Biological Foundations of Swarm Intelligence
Madeleine Beekman1 , Gregory A. Sword2 , and Stephen J. Simpson2
1
2
Behaviour and Genetics of Social Insects Lab, School of Biological Sciences,
University of Sydney, Sydney, Australia
mbeekman@bio.usyd.edu.au
Behaviour and Physiology Research Group, School of Biological Sciences,
University of Sydney, Sydney, Australia
{greg.sword,stephen.simpson}@bio.usyd.edu.au
Summary. Why should a book on swarm intelligence start with a chapter on biology? Because swarm intelligence is biology. For millions of years many biological
systems have solved complex problems by sharing information with group members.
By carefully studying the underlying individual behaviours and combining behavioral observations with mathematical or simulation modeling we are now able to
understand the underlying mechanisms of collective behavior in biological systems.
We use examples from the insect world to illustrate how patterns are formed, how
collective decisions are made and how groups comprised of large numbers of insects
are able to move as one. We hope that this first chapter will encourage and inspire
computer scientists to look more closely at biological systems.
1 Introduction
“He must be a dull man who can examine the exquisite structure of a comb
so beautifully adapted to its end, without enthusiastic admiration.”
Charles Darwin (1872)
When the Egyptians first started to keep honeybees 5,000 years ago, they
surely must have marveled on the beauty of the bees’ comb. Not only is the
honeycomb beautiful to look at, but how did the bees decide to build hexagonal cells and not cells of another form? Initially it was suggested that hexagonal cells hold the most honey, but the French physicist R.A.F. de Réaumur
realized that it was not the content of the cells that counts, but the amount
of material, wax, that is needed to divide a given area into equal cells. Obviously at that time it was assumed that the bees were “blindly using the highest
mathematics by divine guidance and command” (Ball 1999). It was not until
Darwin that the need for divine guidance was removed and the hexagonal cells
were thought to be the result of natural selection. In this view the bees’ ancestors ‘experimented’ with different shaped cells, but the bees that by chance
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M. Beekman, G. A. Sword and S. J. Simpson
‘decided’ to build hexagonal cells did better and, as a result, the building of
hexagonal cells spread. In Darwin’s words, “Thus, as I believe, the most wonderful of all known instincts, that of the hive-bee, can be explained by natural
selection having taken advantage of numerous, successive, slight modifications
of simpler instincts; natural selection having by slow degrees, more and more
perfectly, led the bees to sweep equal spheres at a given distance from each
other in a double layer, and to build up and excavate the wax along the planes
of intersection.” (Chapter 7, Darwin 1872).
It was exactly such ‘Darwinian fables’ that inspired the biologist and mathematician D’Arcy Wentworth Thompson to write his book On Growth and
Form (Thompson 1917). The central thesis of this book is that biologists
overemphasize the role of evolution and that many phenomena can be more
parsimoniously explained by applying simple physical or mathematical rules.
Thompson argued that the bees’ hexagonal cells are a clear example of a pattern formed by physical forces that apply to all layers of bubbles that are
pressed into a two-dimensional space. Bees’ wax is not different, the soft wax
forms bubbles that are simply pulled into a perfect hexagonal array by physical forces. Hence, the pattern forms spontaneously and no natural selection
or divine interference needs to be invoked (Ball 1999).
In fact, many instances of spontaneous pattern formation can be explained
by physical forces, and given the almost endless array of patterns and shapes
found around us, it is perhaps not surprising that such patterns are an inspiration for many people, scientists and non-scientists alike. Upon closer examination, amazing similarities reveal themselves among patterns and shapes
of very different objects, biological as well as innate objects. As we already
alluded above, the characteristic hexagonal pattern found on honeycombs are
not unique; the same pattern can be obtained by heating a liquid uniformly
from below. Autocatalytic reaction-diffusion systems will lead to Turing patterns (think stripes on tigers) in both chemical and biological mediums (Kondo
and Asai 1995; Ball 1999), and minerals form patterns that have even been
mistaken for extra-terrestrial fossils (McKay et al. 1996).
The similarity of patterns found across a huge range of systems suggests
that there are underlying principles that are shared by both biological and
innate objects. Such similarities have been nicely illustrated by work on pattern formation in bacterial colonies. When one manipulates the amount of
food available to bacteria and the viscosity of their medium, patterns emerge
that are remarkably similar to those found in, for example, snowflakes (BenJacob et al. 2000). In fact, the growth of bacterial colonies has proven to be
an important playground for testing ideas on non-living branching systems
(Ball 1999; Ben-Jacob and Levine 2001; Levine and Ben-Jacob 2004). As it
turns out, many branching patterns found across nature can be explained by
the same process, known as diffusion-limited aggregation, resulting from the
interactions of the particles, be they molecules or individual bacteria (Ball
1999).
Biological Foundations of Swarm Intelligence
5
All patterns described above have been explained by approaching the systems from the bottom up: how do the particles interact with each other and
with their immediate environment? One may not really be surprised by the
fact that the same approach helps one to understand bacteria as well as
molecules. After all, bacteria aren’t really that different from molecules, are
they? In the following we will illustrate how such a bottom-up approach can
explain another remarkable feature of honeybees: the typical pattern of honey,
pollen and brood found on combs.
The honeybee’s comb is not only a marvel because of its almost perfect
hexagonal cells, the bees also seem to fill the cells with brood (eggs that
develop into larvae and then pupae and finally emerge as young workers or
males), pollen (to feed the brood) and nectar (which will be converted into
honey) in a characteristic pattern. This pattern consists of three distinct concentric regions: a central brood area, a surrounding rim of pollen, and a large
peripheral region of honey (Fig. 1). If we envision the honeybee colony as
a three-dimensional structure, this pattern is most pronounced in the central combs which intersect a large portion of the almost spherical volume of
brood. How does this pattern come about? The storage of pollen close to the
brood certainly makes sense as it reduces the time needed to get the pollen
to the brood. But how do the bees know this? Do they use a blueprint (or
template) to produce this characteristic pattern, implying that there are particular locations specified for the deposition of pollen, nectar and brood? Or
is the pattern self-organized and emerges spontaneously from the dynamic
interactions between the honeybee queen, her workers and the brood? Scott
Camazine set out to determine which of these two hypotheses is the most
parsimonious (Camazine 1991).
The beauty of working on macroscopic entities such as insects is that you
can individually mark them. Honeybees are particularly suitable because we
can then house them in what we call an observation hive, a glass-walled home
for the bees. This means that we can study the interactions of the individually
marked bees without taking them out of their natural environment (see Fig. 1).
Camazine did just that. He monitored the egg-laying behavior of the queen,
of foragers that returned with pollen or nectar, and of nurse workers, those
that feed the brood. The first thing that he observed was that the queen
is rather sloppy in her egg-laying behavior, moving about in a zig-zag-like
manner, often missing empty cells and retracing her own steps. Camazine
further noticed that she has a clear preference to lay a certain distance from
the periphery of the comb and never more than a few cell lengths of the nearest
brood-containing cell. Interestingly, even though the queen somewhat has a
preference for at least the middle of the comb and the vicinity of brood, bees
returning with pollen or nectar did not seem to have a preference for specific
cells at all. When an empty comb was left in the colony and the deposition
of nectar and pollen observed, both could be found in any cell. Even though
such absence of a preference clearly refutes the blueprint hypothesis, it does
not explain how the characteristic pattern ultimately arises.
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M. Beekman, G. A. Sword and S. J. Simpson
Fig. 1. Because of their relatively large size, we can easily mark individual bees in a
colony. In this particular colony we marked 5,000 bees by combining numbered plates
and different paint colors. This allowed us to study their behavior at an individual
level. Photograph taken by M. Beekman.
As it turns out, bees do have a clear preference when they remove pollen
or honey from cells. Both honey and pollen are preferentially removed from
cells closest to the brood. By following the pattern of cell emptying during a
period in which foraging activity was low (overnight or during rain), Camazine
observed that all the cells that were emptied of their pollen or nectar were
located within two cells or less from a cell containing brood. No cells were
emptied that were further from brood cells. It is easy to see why the bees
would have a preference for the removal (through use) of pollen that is found
closest to the brood, as it is the brood that consumes the pollen. In addition,
nurse bees are the younger bees which restrict most of their activity to the
brood area (Seeley 1982).
The preferential removal of pollen and nectar from cells closest to cells
containing brood and the queen’s preference for laying eggs in cells close to
brood made Camazine realism that this might explain the honeybee’s characteristic comb pattern. But how to prove this? This is where the physicist’s
approach comes in. By constructing a simulation model based on his behavioral observations, Camazine was able to closely follow the emergence of the
pattern. Initially, both pollen and nectar were deposited randomly throughout
the frame with the queen wandering over the comb from her initial starting
point. Despite the random storage of pollen and nectar, the queen’s tendency
to lay eggs in the vicinity of cells that already contain brood rapidly results
in an area in which mostly brood is found. This is enhanced by the bees’ pref-
Biological Foundations of Swarm Intelligence
7
Fig. 2. The typical pattern of honey (grey cells), pollen (white cells), and brood
(black cells) as seen on a honeybee’s comb. Shown is the top-left corner of the comb
erence to remove honey and pollen from cells close to brood, which increases
the availability to the queen of cells to lay eggs in. This further reduces the
number of cells available for storage of honey or pollen. Thus, the brood area
is continually freed of honey and pollen and filled with eggs resulting in a
compact brood structure. But how do the pollen and nectar get separated
(Fig. 2)?
