2903
The Journal of Experimental Biology 208, 2903-2912
Published by The Company of Biologists 2005
doi:10.1242/jeb.01711
Temporal organization of bi-directional traffic in the ant Lasius niger (L.)
Audrey Dussutour1,*, Jean-Louis Deneubourg2 and Vincent Fourcassié1,†
1
Centre de Recherches sur la Cognition Animale, UMR CNRS 5169, Université Paul Sabatier, 118 route de
Narbonne, F-31062, Toulouse Cedex 4, France and 2Service d’Ecologie Sociale and Centre d’Etudes des
Phénomènes Non-linéaires et des Systèmes Complexes, Université Libre de Bruxelles, CP231, Boulevard du
Triomphe, B-1050 Bruxelles, Belgium
*Present address: Biology Department, Concordia University, 7141 Sherbrooke St W., Montreal, Quebec, Canada H4B 1R6
†
Author for correspondence (e-mail: fourcass@cict.fr)
Accepted 24 May 2005
Summary
Foraging in ants is generally organized along wellorganization limits the number of head-on encounters and
defined trails supporting a bi-directional flow of outbound
thus allows to maintain the same travel duration as on the
and nestbound individuals and one can hypothesize that
wide bridge. A model is proposed to assess in various
this flow is maximized to ensure a high rate of food return
conditions the importance of the behavioural rules
to the nest. In this paper we examine the effect of
observed at the individual level for the regulation of traffic
bottlenecks on the temporal organization of ant flow. In
flow. It highlights how the interplay between the value of
our experiments ants had to cross a bridge to go from
the flow and cooperative behaviours governs the
their nest to a food source. Two types of bridges were
formation and size of the clusters observed on the bridge.
used: one with and one without bottlenecks. Traffic counts
show that, in spite of the bottlenecks and the reduction of
path width, the volume of traffic and the rate of food
Supplementary material available online at
http://jeb.biologists.org/cgi/content/full/208/15/2903/DC1
return were the same on both bridges. This was due to a
change in the temporal organization of the flow: when
path width decreases alternating clusters of inbound and
Key words: ants, traffic, cooperation, crowding, foraging, mass
recruitment, trails.
outbound ants were observed crossing the bridge. This
Introduction
The collective displacement of assemblies of organisms is
certainly one of the most spectacular phenomena one can
observe in nature. A column of army ants, a swarm of locusts,
a herd of migrating wildebeests, a flock of birds or a shoal of
fish can sometimes comprise several million individuals.
Collective displacements are characterized by a high degree of
coordination among individuals. This coordination is allowed
by short response latencies: the movement of an individual is
almost immediately followed by a parallel movement of the
neighbouring individuals located within perceptual range.
Each individual in a formation is submitted to conflicting
forces of interattraction and repulsion (Couzin et al., 2002),
and a rupture in the balance between the two categories of
forces can lead to the collapse of the group. A number of recent
reviews attests to the growing interest in the study of collective
motion (Parrish and Hamner, 1997; Boinski and Garber, 2000;
Camazine et al., 2001; Krause and Ruxton, 2002; Couzin and
Krause, 2003; Chowdhury et al., 2004; Ball, 2004).
Ants provide an excellent model for the study of collective
movement because of their highly social organization that
functions in a completely decentralized manner (Camazine et
al., 2001). Collective motion in ants is mainly organized along
well-defined trails that are initially created by the deposition of
pheromone but can turn into more or less permanent trunk-trails
through the physical modification of the environment in the
case of sustained traffic over a long period of time (Hölldobler
and Wilson, 1990). Because social insects are central-place
foragers, these trails, unlike most collective movements that
take place in a migration context, support a bi-directional flow
of outbound and nestbound individuals (John et al., 2004). They
are used for the exchange of food or individuals between nests
in polydomous colonies (i.e. the same colony is distributed
among several nests linked by more or less permanent trunktrails; e.g. Pfeiffer and Linsenmair, 1998) or for the collective
harvesting of abundant food sources (clusters of prey, aphid
honeydew, seeds or leaves in leaf-cutting ants). In the latter
case, it is essential that ants maximize the traffic flow on the
trails to ensure a high rate of food return to the nest.
In this paper, we examine the effect of bottlenecks on traffic
flow in the ant Lasius niger (L.). To go from their nest to a
food source, ants were forced to cross a bridge whose central
part is so narrow that it allows the passage of a maximum of
THEJOURNALOFEXPERIMENTALBIOLOGY
2904 A. Dussutour, J.-L. Deneubourg and V. Fourcassié
two ants at a time across its width. Because of this constraint,
we were interested in the temporal organization of the flow,
and not in its spatial organization, as in previous studies of ant
trail traffic (Burd et al., 2002; Couzin and Franks, 2002;
Dussutour et al., 2004). This kind of situation may occur when
ants or termites are moving between nest chambers through
narrow section galleries. In bi-directional streams of
pedestrians, narrow passages (e.g. doors or narrowing
corridors) give rise to jamming phenomena and to oscillatory
changes in the flow direction (Helbing et al., 2001, 2005).
