[from Gary Cziko 2006.11.30 19:10 GMT]
Interesting how positive feedback is used to explain how the
collective motion begins. But no mention of goal-seeking or negative
feedback to account for gettin where you want to go (or avoiding
where you don't want to go).
--Gary
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Science News Online
Week of Nov. 25, 2006; Vol. 170, No. 22
The Mind of the Swarm
Math explains how group behavior is more than the sum of its parts
Erica Klarreich
Few people can fail to marvel at a flock of birds swooping through
the evening sky, homing in with certainty on its chosen resting
place. The natural world abounds with other spectacular examples of
animals moving in concert: a school of fish making a hairpin turn, an
ant colony building giant highways, or locusts marching across the
plains.
[IMAGE] Many animals, such as these anchovies, move in concert. By
combining experiments and computer simulations, researchers are
elucidating the principles that underlie swarming behaviors.
Photodisc
Since ancient times, scientists and philosophers have pondered how
animals coordinate their movements, often in the absence of any
leader. Coordinated groups can range in scale from just a few
individuals to billions, and they can consist of an intelligent
species or one whose members have barely enough brainpower to
recognize each other.
Despite these differences, similar patterns of motion appear again
and again throughout the animal kingdom. This congruence in behavior
has led researchers to speculate for about 70 years that a few simple
rules might underpin many sophisticated group motions. However,
establishing just what these rules are is no easy matter.
"Imagine a space alien looking at rush hour traffic on the L.A.
freeway," says Julia Parrish of the University of Washington in
Seattle, who studies fish schooling. "It thinks the cars are
organisms and wonders how they're moving in a polarized way without
collisions. The reason is that there's a set of rules everyone knows.
"We're the space aliens looking at fish, and we don't have the
driver's manual," she says.
In recent years, mathematicians and biologists have started to get
glimpses of just what may be in that manual. They have constructed
mathematical models of animal swarms and colonies that take
inspiration from decades of physics research. In physicists' studies
of magnetism, for instance, they have elucidated how simple local
interactions give rise to complex, large-scale phenomena. Using a
combination of computer simulations and experiments with real
animals, researchers are explicating how a trio of physics and
engineering principles—nonlinearity, positive feedback, and
phase transitions—may be basic ingredients from which a wide
variety of animal-swarming behaviors takes shape.
"This is a more and more exciting area in which to work," says Iain
Couzin, who studies collective animal behavior at the University of
Oxford in England and Princeton University. "We have the mathematical
foundations to investigate phenomena quickly and effectively."
Positive food back
Anyone who has left crumbs on the kitchen counter knows the brutal
efficiency with which ants can capitalize on such a mistake. As soon
as one ant discovers a tempting morsel, thousands more create and
follow a trail between the food source and their nest.
[IMAGE] ON THE TRAIL. Ants' foraging behavior may obey simple
mathematical rules.
iStockphoto
"Ants follow only local rules... but the resulting trail structure is
built on a scale well beyond that of a single ant," said David
Sumpter of the University of Oxford in England in an article on
animal groups in the January Philosophical Transactions of the Royal
Society B.
In 2001, using mathematical modeling and lab experiments, Sumpter and
two colleagues studied how foraging pharaoh's ants build trails. The
researchers turned up a striking group behavior: Just as water
abruptly turns to ice at the freezing point, foraging behavior
undergoes a "phase transition" at a certain critical colony size.
If an ant colony is small, foragers wander about randomly and, even
if some of the ants discover food, no trail persists. If a colony is
large, the ants' trails build into a superhighway to the food that
they find. Somewhere in between—in the case of the experimental
ants, at a colony size of 700 members—the colony's behavior
switches suddenly.
While this sharp transition might seem unexpected, the researchers
weren't altogether surprised to find it because the mathematical
principles underlying their model of foraging behavior make such a
transition likely. When an ant discovers a food source, it deposits
chemicals called pheromones along its trail back to the nest. If
another ant happens to wander across the trail, it detects the
pheromones and tends to follow that trail. Once it discovers the
food, it will deposit pheromones of its own along the trail,
reinforcing it and making future ants that encounter it even more
likely to follow it—exemplifying what engineers call a
positive-feedback loop. However, pheromones gradually evaporate, so
if a trail is little used, it will eventually vanish.
If a colony is small, few ants wander around and they are unlikely to
happen upon a trail before the pheromones evaporate. The colony
collects only as much food as each ant, working independently, can
find.
By contrast, in a large colony, many ants are likely to find a given
trail, and their combined deposits of pheromones have a
multiplicative effect on the colony's behavior. There's a jump in
efficiency that makes a large colony more than the sum of
independently working ants, Sumpter says.
In mathematical terms, the ants' behavior is nonlinear: If a colony,
say, doubles in size, its trails more than double in strength. This
happens because, at any moment, a trail's growth reflects the product
of how many ants have already found the trail and how many ants are
now likely to stumble upon it.
