The seventh starling

Last November, a series of Contrarian posts depicted the mesmerizing spectacle of starling murmuration: the undulating patterns made by starling flocks in flight (here, here, and here). Beyond their intrinsic beauty, these scenes provoke a sense of wonder: how do they do it? How do the hundreds of individuals who make up a flock of birds (or a school of sardines, or a swarm of midges) know how to execute their particular roles in the collective ballet.

The standard explanation, recounted by a pair of Italian physicists who have studied the question [PDF], runs like this:

[T]his collective behaviour stems from some simple rules of interaction between the individuals: stay close to your neighbours (but not too close!) and align your velocity to theirs. There is neither a central coordination (a leader), nor any “collective intelligence,” but a distributed behaviour from which coordination emerges. This is the essence of self-organisation.

Unfortunately, as Andrea Cavagna and Irene Giardina acknowledge, these purported rules of interaction boil down to, “just an educated guess as opposed to a well-established scientific fact. Moreover, they are generic and vague.” While computer models based on these rules produce, “swirling dots on our computer screen that look roughly like a flock of birds,” this is “hardly satisfactory science.”

Cavagna and Giardina led an EU-funded research project called STARFLAG (Starlings in Flight) that used stereoscopic cameras to produce 3D images of a real starling flock in motion. This gave them empirical data they could use to see how the birds actually interact in flight.

The clearest structural feature is that a bird’s nearest neighbours are typically found at the bird’s sides, rather than ahead or behind the bird, so that the probability that a bird’s nearest neighbour is approximately ahead or behind is very low. The reason for this is either the anisotropic visual apparatus of starlings—with eyes on the side of their heads they see better sideways than fore-and-aft—or a sort of “motorway effect,” by which birds keep a safe frontal distance to avoid collisions.

This “anisotropic” quality — think of it as side-by-sidedness — declines with distance. A bird’s closest neighbor is directly to its side, the second nearest slightly less so, the third nearest even less so.

The results of this measurement were surprising. All existing models and theories of collective animal behaviour have assumed that each animal interacted with all neighbours within a fixed distance. The STARFLAG data showed something quite different: each bird interacts with a fixed number of neighbours, irrespective of their physical distance. This number is approximately equal to seven. The difference with the assumptions of the models is stark: the data show clearly that the distance within which birds interact is not fixed at all, but rather it depends on the density of the flock. In a packed flock, the seven neighbours you are interacting with are close to you, whereas in a loose, sparse flock they are more distant.

Starlings, and perhaps other schooling, swarming, and flocking critters, perform their complicated pirouettes by adjusting their speed, and staying close but not too close, to their seven nearest neighbors. The critical point, Cavagna and Giardina found, is that the birds interact with a fixed number of nearest neighbors—not, as had been previously supposed, with all neighbors within a fixed distance. This turns out to give them the evolutionary advantage of greater protection from marauding hawks.

By interacting within a fixed number of individuals, rather than meters, the aggregation can be either dense or sparse, change shape, fluctuate and even split, yet maintaining the same degree of cohesion. Thus, the topological interaction is functional to keeping the cohesion in the face of the strong perturbations a flock is subject to, typically predation.

HT: The two Daves