Because initially both are deposited randomly, both pollen and nectar
will be present in the periphery of the comb. However, most pollen that gets
collected on a daily basis is consumed that same day. This means that given
the normal fluctuations in pollen availability, there is often a net loss of pollen,
with pollen present in the periphery being consumed at nearly the same rate
as pollen being stored elsewhere. At the same time, these empty cells are most
likely to be filled with nectar, as the nectar intake is much higher, and soon
there is no longer space to store pollen. Where is pollen stored then?
Eventually the only place left for pollen to be stored is the band of cells
adjacent to the brood. The developmental time from egg to adult is 21 days,
meaning that for three weeks a brood cell cannot be used for anything else.
But in the interface zone between the brood and the stores of honey at the
periphery, the preferential removal of honey and pollen continuously provides
a region in which cells are being emptied at a relatively high rate. And it
is these cells that are available for pollen. Other cells that become available
because bees emerge from them are found in the middle of the brood nest,
but these will then be preferentially emptied and again filled with eggs.
Without his computer simulation Camazine would not have been able to
fully understand how the behavior of the individual bees resulted in the organized pattern of brood, honey and pollen on the comb of the bees. And this
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M. Beekman, G. A. Sword and S. J. Simpson
is a general principle for understanding collective animal behavior: without
tools such as simulations or mathematics, it is impossible to translate individual behavior into collective behavior. And it is exactly with those tools that
originally came from disciplines outside of biology, and with the view that interactions among individuals yield insights into the behavior of the collective,
that we biologists have learned from physics. In fact, we began this chapter by
illustrating that even biological phenomena can often more parsimoniously be
understood using physical explanations, and that many systems, both innate
and living, share the same physical principles. And it has exactly been these
similarities and the wide applicability of the mathematical rules that govern
diverse behaviors that have led to the field of Swarm Intelligence (e.g. Dorigo
et al. 1996; Dorigo and Di Caro 1999).
However, it is important to realise that our biological ‘particles’ are more
complex than molecules and atoms and that the ‘simple rules of thumb’ of
self-organization (Nicolis and Prigogine 1977) have only limited explanatory
power when it comes to biological systems (Seeley 2002). Bacterial colonies
may grow in a similar pattern as minerals, Turing patterns may be found
on fish, in shells and in chemical reactions, and we can understand the bees’
hexagonal cells using physics, but when it comes to biological systems, an
extra layer of complexity needs to be added. Besides the complexity of the
individuals, we cannot ignore natural selection acting on, for example, the
foraging efficiency of our ant colony, or the building behavior of our termites. If
the underlying principles that govern the building behavior of termites results
in colony-level behavior that is far from functional, this would be rapidly
selected against. Moreover, it is of no use to assume that certain systems
must behave similarly simply because they ‘look’ similar. It is true that if the
same mathematical model or behavioral algorithm captures the behavior of
different systems, then we can talk about similarities between systems that
go beyond simple analogy (Sumpter 2005). However, as we will explain in the
concluding section of this chapter, true biological inspiration needs to come not
from the superficial similarities between systems, but from the intricate and
often subtle differences between them. We shall illustrate this standpoint by
drawing examples from our own study systems: decentralized decision making
in social insects and the coordinated movement of animal groups.
2 Decentralized Decision Making
The evolution of sociality, the phenomenon where individuals live together
within a nest such as is found in many bees and wasps, and all ants and termites, has created the need for information transfer among group members.
No longer can each individual simply behave as if solitary, but actions by different group members need to be carefully tuned to achieve adaptive behavior
at the level of the whole group. Insect colonies need to make many collective
decisions, for example where to forage, which new nest to move to, when to
Biological Foundations of Swarm Intelligence
9
reproduce, and how to divide the necessary tasks among the available workforce. It is by now well known that such group-level decisions are the result
of the individual insects acting mainly on local information obtained from
interactions with their peers and their immediate environment (Bonabeau et
al. 1997; Camazine et al. 2001). In other words, decision making in insect societies is decentralized. To illustrate how insect colonies achieve this, we will
describe foraging and nest site selection in ants and honeybees.
2.1 Where to Forage?
In order to organize foraging, social insects need a form of recruitment. Recruitment is a collective term for any behavior that results in an increase
in the number of individuals at a particular place (Deneubourg et al. 1986),
and allows insect societies to forage efficiently in an environment in which
food sources are patchily distributed or are too large to be exploited by single
individuals (Beckers et al. 1990; Beekman and Ratnieks 2000; Detrain and
Deneubourg 2002). In addition, social insects that transfer information about
the location of profitable food sources can exploit an area much larger than
those that lack such a sophisticated recruitment mechanism. Honeybees are a
prime example. Their sophisticated dance language (von Frisch 1967) allows
them to forage food sources as far as 10 km from the colony (Beekman and
Ratnieks 2000).
Exact recruitment mechanisms vary greatly among the social insects but
can be divided into two main classes: direct and indirect mechanisms. Mass
recruitment via a chemical trail is a good example of indirect recruitment.
The recruiter and recruited are not physically in contact with each other;
communication is instead via modulation of the environment: the trail. The
recruiter deposits a pheromone on the way back from a profitable food source
and recruits simply follow that trail. In a way such a recruitment mechanism is
comparable to broadcasting: simply spit out the information without controlling who receives it. The other extreme is transferring information, figuratively
speaking, mouth to mouth: direct recruitment. The best-known example of
such a recruitment mechanism is the honeybees’ dance language. Successful
foragers, the recruiters, perform a stylized ‘dance’ which encodes information
about the direction and distance of the food source found and up to seven
dance followers (Tautz and Rohrseitz 1998), potential recruits, are able to
extract this information based upon which they will leave the colony and try
to locate the advertised food source. Recruitment trails and the honeybee
dance language can be seen as the two extremes of a whole range of different
mechanisms used by social insects to convey information about profitable food
sources.
Many computer scientists are familiar with the double bridge experiment
as an example of the means by which foraging is organized in ant colonies. In
this experiment a colony of trail-laying ants is offered two equal food sources
located at the end of two paths of different lengths. After some time the
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M. Beekman, G. A. Sword and S. J. Simpson
vast majority of foragers converges on the shorter path (Beckers et al. 1993).
This collective choice for the nearest source is the result of a positive feedback
process: Ants finding food mark the environment with pheromone trails during
their return to the nest, and ants searching for food probabilistically follow
these trails.
The same trail-following behavior allows an ant colony to choose the best
food source out of several possibilities without the individual ants directly
comparing the quality of the food sources on offer. Experiments performed
on several species of ants have shown that ants modulate the amount of
pheromone deposited depending on the quality of the food source, such that
the better the quality, the more pheromone is left and the more likely other
ants are to follow the trail to the best food source (Beckers et al. 1990; Beckers
et al. 1993; Sumpter and Beekman 2003).
The success of the pheromone trail mechanism is likely to be due, at least
in part, to the non-linear response of ants to pheromone trails where, for example, the distance that an ant follows a trail before leaving it is a saturating
function of the concentration of the pheromone (Pasteels et al. 1986). In other
words, the probability an ant will follow a trail is a function of trail strength
(expressed as concentration of pheromone), but ants never have a zero probability of losing a trail, irrespective of the strength of the trail. Mathematically,
non-linearity in response means an increase in the number and complexity of
solutions of the model equations that may be thought of as underlying foraging (linear equations have only a single solution). Biologically, a solution
to a differential equation corresponds to a distribution of ants between food
sources and an increase in solutions implies more flexibility as the ants ‘choose’
between possible solutions. Such an allocation of workers among food sources,
which assigns nearly all trail-following foragers to the best food source, is optimal provided the food source has unlimited capacity. When the food source
does not have unlimited capacity, the result is that trail-following ants will
be directed to a food source at which they cannot feed. In a way the colony
gets ‘stuck’ in a suboptimal solution and can only get out of this solution
by adding some layers of complexity, such as negative pheromones signalling
‘don’t go there’, or individual memory so that the individual remembers that
following that particular trail does not yield anything. A second drawback of
relying on pheromone trails is that it may be difficult to compete with an
existing trail, even if a better food source is found. If, due to initial conditions, a mediocre food source is discovered first, ants that have found a better
quality food source after the first trail has been established will not be able
to build up a trail strong enough to recruit nest mates to the newly discovered bonanza (Sumpter and Beekman 2003). Again, the ants are stuck in a
sub-optimal solution.
Because of their fundamentally different recruitment mechanism, honeybees cannot get stuck in a sub-optimal solution. This direct recruitment behavior, the dance, encodes two main pieces of spatial information: the direction
and the distance to the target. Both are necessary as, unlike ants, honey-
Biological Foundations of Swarm Intelligence
11
bees need to deal with a three-dimensional space. During a typical dance the
dancer strides forward about 1.5 times her length vigorously shaking her body
from side to side (Tautz et al. 1996). This is known as the ‘waggle phase’ of
the dance. After the waggle phase the bee makes an abrupt turn to the left
or right, circling back to start the waggle phase again. This is known as the
‘return phase’. At the end of the second waggle, the bee turns in the opposite
direction so that with every second circuit of the dance she will have traced
the famous figure-of-eight pattern of the waggle dance (von Frisch 1967).
