From the first intention movement to the last joiner: Macaques combine mimetic rules to optimize their collective decisions

doi: 10.1098/rspb.2010.2084
published online 17 November 2010Proc. R. Soc. B
 
C. Sueur, J. L. Deneubourg and O. Petit
 
combine mimetic rules to optimize their collective decisions
From the first intention movement to the last joiner: macaques
 
 
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fication. Our study also provides the first complete proof that there is continuity in the decision-making
1. INTR
Anima
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preced
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uthors
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orum
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fishes,
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other
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depends on mimetic rules without any threshold
[15,25]. This mimetic process is anonymous [15,25] or
selective [26] and follows a linear law (absence of
threshold). In white-faced capuchin monkeys, the
on November 17, 2010rspb.royalsocietypublishing.orgDownloaded from * Author for correspondence (cedric.sueur@c-strasbourg.fr).Received
Acceptedprocesses underlying collective movements in mammals from the first intention movement right through
to the last joiner.
Keywords: quorum response; collective movement; social amplification; voting process;
primates; self-organization
ODUCTION
l groups use complex decision-making processes
chronize their activities and movements [1–3].
on collective decision-making have increased
over the last 15 years, and have described mech-
such as social amplification in almost all animal
from amoebae to worms, insects and vertebrae,
ng human beings [2,4–8]. Authors reported the
nce of pre-departure processes such as social
cation (increasing probability to display behaviour
ing to the number of individuals performing this
ur; [9,10]) in wolves [11] and gorillas [12] or
(choice between exclusive alternatives according
majority) in African buffalos [13] and hamadryas
s [14]. In other species, the initiation process
s to suffice in order to propose and to start a
ent [15]. Repeated initiations allowing group
ents could either be carried out by one specific
ual alone—defined as a personal leadership—or
eral group members—defined as a distributed
hip [16]. After initiation of the movement—
ed or not by a pre-departure process—other
members join the movement and hence become
rs [17]. This joining of individuals may follow a
or social relationships [18]. In some species, a
reported that males are more often located at the
and the back of the movement, whereas female
juveniles occupy more central positions [19–21]. A
suggest that this organization may be a strategy for
iles to decrease predation risk and for males to in
their access to food sources. In other species, indiv
join the movement according to their kinship or to
affiliative relationships because being associat
specific related or dominant individuals may in
individual fitness [18–21].
There is a growing body of evidence that pre-dep
and joining processes are ruled by amplification. I
(Temnothorax sp. [22]) or in honeybees (Apis m
[23]), the probability of an individual immigrat
a specific nest depends on a threshold numb
individuals having already chosen this nest. A qu
response could also explain group movement dec
in three-spine sticklebacks (Gasterosteus aculeatus)
two directions are proposed: animals choose the dir
taken by the majority of individuals [24]. Thus, in
ants or bees, individuals respond to a quorum thr
when several exclusive choices are possible. In
species, the individual probability to join a movwith a selective mimetism at departure. This is the first time that transition mechanisms have been
described in mammals, which consequently helps understand how a voting process leads to social ampli-From the first intentio
joiner: macaques co
to optimize their c
C. Sueur1,2,3,*, J. L. Den
1Unit of Social Ecology, Free University of Bruss
1050 Brus
2Department of Ecology and Evolutionary Biolog
3Department of Ecology, Physiology and Ethology, IPH
Mechanisms related to collective decision making
from amoebae to worms, insects and vertebrates, in
related to collective movements—including pre-d
different steps of the movement process, but these s
have no understanding of how these different proce
decision-making event. Here, we consider the w
macaques (Macaca tonkeana), using a stochastic m
macaques vote and choose the majority. Individua
based on affiliative relationships. The pre-departu
probably linked, but we have not yet identified wh
that decision-making related to macaque group m28 September 2010
26 October 2010 1movement to the last
bine mimetic rules
llective decisions
ubourg1 and O. Petit1,3
Campus de la Plaine, Boulevard du Triomphe,
, Belgium
rinceton University, Princeton, 08542 NJ, USA
, 23, rue Becquerel, 67087 Strasbourg, Cedex France
e recently been found in almost all animal reigns
ding human beings. Decision-making mechanisms
rture and joining—have already been studied at
ies were always carried out separately. We therefore
are related when they underlie the same collective
le departure process of two groups of Tonkean
el. When several exclusive choices are proposed,
hen join the movement according to a mimetism
quorum and the joining mimetic mechanism are
transition mechanism is used. This study shows
ements is governed by a quorum rule combined
Proc. R. Soc. B
doi:10.1098/rspb.2010.2084
Published onlineThis journal is q 2010 The Royal Society

ence the decision-making process in any way [17]. Events
2 C. Sueur et al. Combination of mimetic rules in macaques
on November 17, 2010rspb.royalsocietypublishing.orgDownloaded from probability of any individual joining the movement and
the probability of the first departed individual cancelling
its initiation both follow linear rules and lead to a
threshold function: until at least three individuals have
joined the movement, the departure can be cancelled at
any time [15]. After the joining of three individuals, all
group members join the movement as an acceptance of
a sub-majority.
