From bird flocks to fish schools, animal groups often seem to react to environmental perturbations as if of one mind. Most studies in collective animal behavior have aimed to understand how a globally ordered state may emerge from simple behavioral rules. Less effort has been devoted to understanding the origin of collective response, namely the way the group as a whole reacts to its environment. Yet, in the presence of strong predatory pressure on the group, collective response may yield a significant adaptive advantage. Here we suggest that collective response in animal groups may be achieved through scale-free behavioral correlations. By reconstructing the 3D position and velocity of individual birds in large flocks of starlings, we measured to what extent the velocity fluctuations of different birds are correlated to each other. We found that the range of such spatial correlation does not have a constant value, but it scales with the linear size of the flock. This result indicates that behavioral correlations are scale free: The change in the behavioral state of one animal affects and is affected by that of all other animals in the group, no matter how large the group is. Scale-free correlations provide each animal with an effective perception range much larger than the direct interindividual interaction range, thus enhancing global response to perturbations. Our results suggest that flocks behave as critical systems, poised to respond maximally to environmental perturbations. O f all distinctive traits of collective animal behavior the most conspicuous is the emergence of global order, namely the fact that all individuals within the group synchronize to some extent their behavioral state (1-3). In many cases global ordering amounts to an alignment of the individual directions of motion, as in bird flocks, fish schools, mammal herds, and in some insect swarms (4-6). Yet, global ordering can affect also other behavioral states, as it happens with the synchronous flashing of tropical fireflies (7) or the synchronous clapping in human crowds (8).The presence of order within an animal group is easy to detect. However, order may have radically different origins, and discovering what is the underlying coordination mechanism is not straightforward. Order can be the effect of a top-down centralized control mechanism (for example, due to the presence of one or more leaders), or it can be a bottom-up self-organized feature emerging from local behavioral rules (9). In reality, the lines are often blurred and hierarchical and distributed control may combine together (10). However, even in the two extreme cases, discriminating between the two types of global ordering is not trivial. In fact, the prominent difference between the centralized and the self-organized paradigm is not order, but response.Collective response is the way a group as a whole reacts to its environment. It is often crucial for a group, or for subsets of it, to respond coherently to perturbations. For gregarious animals under strong predatory pressure,...

Animal groups represent magni¯cent archetypes of self-organized collective behavior. As such, they have attracted enormous interdisciplinary interest in the last years. From a mechanistic point of view, animal aggregations remind physical systems of particles or spins, where the individual constituents interact locally, giving rise to ordering at the global scale. This analogy has fostered important research, where numerical and theoretical approaches from physics have been applied to models of self-organized motion. In this paper, we discuss how the physics methodology may provide precious conceptual and technical instruments in empirical studies of collective animal behavior. We focus on three-dimensional groups, for which empirical data have been extremely scarce until recently, and describe novel experimental protocols that allow reconstructing aggregations of thousands of individuals. We show how an appropriate statistical analysis of these large-scale data allows inferring important information on the interactions between individuals in a group, a key issue in behavioral studies and a basic ingredient of theoretical models. To this aim, we revisit the approach we recently used on starling°ocks, and apply it to a much larger data set, never analyzed before. The results con¯rm our previous¯ndings and indicate that interactions between birds have a topological rather than metric nature, each individual interacting with a¯xed number of neighbors irrespective of their distances.

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