The Role of Projection in the Control of Bird Flocks
  Swarming is a conspicuous behavioural 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 between 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-ranged information necessary to control their density remains unknown. We show that large flocks self-organize to the maximum density at which a typical individual is still just able to see out of the flock in many directions. Such flocks are marginally opaque - an external observer can also just still see a substantial fraction of sky through the flock. Although seemingly intuitive we show that this need not be the case; flocks could easily be highly diffuse or entirely opaque. The emergence of marginal opacity strongly constrains how individuals interact with each other 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 behavioural perspective it optimizes the information available to each bird while maintaining the protection of a dense, coherent flock. 
Daniel J. G. Pearce and A. M. Miller and George Rowlands and Matthew   S. Turner
q-bio.QM cond-mat.stat-mech nlin.AO