Short
Communication
The Blind
Leading the
Blind:
Modeling
Chemically
Mediated Army
Ant Raid Patterns
J. L. Deiieubourg,'"'
S. Goss,' N.
Franks,^
and J. M. Pasteels'
Acceptée!
7
April 1989; rexised
27
April 1989
KEY WORDS:
army ants; raid patterns;
self-organizalion;
mathemalical
model.
INTRODUCTION
Army
ant colonies are among the
largest
and most cohesive societies. Individual
ants
are typically
less
than 10 mm long, communication between them is
restricted
to local chemical and tactile stimuli, and yet their foraging Systems
coordinate
hundreds of thousands of individuals and cover some 1000
m^
in a
day
(Fig. 1) (Raignier and Van Boven, 1955; Rettenmeyer, 1963;
Schneirla,
1971; Topoff,
1972;
Gotwald,
1982; Franks and Fletcher,
1983;
Burton and
Franks, 1985).
Such swarm raids pose in the strongest possible way the
gênerai
problem
of collective
décision
making without any form of centralized control.
Dur
model shows how their characteristic patterns
could
be seif-organizing.
1.
e., generated
froni
the interactions between many identical foragers, each with
simple trail-laying
and
trail-following
behavior.
MODEL
AND MONTE CARLO SIMULATIONS
Unlike
most other ant species, army ant foragers
lay
pheromone not
only
when
rctuming with prey but
also,
to a lesser extent,
while
advancing with the
swarm
(Schneirla, 1933, 1940). If we
considerthe
swarm to move in a
discrète
network
of points representing continuous
two-dimensional
(2-D) space (Fig.
2,
inset), at each point each ant chooses ahead left or ahead right, moves, and
adds
to the pheromone at the point chosen.
Initially,
the choice is random.
'
Unit of
Behavioural
Ecology, C.P.
231,
Université Libre de Bruxelles,
1050
Bruxelles.
Belgium.
^School
of Biological Sciences,
Balh
University,
Clavetlon
Down,
Bath
BA2 7AY, U.K.
•'TO
whom
corrcspondence
should bc
addrcsscd.
719
08«2.7.tS.VII9/n9m.07l9S06.nn/n & \<m ncnum PuMisliing C»n«>Tali»n
KIg.
I.
Foraging pulicms
of
(hrcc amiy anls, Erium hamiilum,
E.
rcipiL\,
and E.
hurthelli
(fnmi Icfl lo righl), cath covcring somc
50
X
20 m.
(Kedrawn friiiii RcIlL-nmcycr
(1963) and
Hunon
and
Frunks (1985).)
T
Step
300
Step
600
Step
900
Fig.
2. Monte Carlo simulation of the
model
on a network of points reprcscnting 2-D space
(inset).
At each point,
prob.
(choosing
lefi) =
1 - prob. (choosing right) =
1^
+
P\fK(.S
+ (
Pi)"
+
(5
+ P,) ]. where
P,
and P, are the quantities of pheromone ahcad left'and righl. Prob.
(moving
per step)
= 1 + 1 lanh \(P,
+
P,)/P„2
-
U-
e =
j,,. P,i2
=
'00,
P,,,, (advancing ants)
= 1000,
and
(retuming
ants) = 300. Ten ants
leave
the nest per step. Maximum
numbcrof
ants
per point = 20. The unit for P is the quantity of pheromone laid by an advancing ant per
point.
Retuming anls
lay 10
pheromone
unils
per
point
Modeling Chemically Mediated
Army Ant Raid Patierns
721
However,
in marking, each ant that passes a point modifies the following ant's
probabiiity
of choosing
left
or right, an autocalalytic System that rapidly
Icads
to
a symmctry
breaking,
one of the two points ahcad bccoming
more
or
Icss
complclcly
prcfcrrcd to the
other.
This process, rcpeatcd at each point
along
the
swarm's path, is the basis of how the swann forms its trails.