Here, we show that a similar phenomenon can be observed in
ants at high levels of traffic intensity. This temporal
organization, which emerges through a cooperative behaviour
between ants, can minimize the amount of head-on encounters
per ant and per unit distance and explains why a narrow bridge
can sustain the same flow intensity as a large bridge, thus
ensuring the same rate of food return to the nest.
Materials and methods
Species studied and rearing conditions
We used the black garden ant, Lasius niger, a species that
uses mass recruitment through scent trails to exploit abundant
food sources. We collected four colonies of 4000–5000
workers in Toulouse (south-west France) in September 2001.
Each of these colonies was subdivided into two or three
queenless experimental groups, each containing 1000 workers
without brood, yielding a total of 12 experimental groups.
Each experimental group was housed in a plastic box of
100·mm diameter, the bottom of which was covered by a layer
of plaster moistened by a cotton plug soaking in a water
reservoir underneath. The box was connected to an arena
(diameter, 130·mm) whose walls were coated with Fluon® to
prevent ants from escaping. The nests were regularly
moistened and the colonies were kept at room temperature
(25±1°C) with a 12·h:12·h L:D photoperiod. We supplied ants
Nest side
Access
ramp
Bottleneck
(1)
with water and a mixed diet of vitamin-enriched food
(Bhatkhar and Withcombs, 1970), as well as maggots
(Calliphora erythrocephala), three times a week.
Experimental set-up and protocol
In each experiment, an experimental group starved for
5·days was given access to a food source (2·ml of 1·mol·l–1
sucrose solution) placed on a platform (70⫻70·mm) at the
other end of a bridge. The food source was spread over a
surface large enough to accommodate a large number of ants
without crowding. We used two kinds of bridges whose central
part was characterized by a different width: 10·mm (control
bridge) or 3·mm (experimental bridge). The total length of the
bridges was 210·mm. For the purpose of the analysis, the
bridges were divided into six different sections (see Fig.·1): an
access ramp (95·mm long), which began in the small arena
connected to the experimental nests, one bottleneck (15·mm)
and one entrance (15·mm) at both ends of the bridge (hitherto
defined as the nest and source side of the bridge), and a central
part (60·mm). For the 10·mm bridge, all sections had a width
of 10·mm. Fifteen trials were achieved with each type of
bridge. All trials were filmed for 1·h by a video camera placed
over the bridge.
Data collection
Traffic dynamics
The traffic on the bridge was counted over a 1·min period
every three minutes during 1·h. Counting began as soon as the
first ant was observed climbing the bridge. We measured the
flow of ants leaving the nest and that leaving the food source
at the level of the entrances on each side of the bridge.
Traffic organization
In order to investigate the traffic organization in extreme
crowding conditions, we focused our analysis for each bridge
on the trial characterized by the highest flow of ants
Source side
Entrance
(1)
Centre
Entrance
(2)
Bottleneck
(2)
Sugar source 1 mol l–1
10 mm
3 mm
15 mm
15 mm
60 mm
15 mm
15 mm
Fig.·1. Schematic illustration of the 3·mm-width bridge, with the different sectors defined for the analysis of the ants’ individual behaviour.
THEJOURNALOFEXPERIMENTALBIOLOGY
Temporal organization of traffic in ants 2905
Data analysis
The relationship between variables across bridge widths (3 or
10·mm) or bridge sides (nest or source) was examined using
multiple regression analysis. For this purpose, continuous
predictor variables were centred on their means (i.e. the mean
value was subtracted from each observation), and categorical
variables (either bridge width or bridge side) were coded as scalar
numbers. This procedure is recommended in multiple regression
analysis because it reduces the covariation between linear
variables and their interaction terms (Aiken and West, 1991).
In order to investigate whether the sequence of inbound and
outbound ants was random or consisted of an alternation of
groups of ants travelling in opposite directions, we used a onesample runs test of randomness (Siegel and Castellan, 1988).
This test is based on the number of runs in a sequence of
categorical data. A run is defined as a succession of data
belonging to the same category (in our case +1 or –1) and is
delimited at both ends by a value belonging to the other
category. The total number of runs in a sequence gives an
indication of whether or not the sequence is random. The
occurrence of very few runs suggests a time trend or some
bunching owing to a lack of independence between data. The
occurrence of many runs indicates systematic cyclical
fluctuations of short period. In addition, we tested with a
Kolgomorov–Smirnov two-sample test whether the
distribution of the size of the groups of ants travelling in the
same direction was random by comparing it with that given by
a theoretical sequence generated on a basis of equal probability
of occurrence of nestbound and outbound ants.
Results
Traffic dynamics
The recruitment dynamics and the traffic volumes were not
influenced by bridge width (Fig.·2; two-way ANOVA with
repeated measures on time interval; width effect, F1,32=0.62,
P=0.439; interaction width ⫻ time effect, F19,32=1.21,
P=0.247) and were typical of a trail-recruitment process
(Pasteels et al., 1987). The flux reaches a peak after ~12·min
(time effect; F19,32=17.20, P<0.001).