Decision-making mechanisms related to collective
movements—including pre-departure and joining—have
been studied at different steps of the movement process.
These studies showed similarities between species and
these similarities illustrate a parsimony and an optimality
of collective decision-making then illustrated a parsimony
and optimality of collective decision-making [1,22–
24,26]. However, these different steps were always studied
separately. Therefore, we have no real knowledge of how
these different processes are related when they underlie
the same collective decision-making event. In fact, no
study has yet been carried out to elucidate exactly which
transition mechanism links the pre-departure and depar-
ture processes. Here, we consider the whole departure
process—pre-departure, initiation and joining—of two
groups of Tonkean macaques (Macaca tonkeana; 10 and
22 individuals, respectively), using a stochastic model.
In a series of previous studies conducted on this
species, we showed that macaques may have to vote
between several exclusive choices [27]. Wild Tonkean
macaques typically live in primary and secondary forests
in Sulawesi (Indonesia) and are frugivorous. As fruit
trees are scattered throughout the forest, this dispersion
may lead animals to choose between different food
patches and vote. Individuals displayed preliminary beha-
viours in the direction they favoured, irrelevant of their
hierarchical rank, age or sex [17,26,27]. The decision to
start and move was then ruled by a sequence of quorums:
the group went in the direction for which a majority of
individuals had displayed preliminary behaviours. When
a direction was chosen and the initiation completed, indi-
viduals joined the movement according to a selective
mimetism based on affiliative relationships [26]. We also
found that the number of notifying individuals influences
the probability of group members to join the movement
[17]. When a pre-departure period is present, the
quorum response seems to apply on top of the selective
mimetism. This means that mechanisms allowing the col-
lective movement are not different, whether only one
direction is proposed or two. This suggests that the pre-
departure quorum and the joining mimetic mechanism
are probably linked, but the exact transition mechanism
responsible is still unknown.
Moreover, we have yet to establish exactly how far
such combinations of mechanisms could contribute to
optimizing the collective decision, and how the decision-
making process changes from one to two proposed
directions. In order to answer these questions, we analysed
each step of the process—pre-departure, initiation and
joining—and implemented them in a model. Modelling
helps gain a better insight into processes underlying collec-
tive decisions (e.g. [15,28,29]). In this model, individuals
within a resting area have to choose and move together
to one of two possible foraging areas. By using an agent-
based model, we can recapture all data relating to
mechanisms of collective decision-making and implementProc. R. Soc. Bwere only taken into account if more than two-thirds of
group members were present in or around the area �10 m
from the starting point of the first departed individual.them in the chronology they happened. Observed
phenomena are then compared with simulated ones.
2. METHODS
(a) Subjects and environment
The two study groups of Tonkean macaques were bred in
semi-natural conditions at the Strasbourg University Prima-
tology Center. They ranged in a 0.5 ha park (fenced field),
containing different patches of vegetation between which
individuals could collectively switch. The first Tonkean
macaque group studied (November 2005 to March 2006),
consisted of 10 individuals. The second group (study carried
out from December 2003 to April 2004) consisted of 22 indi-
viduals. The composition of both groups was similar to that
found in wild groups [30,31]. Animals had free access to an
inside shelter with commercial pellets and water ad libitum.
Fruit and vegetables were distributed once a week, outside
observation sessions.