The most information rich phase of the dance is the waggle phase. During
the waggle phase the bee aligns her body so that the angle of deflection from
vertical is similar to the angle of the goal from the sun’s current azimuth.
Distance information is encoded in the duration of the waggle phase. Dances
for nearby targets have short waggle phases, whereas dances for distant targets
have protracted waggle phases.
Dance followers need to be in close contact with the dancer in order to
be able to decode the directional information (Rohrseitz and Tautz 1999).
Hence, directional information is transferred to a limited number of individuals. Moreover, more than one dance can take place at the same time, and
these dances can be either for the same site or for different sites. This means
that there is no direct competition between dances, provided the number of
bees available to ‘read’ a dance is infinite (a likely assumption). Dances are
only performed for food sources that are really worthwhile.
In order to assess the quality of the food encountered, a forager uses an
internal gauge to assess the profitability of her source, based on the sugar
content of the nectar and the distance of the patch from the colony, as well
as the ease with which nectar (or pollen) can be collected. A bee’s nervous
system, even at the start of her foraging career, has a threshold calibrated into
it which she uses to weigh these variables when deciding whether a patch is
firstly worth foraging for at all, and secondly worth advertising to her fellow
workers (Seeley 1995).
Dancing bees also adjust both the duration and the vigor of their dancing
as a function of profitability of their current source (Seeley et al. 2000). The
duration of the dance is measured by the number of waggle phases that the
dancer performs in a particular dance, and the vigor is measured by the time
interval between waggle phases (the return phase). The larger the number
of waggle phases, and the smaller the return phase, the more profitable the
source is and the more nest mates will be recruited to it. This means that
when two dances are performed simultaneously, one for a mediocre and one
for a superb site, the dance for the superb site is more likely to attract dance
followers than the one for the mediocre site. At the same time, however, the
dance for the mediocre site will still attract some dance followers, because
potential dance followers do not compare dances before deciding which one to
follow (Seeley and Towne 1992). The result is that a honeybee colony can not
only focus on the best food sources to the extent that most foragers will collect
food at the best sites (Seeley et al. 1991), but is also able to swiftly refocus
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M. Beekman, G. A. Sword and S. J. Simpson
its foraging force in response to day-to-day, or even hour-to-hour, variation
in available forage (Visscher and Seeley 1982; Schneider and McNally 1993;
Waddington et al. 1994; Beekman and Ratnieks 2000; Beekman et al. 2004).
2.2 Exploration Versus Exploitation
Most, if not all, studies on the allocation of foragers over food sources have
used stable environments in which the feeders or forage sites were kept constant (e.g. Beckers et al. 1990; Seeley et al. 1991; Sumpter and Beekman 2003).
When conditions are stable the optimal solution from the colony’s point of
view is to focus solely on the best food source (provided this food source is
so large that it allows an infinite number of individuals to forage it) and this
is exactly what many species of ants do that collect stable food sources such
as honeydew (a sugary secretion produced by aphids) (Quinet et al. 1997), or
leaves (Darlington 1982; Wetterer et al. 1992). These species construct long
lasting trails (trunk trails) that connect the nest to foraging locations. In some
species trails are more or less permanent due to the workers actively changing
the environment by removing vegetation (Rosengren and Sundström 1987;
Fewell 1988). As soon as conditions are not stable, however, which is mostly
the case in nature, it becomes important to have a mechanism that allows
the change-over to another food source or food sources when they have become more profitable or when the initial food source has been depleted. This
means that in order to do well in a dynamically changing environment, insect
colonies should allow the storage of information about food patches which are
currently exploited but at the same time allow the exploration for new sites.
The key to keeping track of changing conditions is the trade-off between
exploitation and exploration: the use of existing information (exploitation)
versus the collection of new information (exploration). How do the two extreme recruitment mechanisms, trail-based foraging and the honeybee’s dance
language, allow for the discovery of new food sources?
As mentioned earlier, trail-following ants never have a zero probability
of losing a trail, irrespective of the trail resulting in some ants getting lost
even when the trail is at its strongest. Assuming that these ‘lost’ ants are
able to discover new food sources and thus serve as the colony’s explorers or
scouts, this ‘strategy of errors’ (Deneubourg et al. 1983; Jaffe and Deneubourg
1992) allows the colony to fine-tune the number of scouts depending on the
profitability of the food source that has already been exploited. This is because
the weaker the trail (indicating the presence of a mediocre food source), the
more the number of ants that get ‘lost’ and hence become scouts. When the
trail is very strong (indicating that a high-quality food source has been found)
a smaller number of ants will lose the trail, resulting in a smaller number of
scouts.
The regulation of scouts in honeybees similarly assures the correct balance
between the number of individuals allocated to exploration and exploitation.
An unemployed forager (an individual that wants to forage but does not know
Biological Foundations of Swarm Intelligence
13
where to forage) will first attempt to locate a dance to follow. If this fails
because the number of dancers is low, she will leave the colony and search
the surroundings, thereby becoming a scout (Beekman et al. 2007). As a
result, the number of scouts is high when the colony has not discovered many
profitable forage sites, as dancing will then be low, whereas the number of
scouts will be low when forage is plentiful and the number of bees performing
recruitment dances high (Seeley 1983; Beekman et al. 2007). This so-called
‘failed follower mechanism’ (Sumpter 2000; Beekman et al. 2007) provides
the colony with the means to rapidly adjust its number of scouts depending
on the amount of information available about profitable forage sites. Even
when the colony is exploiting profitable patches, there may still be other,
undiscovered, profitable sites that are not yet exploited. As soon as there is
a reduction in the number of dances occurring in the colony, the probability
that some unemployed foragers are unable to locate a dance increases, and
the colony therefore sends out some scouts. Such fluctuations in the number
of dances regularly occur in honeybee colonies, even when there is plenty of
forage (Beekman et al. 2004).
2.3 Where to Live?
Amazing as an insect colony’s collective food collection is, even more amazing
is that the same communication mechanisms are often used to achieve a very
different goal: the selection of a new nest. A colony needs to select a new home
under two conditions. Either the whole colony needs to move after the old nest
has been destroyed, or part of the colony requires a new nest site in the case
of reproductive swarming (where the original colony has grown so much that
part of it is sent off with one or more new queens to start a new colony).
This means that colonies of insects need to address questions very similar to
the questions we ask ourselves when changing homes (Franks et al. 2002).
What alternative potential new homes are available? How do their attributes
compare? Has sufficient information been collected or is more needed? House
hunting by social insects is even more piquant, as it is essential for the colony
that the decision be unanimous. Indecisiveness and disagreement are fatal
(Lindauer 1955). House hunting has been studied in detail in two species of
social insect only, in the ant and the honeybee. Both study systems have been
selected for ease with which this process can be studied. The ant Temnothorax
albipennis forms small colonies (often containing about 100 workers) and lives
in thin cracks in rocks (Partridge et al. 1997) and can easily be housed in the
laboratory. By simply destroying their old nest, the ants are forced to select a
new one (Sendova-Franks and Franks 1995). Moreover, because of their small
colony size, it is not that hard to uniquely mark all individuals (and they
don’t sting!), which greatly facilitates the study of their behavior.
Honeybee swarms normally have many more individuals (approximately
15,000 bees (Winston 1987)), but researchers often work with swarms that
contain 4,000 to 5,000 bees (Seeley et al. 1998; Camazine et al. 1999; Seeley
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M. Beekman, G. A. Sword and S. J. Simpson
and Buhrman 1999; Seeley and Buhrman 2001; Seeley 2003; Seeley and Visscher 2004; Beekman et al. 2006). The great benefit of honeybees is that we
can artificially make swarms by simply taking the queen out of the colony and
shaking the 5,000 or so bees needed to produce an experimental swarm. And,
if necessary, we label the bees individually in the same manner as when we
study foraging.
By offering our homeless insects nest sites that differ in quality, we can
carefully study which attributes the ants or bees value in their new home.
At the same time we can get a clear picture of the behavioral repertoire
that underlies collective house hunting. These behaviors can then be used to
construct individual-based models aimed at understanding precisely how the
actions of the individuals result in collective choice.
House Hunting in Honeybees
Tom Seeley was the first to systematically study house hunting in social insects
using the honeybee as his model organism. Seeley started out by determining
what attributes the bees look for when judging the suitability of a potential
new nest site. By working on a tree-less island (this species of honeybee normally inhabits tree hollows but happily lives in man-made hives when no tree
hollows are available), Seeley and his colleague Buhrman could manipulate
the kind of nest sites the bees could choose from. By manipulating the nest
site’s main attributes, such as content and size of the entrance, they could
determine what constitutes a ‘mediocre’ and a ‘superb’ site from the bees’
point of view. This further allowed them to study how good a bee swarm is
at choosing the best nest site out of several possibilities (Seeley and Buhrman
2001). And, not surprisingly, they are pretty good at it because when offered
an array of five nest boxes, four of which were mediocre because they were
too small (bees like large nest sites with a small nest entrance), in four out of
five trials the bees chose the superb nest site. How do they do it?
As with recruitment to forage sites, bees that have found a nest site that
is considered worthwhile will perform a dance upon returning to the swarm.
