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

TLDR

Numerical models suggest that collective animal behavior can arise from simple local interaction rules, yet little is known about the nature of these interactions, leaving most theories reliant on a priori assumptions. The study demonstrates that bird interactions depend on topological rather than metric distance by reconstructing 3D positions of thousands of individuals in airborne flocks. The authors reconstructed 3D positions of thousands of birds and performed numerical simulations to test interaction rules. Each bird interacts with a fixed six‑to‑seven neighbors, and topological interactions provide higher cohesion against density changes and perturbations, as confirmed by simulations.

Abstract

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.