The result of this nonlinear growth is to eliminate the middle
ground. If a trail doesn't evaporate, it will burgeon into a bustling
superhighway.
In each of these extremes, the individual ants are following the same
rules, points out Stephen Pratt, who studies collective animal
behavior at Arizona State University in Tempe. "In the old days, the
focus would have been on what has changed about the animal when it
goes from one state to another," he says. "What's new is to move the
question up a level and ask how changing a single environmental
variable, like density, can cause these dramatic changes in group
behavior."
Positive feedback and nonlinearity, which are ingredients in a wide
range of animal interactions, enable animal groups to generate
behaviors that are more than the sum of their parts, Sumpter says.
Global swarming
Phase transitions, far from being limited to ant colonies, appear to
be a ubiquitous feature of animal groups. In 2002, for instance,
Couzin and his team showed that a few simple rules for fish
interactions yielded phase transitions between swarming behaviors.
[IMAGE] RAPID RESPONSE. Mathematical modeling is explaining how a
school of fish can quickly change shape in reaction to a predator.
Photodisc
Basing their work on a particle-interaction model from physics, the
researchers represented each fish as a single particle. They assumed
three rules about how the particles interact: Each fish tries to
avoid colliding with other fish, stays with the group, and aligns its
swimming direction with that of nearby fish within some defined zone
around itself.
Variations of these rules have been studied for decades, but only
recently has computer power grown to the point where researchers can
simulate the movements of, say, 10,000 fish.
The researchers also assumed that fish can modify their sensitivity
to their neighbors, that is, the size of their alignment zones. The
team found that as the individuals' alignment zones grow, the
school's architecture undergoes two sharp transitions.
When the alignment zone around each fish is negligible in size, so
that the fish barely pay attention to their neighbors' directions,
each fish swims in a random direction within the group. At a certain
critical size of the alignment zone, the fish suddenly start
following each other to produce a doughnut-shaped swarm. As the
alignment zone continues to grow, the fish start swimming in
parallel, as in a migration.
"The model switches very dramatically and quickly between patterns,"
Couzin says.
As fish take into account more and more of their neighbors, the
alignment between them grows nonlinearly, leading to the sharp
transitions that the team observed. While biologists have never, to
Couzin's knowledge, studied a fish school in the act of changing from
one of the three swarming patterns to another, each of the patterns
has been observed frequently in nature.
"When we first saw [the doughnut] pattern in the simulations, I
thought 'That's really weird!'" Couzin recalls. "But then we found in
the literature that it really does appear in nature."
The model shows that simple rules for how fish interact with their
neighbors can give rise to complex, schoolwide patterns. Couzin
reports, "There's nothing in the individual rules that says, 'Go in a
circle,' but it happens spontaneously."
Likewise, the model offers an explanation for how fish schools change
their behaviors on the fly—for instance, if a predator suddenly
appears. "Very subtle adjustments in the rules allow you to create
all these structures without complicated actions on the part of the
individual," Couzin says.
Preliminary experimental evidence suggests that fish can indeed
adjust the sizes of their alignment zones. Parrish and Daniel
Grunbaum, also of the University of Washington, have been filming
fish schools in the lab, then using computerized sensing software to
track each fish's path. "Sometimes, they pay attention to a lot of
neighbors; sometimes, to just one," Parrish says.
However, Parrish and Grunbaum caution, considerably more experimental
data are needed before researchers can say with confidence that the
alignment-zone model captures what fish are doing. At present,
tracking fish is so computationally intensive that Parrish and
Grunbaum can follow only about 16 fish at a time in the lab.
Parrish is optimistic, though, that technological advances will soon
enable researchers both to track fish in their natural habitats and
to quickly crunch the resulting data.
Locusts of control
In the meantime, a team made up of Couzin, Sumpter, and several other
researchers has made progress in explaining one of the most dramatic
of all animal swarms: a locust plague. Locust swarms—which often
appear suddenly and seemingly out of nowhere—can quickly grow to
a billion insects that migrate together, eating every scrap of plant
matter in their path. Even in antiquity, philosophers marveled at the
insects' ability to coordinate their motion: "The locusts have no
King, yet all of them march in rank," the Bible comments.
Couzin, Sumpter, and their colleagues suspected that locusts follow
rules similar to those in the researchers' fish model. In work
published in the June 2 Science, they carried out simulations and lab
experiments to test this hypothesis.
Their simulations suggested that as a locust population grows denser,
its swarming behavior changes from chaos to order. When the
researchers tracked locusts in a small area and gradually increased
the insects' number, the small group's behavior mirrored the model's
predictions. When there were just a few locusts, they wandered
randomly, interacting only occasionally. Once the population reached
10 locusts, the insects formed small bands that changed direction
frequently. At 30 locusts, the insects suddenly started marching as
one.