By filming the dances of bees returning from both mediocre and superb sites,
Seeley and Buhrman (2001) could study how the dances differed between
the two. What they observed was that bees tune their dance in three ways.
Firstly, bees returning from a superb site dance longer than bees returning
from a mediocre site. Secondly, a dance for a superb site contains more waggle
phases (the part of the dance that encodes the distance to the site). Lastly,
dances for superb sites are ‘livelier’, meaning that the period between two subsequent waggle phases is shorter. Hence, there is a clear difference in dance
behavior between bees returning from mediocre and superb sites, but this is
not different from bees dancing for high and mediocre quality food sources
which leads to most, but not all, bees focusing on the best food source. Dances
for forage will never converge; instead there will always be different sites ad-
Biological Foundations of Swarm Intelligence
15
vertised simultaneously. However, a swarm needs to select just one nest site
unanimously and this suggests that dances for nest sites do converge.
Scout bees, those bees that search the environment for suitable new nest
sites, fly out in every direction and return to the swarm with information
about nest sites found. Initially, many dances will take place on the swarm,
advertising all sites that have been judged to be good enough. Within a few
hours, however, many sites are no longer danced for, and just before the swarm
takes to the air to fly to its new home, most, if not all, dances will be for a
single site (Seeley and Buhrman 1999). Such a unanimous decision is reached
without scouts comparing multiple nest sites (Visscher and Camazine 1999)
or potential dance followers selecting dances for the best nest sites. The most
likely reason why the swarm is ultimately able to select one nest site that is
mostly the best is dance attrition. In contrast to the dances for forage, where
bees will keep dancing for a forage site provided it remains profitable, bees
returning from a potential new nest site ultimately cease dancing (Seeley and
Buhrman 2001; Seeley 2003) even when their discovered nest site is of superb
quality.
The process goes like this. A bee that has returned from the best site
possible will perform, say, 100 waggle phases during the first dance that she
performs for that nest site. After she has finished her dance, she returns to the
nest site to confirm that it is still superb. Upon returning to the swarm, she
will advertise her site again, but will now reduce the number of waggle phases
to 80. After this dance she flies off again to her site and the process repeats
itself. This means that after five trips, this bee will not perform a dance upon
her return (as she will have reduced the number of waggle phases after each
return trip), but in the meantime she will have performed protracted and
lively dances for her site. Compare this with a bee that has found a mediocre
site. This bee will perform, say, only 60 waggle phases during her first dance,
40 on her second dance, etc. until she ceases dancing altogether. She not only
dances for a shorter period, but the number of dances performed for her site
is also less than the number of dances performed by the bee that found the
superb site. Hence, the ‘length of advertising’ differs significantly between the
mediocre and superb site and, as a result, more bees will be recruited to the
superb site than to the mediocre site, and those bees, provided they also rate
the site as superb, will perform lengthy dances and recruit more bees. It has
been suggested, based on a mathematical model, that this dance attrition is
crucial to the swarm’s ability to decide on one site (Myerscough 2003), but
this assumption awaits empirical testing.
Even though many behaviors of the bees involved in the swarm’s decisionmaking process have been described in great detail (for a nice overview see
Visscher 2007), without the use of a mathematical or simulation model it is
not immediately obvious how individual behavior is translated into collective
behavior and the swarm’s ability to choose the best nest site. Understanding
in more detail the swarm’s decision-making process led one of us, Madeleine
Beekman, together with two computer scientists, Stefan Janson and Martin
16
M. Beekman, G. A. Sword and S. J. Simpson
Middendorf, to construct an individual-based model of a honeybee swarm
choosing a new home (Janson et al. 2007). Not only did we want to construct
a model that would behave in a realistic way, we wanted also to use that
model to get an idea about two aspects in particular which are hard to study
using real honeybee swarms: how a swarm regulates the number of individuals
that explore the surroundings for nest sites (as opposed to recruiting individuals to nest sites that have already been discovered), and how scouts search
their environment. Both questions address the trade-off between using existing information (exploitation) and acquiring new information (exploration)
and how this trade-off affects the quality of the decision made at the level of
the swarm.
We assumed that the bees would use the same behaviors and decision rules
both when foraging and when deciding on a new home. We therefore started by
applying the same exploration decision rule as had been applied in the context
of foraging: an individual bee that has not yet decided where to search will
always start by attempting to locate a dance to follow. The longer it takes to
find a dance, the more likely this bee is to fly off and search independently
(explore). This simple decision rule gave the following result (see Fig. 3): when
the nest site known to the swarm is only of mediocre quality, not many bees
will dance for that nest site and many bees will search independently because
they have a low chance of finding a dance to follow; the reverse is true when a
superb nest site has been found, as now most returning bees will dance for this
nest site (note that we included individual variation in our bees such that an
individual has a probability of dancing that increases with increasing quality
of nest site). Clearly, applying the failed follower mechanism also works very
well in house hunting and ensures an elegant balance between the number of
bees recruiting to a known nest site and the need to search the environment
for a better nest site.
All experimental work done so far on nest site selection in honeybee swarms
used nest sites which were located at equal distance from the swarm, a situation which is highly unlikely under natural conditions where nest sites are
present at all distances. Imagine a situation in which the swarm has discovered
a nest site nearby, but this nest site is only of very mediocre quality. We now
know that under this condition the swarm allows for more bees to explore the
surroundings in case a better nest site is found; but how should the swarm
distribute its scouts over the environment to allow the discovery of such a
further site in the first place? The great benefit of using models is that one
can manipulate the experiment. Hence, in our simulation model we were able
to control which nest site was discovered first by the swarm by simply sending
the first scout to that particular nest site. At the same time we could give our
scouts different ‘search rules’ to investigate how these rules affect the swarm’s
decision. The search rules we used were the following: scouts were sent out
such that all nest sites irrespective of their distance were equally likely to be
discovered (uniform Pu =1/250); the chance of discovery decreased with increasing distance from the swarm (distance Pd =1/distance); sites nearby had
Biological Foundations of Swarm Intelligence
17
400
Average number of bees
350
300
250
Bees at Site
200
Site Quality 45
Site Quality 50
Site Quality 70
150
Scouts
100
50
0
0
4
8
12
16
20
Time [h]
24
28
32
Fig. 3. Average number of bees scouting for a nest site and average number of bees
assessing a nest site (e.g., the number of bees that already know about the location
of a potential new nest site) when nest sites of different quality (70: good site, 50:
mediocre site, 45: poor site) were offered to the swarm. The vertical bars indicate
the standard variation (50 runs per experiment). (Fig. 6 in Janson et al. (2007).)
a much higher probability of being discovered than sites present further from
the swarm (distance squared Ps =250/distance2 ). Our results showed that the
best search strategy from the swarm’s point of view would be to focus on
nearby sites without ignoring possible sites further away. Hence, most scouts
are expected to search in the vicinity of the swarm, whereas some are likely
to fly out further. This prediction can relatively easily be tested using real
honeybee swarms.
Ants Moving House
The ant Temnothorax albipennis is rather different from the honeybee. Not
only are its colonies much smaller, decision making seems much more dependent on individual decisions. For example, when offered a choice between two
nest sites, about half of the ants directly compare the quality of those sites
and can therefore make an informed choice (Mallon et al. 2001). At the same
time, however, the other half does not directly compare the different options
but these poorly informed ants still contribute to the colony’s overall decision.
How does their decision-making mechanism work?
Individual behavior of T. albipennis during nest site selection has been
described in great detail (Mallon et al. 2001; Pratt et al. 2002). T. albipennis
does not use pheromone trails to recruit nest mates but instead relies on
18
M. Beekman, G. A. Sword and S. J. Simpson
tandem running, where one individual guides a second individual by staying
in close contact, and social carrying, where the recruiter simply picks up
another ant and carries it across to the new nest site (the queen is always
carried!). In the beginning of the process, only tandem runs are performed by
scouts that have discovered a potential new nest. Similarly to the honeybee, T.
albipennis scouts know what they want in a new home: it should be spacious
and the entrance should be relatively small so that it can easily be defended.
The probability that a scout will initiate tandem recruitment to the site that
it has just found depends on the quality of that site. Moreover, assessment
duration (the time spent inspecting the potential new nest) varies inversely
with the quality of the site. Hence, the better the scout judges that site to be,
the faster it will start recruiting. By leading a single individual towards the
nest site discovered, the scout basically teaches the recruit how to get to the
new nest site so that this recruit, if it decides that the nest site is indeed of
good quality, can lead other ants to that site. The result is a build-up of ants
at good quality sites, whereas sites of poor quality will not attract many ants.
When the number of ants present at a particular nest site reaches a certain
level, the quorum threshold, no more tandem recruitment takes place but
instead ants still present in the old nest are picked up and simply carried to
the new nest site. Brood items (eggs, larvae and pupae) will also be moved
in this way. Why does T. albipennis have two recruitment methods, one slow
(tandem runs) and one fast (social carrying)?
During the period in which tandem recruitment takes place, the quality
of the nest site discovered is assessed independently by each ant that either
discovered that site via scouting or was led to it via tandem recruitment. This
ensures that the ‘opinions’ of many ants about the site’s quality are pooled,
thereby increasing the likelihood that that site is indeed of sufficient quality.