(b) Observational protocol
The beginning of a group movement was defined by the first
departure of an individual who walked more than 10 m in
less than 40 s, according to criteria used by Leca et al. [16]
and Sueur & Petit [17,18]. The departure of the first individ-
ual over a distance of more than 10 m was an obvious signal
for other group members. A ‘joiner’ was defined as any indi-
vidual walking more than 5 m in a direction that formed an
angle of less than 458 with the direction of the first departing
individual. The following behaviours were recorded and
named as ‘preliminary behaviours’ when exhibited before
departure [17,27]: back glance and intention movement.
A back glance is defined as an individual turning its head
and looking towards other group members. If the eyes of
animals could not be observed, we used the direction of
the head—with an angle greater than 1358 from the direction
of the movement—to determine a back glance (see [32] for
more details). An intention movement is considered to have
occurred when an individual walks between 1 and 5 m, in a
specific direction. A stop of more than 2 s after an advance
was considered to show the end of the behaviour. Direction
of the body axis of individuals indicated the direction of
the future group movement [13]. We considered the back
glances as preliminary behaviours when an individual had
previously made at least one intention movement and had
moved away from the group. These preliminary behaviours
are formal indications of a choice between two candidates
and could be considered as a vote [13,14,27]. We called
individuals displaying preliminary behaviours notifying
individuals. We considered a direction to exist when there
were at least two preliminary behaviours for that direction.
If the directions of at least two individuals displaying prelimi-
nary behaviours formed an angle greater than 458, we
considered these directions to be different. The enclosure
where each group lived was marked with reference points,
and the position (+1 m) of each animal as well as the dis-
tance it walked was recorded. Group movements occurring
in agonistic or sexual contexts were discarded from the
analysis. Previous studies showed that the different possible
activities of individuals, before or after moving, did not influ-

Even though many routes were available and taken by the
group in the enclosure, no event was recorded in which
the second direction seemed to mimic (for the time
Combination of mimetic rules in macaques C. Sueur et al. 3
on November 17, 2010rspb.royalsocietypublishing.orgDownloaded from more than two directions were displayed before the departure
of a group. We used analysis of probability distribution (sur-
vival analysis) to analyse the probability of displaying a
preliminary behaviour [15]. Relations between variables
were analysed using curve estimation tests [26,27,35]. Only
the values of the model fitting best with the observed data
are indicated in the results. Tests were performed using
SPSS v. 10 (SPSS Inc., Chicago, USA). a was set at 0.05.
Means were +s.e.m.
3. RESULTS
(a) Probability to display a first
preliminary behaviour
We first analysed the process(es) used to display first pre-
liminary behaviours in one or two directions and thus
assessed how two different directions of movement
appear.
Analyses of observed data show that the probability
c p1d1 to display a first preliminary behaviour p1 in one
direction d1 is constant per time unit: the distribution of
the durations between the end of the previous collective
movement and the first preliminary behaviour of a new
collective movement follows an exponential curve (curve
test estimation: F1,30 ¼ 470; R2 ¼ 0.94; s.e.m. ¼ 0.168;
p , 0.00001 for group 1; F1,27 ¼ 918; R2 ¼ 0.97;
s.e.m. ¼ 0.146; p , 0.00001 for group 2). This prob-
ability c p1d1 equals 0.0013 for group 1 and 0.0015 for
group 2. The probability li;p1d1 per individual therefore
equals 0.00013 for group 1 and 0.00007 for group 2:
c p1d1 ¼
Xn
i¼1
ðli;p1;d1Þ; ð3:1Þ
where n is the number of resting individuals. For equation
(3.1), n ¼ N, the number of individuals in the group. N ¼
10 for group 1, and 22 for group 2.Using video scoring, C.S. recorded the type as well as the fre-
quency of any behaviour displayed by each group member.
Measurements were taken using the all occurrence sampling
method, both during the 20 minutes prior to a group
movement, and after the start of the group movement [33].