Traffic organization
Travel duration and interactions between ants
There was no significant difference between the two bridge
widths in the time required to cross the bridge without
interaction [mean ± S.D., 2.96±0.61·s and 2.93±0.56·s (N=50)
for 10·mm and 3·mm bridges, respectively; Student’s t-test;
t=0.73, P=0.735]. Therefore, the geometry of the system alone
did not have any effect on the mean travel speed of the ants.
The regression model of the net travel duration on the
number of contacts across bridge width was significant (Fig.·3;
ANOVA for the whole model; F3,255=626.43, P<0.001) and
accounted for 88.1% of the variance. As a confirmation of the
preceding analysis, the model indicates that, in the absence of
contacts, there was no effect of bridge width on the time
required for an ant to cross the bridge [intercept of the
regression lines with the y-axis (±C.I.0.95) indicated on Fig.·3:
120
Mean no. of ants (min–1)
(approximately 120·ants·min–1). The following data were
collected.
Travel duration and interactions between ants. For both
types of bridges, we first computed, for a sample of 50
outbound ants, the time required for an ant to travel the length
of the bridge between the two bottlenecks in the absence of
interactions with other ants. The times were measured from the
time stamp of the video frames, allowing a precision of
1/25=0.04·s. Because 120·ants·min–1 was too high to allow the
passage of an ant without interactions, these data were obtained
for each bridge from another trial, characterized by a smaller
traffic volume (∼60·ants·min–1).
We then counted for both types of bridge, on a sample of
150 outbound ants on the trial characterized by the highest flow
of ants, the number of encounters occurring per ant when
travelling between the two bottlenecks. An encounter was
counted each time an ant passed another one in the same or in
the opposite direction, with or without contact. A contact could
be the result of either a collision (when the heads of two ants
enter into contact) or a push (when the head of an ant enters
into contact with the gaster of the ant preceding it). The net
travel duration (i.e. including the time spent in interactions) for
each ant was also measured. The measurements began 10·min
after the beginning of the experiment, when the outbound and
nestbound flow of ants was at equilibrium.
The time lost per interaction with contact was estimated by
regressing the net travel duration on the number of encounters
with contact. The probability to be contacted during an
interaction was estimated by regressing the number of
encounters with contact on the total number of encounters with
or without contact.
Temporal organization of the flow of ants. For both types of
bridges, we noted the travel direction for a sequence of 2700
successive ants (+1 for inbound ants, –1 for outbound ants) and
the time at which each ant crossed the line between the
bottleneck and the entrance on the nest side of the bridge. The
sequence lasted approximately 20·min.
3 mm
10 mm
100
80
60
40
20
0
0
5 10 15 20 25 30 35 40 45 50 55 60
Time (min)
Fig.·2. Mean number of ants per minute crossing the bridge in both
directions every 3·min. Values are means ± S.E.M. N=15 trials for both
bridge widths.
THEJOURNALOFEXPERIMENTALBIOLOGY
2906 A. Dussutour, J.-L. Deneubourg and V. Fourcassié
20
45
3 mm
10 mm
40
3 mm
10 mm
35
Number of contacts
Travel duration (s)
15
10
y=0.48x+2.46 r2 =0.88
5
30
25
20
15
10
y=0.68x r2 =0.96
5
y=0.36x r2 =0.96
y=0.43x+2.49 r2 =0.83
0
0
5
10
15
20
25
10
2.46±0.27·s and 2.49±0.47·s for 10·mm and 3·mm bridges,
respectively]. Travel duration increased significantly with the
number of contacts (t=38.87, P<0.001) and was significantly
affected by bridge width (t=4.87, P<0.001): for the same
number of contacts, the duration of travel was higher for
10·mm bridges than for 3·mm bridges. Moreover, there was a
significant interaction effect between bridge width and the
number of contacts (t=2.43, P=0.016). Travel duration
increased slightly more rapidly for 10·mm than for 3·mm
bridges: the time lost per contact (which corresponds to the
slope of the regression lines indicated in Fig.·3) amounted to
0.430±0.017·s (mean ± S.E.M.) on the 3·mm bridge and to
0.480±0.015·s (mean ± S.E.M.) on the 10·mm bridge.
Examination of the standardised regression coefficients (which
are in units of S.D. and therefore can be compared directly) of
the multiple regression model shows, however, that travel
duration was almost entirely determined by the number of
contacts with other ants (β=1.00, 0.12 and 0.05 for the effect
of the number of contacts, bridge width and the interaction
term between the two variables, respectively).