At the same time, the slow build-up of ants at the discovered site allows
for a better site to be discovered, as recruitment to this site will be faster
and hence the number of ants will rapidly increase. Because of the different
recruitment to sites depending on their quality, the quorum will be reached
faster at the better site, after which social carrying will be initiated. This last
phase enables the colony to move into the chosen site rapidly (remember that
these ants move when their old nest site has been destroyed).
The above is a verbal description of the ants’ collective choice based on
observations of their individual behaviors. But can this sequence of behaviors
really account for the ants’ collective choice? To answer this question Stephen
Pratt and his colleagues (Pratt et al. 2005) incorporated everything they knew
about individual behavior into an agent-based model of collective nest choice.
They then used this model to simulate emigrations and compared the outcomes of these in silico emigrations with those performed by real ant colonies.
When the simulated ants were presented with a single site, the time course of
the emigration generally conformed to experimental data. More interesting,
however, was what the simulated ants did when confronted with two potential sites that differed in quality. The model predicted that about 10% of each
Biological Foundations of Swarm Intelligence
19
colony should typically be carried to the site of lower quality by the time the
old nest is completely empty, a result of many individuals basing their decision on information on one nest site only. This prediction was confirmed by
using real colonies and offering them the same choice as the in silico ants. The
agent-based model therefore provides strong support for the interpretation of
the ants’ individual behavior.
3 Moving in Groups
In many animal species, individuals move in groups as they perform seasonal
migrations, travel to food sources and return to safe havens, often over considerable distances (Boinski and Garber 2000; Krause and Ruxton 2002; Couzin
and Krause 2003). The movement of these groups is commonly self-organized,
arising from local interactions between individuals rather than from a hierarchical command center. Self-organized group movement is not restricted to
groups of relatively ‘simple’ creatures such as insect swarms or schools of fish,
but may even include ‘intelligent’ species like us. One of the most disastrous
examples of collective human group movement is crowd stampede induced by
panic, often leading to fatalities as people are crushed or trampled (Helbing
et al. 2000).
There are two extreme ways in which groups can ‘decide’ on a direction of
movement. Either all individuals within the group contribute to a consensus,
or else relatively few individuals (for convenience we will call these ‘leaders’)
have information about the group’s travel destination and guide the uninformed majority. Thus, in some species, all individuals within a group share
a genetically determined propensity to travel in a certain direction (Berthold
and Querner 1981; Berthold et al. 1992) or all are involved in choosing a
particular travel direction (Neill 1979; Grünbaum 1998). In contrast, a few informed individuals within a fish school can determine the foraging movements
of the group and can steer a group towards a target (Reebs 2000; Swaney et
al. 2001). Similarly, very few individuals (approx. 5%) within a honeybee
swarm can guide the group to a new nest site (Seeley et al. 1979).
When leaders are present, the question arises as to how these informed
individuals transfer directional information to the uninformed majority. Similarly, in the absence of leaders how is a consensus reached about travel direction? Such questions are almost impossible to address without having first
developed a theoretical framework that explores possible mechanisms.
Recently, two theoretical studies have addressed the issue of information
transfer from informed to uninformed group members. Stefan Janson, Martin
Middendorf and Madeleine Beekman (2005) modeled a situation in which
the informed individuals make their presence known by moving at a higher
speed than the average group member in the direction of travel. Guidance
of the group is achieved by uninformed individuals aligning their direction
of movement with that of their neighbors. Because the informed individuals
20
M. Beekman, G. A. Sword and S. J. Simpson
initially move faster, they have a larger influence on the directional movement
of the uninformed individuals, thereby steering the group.
A second model by Iain Couzin and colleagues (2005) shows that the movement of a group can be guided by a few informed individuals without these
individuals providing explicit guidance signals and even without any individual in the group ‘knowing’ which individuals possess information about travel
direction. Only the informed members of the group have a preferred direction, and it is their tendency to go in this direction that steers the group. The
main difference between the two models lies in the presence or absence of cues
or signals from the informed individuals to the uninformed majority. Janson
et al.’s (2005) leaders clearly make their presence known, whereas Couzin et
al.’s (2005) model suggests that leadership can arise simply as a function of
information difference between informed and uninformed individuals, without
the uninformed individuals being able to tell which ones have more information. It seems likely that the exact guidance mechanism is species-dependent.
When the group needs to move fast, for example a swarm of honeybees that
cannot run the risk of losing its queen during flight, the presence of leaders
that clearly signal their presence might be essential, as the group otherwise
takes a long time to start moving into the preferred direction. However, when
the speed of movement is less important than group cohesion, for example
because being in a group reduces the chance of predation, leaders do not need
to signal their presence.
If there are no leaders, the essential first step before a group can start
to move cohesively is some level of consensus among the individuals in their
alignment. How is this achieved when there are no leaders? Most likely there
are a minimum number of individuals that need to be aligned in the same
direction before the group can start to move in a particular direction without breaking up. If the number of equally aligned individuals is below this
threshold, the group does not move cohesively. As soon as this threshold is
exceeded, coordinated movement is achieved. Such a non-linear transition at
a threshold is known in theoretical physics and mathematics as a phase transition. Interestingly, we have recently discovered, for the first time, similar
transitions in biological systems (Beekman et al. 2001). Theoretical physicists
have developed a suite of models, termed self-propelled particle (SPP) models,
which attempt to capture phase transitions in collective behavior (Vicsek et
al. 1995). SPP models aim to explain the intrinsic dynamics of large groups
of individuals. Later we shall show how this theoretical framework can be
applied to the collective movement of locusts. But first we will describe some
experimental results on group movement in honeybee swarms, locusts and
Mormon crickets.
3.1 Honeybees on the Move
Deciding where to live is only one part of a honeybee swarm’s problem. The
second problem arises once that decision has been made: how does the small
Biological Foundations of Swarm Intelligence
21
number of informed bees (about 5%) convey directional information to the
majority of the uninformed bees in such a way that the swarm moves in unison? In the previous section we already described two theoretical possibilities:
either leaders signal their presence to the uninformed majority, or they do not
but simply move in their preferred direction. In fact, the model by Janson
and colleagues was inspired by a suggestion made in the early 1950s by Martin Lindauer (1955). Lindauer observed in airborne swarms that some bees
fly through the swarm cloud at high speed and in the correct travel direction, seemingly ‘pointing’ the direction to the new nest site. He suggested
that these fast-flying bees, later named ‘streakers’ (Beekman et al. 2006), are
the informed individuals or scouts. Lindauer got this idea while working in
war-ravaged Munich where he used to run with his honeybee swarms in an
attempt to find out where they were going. Like every scientist who takes
himself or herself seriously, at least at that time, Lindauer used to wear a
white lab coat, even when he was out in the field with the bees. One of his
field sites was near a mental hospital and rumor has it that one day he was
mistaken for an escaped mentally ill patient (Tom Seeley, personal communication). Luckily, Lindauer ran faster than the guards who tried to catch him,
which gives one an indication of how fast a swarm of bees flies!
An alternative to Lindauer’s hypothesis (which we will refer to as the
‘vision’ hypothesis) is the olfaction hypothesis of Avitabile et al. (1975). They
proposed that the scouts provide guidance by releasing assembly pheromone
from their Nasanov glands (a gland found between the last two tergites of
the bee’s abdomen) on one side of the swarm cloud, thereby creating an odor
gradient that can guide the other bees in the swarm. Until very recently
neither the vision hypothesis nor the olfaction hypothesis had been tested
empirically, though other investigators have confirmed Lindauer’s report that
there are streakers in flying swarms (Seeley et al. 1979; Dyer 2000).
Madeleine Beekman, Rob Fathke and Tom Seeley (2006) decided that it
was time to shed some light on this issue. In that study they did two things.
They studied in detail the flights of normal honeybee swarms (containing
approximately 15,000 bees) and smaller (4,000–5,000 bees) swarms in which
the bee’s Nasanov gland was sealed shut by applying paint to every single bee
in the swarm. This meant that sealed-bee swarms could not emit the Nasanov
pheromone (they had to apply paint to all bees in the swarm because they
had no means of knowing which bees would be the scouts). By using a ‘baitnest site’ that they made extremely attractive to a bee swarm, they could
be almost certain that their swarms would select that nest site. This allowed
them to follow the swarm (as Lindauer did through Munich, though they used
an open field), measure its speed and the time it took the swarm to settle in its
new home. Using this procedure and several sealed-bee swarms allowed them
to show that even if every single bee in the swarm was unable to produce
the Nasanov pheromone, the swarm was still able to fly more or less directly
towards the new nest site. From this they concluded that scouts do not use
pheromones to guide the swarm.
22
M. Beekman, G. A. Sword and S. J. Simpson
Proving the vision hypothesis was more difficult. They decided that a first
step would be to show that there is variation in flight speed and flight direction
among the individual bees within a flying swarm by taking photographs of a
large swarm during its flight to the bait hive such that individual bees appear
as small, dark streaks on a light background. The faster the flight speed of a
bee, the longer the streak it produced using this technique (provided the bee
flew in the plane of vision). Each photograph was analyzed by projecting it
onto a white surface to create an enlarged image. They then measured the
length (in mm) and the angle (in degrees, relative to horizontal) of each dark
streak that was in focus in the enlarged image. Because a size reference was
present in each photograph, and because each photograph recorded the bees’
movements during a known time interval (1/30 s), they were able to calculate
for each photograph the conversion factor between streak length and flight
speed. Using this procedure they could quantify what they saw while running
with the swarms: that a portion of the bees fly much faster in the direction of
travel while the majority of the bees seem to fly much slower and with curved
flight paths. Moreover, the fast-flying bees, the streakers, appeared to be most
common in the upper region of a swarm. For humans, and probably also for
bees, streakers are much more easily seen against the bright sky rather than
the dark ground or vegetation, so by flying above most of the bees in a swarm,
the streakers may be facilitating the transfer of their direction information to
the other bees. Future work should focus on determining if it is indeed the
streakers that are the scouts, those with information about the location of the
new nest site.