This modcl
is subject to three refincments. First, it is obscrvcd that the
foragers
on the
trail
move rapidly and directly (Schneirla, 1940; Franks, 1985),
whereas
those at the front are much slower, more
hésitant
and random, making
characteristic
looping movements. This is linked to the fact that the trail is
extremely well
marked,
while
the leading edge of the front is unmarked. We
simulate
this by making the probabiiity of each ant's moving at each step
incrcasc
sigmoidally with
the pheromone
quantity ahcad of it.
Second,
there is a maximum
numbcrof
ants that can occupy onc point. At
each
point the
foragers décide
whethcr to move and, if so, whcther lo move
ahcad Icft
or ahcad right. Should the point ahcad right not have cnough room
for ail
those wishing to move
there,
the surplus move ahcad
Icit
instcad, and
vice
versa. Should both points ahead be
full,
thcn the surplus ants stay where
thcy
arc |cf. Schneirla's (1940)
pressure/drainage analogy).
Third,
a fixed fraction,
e,
of the
pheromone
at each point
évaporâtes per
step. Only
moving ants lay
pheromone,
at the point at which thcy
arrive,
although
not if the quantity of pheromone there is greater than a
salurali(m
value, P,.„.
Figure
2 shows a Monte Carlo simulation of this model.
The
choicc func-
tion
proposed is based on an
expérimental
study of similar but smallcr explor-
atory swanns
in the Dolychoderine ant,
Iridomynnex liumilis (Dencubourg
et
al.,
1989), and an analytical model (Deneubourg, 1979). A diffuse front is
formed
and advances with a concentrated trail extending from its trailing edge
to
the nest. At the front, the ground is relatively unmarked and the ants move
slowly
and randomly, thus accumulating and spreading out. At the trailing edge
of
the front, the number of passages is suffcient for one path, the trail, to have
become
preferred to
ail
other possibilities.
So
far we have defined only ants that advance, but what about those that
retum?
We state that they retum when they have found a food item. How is the
food
distributed? We first consider that each point has a fixed probabiiity of
containing
one nonrenewable food item, transportable by one ant. This approx-
imates
the situation of Eciton
burchelli,
which feeds largely on scattered arthro-
pods
(Franks and Bossert, 1983).
The
first ant that arrives at a point containing a food item takes it and retums
toward
the nest, obeying exactly the same
mies
as an advancing ant, laying,
however,
a greater
amouiit
of pheromone per step. Arriving at the nest, it lays
down
the food item and retum outward once more. (Note that should there be
,
at
any point no guiding pheromone in front of them, they move toward
the*
rfnfrtl ll lil 'ilthniinh thit- ml ' i'- nnl" rtri>l\' iti-'.-l o,l N
722
Siep
300
Sfep
700 Step
1100
Fig.
3. The
same
as Fig. 2,
wilh
each
poini
having a
l-in-2 probability
of conlaining one food
ilem.
With
a
low
food density, the retuming ants do not modify the swarm pattem
seen
in Fig. 2. However, with higher densities, they cause the central
trail
to
split
into
latéral
trails which
themscives
branch out, giving a swarm
like
a river
delta
(Fig. 3), characteristic of E. burchelli. As the swarm advanccs the older
latéral
trails are
progressively
abandoned,
while
new ones are formed just behind
the
diffuse front.
Finally,
E.
hamatum
feeds more on dispersed social insect colonies, and
its
food distribution can be represented by each point having a very small prob-
ability
of containing a very large
numberof
food items. E.
rapcix
has an inter-
mcdiary
diet. With this more hetcrogencous food distribution, the swarm splits
up
into a
numberof
small columns and deltas (Fig. 4), characteristic of
E. rapax
[see
also
Moffet
(1988)
for
the
différent
pattems of
Pheidologeton
diversus when
presented
with dispersed or concentrated food sources).
