Group movement decisions in capuchin monkeys : the utility of an experimental study and a mathematical model to explore the relationship between individual and collective behaviours

Abstract

In primate groups, collective movements are typically described as processes dependent on leadership mechanisms. However, in some species, decision-making includes negotiations and distributed leadership. These facts suggest that simple underlying processes may explain certain decision mechanisms during collective movements. To study such processes, we have designed experiments on white-faced capuchin monkeys (Cebus capucinus) during which we provoked collective movements involving a binary choice. These experiments enabled us to analyse the spatial decisions of individuals in the group.We found that the underlying process includes anonymous mimetism, which means that each individual may influence all members of the group. To support this result, we created a mathematical model issued from our experimental data. A totally anonymous model does not fit perfectly with our experimental distribution. A more individualised model, which takes into account the specific behaviour of social peripheral individuals, revealed the validity of the mimetism hypothesis. Even though white-faced capuchins have complex cognitive abilities, a coexistence of anonymous and social mechanisms appears to influence their choice of direction during collective movements. The present approach may offer vital insights into the relationships between individual behaviours and their emergent collective acts.

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1) Corresponding author’s e-mail address: helene.meunier@c-strasbourg.fr






Group movement decisions in capuchin monkeys: the utility of an experimental study
and a mathematical model to explore the relationship between individual and collective
behaviours

Short title: Group movement decision in capuchin monkeys

H. Meunier1,2), J.-B. Leca1), J.-L. Deneubourg2) & O. Petit1)

1) Ethologie des Primates, IPHC, Département Ecologie Physiologie et Ethologie, UMR 7178
CNRS-ULP, 67087 Strasbourg Cedex 2, France
2) Service d’Ecologie Sociale, Université Libre de Bruxelles, Belgium




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Summary
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In primate groups, collective movements are typically described as processes dependent on
leadership mechanisms. However, in some species, decision-making includes negotiations
and distributed leadership. These facts suggest that simple underlying processes may explain
certain decision mechanisms during collective movements. To study such processes, we have
designed experiments on white-faced capuchin monkeys (Cebus capucinus) during which we
provoked collective movements involving a binary choice. These experiments enabled us to
analyse the spatial decisions of individuals in the group. We found that the underlying
process includes anonymous mimetism, which means that each individual may influence all
members of the group. To support this result, we created a mathematical model issued from
our experimental data. A totally anonymous model does not fit perfectly with our
experimental distribution. A more individualised model, which takes into account the
specific behaviour of social peripheral individuals, revealed the validity of the mimetism
hypothesis. Even though white-faced capuchins have complex cognitive abilities, a
coexistence of anonymous and social mechanisms appears to influence their choice of
direction during collective movements. The present approach may offer vital insights into the
relationships between individual behaviours and their emergent collective acts.

Keywords: animal societies; collective decision-making; primates; group movement;
mathematical modelling

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Introduction
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In group-living animals, a wide range of behaviours like resting, foraging or moving may be
performed collectively. The functions of such groupings are diverse: antipredation (van
Schaik, 1983; Sterck et al., 1997; Isbell, 1994), foraging benefits (Wrangham, 1980;
Terborgh, 1983) and energy saving (Weimerskirch et al., 2001). In a social group, animals
have different motivations and have to compromise between their own interests and the costs
of a collective choice which could differ from their own needs. In the case of group
movement, if all members choose different directions, the group will split and its members
may lose many of the advantages of group living (Krause & Ruxton, 2002). Observational
and empirical evidence shows that animal groups move across the landscape quite cohesively
(Stewart & Harcourt, 1994; Boinski & Campbell, 1995; Boinski, 1996, 2000; Byrne, 2000;
Parrish et al., 2002; Conradt & Roper, 2003), which strongly suggests that a collective
decision has been taken. Thus it could be assumed that individual decisions lead to a common
decision, allowing the group to remain cohesive (Conradt & Roper, 2005).
Classically, collective movements in primate groups are described as processes
dependent on leadership mechanisms where a single individual initiates a group movement
and is followed by other individuals (Boinski & Garber, 2000). Mountain gorillas (Gorilla
gorilla beringei) are the best known example of such leadership concentrated on a single
individual (Schaller, 1963). However, it has been suggested that instead of one individual
being responsible for a decision, a division of roles among an initiator and other decision-
making individuals may exist (Byrne, 2000). In Drakensberg mountain baboons (Papio
ursinus), Byrne et al. (1990) have described several scenarios ranging from a single
individual who initiates and determines the direction and the departure time, to the case where
the initiator seems to be ineffective alone and needs the adhesion of a first follower to
influence the group. In white-faced capuchins (Cebus capucinus), Leca et al. (2003) showed