3.2 Locusts
To this point we have considered examples of self-organization and swarm
intelligence in highly structured social groups, in which there is a distinction
between reproductive individuals and more or less sterile workers and pronounced division of labor among workers. But not all cohesively behaving
animal groups are so structured. Some consist of individuals that are essentially all the same. And, as we shall see in the next section, the forces that
bind and propel such groups may be very sinister indeed.
Of the approximately 13,000 described species of grasshopper that exist
across the world, 20 or so are particularly notorious. For much of the time
they are just like any other harmless grasshopper — but, occasionally, and
catastrophically, they change and instead of living solitary lives, produce massive, migrating aggregations. As juveniles they form marching bands that may
extend for kilometers. Once they become winged adults, they take to the air
as migrating swarms that may be hundreds of square kilometers in area and
travel hundreds of kilometers each day. More than one fifth of the earth’s land
surface is at risk from such plagues and the livelihood of one in ten people on
the planet may be affected. These grasshoppers are called locusts.
Biological Foundations of Swarm Intelligence
23
Fig. 4. The two extreme forms of juvenile desert locusts. When reared in a crowd,
locusts develop into the gregarious phase, whereas the same individual if reared
alone would develop into the solitarious phase (photo by S. Simpson).
Phase Polyphenism: The Defining Feature of Locust Biology
Unlike other grasshoppers, locusts express an extreme form of density dependent phenotypic plasticity, known as ‘phase polyphenism’. Individuals
reared under low population densities (the harmless, non-migratory ‘solitarious’ phase) differ markedly in behavior, physiology, color and morphology
from locusts reared under crowded conditions (the swarm-forming, migratory
‘gregarious’ phase) (Pener and Yerushalmi 1998; Simpson et al. 1999; Simpson and Sword 2007). In some species, such as the infamous migratory locust
of Africa, Asia and Australia (Locusta migratoria), the phenotypic differences
are so extreme that the two phases were once considered to be separate species
(Uvarov 1921; Fig. 4). In fact, not only are the two phases not different species,
they are not even different genotypes: the same animal can develop into the
solitarious or the gregarious phase depending on its experience of crowding.
The genetic instructions for producing the two phases are, therefore, packaged
within a single genome, with expression of one or other gene set depending
on cues associated with crowding.
At the heart of swarm formation and migration is the shift from the shy,
cryptic behavior of solitarious phase locusts, which are relatively sedentary
and avoid one another, to the highly active behavior and tendency to aggregate
typical of gregarious phase insects. In the African desert locust, Schistocerca
gregaria, this behavioral shift occurs after just one hour of crowding (Simpson
et al. 1999). In recent years progress has been made towards understanding the
physiological and neural mechanisms controlling behavioral phase change in
locusts. In the desert locust the key stimulus evoking behavioral gregarization
is stimulation of touch-sensitive receptors on the hind (jumping) legs. These
receptors project via identified neural pathways to the central nervous system
and cause release of a suite of neuro-modulators, among which serotonin initiates phase transition through its action on neural circuits controlling behavior
(Simpson et al. 2001; Rogers et al. 2003, 2004; Anstey et al., unpublished).
24
M. Beekman, G. A. Sword and S. J. Simpson
Phase characteristics, including behavior, not only change within the life of
an individual, they also accumulate epigenetically across generations (Simpson
et al. 1999; Simpson and Miller 2007). Solitarious females produce hatchlings
that are behaviorally gregarized to an extent that reflects the degree and
recency of maternal crowding. If crowded for the first time at the time of
laying her eggs, the mother will produce fully gregariously behaving offspring.
In contrast, if a gregarious female finds herself alone when laying eggs, she
will produce partially behaviorally solitarized young (Islam et al. 1994a,b;
Bouaı̈chi et al. 1995). The gregarizing effect is mediated by a chemical which
the mother produces in her reproductive accessory glands and adds to the
egg foam in which she lays her eggs in the soil (McCaffery et al. 1998). In
effect, female locusts use their own experience of being crowded to predict the
population density that their young will experience upon emerging from the
egg and predispose them to behave appropriately. As a result phase changes
accumulate across generations.
Group Formation
Behavioral phase change within individuals sets up a positive feedback loop,
which under appropriate environmental conditions promotes the rapid transition of a population from the solitarious to the gregarious phase. If they
can, solitarious locusts will avoid each other. However, if the environment
forces them to come together, close contact between individuals will rapidly
induce the switch from avoidance to active aggregation, which will in turn
promote further gregarization and lead to formation of groups. Given that
gregarious phase locusts are migratory and move together, either as marching
bands of juveniles or swarms of winged adults, there is the likelihood that local
groups coalesce, ultimately seeding the formation of massive regional swarms.
In contrast, when previously aggregated individuals become separated, they
will begin to solitarize, hence reducing their tendency to aggregate and so
promoting further solitarization. If the habitat tends to keep locusts apart,
then this will ultimately lead to resolitarization of a gregarious population. Interestingly, the switch from solitarious to gregarious occurs more rapidly than
the reverse transition (Roessingh and Simpson 1994), indicating a hysteresis
effect.
Small-scale features of resource distribution determine the extent to which
phase change occurs in a local population of desert locusts. Clumping of resources such as food plants, roosting sites, and areas of favorable microclimate
encourages solitarious locusts to come together and as a consequence to gregarize and aggregate (Bouaı̈chi et al. 1996). The degree of clumping of food
plants in the parental environment in turn influences the phase state of the
offspring (Despland and Simpson 2000a).
The relationships between resource distribution, resource abundance, and
locust population size have been explored using individual-based computer
simulations, parameterized using experimental data from locusts (Collett et
Biological Foundations of Swarm Intelligence
25
al. 1998) . The extent of gregarization within a simulated population increases
with rising locust population density and increasing clumping of food resources. Critical zones at which solitarious populations gregarize precipitously
appear in the model across particular combinations of resource abundance,
resource distribution and population size. Subsequent experimental data support the predictions from the simulation model (Despland et al. 2000).
The spatial pattern of food distribution interacts with the nutritional quality of foods to determine the spread of phase change within local populations
(Despland and Simpson 2000b). Nutritional effects are mediated through differences in locust movement (Simpson and Raubenheimer 2000). Insects provided with poor quality food patches are highly active and are likely to contact
one another and gregarize even when food patches are not clumped. In contrast, locusts with nutritionally optimal food patches do not move far after
feeding, resulting in limited physical interactions between individuals, even
when food patches are highly clumped.
It is clear that small-scale features of the habitat such as resource abundance, quality and distribution either promote or impede phase change within
local populations. The same pattern seems to apply at intermediate scales of
a small number of kilometers (Babah and Sword, 2004) but at higher spatial
scales the relationship between vegetation distribution and desert locust outbreaks changes as different ecological processes come into play. At the scale of
individual plants, a fragmented habitat with multiple dispersed patches encourages solitarization, whereas at the landscape scale the pattern is reversed:
habitat fragmentation brings migrating locusts together and encourages outbreaks (Despland et al. 2004).
Understanding patterns of collective movement across local to landscape
scales requires answering two questions: what causes bands of marching hoppers (the juvenile stages) and flying adults to remain as cohesive groups, and
what causes them to move synchronously and collectively between patches at
different scales?
Collective Movement
Locust aggregations will build into major outbreaks only if locally gregarized
populations remain together and move collectively into neighboring areas of
habitat, where they can recruit further locusts to the growing band. Unless
such cohesive movement occurs, local aggregations will disband and individuals will return to the solitarious phase.
Within marching bands of juvenile locusts, individuals tend to synchronize
and align their directions of travel with those of near neighbors (Despland and
Simpson 2006). It had been shown in the laboratory that marching begins only
at high locust densities (Ellis, 1951), but these experiments did not measure
how and why alignment increases with density to the point that an aggregation
of locusts suddenly commences collective marching.
26
M. Beekman, G. A. Sword and S. J. Simpson
Fig. 5. An image from the Mexican hat marching arena and tracking software used
in Buhl et al.’s (2006) study of collective marching in gregarious locusts. For a movie
see http://www.sciencemag.org/cgi/content/full/312/5778/1402/DC1.
This problem has recently been studied by Jerome Buhl and colleagues
(2006) by modeling locusts as self-propelled particles (SPP), each ‘particle’
adjusting its speed and/or direction in response to near neighbors. The model
developed by Vicsek et al. (1995) was used because of its small number of underlying assumptions and the strength of the universal features it predicts. A
central prediction from the model is that as the density of animals in the group
increases, a rapid transition occurs from disordered movement of individuals
within the group to highly aligned collective motion. Since SPP models underlie many theoretical predictions about how groups form complex patterns,
avoid predators, forage, and make decisions, confirming such a transition for
real animals has fundamental implications for understanding all aspects of
collective motion. It is also particularly important in the case of locusts as it
could explain the sudden appearance of mobile swarms.