The regression model of the number of encounters with
contacts on the number of encounters per ant across bridge
width yielded a significant linear relationship (Fig.·4; ANOVA
for the whole model; F3,258=323.52, P<0.001) and accounted
for 79% of the variance. The model indicates a significant
effect of the number of encounters (t=24.30, P<0.001), of
bridge width (t=–24.05, P<0.001) and of the interaction term
between these two variables (t=–4.80, P<0.001). Examination
of the standardised regression coefficients shows that the main
effect on the number of contacts was due to the number of
30
40
50
60
Number of encounters
Number of contacts
Fig.·3. Effect of the number of encounters with contact on the duration
of travel between the two bottlenecks of the bridge for the two bridge
widths studied. The slope of the linear regression lines corresponds
to the time lost by each ant per interaction; its intercept gives the
duration of travel without interaction. N=133 and N=126 for the 3·mm
and 10·mm bridge, respectively.
20
Fig.·4. Relationship between the number of encounters with contact
and the total number of encounters per ant for each bridge width
studied. The slope of the lines corresponds to the probability of an ant
travelling on the bridge to be contacted by another ant during an
encounter. N=133 and N=126 for the 3·mm and 10·mm bridge,
respectively.
encounters (β=0.780), followed by bridge width (β=–0.710)
and the interaction between these two variables (β=–0.149). A
separate regression analysis on the data for each bridge width
explains 95.7% and 96.4% of the variance for 3·mm and
10·mm bridges, respectively (Fig.·4). The slope of the
regression lines on Fig.·4 gives the probability of contacting
another ant during an encounter. It is significantly higher for
the 3·mm (0.681±0.013, mean ± S.E.M.) than for the 10·mm
(0.360±0.06, mean ± S.E.M.) width. The fact that we obtained
a good fit with a linear regression shows that the probability of
contact does not increase with the volume of traffic and
depends only on the width of the bridge.
Since the volume of traffic was not significantly different on
the two bridge widths (see Fig.·2), one would have expected the
number of encounters (with and without contacts) per ant on the
3·mm bridge to be at least equal to that on the 10·mm bridge.
However, this is not what we actually observed. In fact, the
number of encounters per ant was lower on the 3·mm bridge than
on the 10·mm bridge [mean ± S.D., 19.86±5.53 (N=126) and
23.09±8.29 (N=133) for 3·mm and 10·mm bridges, respectively;
Student’s t-test; t=3.67, P<0.001]. This discrepancy suggests
that there is some temporal organization in the flow of ants,
decreasing the number of interactions on the 3·mm bridge. This
is indeed what is shown in the following section.
Temporal organization of the flow of ants
The one-sample runs test of randomness allowed us to
identify the formation of groups of successive ants travelling
in the same direction in the sequence of ants observed on the
3·mm bridge (Z=–26.15, P<0.001; see Movie 2 in
THEJOURNALOFEXPERIMENTALBIOLOGY
Temporal organization of traffic in ants 2907
Random
10 mm
3 mm
0 .6
0 .5
0 .4
0 .3
0 .2
0 .1
0
1
2
3
4
5
6
7
Group size
8
9
>10
Fig.·5. Experimental results. Distribution frequency of the size of the
groups of successive ants travelling in the same direction identified at
the level of the line between the bottleneck and the entrance on the
nest side of the bridge for each bridge width. The distribution
frequency of group size obtained with a random sequence of ants
generated on the basis of an equal probability of occurrence of
nestbound and outbound ants is also represented. N=1203 and N=905
for the 10·mm and 3·mm bridge, respectively.
supplementary material). The distribution of the size of the
groups identified in the sequence was significantly different
from that given by a random sequence of nestbound and
outbound ants (Fig.·5; Kolmogorov–Smirnov; Z=1.58,
P=0.013). The mean size of a group on a 3·mm bridge was 3.3.
By contrast, the sequence of ants on a 10·mm bridge was not
different from random (Z=0.58, P=0.560) and the distribution
of group size observed on a 10·mm bridge was not different
from that computed from a random sequence (Fig.·5;
Kolmogorov–Smirnov; Z=0.67, P=0.759; see Movie 1 in
supplementary material). A Fourier analysis conducted to test
the periodicity between groups of opposite direction for 3·mm
bridges did not give any conclusive results.
To investigate the mechanisms allowing the formation of
alternating groups of ants travelling in opposite direction on a
3·mm bridge, we noted, for both travel directions and for both
sides of the bridge, the time at which 500 successive ants
travelling in the same direction crossed (Fig.·1) (1) the line
between the access ramp (or the platform) and the bottleneck,
(2) the line between the bottleneck and the entrance and (3) the
line between the entrance and the centre of the bridge. The
sequence of inbound and outbound ants crossing each line was
then reconstructed from the time tag of each ant. A total of
2000 ants was followed: 500 ants for each direction and each
side of the bridge.
