than the group moves itself. The specific manoeuvre underlying a wave is typically known, but not so in starlings (Sturnus vulgaris). Although waves of agitation in starling flocks have been suggested to reflect density waves, exact escape manoeuvres cannot be distinguished because flocks are spatially too far away. Therefore, waves may also reflect orientation waves (due to escape by rolling). In the present study, we investigate this issue in a computational model, StarDisplay. We use this model because its flocks have been shown to resemble starling flocks in many traits. In the model, we show that agitation waves result from changes in orientation rather than in density. They resemble empirical data both qualitatively in visual appearance and quantitatively in wave speed. In the model, local interactions with only two to seven closest neighbours suffice to generate empirical wave speed. Wave speed increases with the number of neighbours mimicked or repeated from and the distance to them. It decreases with reaction time and with time to identify the escape manoeuvre of others and is not affected by flock size. Our findings can be used as predictions for empirical studies

Damping of waves of agitation in starling flocks

When a predator attacks a flock of starlings (Sturnus vulgaris), involving thousands of individuals, a typical collective escape response is the so-called agitation wave, consisting of one or more dark bands (pulses) propagating through the flock and moving away from the predator (usually a Peregrine falcon, Falco peregrinus). The mechanism underlying this collective behavior remains debated. A theoretical study has suggested that the individual motion underlying a pulse could be a skitter (in the form of a zigzag), that is copied by nearby neighbors, and causes us to temporarily observe a larger surface of the wing because the bird is banking during turning while zigzagging. It is not known, however, whether pulses during a wave event weaken over time. This is of interest, because whereas during the usual turning by an undisturbed flock the motion is copied completely without weakening, we may expect that pulses dampen during a wave event because individuals that are further away from a predator react less because of reduced fear. In the present paper, we show in empirical data that pulses during a wave event weaken over time. Our computational model, StarDisplay, reveals that this is most likely a consequence of a reduction of the maximum banking angle during the zigzag escape maneuver rather than by a reduced tendency to copy this maneuver with time. The response seems adaptive because of lowered danger at a larger distance to the location of attack

Scale-free correlations, influential neighbours and speed control in flocks of birds

Coordination of birds in large flocks is amazing, especially, since individual birds only interact with a few neighbors (the so-called 'influential neighbours'). Yet, empirical data show that fluctuations of velocity and speed of different birds are correlated beyond the influential neighbours and are correlated over a larger distance in a larger flock. This correlation between the correlation length of velocity or speed and flock size was found to be linear, called a scale-free correlation. It depends on the way individuals interact in the flock, for instance, on the number of influential neighbours and speed control. It is unknown however, how exactly the number of influential neighbours affects this scale-free correlation. Recent empirical data show that different degrees of control of speed affect the scale-free correlation for speed fluctuations. Theoretically, based on statistical mechanics, it is predicted that at very high speed control, the correlation is no longer scale-free but saturates at a certain correlation length and this hampers coordination in flocks. We study these issues in a model, called StarDisplay, because its behavioural rules are biologically inspired and many of its flocking patterns resemble empirical data. Our results show that the correlation length of fluctuations of velocity as well as speed correlate with flock size in a scale-free manner. A higher number of influential neighbours causes a diminishing increase of the slope of the scale-free correlation with velocity, resulting thus in flocks that coordinate more uniformly. Similar to recent empirical data higher speed control reduces the correlation length of speed fluctuations in our model. As predicted theoretically, at very high speed control the model generates a non-scale free correlation, and although there are still flocks, they are in the process of disintegrating

