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Numerical models indicate that collective animal behaviour may emerge fromsimple local rules of interaction among the individuals. However, very littleis known about the nature of such interaction, so that models and theoriesmostly rely on aprioristic assumptions. By reconstructing the three-dimensionalposition of individual birds in airborne flocks of few thousands members, weprove that the interaction does not depend on the metric distance, as mostcurrent models and theories assume, but rather on the topological distance. Infact, we discover that each bird interacts on average with a fixed number ofneighbours (six-seven), rather than with all neighbours within a fixed metricdistance. We argue that a topological interaction is indispensable to maintainflock's cohesion against the large density changes caused by externalperturbations, typically predation. We support this hypothesis by numericalsimulations, showing that a topological interaction grants significantly highercohesion of the aggregation compared to a standard metric one.

Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study