The run test applied to the sequences of ants travelling
between the different sections of the 3·mm bridge yielded a
non-significant result for the sequence of ants crossing the line
between the access ramp and the bottleneck for the nest side
of the bridge (Z=0.59, P=0.555), and for that between the
platform and the bottleneck for the source side of the bridge
(Z=0.74, P=0.458). By contrast, the formation of groups of
successive ants travelling in opposite direction was detected on
the line between the bottleneck and the entrance (Z=–8.81,
P<0.001 and Z=–9.43, P<0.001, for the nest and source side
of the bridge, respectively), as well as on the line between the
entrance and the centre of the bridge (Z=–9.777, P<0.001 and
Z=10.247, P<0.001, for the nest and source side of the bridge,
respectively). This result suggests that the formation of groups
was generated at the level of the two bottlenecks, and not at
the moment the ants left the nest or the food source.
In order to investigate the priority rules between ants at the
level of the two bottlenecks, the following variables were
measured. (1) The time spent crossing the two bottlenecks and
the two entrances (N=500 for each bridge side). (2) The
number of encounters at the level of the two bridge
constrictions, on the line between the bottleneck and the
entrance (Fig.·1); the delay between the time each ant was
stopped by an encounter and the time it started again was also
noted). (3) The number of contacts in the two bottlenecks
(N=250 for each bridge side).
A three-way ANOVA was used to test for the effect of sector
(bottleneck vs entrance), travel direction (ants travelling
towards the centre of the bridge vs those travelling out of the
centre) and bridge side (nest vs source) on the time spent by
ants to cross the bottlenecks and the entrances. Since the ants
were individually followed when travelling across the
bottlenecks and the entrances on both sides of the bridge, the
sector effect was treated as a repeated measure factor. The data
were log-transformed to allow for normality.
Examination of the estimates of effect size of the ANOVA
(partial correlation effect size; Kline, 2004) shows that the main
effect on the total variance of the scores was due to the
interaction between sector and travel direction (Fig.·6; Table·1;
Bottleneck
Entrance
Time to cross a sector (s)
Proportion of groups
0 .7
6
4
2
0
Travel direction
Fig.·6. Distribution of the time spent crossing the bottlenecks and the
entrances for ants travelling to and from the centre of a 3·mm bridge
(for each sector, the results for the nest and source sides of the bridge
have been pooled). The dotted lines within the boxplots represent the
median, the lower and upper boundaries of the boxes represent,
respectively, the 25th and 75th percentiles, while the whiskers extend
to the smallest and largest values within 1.5 box lengths. The open
circles represent the outliers. N=500 for each box plot.
THEJOURNALOFEXPERIMENTALBIOLOGY
2908 A. Dussutour, J.-L. Deneubourg and V. Fourcassié
Table·1. Results of a three-way ANOVA to test for the effect of
the travel direction (ants travelling from the bridge ends
towards the centre of the bridge vs those travelling from the
centre towards the bridge ends), the bridge side (nest vs
source) and the sector (bottleneck vs entrance) on the time
required to cross a sector by an ant
Mean
squares
d.f.
F
P
Between ants
Travel direction
Bridge side
Travel direction ⫻ bridge
side
5.469
0.082
2.520
1
1
1
74.04
1.07
33.03
<0.001
0.301
<0.001
Within ants
Sector
Sector ⫻ travel direction
Sector ⫻ bridge side
Sector ⫻ travel direction
⫻ bridge side
2.657
9.448
0.004
0.321
1
1
1
1
44.80
158.14
0.07
5.37
<0.001
<0.001
0.792
0.021
Source of variation
As ants were individually followed across the two sectors, the
sector effect was treated as a repeated measure factor. The data were
log-transformed to allow for normality.
P<0.001, ηp2=0.074): ants spent more time crossing the
bottleneck than the entrance when they were travelling towards
the centre than when they were travelling out of the centre.
Overall, the effect of travel direction was significant for both
sectors (Table·1; P<0.001, ηp2=0.036), and the time spent
crossing the two sectors did not depend on whether ants came
from or went to the food source or the nest (Table·1; P=0.301).
The other significant effects accounted for a minor part of the
total variance (Table·1). We conclude from this analysis that the
ants going to the centre of the bridge were slowed down in their
progression at the level of the two bridge constrictions. This
was not the case for the ants moving away from the centre. This
asymmetry suggests that ants coming away from the centre are
given way by the ants coming from the opposite direction.
Close observations of the encounters occurring at the level
of the two bridge constrictions between ants travelling in
opposite directions indeed show that the majority of ants
travelling towards the centre stopped and gave way to those
coming from the opposite direction, whether a contact occurred
or not during the encounter (in 99 out of 105 and in 103 out
of 106 encounters with contact, for the nest and source side of
the bridge, respectively, and in 86 out of 87 and in 166 out of
168 encounters without contact, for the nest and source side of
the bridge, respectively; see Movie 2 in supplementary
material). The proportion of ants that encountered another ant
at the level of the bridge constriction was the same for the nest
and source side of the bridge (0.47 and 0.51 respectively,
χ2=0.84, P=0.358).