Buhl et al.’s experiments involved studying marching in the laboratory in a
ring-shaped arena, rather like a Mexican hat in shape, with a central dome to
restrict optical flow in the direction opposite to that of individual motion. For
data analysis, Iain Couzin developed an automated digital tracking system,
allowing the simultaneous analysis of group-level and individual-level properties, which is technically extremely challenging but essential for discovering
the link between these levels of organization (Fig. 5).
Biological Foundations of Swarm Intelligence
27
Juvenile locusts readily formed highly coordinated marching bands under
laboratory conditions when placed in the Mexican hat arena. Individuals selected collectively either a clockwise or counter-clockwise direction of travel
(the choice of which was random) and maintained this for extended periods.
Experiments were conducted in which the numbers of locusts in the arena
ranged from 5 to 120 insects (densities of 13 to 295 m2 ). The locusts’ motion
was recorded for eight hours and the resulting data were processed using the
tracking software to compute the position and orientation of each locust.
Coordinated marching behavior depended strongly on locust density (Figs.
6, 7). At low densities (2 to 7 locusts in the arena, equating to 5 to 17 locusts
per m2 ) there was a low incidence of alignment among individuals. In trials
where alignment did occur it did so only sporadically and after long initial
periods of disordered motion. Intermediate densities (10 to 25 locusts; 25 to
62 per m2 ) were characterized by long periods of collective marching with
rapid, spontaneous reversals in rotational direction. At densities higher than
74 per m2 (30 or more locusts in the arena) spontaneous changes in direction
did not occur, with the locusts quickly adopting and maintaining a common
rotational direction.
Hence Buhl et al.’s experiments confirmed the theoretical prediction from
the SPP model of a rapid transition from disordered to ordered movement
(Figs. 6, 7) and identified a critical density for the onset of coordinated
marching in juvenile locusts. In the field, small increases in density past this
threshold would be predicted to result in a sudden transition to a highly
unpredictable collective motion, making control measures difficult to implement. The experiments also demonstrated a dynamic instability in motion at
densities typical of locusts in the field, whereby groups can switch direction
without external perturbation, potentially facilitating rapid transfer of directional information. Buhl et al.’s data and model also suggest that predicting
the motion of very high densities is easier than predicting that of intermediate
densities.
Of course, it cannot be assumed that all of the collective behavior seen
in laboratory experiments translates directly to that observed in the field.
However, the wealth of mathematical and simulation-based understanding of
SPP models provides tools for performing such scaling. In combination with
the detailed understanding of the role of the environment in behavioral phase
change, as discussed above, SPP models could now form the basis of prediction
to improve control of locust outbreaks.
3.3 Mormon Crickets
As we have noted, superficial similarities in group-level characteristics of biological systems may mask subtle, but important, underlying differences among
them. This scenario rings true for mass-migrating Mormon crickets (Anabrus
simplex). Just like locusts, Mormon crickets form cohesive migratory bands
during outbreak periods that march en masse across the landscape (Fig. 8a).
28
M. Beekman, G. A. Sword and S. J. Simpson
Fig. 6. Similarity between the self-propelled particles model of Vicsek et al. (1995)
and experimental data as density of locusts in the arena was manipulated: (A) 7,
(B) 20 and (C) 60 individuals in the arena (from Buhl et al. 2006). See text for
explanation.
These bands can be huge, spanning over ten kilometers in length, several in
width, containing dozens of insects per square meter, and capable of traveling
up to 2.0 km per day (Cowan 1929; Lorch et al. 2005). Mormon cricket bands
can cause serious damage when they enter crop systems and usually elicit
prompt chemical control measures when they appear.
Although studied far less than locusts, laboratory and field analyses of
Mormon cricket migratory behavior have provided important insights into the
mechanisms underlying group formation and subsequent collective movement
patterns. In addition, Mormon crickets have served as a key study system
in the development of the nascent field of insect radiotelemetry in which the
movement patterns of individual insects can be tracked across the landscape
using small radiotransmitters. The use of this technology has enabled the
study of landscape-scale collective movement to move beyond descriptions of
observed patterns and into the realm of empirical hypothesis testing using
manipulative field experiments.
Despite their name, Mormon crickets are not true crickets, but rather are
classified as katydids or bush-crickets. They are flightless throughout their
lives and possess small vestigial wings used by males for sound production
and mate attraction (Gwynne 2001). As a result, they are incapable of forming flying swarms and travel on the ground as both juveniles and adults.
Their religious name originates from a now legendary incident that occurred
in the spring of 1848 involving the first Mormon settlers to arrive in the Great
Salt Lake Valley in the western US. After surviving a difficult westward jour-
Total time spent in the ordered phase (min)
Biological Foundations of Swarm Intelligence
500
500
450
A
450
400
400
350
350
300
300
250
250
200
200
150
150
C
100
100
10
70
Total number of changes
in the alignment state
29
0
1
10
10
2
10
70
B
60
60
50
50
40
40
30
30
20
20
10
0
1
10
10
2
D
10
0
10
0
1
10
Mean number of moving locusts
10
2
0
10
0
1
10
10
2
Number of locusts
Fig. 7. The relation between the average number of moving locusts and the mean
total time spent in the aligned state (A and C) and the mean number of changes
in the alignment state (B and D) are displayed on a semi-log scale. Error bars,
standard deviation. The ‘ordered phase’ refers to periods where the insects exhibited
high alignment (> 0.3), and thus were moving collectively in one direction (either
clockwise or anti-clockwise). From (Buhl et al. 2006).
ney and ensuing winter, the pioneers were enjoying what appeared to be a
bountiful first spring in their newly established homeland. This serenity was
shattered when their fields, planted with over 5,000 acres of wheat, corn and
vegetables were invaded by marching hoards of large black ‘crickets’ that set
upon their standing young crops (Hartley 1970). The devout surely interpreted
this assault as an act of God analogous to the well-known Biblical plagues of
Old World locusts. The settlers’ attempts to battle the crickets using sticks,
shovels, brooms, fire and trenches were futile, but their prayers for relief were
answered by the arrival of seagulls that flew in from the Great Salt Lake and
began to devour the marauding crickets. The gulls reportedly gorged themselves on crickets in the fields, often to the point of regurgitation, after which
they would return to feast again (Hartley 1970). The gulls were credited with
saving the remaining crops, and by extension the first settlers; a multi-trophic
level interaction that resulted in the California Sea Gull being selected as the
state bird of Utah. The Miracle of the Gulls was also commemorated by the
erection of a monument at the headquarters of the Mormon Church in Salt
Lake City, one of the few monuments, if not the only one, in the world dedicated to an insect predator (Gwynne, 2001).
30
M. Beekman, G. A. Sword and S. J. Simpson
Phase Polyphenism and Migratory Band Formation
Until recently, it had been widely assumed that Mormon crickets express
density-dependent phase polyphenism similar to that known to occur in locusts. This assumption was due in large part to the similarities between migratory bands of locusts and those of Mormon crickets. The possibility of phase
polyphenism in Mormon crickets was further supported by observed phenotypic differences in migratory behavior, coloration and body size between individuals from low-density, non-outbreak populations and their counterparts
in high-density, band-forming populations (MacVean, 1987; Gwynne, 2001;
Lorch and Gwynne, 2000). MacVean (1987) noted that the formation of migratory bands in the Mormon cricket “bears a striking resemblance to phase
transition in the African plague locusts,” and Cowan (1990) described the
Mormon cricket as having gregarious and solitarious phases similar to locusts.
Mormon crickets and locusts also share phase-related terminology in the scientific literature with Mormon crickets in non-outbreak populations, commonly
referred to as inactive solitary forms (i.e. solitarious phase), whereas those in
band-forming populations are referred to as gregarious forms (e.g. Wakeland
1959; MacVean 1987, 1990; Lorch and Gwynne 2000; Gwynne 2001; Bailey et
al. 2005).
Two lines of recent evidence suggest that the expression density-dependent
phase polyphenism in Mormon crickets plays little if any role in either the
initial formation of migratory bands or the observed phenotypic differences
between insects from high-density band-forming and low-density non-bandforming populations. Sword (2005) failed to find an endogenous effect of rearing density on Mormon cricket movement behavior in the lab, but rather
demonstrated that individual movement was induced simply by the shortterm presence of other nearby conspecifics. Although the lack of a behavioral
phase change does not rule out the possibility of density-dependent changes in
other traits, a recent phylogeographic analysis of genetic population structure
suggests considerable divergence between the migratory and non-migratory
forms (Bailey et al., 2005). Thus, the differences between crickets in migratory
and non-migratory populations could primarily be due to genetic differences
rather than the expression of phase polyphenism mediated by differences in
population density.
Taken together, these studies strongly suggest, in contrast to the case
with locusts, that the expression of phase polyphenism is not involved in the
formation of Mormon cricket migratory bands. In other words, the expression
phase polyphenism in not a prerequisite for migratory band formation.