Self-organization of collective escape in pigeon flocks

Bird flocks under predation demonstrate complex patterns of collective escape. These patterns may emerge by self-organization from local interactions among group-members. Computational models have been shown to be valuable for identifying what behavioral rules may govern such interactions among individuals during collective motion. However, our knowledge of such rules for collective escape is limited by the lack of quantitative data on bird flocks under predation in the field. In the present study, we analyze the first GPS trajectories of pigeons in airborne flocks attacked by a robotic falcon in order to build a species-specific model of collective escape. We use our model to examine a recently identified distance-dependent pattern of collective behavior: the closer the prey is to the predator, the higher the frequency with which flock members turn away from it. We first extract from the empirical data of pigeon flocks the characteristics of their shape and internal structure (bearing angle and distance to nearest neighbors). Combining these with information on their coordination from the literature, we build an agent-based model adjusted to pigeons’ collective escape. We show that the pattern of turning away from the predator with increased frequency when the predator is closer arises without prey prioritizing escape when the predator is near. Instead, it emerges through self-organization from a behavioral rule to avoid the predator independently of their distance to it. During this self-organization process, we show how flock members increase their consensus over which direction to escape and turn collectively as the predator gets closer. Our results suggest that coordination among flock members, combined with simple escape rules, reduces the cognitive costs of tracking the predator while flocking. Such escape rules that are independent of the distance to the predator can now be investigated in other species. Our study showcases the important role of computational models in the interpretation of empirical findings of collective behavior

Emergence of splits and collective turns in pigeon flocks under predation

Complex patterns of collective behaviour may emerge through self-organization, from local interactions among individuals in a group. To understand what behavioural rules underlie these patterns, computational models are often necessary. These rules have not yet been systematically studied for bird flocks under predation. Here, we study airborne flocks of homing pigeons attacked by a robotic falcon, combining empirical data with a species-specific computational model of collective escape. By analysing GPS trajectories of flocking individuals, we identify two new patterns of collective escape: early splits and collective turns, occurring even at large distances from the predator. To examine their formation, we extend an agent-based model of pigeons with a ‘discrete’ escape manoeuvre by a single initiator, namely a sudden turn interrupting the continuous coordinated motion of the group. Both splits and collective turns emerge from this rule. Their relative frequency depends on the angular velocity and position of the initiator in the flock: sharp turns by individuals at the periphery lead to more splits than collective turns. We confirm this association in the empirical data. Our study highlights the importance of discrete and uncoordinated manoeuvres in the collective escape of bird flocks and advocates the systematic study of their patterns across species

Diffusion during collective turns in bird flocks under predation

Moving in groups offers animals protection against predation. When under attack, grouped individuals often turn collectively to evade a predator, which sometimes makes them rapidly change their relative positions in the group. In bird flocks in particular, the quick reshuffling of flock members confuses the predator, challenging its targeting of a single individual. This confusion is considered to be greater when the internal structure of the group changes faster (i.e. the ‘diffusion’ of the group is higher). Diffusion may increase when individual birds turn collectively with equal radii (same angular velocity) but not when individuals keep their paths parallel (by adjusting their speed). However, how diffusion depends on individual behaviour is not well known. When under attack, grouping individuals change the way they interact with each other, referred to as ‘alarmed coordination’ (e.g., increase their reaction frequency or their cohesion tendency), but the effect of such changes on collective turning is unknown. Here, we aimed to gain an understanding of the dynamics of collective turning in bird flocks. First, to investigate the relation between alarmed coordination and flock diffusion, we developed an agent-based model of bird flocks. Second, to test how diffusion relates to collective turns with equal-radii and parallel-paths, we developed a metric of the deviation from these two types. Third, we studied collective turning under predation empirically, by analysing the GPS trajectories of pigeons in small flocks pursued by a RobotFalcon. As a measure of diffusion, we used the instability of neighbours: the rate with which the closest neighbours of a flock member are changing. In our simulations, we showed that this instability increases with group size, reaction frequency, topological range, and cohesion tendency and that the relation between instability of neighbours and the deviation from the two turning types depends in often counter-intuitive ways on these coordination specifics. Empirically, we showed that pigeons turn collectively with less diffusion than starlings and that their collective turns are in between those with equal-radii and parallel-paths. Overall, our work provides a framework for studying collective turning across species