To check whether the delay we observed in ants crossing the
bottlenecks towards the centre (Fig.·6) was due to the time lost
during an encounter at the level of the bridge constrictions, and
not to an increased time lost in interactions while crossing the
bottleneck, we selected a sample of ants that did not encounter
another ant at the level of the bridge constrictions. We then
compared the time that these ants spent crossing successively
the bottleneck and the entrance of the bridge. These times were
not significantly different (mean ± S.D., 1.09±0.10·s vs
1.23±0.04·s; Student’s t-test for matched samples; t=–1.74,
P=0.084), showing that indeed the delay in crossing the
bottlenecks was essentially due to the ants stopping and giving
way to those coming from the opposite direction, and not to
the interactions occurring inside the bottlenecks.
Model
To better understand the interaction rules governing the
organization of traffic on the bridge, we devised a model that
we implemented in a ‘Monte-Carlo’ simulation. The model,
based on the interactions measured in the experiments,
describes the traffic on the bridge in both directions (inbound
and nestbound). The simulation output gives the distribution
of the size of the groups travelling in both directions.
The bridge in the model is divided into five different sectors,
as in the experiments: one bottleneck followed by one entrance
at both ends of the bridge, and a single central sector. The
model is not spatially explicit, i.e. the lengths of each sector
are not encoded in the model. Interactions between ants are
considered only at the level of the bottlenecks and the
entrances. Interactions occurring on the central part of the
bridge are ignored. Since no significant effect of bridge side
on the behaviour of the ants was found in the experiments, the
behavioural rules followed by ants at either side of the bridge
were the same in the model. A time step in the simulation lasts
0.5·s, and the simulations were run for 7200 time steps,
corresponding to 1·h of experiment.
The first decision concerns the arrival of an ant in the
bottleneck. At each time-step there is a probability, p, that one
ant leaves the nest and enters the bottleneck on the nest side
of the bridge. As the inbound and nestbound flows of workers
were equal in the experiments, the probability to leave the food
source and to enter the bottleneck on the source side of the
bridge is also set to p. The value of the probability p
corresponds to the value of the flow parameter. In the
simulations, a random number is sampled from a uniform
distribution between 0 and 1. If its value is less than or equal
to p an ant enters the bottleneck.
The second decision corresponds to the crossing of the line
between the bottleneck and the entrance on both sides of the
bridge. If the entrance is empty, i.e. if there is no ant coming
from the opposite direction, the ant in the bottleneck always
enters the entrance. On the other hand, when the ant in the
bottleneck is facing another ant in the entrance, coming from
the opposite direction, the latter always has priority. The ant in
the bottleneck gives way and does not move until the ant in the
entrance has completely entered the bottleneck. This priority
rule is always followed except if the ant in the bottleneck
follows a previous ant that has just entered the entrance, in
which case it has priority over the ants in the entrance. This
THEJOURNALOFEXPERIMENTALBIOLOGY
Temporal organization of traffic in ants 2909
Proportion of groups
0.6
Random
Model: without cooperation
Model: with cooperation
Experiments: 3 mm
0.5
0.4
Fig.·7. Simulation results. Distribution frequency of the size of
the groups of successive ants travelling in the same direction
at the level of the line between the bottleneck and the entrance
on the nest side of the bridge when the simulations were run
with a flow of ants entering the bottlenecks of the bridge equal
to 0.5 ants per time step, corresponding to the flow measured
in the experiments on a 3·mm bridge. The simulations were run
with and without implementing a cooperative rule between
following ants. For explanations on the random distribution,
see Fig.·5.
0.3
0.2
0.1
0
1
2
3
4
5
6
Group size
7
8
9
>10
effect corresponds to a cooperative behaviour between ants
because the second ant benefits from the passage of the first
ant. When this rule is not introduced, we consider that there is
a non-cooperative behaviour.
To take into account the fact that ants can follow each other
very closely when the number of ants in the bottleneck or in
the entrance is greater than one, there is a probability, q=0.33,
that, during the same time step (0.5·s), one ant crosses the line
between the bottleneck and the entrance, and a probability
(1–q) that two ants cross the line within the same time step.
The probability that three or more ants cross the line during
one time-step is equal to zero. This value is based on
measurement of the time delay between two ants following
each other and crossing the line between the bottleneck and the
entrance. This delay was less than 0.4·s (0.5·s) for 31% (51%)
of the total number of pairs of successive ants (N=242 pairs).
The fraction of groups of three or more ants crossing the line
during the same time step is negligible. Seven percent of the
groups of three ants (N=135) took less than 0.5·s to cross the
line; for larger groups (4, 5 and 6 ants; N=183), this time was
always greater than 0.5·s. The time required for an ant to cross
the central part of the bridge is set to a constant value of τ=12
time steps (6·s), corresponding to the mean time required for
an ant to cross the centre of the bridge.
First, we ran the simulations with a value of p equal to 0.5,
corresponding to the average flow of ants we observed in our
experiments (~60·ants·min–1). The distribution of group size
we obtained when the cooperative effect was implemented in
the model is close to the experimental one (Fig.·7), although a
little bit skewed towards high-size groups. In the absence of a
cooperative effect, however, the distribution is closer to the
theoretical distribution, corresponding to a random sequence
of workers, than to the distribution observed in the
experiments.