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that: (1) several individuals, not necessarily the most dominant ones, can initiate movements,
and (2) the spatial and temporal distribution of the group affects the probability that other
group members respond positively to an initiation.
These observations lead us to consider alternative mechanisms which may help us to
understand exactly how a collective decision is reached. Mimetic interactions between group
members could play a key role in collective movements. Mimetic behaviour, where animals
act like their conspecifics, is widespread in animal societies and is an example of positive
behavioural feedback (Sumpter, 2006). Distributing the team within the environment and
introducing positive feedback among animals allows amplification of the decision taken by a
few individuals. Through competition among different amplifications, all individuals reach a
consensus decision and maintain group cohesion (Deneubourg & Goss, 1989; Bonabeau et
al., 1997; Detrain et al., 1999; Camazine et al., 2001; Deneubourg et al., 2002; Jeanson et al.,
2004; Couzin et al., 2005; Amé et al., 2006). Such self-organized processes allow groups to
carry out collective actions in various environments without any lead, external control or
central coordination. They are used by many species living in large societies (Conradt &
Roper, 2005) with low individual levels of cognition but also by vertebrates, including
primates, living in small or large groups (Parrish & Edelstein-Keshet, 1999; Hemelrijk, 2002;
Couzin & Krause, 2003).
Our objective was to test whether anonymous or social processes govern the choice of
a given direction for collective movements in a white-faced capuchin monkey group. In order
to assess the mechanisms of the collective movements and their dynamics, we have designed
experiments where we provoked collective movements to explore the process in a purest
form, which is practically impossible to achieve in a natural environment. Based on these
experiments, we analysed spatial decisions within the group. Our hypothesis is that the nature
of the underlying processes concerns mimetism (acting as a catalyst for the collective

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decision) combined with individualities. To validate this hypothesis, we use a mathematical
model to explore the relation between individual behaviour and collective phenomena.

Material and methods
Subjects and environment
The group of white-faced capuchins was established in 1989 at the Louis Pasteur University
Primate Centre, Strasbourg, France. During our study, the group contained 13 individuals of
three separate lineages: Five males (aged 2, 4, 8, 9 and 20 years or more) and eight females
(2, 2, 2, 7, 8, 9 years old, and two individuals aged 20 years or more).
The group was kept in a one-acre outdoor enclosure with natural vegetation and
uneven ground with free access to an indoor shelter. Commercial primate pellets and water
were available ad libitum. Fresh fruits and vegetables were provided once a week but not
during testing.

Observation procedure
Observations took place between 0900 and 1200 hours and between 1400 and 1800 hours
from May to August 2001. Three observers collected data with video and tape recorders and
communicated using walkie-talkies.
The first phase of the experiment consisted in training the capuchins to move to the
sound of a whistle. The sound of the whistle was gradually associated with the subsequent
presentation of food located further and further away from the starting point where the sound
was emitted. At the end of the training period, the blast of the whistle was perceived as a
food-anticipatory signal leading to the possible presence of food in a remote location. The
second phase of the experiment consisted of 108 tests during which the capuchins had the
opportunity to choose between two opposite directions leading to two distinct areas in the

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park. In non-experimental baseline context, animals spontaneously used a particular zone of
the enclosure for social and resting activities. This zone is referred to as the “departure zone”.
The two areas to choose from are natural foraging areas situated 60 meters away from the
departure zone. A manger was placed in each of the areas but was not visible from the
departure zone.
During each test, only one randomly selected manger contained figs. The other one
was left empty. The same manger could not be filled more than three times successively to
prevent learning of reward position. Each manger was 2 meters long thus all monkeys could
feed simultaneously from the same manger. When all animals were grouped in the departure
zone, the whistle was sounded, and the mangers were opened. The choice for left or right
manger was made from the very beginning. The initial direction taken by the animals from the
departure zone was systematically maintained until the chosen manger was reached. The
direction taken by each monkey was recorded for each test and coded by an “L” when animals
chose to go left and by an “R” when they chose to go right.

