• DOI:10.1073/pnas.0711437105
• Corpus ID: 2048695

Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study

@article{Ballerini2008InteractionRA,
  title={Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study},
  author={Michele Ballerini and Nicola Cabibbo and Rapha{\"e}l Candelier and Andrea Cavagna and Evaristo Cisbani and Irene Giardina and Vivien Lecomte and Alberto Orlandi and Giorgio Parisi and Andrea Procaccini and Massimiliano Viale and Vladimir Zdravkovic},
  journal={Proceedings of the National Academy of Sciences},
  year={2008},
  volume={105},
  pages={1232 - 1237}
}

• M. Ballerini, N. Cabibbo, +9 authors V. Zdravkovic
• Published 12 September 2007
• Biology
• Proceedings of the National Academy of Sciences

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.