When we explored the model for different values of p, we
found that for small values of p (p⬇0.1) the distribution of
group size was different from a random distribution (Fig.·8).
The mean group size was close to 2 (Fig.·8, inset). Up to a
value of p=0.35, the distribution was weakly modified: the
most frequent size was 1, and the greater the size of the group,
the lower its frequency. When p took values higher than 0.35,
the mean size of the group increased abruptly. For p=0.6, largesize group became predominant.
Discussion
This study shows that crowding induced by a reduction of
path width is avoided in ants by a change in the temporal
organization of the flow of individuals going to and coming
back from a food source. When path width decreases, the rate
of contacts between workers coming from opposite direction
is regulated by a desynchronisation of inbound and outbound
traffic. This desynchronisation limits the number of head-on
encounters and thus allows the decrease in travel duration. The
0. 5
0. 4
Random
Flow: 0.1 ants time step–1
Flow: 0.5 ants time step–1
Flow: 0.6 ants time step–1
0. 3
Mean group size
Proportion of groups
0. 6
14
12
10
8
6
4
2
0
0
0. 2
0. 2
0. 4
0. 6
Flow (ants time step–1)
0. 1
0
1 2 3
4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19 >20
Group size
Fig.·8. Simulation results. Distribution frequency of the
size of groups of successive ants travelling in the same
direction at the level of the line between the bottleneck
and the entrance on the nest side of the bridge, when
the simulations were run with increasing values of the
flow of ants entering the bridge. For explanations on the
random distribution, see Fig.·5. The inset shows the
mean group size obtained for different values of
entrance flow.
THEJOURNALOFEXPERIMENTALBIOLOGY
2910 A. Dussutour, J.-L. Deneubourg and V. Fourcassié
same rate of food return to the nest is maintained, whatever the
path width.
We found that the duration of travel of L. niger workers
moving on a recruitment trail was significantly affected by the
number of contacts with other ants. This result concords with
that found by Burd and Aranwela (2003) in Atta cephalotes. In
the latter species, however, the effect of encounter rate on the
speed of the ants is small compared with the effect of their size
and the mass of the load they carry. In L. niger, crop load does
not have an influence on forager speed, since the speed of
outbound emptied ants and nestbound loaded ants is not
significantly different (Mailleux et al., 2000). Therefore, in the
absence of polymorphism in L. niger, the overall increase in
travel duration observed on a narrow bridge compared with a
wider bridge is essentially explained by a higher rate of
contact.
Independent of contact rate, we found that the duration of
travel was slightly higher on a wide bridge than on a narrow
bridge (multiple regression of Fig.·3; bridge effect). This
result is related to the fact that the time lost per contact was
slightly higher on a wide bridge than on a narrow bridge
(Fig.·3; differences in the slope of the two regression lines).
This could be due to the fact that the value of the angular
deviation induced by a head-on encounter on a wide bridge
could be larger than on a narrow bridge since ants have more
lateral space available to stray from their initial trajectory.
Finally, the duration of travel in the absence of contacts was
slightly longer when traffic volume was low (60·ants·min–1;
2.96 and 2.93·s, for 10·mm and 3·mm bridge, respectively)
than when it was high (120·ants·min–1; 2.46 and 2.49·s, for
10·mm and 3·mm bridge, respectively). This result suggests
an effect of the concentration of the trail pheromone on the
speed of the ants. Indeed, the concentration of the trail
pheromone is directly related to the volume of traffic on the
bridge and it is known that the speed of the ants increases
with the concentration of the pheromone on the trail they
follow (Beckers et al., 1992; see also Franks et al., 1991 in
Eciton burchelli; Roces and Nuñez, 1993 in Acromyrmex
lundi).
Surprisingly, in spite of the fact that the volume of traffic
did not vary with bridge width (Fig.·2), the mean rate of
encounters per ant on a narrow bridge was lower than that on
a wide bridge. This means that ants regulate their density on
a narrow bridge in order to avoid the delay incurred by too
high a rate of contact. The analysis of the sequence of outand nestbound ants reveals that this regulation is allowed by
a change in the temporal organization of the traffic on the
bridge. Whereas on wide bridges this sequence is not
different from random, on narrow bridges alternating groups
of inbound and outbound ants were observed. This
organization limits the number of head-on encounters
because ants progress on the bridge as clusters of individuals
moving in the same direction.
Examination of the sequence of out- and nestbound ants at
different levels of the bridge shows that clusters arise at the
bridge bottleneck. Ants arriving in the bottleneck give way to
ants coming from the narrow part of the bridge and therefore
accumulate at the level of the constrictions. When the path is
free, the waiting ants cross the narrow part of the bridge, where
they are given way by ants in the bottleneck at the other side.