(c) Modelling
We implemented the model in NETLOGO v. 3.1.4 [34]. At the
start of a simulation, all agents (N) are in an area called the
resting area and have to move to another area qualified as a
foraging area. Two foraging areas are present in order to
induce the voting process. At each time step (one second)
in the model, a number between 0 and 1 is randomly attrib-
uted for each resting agent (i.e. at the resting area); when this
number is smaller than the theoretical probability of each
equation (from 1 to 6), the individual changes its state (i.e.
decides to move, chooses a direction and so on); if this
number is higher than the theoretical departure probability,
the agent stays in the same state. We include individual
identities and the network of affiliative relationships for
the observed group in the model. Affiliative relationships
are taken from previous studies [18,26,27,32]. We set the
number of simulations to 10 000 for each group.
(d) Statistical analysisProc. R. Soc. Bdimension but not for the spatial dimension) the
behaviour of the first individual notifying in the first
direction. These two individuals shared the same time
decision (consensus on time) but not the same direction
decision.
(b) Probability to take part in the voting process
After the first preliminary behaviour is displayed, other
individuals participate in the voting process and display
preliminary behaviours in turn [17,27]. The time
elapsed between the notifying of two different individ-
uals involved in the voting process in one direction (d1
or d2) is 26.56+39.64 s for group 1 and 17.89+
23.85 s for group 2. For both groups, these durations
are about 34 times lower than the mean duration
between the end of a previous collective movement
and a first preliminary behaviour for a new collective
movement. Moreover, the time elapsed between the
first preliminary behaviour in one direction and the
first one in the second direction is 28.14+33.58 for
group 1 and 18.54+22.44 for group 2. This suggests
an influence of the behaviour in the first direction on
the second one rather than an independent probability
to notify in the second direction. These results show
that displaying preliminary behaviour involves a mimetic
process following notifying behaviour by some group
members.
However, the probability of an individual to display a
preliminary behaviour in one direction may be dependent
either on the number of notifying individuals in this direc-
tion or on the number of notifying individuals in both
directions, as suggested by the results of the previous sec-
tion concerning probability to display a first preliminary
behaviour in direction 2.Comparisons between observed and simulated data
show that the simulated durations between the end
of a previous collective movement and a first preliminary
behaviour of a new collective movement are similar to the
observed ones (Mann–Whitney test; group 1: Nobs ¼ 37,
Nsim ¼ 10.000, meanobs ¼ 893.81+1253.73, meansim ¼
891.37+900.34; Z ¼ 21.707, p ¼ 0.074; group 2:
Nobs ¼ 30, Nsim ¼ 10.000, meanobs ¼ 616.56+578.87,
meansim ¼ 548.39+521.20; Z ¼ 20.679, p ¼ 0.497).
This suggests that macaques proposed either one or
two different directions prior to their collective move-
ments. In this study, the simulations show that if the
two first preliminary behaviours are not connected,
the number of collective movements with two proposed
directions should not exceed 1/10 of the collective
movements performed when only one direction is pro-
posed. This ratio of 1/10 can be obtained analytically
by dividing the probability to independently display a
first preliminary behaviour in the second direction
(c p1d1 ¼ 0.0013 for group 1) by the mean probability to
depart in only one proposed direction (C01,t � 0.0126
for group 1). However, the observed ratio is about
one-third in both groups (respectively, 29.5% for
group 1 and 38% for group 2). This means that the pro-
bability Cp1d2 to display a first preliminary behaviour p1 in
the second direction d2 is not independent of the first pre-
liminary behaviour emitted in the first direction d1. This
last analysis shows that the first individual notifying in

process:
individuals in direction 1 and direction 2. This
threshold—for which the probability that individuals
initiate a movement equals 0.5—equals 9 for group 1
and 5 for group 2. q1 represents the degree of sensitivity
of individuals to the system and equals 5 for both
groups. This degree of sensitivity affects the slope of the
sigmoid curve that has been fitted to the data. Higher
values of l correspond to the fitted curves having a stee-
per slope, particularly around the threshold value. In
essence, a higher degree results in a quicker transition
between resting and departing as the difference between
notifying individuals for both directions increases and
then a higher discrimination from animals [36,37]. For
instance, fishes or ants only show a degree of sensitivity
of 2 [24,38].