DISCUSSION
It
is known that the army ant syndrome has evolved convergently at
least
seven
times (Wilson, 1958) and that "group raiding" behavior is found in a
number
of distantly related social insects (Pasteels, 1965; Stuart, 1969;
Maschwitz
and Miihlenberg,
1975;
Leuthold et al., 1976;
Oloo
and Leuthold,
Modeling
Chemically
Mediated
Army Ant Raid Palterns
723
Sfep 500
Step 1000 Step 1300
Fig.
4. The same as Fig. 3, wilh each point having a
1-in-lOO
probabilily of conlaining 400
food ilcnis.
1979; Hôlldobler
et al., 1982; Moffet, 1984) and even in some grcgarious cat-
erpillars
(Fitzgerald and Peterson, 1988). This appears
less
surprising if we
consider tlie
essential simplicity of the mechanism needed ta coordinate the very
large
numbers of participants, namely, laying
trail-pheromone
both while
advancing
and while retuming. Furthermore, the manner in which the environ-
ment détermines
the
différent
swarm pattems
leads
us to suggest that they orig-
inally
arose from the same behavior associated with
différent
prey
préférences
and
that gradually additional mechanisms evolved to reinforce and accentuate
thèse pattems,
which then became species
spécifie.
For
example, Chadab and Rettenmeyer (1975) showed how a single E.
hamatum
forager can divert nestmates from a dense foraging column toward an
important
food source, using tactile stimuli and probably a
différent
chemical
signal
from that used on the main foraging trails, thereby accentuating the
swarm's
branching. Topoff et al. (1980) have shown a similar behavior in Nei-
vamyrmex
nigrescens. (Note that while the
model
does not distinguish between
exploration
and recmitment, considering the same pheromone to be used in both
processes,
those that retum with food
lay
considerably more trail pheromone
than
those advancing and are responsible for the branching observed in Figs. 3
and
4.) Schncirla's (1940) pressure/drainage analogy also
accentuâtes
the
rôle
724
Deneubourg,
Goss, Franks, and Pasteels
of
physical contact between workers.
Nevertheless,
in our wish to stress how
maximum
collective complexlty can be compatible with maximimum individual
simplicity,
we have ignored
thèse
and other possible factors, such as surface
heterogeneity,
that may influence the swarm's pattem.
We
have shown how swarm pattems can resuit from the interplay between
chemical
communication and food exploitation.
While
most ant and termite
species
do
net
exhibit legionary behavior (and do not
lay trail
pheromone as
they
explore), the majority nevertheless relies on trail
pheromone
to
coordinate
their
foraging activity. The basic script is simple. A
numberof
scouts
leave
the
nest.
Those that find food retum, laying a trail whose strength
dépends
on the
size
and quality of the food, the forager's species, etc. Other foragers waiting
in
the nest follow
thèse
trails more or
less
successfully. Taking into account
spécifie
characteristics such as colony size, type, and distribution of prey, etc.,
a small
set of simple
rules
similar to those presented for the army ants
could
explain
many
différent
types of spatiolcmporal forager distribution (Goss and
Deneubourg,
1989, in
préparation),
such as the formation of
trunk-traiis
(Hôlldobler
and Lumsden, 1980), the
sélection
of the best food sources (Pas-
teels
et al., 1987), the sequential exploitation of contiguous foraging zones
(Bemstein,
1975; Franks and Fletcher, 1983), and the switch from diffuse to
concentrated
foraging (Hahn and Maschwitz,
1985).
AU thèse
Systems have in common simplicity and equality of the individ-
uals,
communicating chemically with a single pheromone.
Thèse
minimalistic
assumptions,
deliberately ignoring other factors such as
âge
and memory, are
justified
in that we wish to show the
rôle
and limits of such self-organization
mechanisms.
The resulting structures are dynamic and adapt as the actors inter-
act
with the environment,
conferring
a degree of intelligence to the society that
far
exceeds the capacity of its individual members.
ACKNOWLEDGMENTS
This
work is supported in part by NATO
Scientific
Affairs Division Grant
034/88,
the Belgian program on interuniversity attraction
pôles,
and Les Insti-
tuts
Internationaux de Physique et de Chimie.
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