Social relationships
To establish the dominance hierarchy, we ranked individuals over 1 year of age in a matrix
according to the direction of avoidances and unidirectional aggressions. We used data from
two contexts: (1) spontaneous events and (2) drinking competition around a single source of
orange juice (three series of nine 2-h tests). We carried out hierarchical rank order analysis
using Matman, (de Vries et al., 1993). We verified the linearity of the dominance hierarchy,
h′=0.91 (P<0.001; de Vries, 1995). The dominance scores ranged from one for the most
dominant individual to thirteen for the most subordinate one.
Affiliation was quantified by the frequency of body contacts among all identified
group members, recorded by using instantaneous sampling every 5 minutes (Altmann, 1974).

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We collected 728 scans, but not during fruit provisioning. The affiliation score within each
dyad was assessed by the number of scans during which the two partners were in body
contact.

Data analysis
For each individual, we obtained a total of spatial association, defined as the total number of
group members that chose the same direction as this individual across all tests. Several
matrices were built to analyse the effect of socio-demographic variables on spatial
association. We firstly reported in a symmetrical matrix when one animal chose the same
direction as another one, i.e. the frequency of spatial association choice for each dyad. We
also reported the affiliation scores in a symmetrical matrix. Finally, we assessed the degree of
closeness in maternal kin relationships by distinguishing three types of dyads: non-kin, far-kin
(siblings, half siblings, grandmother-grandchildren, aunt-nephew/niece), and close-kin
(mother-offspring) dyads. We implemented the degree of kinship in the three types of kin
dyads in a matrix. Matrix correlations were tested by using Matman (de Vries et al., 1993).
We set the number of automatic permutations of matrices at 10000 and used Pearson’s
correlation coefficient.
Non-parametric statistical tests used were the Kolmogorov-Smirnov test, Kruskal-
Wallis test, Spearman rank correlation test and the chi-square test (Siegel & Castellan, 1988).
All tests were two-tailed and the significance level was fixed at 0.01.
For decision analysis, only 64 tests were used because of missing data on individual
direction choice in the other tests.

Results
Description of the experiment

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At the sound of the whistle, individuals started to move, one after one. The mean starting time
was 7.5 ±0.6 sec for the first individual and 170.2 ±16.5 sec for the whole group to have
moved. When leaving the departure zone, the monkeys chose between the two directions
leading to the two mangers one after one. All decisions were made prior to vocalizations from
travelling individuals who had already arrived at the manger. Before reaching the manger
corresponding to the initial direction chosen, no animal was observed returning to the
departure zone or going towards the opposite manger.

Independency of the tests
The localisation of the reward in a given test (in the left or the right manger) did not affect the
choice of the animals in the subsequent test: the majority of the group chose 50 times the
manger filled previously in the following test (out of 107 subsequent choices). This result
suggests that reward-reinforcement bias should not be invoked in our study.

Individualities and relationships
During collective movements, capuchins were not significantly associated according to sex
(Kruskal-Wallis test: χ2=3.45, Nmale-male =10, Nfemale-female =28, Nmale-female=40, p=0.178) or
dominance rank (Spearman rank correlation test: rs = -0.110; N = 13; p = 0.721 ) regarding
direction choice. Moreover, matrix correlations revealed that kinship (Pearson’s correlation
coefficient r = -0.027; p = 0.506) and affiliation (Pearson’s correlation coefficient r = 0.236; p
= 0.054) did not influence the spatial associations of capuchins.
Twelve out of thirteen individuals started to move first at least once. First position
frequency was not significantly correlated with dominance rank (Spearman rank correlation
test: rs=0.397, N=13, p=0.180).


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Decision Analysis
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We tested whether the monkeys followed their conspecifics or if they chose a direction
independently of other group members. Of the 64 tests, the total number of choices was 832
(13 individuals x 64 tests), and the proportions were respectively 0.4 for the L side and 0.6 for
the R side. This asymmetry suggests a weak preference for the right side and was taken into
account in the subsequent analysis.
The frequency of tests where i individuals (i = 0,…,13) chose the same direction was
measured. Assuming that the individuals selected their side independently with the
probabilities PL = 0.4 and PR = 0.6, the theoretical distribution of the tests as a function of the
number of individuals choosing the L or R is a binomial distribution (Figure 1a). However,
our experimental distribution is bimodal, a characteristic of a collective choice (Camazine et
al., 2001), and differs from the binomial theoretical one (Chi-square test: χ2=37.067, df=13,
p=0.004, Figure 1). To test the process of collective choice and inter-individual influence, we
made a further analysis by considering the directions taken by the n first individuals
(n=2,…,13). If the n first individuals chose their direction independently, the probability (Pn)
that they chose L (R) is PLn (PRn). We compared the number of tests where at least n first
individuals have taken the same direction to the theoretical ones (64 x (PLn +PRn)). The
experimental distribution was statistically different and higher than the theoretical one and the
maximum difference was observed for the six first individuals (Kolmogorov-Smirnov two-
sample test: D=0.67, N1=N2=13, p=0.015). The ratio between Pn/Pn-1 increases with n,
showing that the larger the number of individuals having chosen one side, the higher the
probability is that the following individuals will also choose this side. The experimental
probabilities are always higher than the theoretical ones.