Results show that the simulated probability to initiate a
movement, following the above rule, is similar to those
observed in group 1 (curve estimation test: F1,19 ¼ 404;
R2 ¼ 0.95; s.e.m. ¼ 0.091; p , 0.00001; figure 1a) and
in group 2 (curve estimation test: F1,19 ¼ 859; R2 ¼
0.97; s.e.m. ¼ 0.056; p , 0.00001; figure 1b). In
figure 1, the number of notifying individuals may be
–0.2
0
0.2
0.4
0.6
0.8
0 10 20
pr
ob
ab
ili
ty
to
d
ep
ar
t i
n
fir
s
number of notifying individuals
Figure 1. Probability to depart first, i.e. to initiate a collective
movement, according to the number of notifying individuals
(a) for group 1 and (b) for group 2. Black squares represent
the observed data. Lines represent the simulated data.
4 C. Sueur et al. Combination of mimetic rules in macaques
on November 17, 2010rspb.royalsocietypublishing.orgDownloaded from c p;d ¼ ðl p;d � nÞ þ ðCp � Pd1þd2Þ ð3:2Þ
with Cp, the mimetic coefficient, equalling approximately
0.002 for both groups. Pd1þd2 is the number of notifying
individuals in direction 1 and in direction 2.
Following this rule, the simulated ratio, ‘number of
collective movements with two proposed directions
divided by the number of collective movements with
only one proposed direction’ (see §2), equals 28.6 per
cent for group 1 and 38.8 per cent for group 2 and is
similar to that observed for group 1 (x2-test: x2 . 0.60;
d.f. ¼ 1; p ¼ 0.806) and for group 2 (x2 . 0.27; d.f. ¼
1; p ¼ 0.870). This result confirms that the first individ-
ual notifying in the second direction is influenced by the
first individual notifying in the first direction. The third
notifying individual, whatever the direction, is influenced
by the two first notifying individuals, and so on.
(c) Probability to depart in a given direction
The voting process described above allows the group to
choose one direction among two alternatives. This
decision is observed through the departure of one individ-
ual—the initiator—who moves in the direction of the
majority, i.e. the direction for which the most individuals
have notified. A previous study showed that this pro-
bability to depart in the direction taken by the majority
depended on two decisions: (i) the departure time
decision and (ii) the departure direction decision [27].
This previous study also showed that the departure
time decision is ruled by a quorum. The probability
C01,t to initiate the group movement is
c01;t ¼ li;t þ 1 �
1
1 þ ððPd1 þ Pd2Þ=Sd1þd2Þ
q1
� �
: ð3:3Þ
This function is a sigmoid where li,t is the intrinsic prob-
ability per individual to initiate a movement [27]. While
individuals of each group may have different intrinsic
probabilities li,t, these differences are not influenced by
dominance, age or sex of group members. Sd1þd2 rep-
resents a threshold, namely the sum of the notifyingWe tested both hypotheses in our model. The influ-
ence of the number of notifying individuals in both
directions seems to be confirmed by the shape of the dur-
ation distribution between the joining of two notifying
individuals. The duration distribution for both directions
followed a parabolic curve for group 1 (curve estimation
test: F1,6 ¼ 9.44; R2 ¼ 0.61; s.e.m. ¼ 6.446; p ¼ 0.02)
and group 2 (curve estimation test: F1,5 ¼ 11.24; R2 ¼
0.70; s.e.m. ¼ 4.535; p ¼ 0.02). However, if we only con-
sider the direction in which the behaviour is displayed, the
duration distribution is a parabolic curve for group 1
(curve estimation test: F1,6 ¼ 8.01; R2 ¼ 0.56; s.e.m. ¼
6.544; p ¼ 0.03) but not for group 2 (curve estimation
test: F1,5 ¼ 0.64; R2 ¼ 0.1; s.e.m. ¼ 6.346; p ¼ 0.457).
The probability that an individual will take part in the
voting process is influenced by the number of notifying
individuals in both directions and not simply by the
number of individuals notifying the direction in which
the individual displayed its preliminary behaviour.
After the display of a first preliminary behaviour, the
probability Cp,d to display a preliminary behaviour p,
whatever the direction, therefore, depends on a mimeticProc. R. Soc. B–0.2
0
0.2
0.4
0.6
0.8
1.0
1.2(a)
pr
ob
ab
ili
ty
to
d
ep
ar
t i
n
fir
st
1.0
1.2
t
(b)