"I think it's surprising that it worked out that cleanly," Grunbaum
comments. "In the overwhelming majority of biological situations, you
have a nice, plausible theory, but the reality works out differently."
The model illuminates why it's so hard to control locust swarms once
they reach the density at which the insects start to march in unison:
The laws of physics overwhelm human efforts to resist the migration.
Reaching a consensus
As with the pheromone model of ant foraging, the positive feedback
built into the alignment-zone model helps explain how an animal swarm
achieves behavior that is more than the sum of its parts. In the Feb.
3, 2005 Nature, Couzin and a group of coauthors demonstrated, through
computer simulations, how a handful of informed individuals can guide
the rest of a group along a migration route or to a food source, even
if the group members are incapable of recognizing which individuals
have expert knowledge.
[IMAGE] MIGRANT WORKERS. Positive feedback explains how a few
experienced birds may lead the rest during a migration.
Photodisc
"We're not assuming anything about what these animals know—they
don't know if anyone agrees with them, and they can't tell anyone,
'Follow me,'" Couzin says.
The researchers assumed, simply, that the experts' choice of
direction at any given moment is balanced between their desire to
move in the correct direction and their desire to align with their
neighbors; by contrast, ignorant animals simply do the latter.
These alignment rules create a positive-feedback effect: The more
animals are already turned in the correct direction, the more animals
are likely to turn that way in the future. As long as the number of
expert animals is big enough for the correct direction to get a
toehold, positive feedback amplifies the experts' influence.
The team found that the larger the group, the smaller the proportion
of experts needed to get the group moving in the correct direction.
In the researchers' simulations, for example, a group of 30 ants
needed four or five experts to get the group moving in the right
direction, while a group of 200 could also be led accurately by just
five of its members.
The researchers also studied what happens if the experts disagree.
They found that the group will quickly reach a consensus and move in
the direction preferred by a slight majority of the
experts—although no individual knows how the experts'
preferences stack up or even who the experts are. Once again,
positive feedback amplifies the majority's tiny edge into a
commanding lead.
"For humans, to reach consensus is very complicated—it requires
language and recognition capabilities," Couzin says. "But animals can
do it using very simple behavioral rules."
This simplicity has important implications. Couzin says, "It means
natural selection is much more likely to find this kind of consensus
behavior" than it would if consensus building required fancy
cognitive skills.
Couzin and his collaborators are now testing their model in a wide
range of systems, including fish and people. For instance, they're
training a few lab-kept fish in the location of a food source and
then seeing whether they lead a group there.
One of the most important contributions that the mathematical models
can make, Couzin says, is to give biologists concrete, testable
hypotheses to pursue. "It's so difficult to do experiments, that
starting with a good theoretical basis is important," he says.
"Theory can drive new ways of doing experiments."
If you have a comment on this article that you would like considered
for publication in Science News, send it to editors@sciencenews.org.
Please include your name and location.
References:
Beekman, M., D. Sumpter, and F. Ratnieks. 2001. Phase transition
between disordered and ordered foraging in Pharaoh's ants.
Proceedings of the National Academy of Sciences 98(Aug.
14):9703-9706. Available at
http://www.pnas.org/cgi/content/full/98/17/9703.
Buhl, J., D.J.T. Sumpter, I.D. Couzin, et al. 2006. From disorder to
order in marching locusts. Science 312(June 2):1402-1406. Abstract
available at
http://www.sciencemag.org/cgi/content/abstract/312/5778/1402.
Couzin, I.D., et al. 2005. Effective leadership and decision-making
in animal groups on the move.
Nature 433(Feb. 3):513-516. Abstract available at
http://dx.doi.org/10.1038/nature03236.
______. 2002. Collective memory and spatial sorting in animal groups.
Journal of Theoretical Biology 218(Sept. 7):1-11. Abstract available
at http://dx.doi.org/10.1006/jtbi.2002.3065.
Sumpter, D. 2006. The principles of collective animal behaviour.
Philosophical Transactions of the Royal Society B 361(Jan. 29):5-22.
Abstract available at http://dx.doi.org/10.1098/rstb.2005.1733.
Sources:
Iain Couzin
Department of Zoology
University of Oxford
Oxford OX1 3PS
United Kingdom
Daniel Grunbaum
School of Oceanography
University of Washington
Seattle, WA 98195
Julia Parrish
School of Aquatic and Fishery Sciences
University of Washington
Seattle, WA 98195
Stephen Pratt
School of Life Sciences
Arizona State University
Tempe, AZ 85287
David Sumpter
Department of Zoology
University of Oxford
Oxford OX1 3PS
United Kingdom
http://www.sciencenews.org/articles/20061125/bob10.asp
From Science News, Vol. 170, No. 22, Nov. 25, 2006, p. 347.
Copyright (c) 2006 Science Service. All rights reserved.
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