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This result shows a correlation between the choices of the individuals, which probably
results from a mimetic effect: each individual seems to be both influenced by the choice of the
others and have a tendency to follow the direction taken by the previous one(s).

Independent Individuals
In this experimental group, individuals have two different profiles. For each individual, we
compare the distribution of the number of tests in which it has taken the same direction as 0,
1, 2, …, 12 of its groupmates, with a distribution calculated from the mean of the
corresponding values of all the other individuals (number of times that 0,…,12 individuals
take the same direction). Ten individuals have similar profiles (their individual distributions
do not show significant differences to the calculated one), and they present a tendency to
follow other group members (‘dependent’ individuals). The three other individuals
(subordinate females) behave differently from the other groupmates (chi-square test:
χ2=44.26, 85.66 and 86.39 for those three animals, df=12, p=0.010). These ‘independent’
individuals tended to choose a side independently of others and thereby move either to the
side mainly chosen by group members or to the other side.

Anonymous model: all individuals identical
Here we test the mimetic hypothesis to explain the collective mechanisms involved in the
group choice. In this model, all individuals (N) are identical. Any individual has the
probabilities PL to go L and PR to go R that depend on its intrinsic preference to choose the
left (αL) or right (αR) side and on the decision of the previous individuals.
The first decision is the choice of the first individual to take the left or the right path.
In this case, PR = αR and PL = αL.

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Similarly we simulate the decision of the second,…, thirteen individual. To take into
account the mimetic behaviour, P
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L (PR) must increase with NL (NR) and decrease with NR (NL).
NL and NR are the number of individuals having chosen the left and right side and NL + NR are
the individuals having moved before the individual. The simplest form of PR or PL is:
PL=
αL+βNL
1+β(NL+ NR)
αR+βNR
1+ β(NL+ NR)
PR+ PL=1
(1,a)
PR=
(1,b)
αR+αL=1
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β is the mimetic coefficient that takes account of the influence of the individual having
previously moved and decided. If β = 0, there is no mimetic behaviour and the individuals act
independently of each other. The greater the value of β the greater the mimetism.
In order to establish the main factors causing the fluctuations of the experimental
results, we used Monte Carlo simulations. In such a numerical simulation, the random aspects
of the process are thus automatically incorporated.
We can summarize the different steps as follows:
- Initial condition: At the beginning of the simulation, all the individuals are at rest, (NR = NL
= 0).
- Decision process: The decisions of the N individuals are tested.
To determine the choice of an individual, the value of a random number is compared to PL
(equation 1,a) , depending on the choice of the previous individuals. For each monkey, the
random number is drawn from a uniform distribution between 0 and 1. If its value is less than
or equal to PL the monkey chooses the left side and if the number is greater than PL, it chooses
the right side. The delay between two departures was not considered.

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The simulations are run 1000 times for the N animals and we calculate the distribution
of the simulations as a function of the number of individuals having chosen the left side.
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We let the β mimetic parameter vary and run simulations for frequency of choices for
the same side. The case β = 0 corresponds to individuals acting independently and the
distribution is binomial (Figure 1a). For very low values of β, the model also exhibits
unimodal distributions. Three simulations with three different β ≥ 1 are presented in Figure 2.
A strong bimodal distribution is only observed for large values of β (β ≥ 3) but the fraction of
the simulations characterized by most of the individuals having chosen the same side is much
greater than the corresponding experimental ones (Figure 2b & 2c).

Individualised Model
We modified the previous model by individualising the process of directional choice. In this
model, each individual is characterized by a specific function PLi and PRi.
We assume two categories of individuals: (1) mimetic individuals having the same
behaviour as in the previous models, (2) independent subjects that are not influenced by and
reciprocally do not influence the other individuals (no mimetic process for direction choice
process). The behaviour of these independent subjects corresponds to the behaviour of the
three experimental peripheral females.