Collective Movement
The initial formation of migratory bands in Mormon crickets and locusts appears to have convergently evolved via different underlying behavioral mechanisms. Is the same true for the mechanisms governing patterns of collective
Biological Foundations of Swarm Intelligence
31
movement once these groups have formed? Are there general rules applicable
to the movement patterns of both Mormon crickets and locust bands (not to
mention other organisms), or do these differ as well? The answers to these
questions have important implications for the broader understanding of collective animal movement as well as considerable practical implications for the
development of predictive movement models that can aid in the management
of these and other migratory pests.
Given that the frequency of contact among individuals will increase with
local population density, the finding that Mormon cricket movement is induced
by immediate behavioral interactions among nearby individuals predicts that
there should be some threshold population density above which mass movement is induced (Sword 2005). Although this remains to be demonstrated in
Mormon crickets, the recent application of SPP models by Buhl et al. (2006)
to explain the induction of mass movement in locusts with increasing local
density stands as a promising general framework to explain the onset of mass
movement in Mormon cricket bands as well. Furthermore, as we shall discuss
in detail later, understanding how individual insects contend with the ecological costs and benefits of living in a group has provided considerable insight
into the general mechanisms that may drive migratory band movement.
Radiotelemetry is an extremely valuable tool available to biologists for
tracking the movement patterns of individual animals in the wild. The approach has traditionally been limited to larger vertebrates capable of carrying
the extra weight of a radiotransmitter. However, technological advances have
reduced the size of transmitters such that they can be used to track the movements of individual insects on the ground (e.g. Lorch and Gwynne 2000; Lorch
et al. 2005) (Fig. 8b) as well as in flight (Wikelski et al., 2006). Lorch and
Gwynne (2000) first demonstrated the utility of small radiotransmitters to
track individual Mormon crickets. Their study was followed by a similar, but
much more rigorous analysis by Lorch et al. (2005) who compared the individual movement patterns of insects from several different band-forming and
non-band-forming populations. These studies confirmed that Mormon crickets
in migratory bands cover much greater distances (up to 2 km/day) and tend
to move collectively in the same direction relative to insects from low-density,
non-band-forming populations (Fig. 8c, d).
In addition to consistent group directionality within as well as across
days, migratory bands also exhibit group-level turns in which similar direction changes are made by individuals regardless of their position in the band
(Lorch et al. 2005). Two possible explanations for these synchronous turns are
that either (i) group movement direction is determined by orientation towards
some landscape-scale environmental cue such as wind direction that can be
detected and responded to by all group members, or (ii) they are similar to
turns in bird flocks or fish schools in which individuals adjust their direction
in response to the movement of near neighbors and these turns are propagated through the group like a wave (Couzin and Krause 2003). Although the
Lorch et al. (2005) experiment was not designed to examine the effect of wind
32
M. Beekman, G. A. Sword and S. J. Simpson
Fig. 8. Collective movement in Mormon cricket migratory bands. (a) A large migratory band crossing a dirt road in northeastern Utah, USA (photo by G. Sword). (b) A
female Mormon cricket affixed with a small radiotransmitter (photo by D. Gwynne).
(c) Example of individual movement patterns by radiotracked Mormon crickets in
a high-density, migratory-band-forming population. Each line represents a single
individual and each line segment depicts one day of movement. (d) Examples of radiotracked Mormon cricket movement patterns in a low-density, non-band-forming
population. Note the differences in group directionality and scale of movement between the band-forming and non-band-forming populations. Radiotracking examples
are from Lorch et al. (2005).
direction on migratory band movement, local wind direction data collected
concurrently with the radiotracking data hinted that wind directions early in
the day might correlate with migratory band directions. However, no effect
whatsoever of wind direction on the movement of individuals within migratory bands was found in a follow-up study specifically designed to test the
wind direction hypothesis. Migratory bands simultaneously tracked at three
nearby sites in the same vicinity were found to travel in distinctly different
directions despite experiencing very similar wind directions and other weather
conditions (Sword et al., unpublished).
So what cues determine the direction in which a migratory band will move?
One possible answer provided by simulation models of collective animal movement patterns is that nothing is responsible. A variety of movement models
Biological Foundations of Swarm Intelligence
33
in which individuals modify their direction and movement rate in response
to others have shown that group directionality can arise from inter-individual
interactions as a result of self-organization (Krause and Ruxton 2002; Couzin
and Krause 2003). The hypothesis that Mormon cricket migratory band movement direction and distance are collectively determined was tested by conducting a manipulative transplant experiment in the field as originally described in
Sword et al. (2005). Insects traveling in naturally occurring migratory bands
were captured and radiotracked. Half of these insects were released back into
the band while the other half were transported and released at a nearby site
where bands had previously been, but were absent at the time. The resulting differences in movement patterns between the crickets released into the
migratory band versus those that were isolated from the band were dramatic
and closely resembled the previously documented differences between crickets from band-forming versus non-band-forming populations shown in Figs. 8c
and d. Insects isolated from the band moved shorter distances, and were much
less directional as a group relative to the insects released back into the band
(Sword et al., unpublished). These findings quite clearly show that the distance and direction traveled by insects in a migratory band are group-level
properties that differ considerably from the movement patterns of individuals
when they are removed from the social context of the band.
A Forced March Driven by Cannibalism
Mormon crickets provide a unique model system in which understanding the
costs and benefits of migratory band formation has provided a unifying framework that explains both how and why inter-individual interactions can lead
to landscape-scale mass movement. The evolution and maintenance of migratory band formation in insects necessarily requires the benefits of such a
strategy to outweigh its costs in terms of individual survival and reproduction.
The radiotelemetry-based transplant study of Sword et al. (2005) mentioned
above was originally designed to study collective movement, but it unexpectedly yielded a critical insight into the benefits and selection pressures that
favor the formation of migratory bands. Individual band members were much
less likely to be killed by predators than were crickets that had been separated
from the group. The precise mechanisms by which individuals in bands gain
protection from predators were not identified (see Krause and Ruxton 2002 for
potential mechanisms), but 50–60% of the crickets removed from migratory
bands were killed by predators in just two days while none within the bands
were harmed during the same period. Thus, migratory bands form as part of
an anti-predator strategy and there is a very strong adaptive advantage to
staying in the group.
Although migratory bands confer anti-predator benefits, living in a huge
group of conspecifics also has a variety of potential costs (see Krause and
Ruxton 2002). It is precisely the interplay between these costs and benefits
that promotes cohesive and coordinated mass movement among individual
34
M. Beekman, G. A. Sword and S. J. Simpson
Mormon crickets living in bands. Recent field experiments revealed that individual band members are subject to increased intraspecifc competition for
nutritional resources. Individual crickets within migratory bands were shown
to be deprived of specific nutrients, namely protein and salt (Simpson et al.
2006). When provided with augmented dietary protein, individual crickets
spent less time walking; a response that was not found when crickets had
ample carbohydrate. Thus, group movement results in part from locomotion
induced by protein deprivation and should act to increase the probability
that individual band members will encounter new resources and redress their
nutritional imbalances.
An additional cost of group formation is that Mormon crickets are notoriously cannibalistic (MacVean 1987; Gwynne 2001). Their propensity to
cannibalize is a function of the extent to which they are nutritionally deprived. Given that Mormon crickets are walking packages of protein and salt,
the insects themselves are often the most abundant source of these nutrients
in the habitat. As a result, individuals within the band that fail to move risk
being attacked and cannibalized by other nutritionally deprived crickets approaching from the rear (Simpson et al. 2006). Thus, the mass movement of
individuals in migratory bands is a forced march driven by cannibalism due to
individuals responding to their endogenous nutritional state. The fact that migratory bands are maintained as cohesive groups despite these seemingly dire
conditions suggests that the risk of predation upon leaving the band must
outweigh the combined costs of intraspecific competition for resources and
cannibalism. Importantly, ongoing experimental work strongly implicates the
threat of cannibalism as a general mechanism that mediates migratory band
movement in locusts as well as Mormon crickets (Couzin et al., unpublished).
4 Concluding Remarks
We have discussed in detail three cases of collective movement of large groups
of animals: honeybees, locusts and Mormon crickets. A description of their
movement would yield striking similarities: individuals in the group seem to
keep an almost fixed distance from their neighbors; they tend to align themselves with their nearest neighbor, and show a clear tendency to stay with the
group. In fact, this description can easily be extended to many other animals
that move in groups, such as to schools of fish and flocks of birds (Couzin
et al. 2005). However, the reasons for their collective movement are fundamentally different. For individual bees in a swarm it is critically important
to stay with the swarm, as an individual bee cannot live. Cohesive movement
in locusts is induced by the fine-scale structure of the environment they find
themselves in. And if you are a Mormon cricket, moving faster than the ones
behind you is essential to prevent yourself from becoming your neighbor’s next
meal.
Biological Foundations of Swarm Intelligence
35
We as biologists are fascinated by nature’s diverse tapestry. Often, biologists tend to argue that nature is too diverse to allow its manifestations to
be captured by generalist models. This is not the message that we want to
convey in this chapter. As we have illustrated, many behaviors can only be
understood by constructing models, which, by definition, are an abstract representation of reality. It is helpful to think about unifying theories that have
the power to explain behaviors across a range of biological systems. We encourage computer scientists and mathematicians to look at biological systems
and to become inspired, see patterns, and seek applications beyond biological
systems. But in doing so, we hope that researchers will be awed not by the
superficial similarities between natural systems but by the intricate and often
subtle differences that distinguish them.
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