Scientists use Brownian Motion to Explore How Birds Flock Together

January 23, 2009 By Lisa Zyga, feature

Inspired by recent research on locust swarms, scientists have used Brownian motion to model how individuals form swarms through escape and pursuit interactions. Image credit: Quarkfolio.
( -- How do thousands of fish swim together in giant schools, seemingly moving as a single body? Flocks of birds, herds of beasts, and a variety of other animals in nature seem to share this same “property” of coming together and moving in unison.

The phenomenon, called collective motion, is common in nature, exhibited by groups that fly, run, and swim, such as swarms of insects and colonies of bacteria. In collective motion, groups move together to form patterns as an organized (but not necessarily cooperative) single body. Scientists aren’t sure exactly what mechanisms cause the emergence of collective motion. However, the natural phenomenon has attracted the interest of researchers in diverse fields such as physics and computer science.

In a recent study, researchers have modeled collective motion using Brownian particles, and they observed as individual particles interact via escape and pursuit movements. Motivated by a previous study that observed cannibalistic interactions in locust and cricket swarms, the scientists found that both escape and pursuit movements can cause collective motion, but escape movements dominated the particular case of insect swarming. Pawel Romanczuk and Lutz Schimansky-Geier of Humboldt University Berlin, and Iain D. Couzin of Princeton University, have published their study in a recent issue of Physical Review Letters.

“Our work can be considered as a link between the simplest models of collective motion with a general (not further specified) velocity alignment interaction and more complicated models from biology based on behavioral rules,” Romanczuk told “By assuming that the escape and pursuit are the actual behavioral responses of individuals underlying collective motion in nature, it is possible to determine which one of these responses dominates the individual behavior by simply looking at the global migration patterns.”

In their study, the researchers modeled an individual as a Brownian particle that possesses internal energy so that it can move at various speeds in reaction to external stimuli. In Brownian motion, a solitary individual explores its environment by a continuous random walk. If approached from behind by another individual, the individual in question escapes by increasing its velocity in the forward direction to prevent getting attacked from behind. If the individual senses another individual in front moving away, it pursues that individual, increasing its velocity toward the escapee. In short, an individual has two movements: escape and pursuit.

The scientists found that, at sufficiently high particle densities, the escape and pursuit interactions can both lead to global collective motion. Interestingly, each interaction by itself has a different effect on the particle distribution. In general, escape interactions homogenize and spread out the particle distribution, while pursuit interactions facilitate the formation of clusters. Overall, the combined escape and pursuit interactions seem to consist of a competition between two opposing effects, in which the outcome is determined by the relative interaction strengths.

The researchers suggest that the Brownian model can help explain the mechanisms behind a wide range of swarming phenomena in nature, from marching insects to schools of fish. Different kinds of swarm formations are likely dominated by either escape or pursuit interactions, depending on how aggressive or non-aggressive the individuals are, respectively. For instance, marching insect formations seem to be dominated by escape behavior, while fish school formations seem to be dominated by pursuit interactions.

“The understanding of collective motion has a clear application in evolutionary biology,” Romanczuk said. “As all animal behavior was subject to evolution, a behavior leading to formation of swarms might have given the corresponding individuals an evolutionary advantage: protection from predators, increased foraging success or, as in our case, prevention from being cannibalized by others. The understanding and the study of collective motion might help to identify the involved evolutionary pressures. Furthermore, the understanding of the onset of collective motion in locust swarms may help us to understand the formation of locusts plagues which affect millions of people and in the last consequence help to predict, or even to control, these events.”

Romanczuk added that understanding collective motion could have applications beyond biology. “The understanding of collective motion is of particular interest to engineers and computer scientists working on the design of autonomous robots. The idea is that simple communicating agents may perform complex tasks as a group without the permanent control of a human for each individual, and which are also robust against the failure of individual agents within the group. Examples of such applications are coordinated automated investigation of environments, which are dangerous and/or difficult to access.

“Finally, mathematical models describing collective motion of animals find applications in computer science and in the production of realistic computer animations of large animal swarms or even human crowds, which are also used in movie productions.”

More information: Romanczuk, Pawel; Couzin, Iain D.; and Schimansky-Geier, Lutz. “Collective Motion due to Individual Escape and Pursuit Response.” Physical Review Letters 102, 010602 (2009).

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5 / 5 (1) Jan 23, 2009
This is genius. We need to draw more lines to the macro structures of nature to understand the true implications of quantum mechanics. Well, I don't, You left brainers do.
Jan 23, 2009
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1 / 5 (1) Jan 23, 2009
This behavior of every density blob is caused by limited speed of energy spreading through such blob. Therefore the repulsive forces are always a tiny bit more stronger, then the attractive ones (this is the reason of CP symmetry violation). Which keeps the particles of space-time at distance - at least temporarily.
4 / 5 (2) Jan 23, 2009
surely there is a misconception in this comparison as fish and birds have an aversion to coliding into each other whereas the paricle collisions known as brownian motion have no such problem and readily colide with each other, which is just as well as it is these collisions which provide heat/energy transmission.
not rated yet Jan 23, 2009
Quantum leads to chaos and chaos leads to deterministic order. Within the flocking mechanism, I would bet there is underlying order with a strange attractor at work in enabling the flock to hold together and move in 3 space. Terrific article. I learned a lot from it.
not rated yet Jan 24, 2009
There has been some other research - sorry cannot recall the source - which suggests that behaviour of flocking birds has the objective of achieving minimum levels of turbulence.
not rated yet Jan 25, 2009
surely there is a misconception in this comparison as fish and birds have an aversion to coliding into each other whereas the paricle collisions known as brownian motion have no such problem and readily colide with each other, which is just as well as it is these collisions which provide heat/energy transmission.

Im not so sure about that. Do two particles ever really collide? Verily, does a speeding motorcycle actually touch the telephone pole, or is it prevented from traveling any further by the strong force?
not rated yet Jan 27, 2009
Awesome! I so love swarms. They are the perfect example of how individuals can form a swarm without an intention or even desire. It's simply a collective phenomena. And collectivism in nature usually means one-cool new properties to explore, use and abuse :)
not rated yet Jan 29, 2009
You mean it might explain how Dubya got "elected" !!
not rated yet Jan 30, 2009
I think the link behind will be helpful to the discussion.
And I think sometimes mathematical explanations are not sufficient for explain the processes in the nature, we sometimes need to look more in the detail. We must also remember the 4 levels of response to a question in biology, maybe this matehmatical approach is one of the possible answers, but not enough.

Serotonin Mediates Behavioral Gregarization Underlying Swarm Formation in Desert Locusts
M. L. Anstey et al.
Serotonin induces the phenotypic switch from solitary to gregarious behavior in desert locusts.
not rated yet Jun 02, 2009
There has been one independent work done in this field by Mr. Craig W. Reynolds "Flocks, herds and schools:a distributed behavioural model" published in Computer Graphics, 21(4), July 1987, pp. 25-34.
(ACM SIGGRAPH '87 Conference Proceedings, Anaheim, California, July 1987.) The boid model he has proposed for flocking seems to capture the details of the intrinsic motion of particles with orientation. I would like to know the differences in his approach and the current work done here and does the current work supersedes the previous work?

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