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11
) , 2 (
)(1
), 2 (
)(1
1
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++
+
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+
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∑
=
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∑
=
j
∑
=
j
∑
=
j
i
L Ri
i
L Ri
N
jj iji
N
j iji Ri
Ri
N
jj iji
N
j iji Li
i
L
PP
b
LR
R
P
a
LR
L
P
αα
δβ
δβα
δβ
δβα
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βi = 0 corresponds to an independent individual not influenced by the others. δij = 1 if the
individual j could influence the individual i. δij = 0 if the individual j could not influence the
individual i. Lj = 1 and Rj = 0 (Lj = 0 and Rj = 1 ) if the individual j has previously chosen the
left side (right side). Lj = 0 and Rj = 0 if the individual j has not yet moved. We can note that
if all the dependent individuals present the same mimetic behaviour (β1 = … = βN, , δij = 1),
equations 2 are equal to equations 1. We have performed simulations based on our
experimental observations with three independent individuals and ten mimetic individuals.
We plot the same distribution as for the anonymous model: the distribution of the
simulations as a function of the number of individuals having chosen the left side for three
mimetic coefficients (Figure 3). The results taking into account the two types of individuals
were similar to the experimental distributions: the obtained distribution was bimodal and the
maximum values of the two modes were very close to those of the experimental distribution.

Discussion
In this study we have demonstrated that most capuchin monkeys tend to follow the travel
route previously taken by their groupmates when given a binary choice, but that a minority of
individuals consistently decides their route independently from their groupmates behaviour.

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Experimental spatial decisions
The experimental distributions of the number of individuals moving in the same direction are
bimodal, which is the signature of a phenomenon involving interactions between individuals
(Camazine et al. 2001). At departure time, all group members were grouped together in the
departure area, where each capuchin had the opportunity to observe the behaviour of other
group members. One can propose facilitation of the response in this case. In such a process,
the presence of a group member performing an act already within the observer’s repertoire
increases the probability of the observer reproducing that act (Byrne 1994). In our study, the
facilitated response was the directional choice. The departure of one or more individuals to a
given side can draw the attention of the others. This would involve a facilitation of the
moving of individuals still present in the departure zone, in the same direction. This
phenomenon could also be interpreted from the perspective of group cohesion in relation to
predation risk. As more individuals have left the departure area, the chance for a capuchin to
be left alone in this area increases. In many cases, such situation is potentially hazardous in
terms of predation for an individual living in a wild primate group. This may account for a
natural tendency to grouped departures in travelling primates.
We found that this collective pattern is not a consequence of demographic and social
relationships between group members. Indeed, during movements, capuchins do not follow
their groupmates according to their sex, dominance rank, kin or affiliative relationships. It
seems that this phenomenon is anonymous from a social point of view, i.e. does not depend
on individualities or social relationships. Moreover, no vocalization was emitted by capuchins
en route for the arrival area. The environmental differences between our captive conditions
and the wild may partly explain the absence of trill vocalizations in this specific experimental
context, where the locations of the mangers were well known by the monkeys. Conversely,

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trills have been emitted by the same group members in the context of spontaneous moves
where only the initiator took the lead (Leca et al., 2003). In the wild, where food sources are
more dispersed and less limited, white-faced capuchins also use trill vocalizations to
coordination troop movements (Boinski & Campbell, 1995).
Distributions observed experimentally also show that the group was split into two
subgroups. Subgroup sizes were asymmetrical with generally one sub-group of ten or eleven
individuals and the other of two or three. This supports the hypothesis of a collective
movement and discredits the hypothesis proposing that all individuals should behave
independently of each other. In the case of truly independent individuals, the distribution
obtained would have been of a binomial type.
This result however gives no indication of the underlying mechanisms of the
asymmetrical division of the group. A finer analysis of spatial decisions whatever the identity
of the individuals reveals that the greater the number of individuals choosing one side, the
greater the probability that the other remaining individuals will choose the same side. This
behaviour has been described by the concept of contagion (Thorpe 1963), which is realised
through mimetic processes. However our results show that not all group individuals are
involved in the chain of contagion or display mimetic behaviour.

Modelling
To validate our hypothesis of mimetic processes, it was important to draw up models
(Deneubourg & Goss 1989; Camazine et al. 2001; Sumpter 2006). This approach enables the
simulation of a large number of events starting from a model. We could implement
mechanisms deduced from our decision analysis. In the anonymous model, all individuals
were considered as identical entities. Regarding non-human primates, it is clear that the
hypothesis of equal individuals is coarse (Stevenson-Hinde 1983) but this simple formulation

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