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Flights of Fancy

How birds (and bird-watchers) compute the behavior of a flock on the wing

Brian Hayes

Flattened Flocks

2011-01HayesFC.jpgClick to Enlarge ImageThe findings of the STARFLAG program support the existing theoretical framework—the basic idea that flocks are held together by local interactions—but the results have also brought some surprises. For example, it turns out that the overall shape of starling flocks is not what it appears to be. To a casual observer, most flocks look globular; they appear to be deformed but fully rounded spheres or cylinders. But the 3D reconstructions show that the typical flock is quasi-two-dimensional: It is extended along two dimensions but squashed to a fairly thin layer along the third dimension. The average aspect ratio of length to width to thickness is 6:3:1. In general, the shortest axis is vertical, so that the flock is spread out in a thin horizontal sheet.

Cavagna and his colleagues suggest a physical or physiological reason for this flight formation: Vertical movements have a higher energy cost than lateral ones, and so birds favor flight at constant altitude. What’s harder to explain is why most observers of flocks have a very different impression of their shapes and motions. The suggested explanation is a perceptual effect: Looking up at a steep angle makes it hard to distinguish between vertical motion of the flock and a component of horizontal motion directed toward or away from the observer.

Another curious finding is that starling flocks have a dense outer rind and a mushy interior. The density of birds is greatest at the boundary of the flock, and it declines steadily toward the core. This is the opposite of the distribution that evolves when free-moving objects are bound together by a long-range force such as gravity; globular clusters of stars, for example, are densest in the middle and sparse at the edges. The Rome investigators discuss some ideas about why the inside-out density gradient might be useful as a defense against predators, but they do not propose a mechanism for generating the gradient. What modification of the Reynolds boid rules would account for this observation?

The Rome group does introduce another, more fundamental revision of the Reynolds model. In the original simulation, a bird’s neighborhood is defined geometrically: The bird keeps track of all other birds within a certain radius of its own position. Cavagna and his colleagues propose a “topological” alternative: A bird interacts with a fixed number of nearest neighbors, regardless of their geometric distance. The number of birds comprising the neighborhood is probably six or seven.

What led to this proposal was the discovery that flocks differ substantially in overall density—by a factor of two or more. If interactions were limited to a fixed radius, then birds in dense flocks would effectively have more neighbors than those in looser groupings. But the observed behavior of the flocks is identical across the range of densities.

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