Role of projection in the control of bird flocks

Significance We propose a new model for long-range information exchange in bird flocks based on the projected view of each individual out through the flock. Visual input is coarse grained to a pattern of (dark) bird against (light) sky. We propose the simplest hybrid projection model that combines metric-free coalignment, and noise, with this projected view; here the birds fly toward the resolved vector sum of all the domain boundaries. This model leads to robustly coherent flocks that self-assemble to a state of marginal opacity. It therefore provides a mechanism for the control of density. Although it involves only two primary control parameters, it also gives rise to several distinct phenotypes. We compare our predictions with experimental data. Swarming is a conspicuous behavioral trait observed in bird flocks, fish shoals, insect swarms, and mammal herds. It is thought to improve collective awareness and offer protection from predators. Many current models involve the hypothesis that information coordinating motion is exchanged among neighbors. We argue that such local interactions alone are insufficient to explain the organization of large flocks of birds and that the mechanism for the exchange of long-range information necessary to control their density remains unknown. We show that large flocks self-organize to the maximum density at which a typical individual still can see out of the flock in many directions. Such flocks are marginally opaque—an external observer also still can see a substantial fraction of sky through the flock. Although this seems intuitive, we show it need not be the case; flocks might easily be highly diffuse or entirely opaque. The emergence of marginal opacity strongly constrains how individuals interact with one another within large swarms. It also provides a mechanism for global interactions: an individual can respond to the projection of the flock that it sees. This provides for faster information transfer and hence rapid flock dynamics, another advantage over local models. From a behavioral perspective, it optimizes the information available to each bird while maintaining the protection of a dense, coherent flock.