Numerical models indicate that collective animal behavior may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional positions of individual birds in airborne flocks of a few thousand members, we show that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discovered that each bird interacts on average with a fixed number of neighbors (six to seven), rather than with all neighbors within a fixed metric distance. We argue that a topological interaction is indispensable to maintain a flock's cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared with a standard metric one.animal groups ͉ behavioral rules ͉ flocking ͉ self-organization C ollective behavior of large aggregations of animals is a truly fascinating natural phenomenon (1). Particularly interesting is the case when aggregations self-organize into complex patterns with no need of an external stimulus (2). Prominent examples of such behavior are bird flocks (3), fish schools (4) and mammal herds (5). Apart from its obvious relevance in ethology and evolutionary biology, collective behavior is a key concept in many other fields of science, including control theory (6), economics (7), and social sciences (8).How does collective behavior emerge? Numerical models of self-organized motion, inspired both by biology (9-15) and physics (16)(17)(18)(19)(20), support the idea that simple rules of interaction among the individuals are sufficient to produce collective behavior. Unfortunately, we have very scarce empirical information about the precise nature of such rules. The main theoretical assumptions (attraction among the individuals, short range repulsion, and alignment of the velocities) are reasonable, but generic, and there are as many different models as different ways to implement these assumptions. Without decisive experimental feedback it is difficult to select what is the ''right'' model and, therefore, to understand what are the underlying fundamental rules of animal collective behavior.The main goal of the interaction among individuals is to maintain cohesion of the group. This cohesion is a very strong biological requirement, shaped by the evolutionary pressure for survival: Stragglers and small groups are significantly more prone to predation than animals belonging to large and highly cohesive aggregations (4). Consider a flock of starlings under attack by a peregrine falcon: The flock contracts, expands, and even splits, continuously changing its density and structure. Yet, no bird remains isolated, and soon the flock reforms as whole. The question we want to answer i...

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The formation of waves is a vivid example of collective behaviour occurring in insects, birds, fish and mammals, which has been interpreted as an antipredator response. In birds a quantitative characterization of this phenomenon, involving thousands of individuals, is missing and its link with predation remains elusive. We studied waves in flocks of starlings, a highly gregarious species, by both direct observation and quantitative computer vision analysis of HD video recordings, under predation by peregrine falcons, Falco peregrinus. We found that waves originated from the position of the attacking predator and always propagated away from it. We measured their frequency and velocities, the latter often being larger than the velocity of the flock. A high positive correlation was found between the formation of waves and reduced predation success. We suggest that the tendency of a prey to escape, when initiated even by a few individuals in a cohesive group, elicits self-organized density waves. Such evident fluctuations in the local structure of the flocks are efficient in confusing predators. (C) 2011 The Association for the Study of Animal Behaviour. Published by Elsevier Ltd. All rights reserved

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