The mere presence of a bottleneck did not induce an additional
delay in the ant progression, as shown by the fact that the ants
that did not encounter another ant at the level of the bridge
constriction spent the same amount of time crossing the
bottleneck and the entrance. Examination of the sequence of
inbound and outbound ants at different levels of the bridge
shows that the clusters did not exist before the bottlenecks and
thus that they were not formed at the departure from the nest
or the food source.
The system is completely symmetrical and the mechanisms
generating the ant clusters are the same at both ends of the
bridge. This means that loaded ants coming from the food
source do not behave differently from emptied ants coming
from the nest. The rules are different in species carrying
external loads. In the leaf-cutting ant Atta colombica, for
example, workers carrying a leaf fragment and coming back to
the nest are always given way by the workers going to the food
source (Dussutour, 2004). This behaviour has also been
observed in the workers of army ants loaded with prey items
(Dorylus sp., Gottwald, 1995; Eciton burchelli, Couzin and
Franks, 2002) or in the termites Longipeditermes longipes and
Hospitalotermes loaded with food pellets (Miura and
Matsumoto, 1998a,b). The priority towards loaded ants
generally results in the emergence of lane formation, with
loaded workers progressing in the centre of the recruitment
column and outbound unloaded ones moving on both of its
margins. Although workers of L. niger transporting a full crop
load of sugar solution are bigger than emptied ones because of
their distended abdomen, they are not as bulky and may not be
as ill-at-ease as the workers of the species transporting external
loads. This probably explains the differences in priority rules
observed between species of ants carrying internal and external
food load.
The priority rules we identified in our experiments are
similar to those observed when branching occurs on a path at
high traffic density; when an ant that has just engaged on one
branch encounters another ant coming from the opposite
direction it is immediately redirected to the other branch
(Dussutour et al., 2004). The ant that gives way is thus always
the one that has the possibility to do it, whether by veering
towards the other branch at a bifurcation or by moving aside
and waiting before entering the narrow passageway, as in our
experiment.
We were unable to detect a periodicity in the alternating
groups of inbound and outbound ants, either regarding the size
of the clusters or on a temporal scale. We hypothesize that
there was too much fluctuation in the interval of time between
ants coming from the nest or the food source to generate
clusters of ants of equal size alternating regularly over time: as
soon as there was a gap in the group of ants coming from the
narrow part of the bridge, ants waiting in the bottlenecks went
ahead. Our theoretical model shows that a periodicity could
THEJOURNALOFEXPERIMENTALBIOLOGY
Temporal organization of traffic in ants 2911
have been generated with a stronger cooperative effect between
ants, i.e. by extending beyond the second following ant the
cooperative effect due to the passage of a first ant in the
entrance from the bottleneck.
The model shows how the interplay between the value of the
flow and the priority rules governs the formation and the size
of the clusters. For low flow of ants, the distribution of the size
of the clusters obtained through the simulations is similar to a
random distribution, whereas for a flow corresponding to the
experiments, the distribution is close to the experimental one.
Most importantly, the model underlines the importance of
cooperation between ants: without cooperative effect, no
desynchronisation emerges for the values of the flow
corresponding to those observed in the experiments. Moreover,
the model predicts a collective phenomenon similar to a phase
transition: the mean size of the cluster remains constant (close
to a value corresponding to randomness) for P<0.4 and
increases abruptly afterwards.
The temporal organization of the flow of ants we observed
is reminiscent of that observed in bidirectional pedestrian flows
moving through a narrow passageway in a corridor (Helbing
et al., 2005). The speed of individuals is reduced at the level
of the bottleneck, and oscillations in the passing direction are
observed. When an individual enters the bottleneck, it is
immediately followed by other individuals. This releases the
pressure in the pedestrian crowd on one side of the passageway
while it increases the pressure on the other side. When the
pressure difference becomes too large, the people from the
other side enter and pass the bottleneck. For long, narrow
passageways, the frequency of the oscillations decreases and
there is a high tendency for the passageways to be passed by
clusters of individuals moving in the same direction rather than
by single individuals, which is exactly what we observed in
ants. In ants, as in pedestrians, the temporal organization of the
flow can therefore be described as a self-organized process
emerging from the simple rules of priority between individuals
moving in opposite directions (Helbing et al., 2001).
The temporal organization of flow that we observed in our
experiments should be particularly adapted to the movement
of ants through the tunnels of their hypogaeic nest. In L. niger,
the subterranean galleries have a small diameter (down to
2·mm, allowing the passage of a maximum of two individuals)
and their length ranges from 4 to 12·cm (Rasse, 1999), which
includes the length of the bridge we used in our experiments.
One can thus imagine that, up to a critical flow volume for
which clogging may occur, the temporal organization we
observed will allow maintenance of the same flow of
individuals through a gallery without engaging in the costly
work of enlarging it (Berghoff et al., 2002).
The authors would like to thank R. Jeanson for his help in
analysing the data. A.D. was supported by a doctoral grant
and a mobility fellowship (‘bourse de co-tutelle BelgiqueFrance’) from the French Ministry of Scientific Research.
J.-L.D. is a research associate from the Belgian National
Funds for Scientific Research.
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