E19 Collective dynamics

Topic

The collective behavior of a flock of birds emerges from local interactions among the individuals that compose it, without the existence of any central coordinator or global plan directing the flock as a whole.

Starling murmurations are the most spectacular example of this collective behavior: groups of up to a million birds that form and reform—while in flight—patterns of extraordinary mathematical beauty, with no single leader coordinating the collective movement from the center or the front of the flock.

Instead of responding to a leader, each starling in the murmuration follows only simple rules based on the position of its six or seven nearest neighbors, regardless of the actual physical distance separating it from them; what matters to each starling is not the distance in meters separating it from those neighbors, but rather the number of neighbors it has—specifically, the same six or seven closest ones.

The macroscopic result of each starling following these simple rules based on its nearest neighbors is the murmuration itself: a complex system whose properties—such as the shifting shape of the bird cloud or the speed at which a disturbance propagates through it—emerge from the microscopic level of interaction between each starling and its neighbors, without any of those macroscopic properties being programmed into the individual rules of a single starling.

Furthermore, this collective behavior serves two specific ecological functions. The first is defense against predators: a dense flock confuses a predator attempting to intercept a specific individual within it and dilutes the risk faced by each individual bird, because a predator attacking an entire murmuration faces a much more difficult geometric interception problem than it would when targeting an isolated bird. The second ecological function is collective energy optimization: in migratory formations, the lead position rotates among different individuals over time. Consequently, the energy savings gained by a bird following in the correct position are—through this rotation—shared among all members of the flock in turn, rather than benefiting only the few individuals who never take the lead.

The physical laws governing this collective behavior—ranging from simple nearest-neighbor rules to the way a disturbance propagates through the entire flock—are the same laws that govern the collective behavior of fish, insects, or even molecules during a phase transition; thus, understanding starling murmuration and understanding a material's phase transition ultimately involve the same physics of collective behavior.

ID:2345