Differences in nutrient requirements imply a non-linear emergence of leaders in animal groups.

Differences in Nutrient Requirements Imply a Non-Linear
Emergence of Leaders in Animal Groups
Ce´dric Sueur1,2,3*, Jean-Louis Deneubourg1, Odile Petit1, Iain D. Couzin3
1Unit of Social Ecology, The Free University of Brussels, Brussels, Belgium, 2 Ethologie des Primates, Department of Ecology, Physiology, and Ethology, Institut
Pluridisciplinaire Hubert Curien, Strasbourg, France, 3Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, United States of America
Abstract
Collective decision making and especially leadership in groups are among the most studied topics in natural, social, and
political sciences. Previous studies have shown that some individuals are more likely to be leaders because of their social
power or the pertinent information they possess. One challenge for all group members, however, is to satisfy their needs. In
many situations, we do not yet know how individuals within groups distribute leadership decisions between themselves in
order to satisfy time-varying individual requirements. To gain insight into this problem, we build a dynamic model where
group members have to satisfy different needs but are not aware of each other’s needs. Data about needs of animals come
from real data observed in macaques. Several studies showed that a collective movement may be initiated by a single
individual. This individual may be the dominant one, the oldest one, but also the one having the highest physiological
needs. In our model, the individual with the lowest reserve initiates movements and decides for all its conspecifics. This
simple rule leads to a viable decision-making system where all individuals may lead the group at one moment and thus suit
their requirements. However, a single individual becomes the leader in 38% to 95% of cases and the leadership is unequally
(according to an exponential law) distributed according to the heterogeneity of needs in the group. The results showed that
this non-linearity emerges when one group member reaches physiological requirements, mainly the nutrient ones –
protein, energy and water depending on weight - superior to those of its conspecifics. This amplification may explain why
some leaders could appear in animal groups without any despotism, complex signalling, or developed cognitive ability.
Citation: Sueur C, Deneubourg J-L, Petit O, Couzin ID (2010) Differences in Nutrient Requirements Imply a Non-Linear Emergence of Leaders in Animal
Groups. PLoS Comput Biol 6(9): e1000917. doi:10.1371/journal.pcbi.1000917
Editor: Raluca Eftimie, McMaster University, Canada
Received April 19, 2010; Accepted August 3, 2010; Published September 2, 2010
Copyright: � 2010 Sueur et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: CS was funded by Wallonia Brussels International, the Franco-American Commission, the Alsace Region, and the Fyssen Foundation. JLD was funded by
Belgian National Funds for Scientific Research. IDC is pleased to acknowledge support from Searle Scholar Award 08-SPP-201, National Science Foundation Award
PHY-0848755, Office of Naval Research Award N00014-09-1-1074 and Defense Advanced Research Projects Agency (DARPA) grant HR0011-09-1-0055. The funders
had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: cedric.sueur@c-strasbourg.fr
Introduction
Social animals have to coordinate their activities in order to
maintain the advantages of group living [1–3]. This coordination
constitutes one of the major challenges of any animal society,
including human beings, and arouses the interest of scientists,
sociologists, and politicians [4–9]. Whatever the group size or the
level of communication – global or local [8,9] – several categories of
group decision making have been described: a leadership process
where one individual will propose or impose a decision that other
group members will follow [10–15], and a voting process in which
each individual indicates a direction, for instance, and after which
the group will move in the direction of the majority [4,16–18]. A
group leader is usually defined as the individual initiating group
movements but also as the individual coordinating individual during
the group progression, and then mainly at the front of the
progression [4,8–13]. In different species of animals, leadership is
not necessarily homogeneously distributed among group members
[8–15]. Some individuals are more likely to become leaders thanks
to specific internal or social traits increasing their probability of
initiating a movement [10–12]. Studies of elephants [19], ravens
[20], or fishes [21] have reported that some individuals may have a
greater knowledge about their environment – which is the best site
to eat or to drink – and these individuals have been observed leading
the group more often than their conspecifics. In other species,
individuals having a high social status, in terms of dominance or
affiliation, also have a greater likelihood of being leaders. Probably
the best known examples come from wolves and gorillas [10,22]
where the dominant male or couple is described as always deciding
for the entire group. In Tonkean macaques, however, the most
affiliated individuals – who are not necessarily the most dominant
ones – seem to have a greater influence than their conspecifics in
collective decision making [23].
However, one of the major factors influencing leadership should
be the different physiological requirements of group members [10–
12]. Such heterogeneity implies conflicts of interests between
individuals that must be resolved in order to maintain group
cohesion. Leaving the leadership to highly motivated individuals
seems to be one compromise. Indeed, the moving decision seems
to be taken by those with highest needs in fishes, zebras, and
primates [8,9,14,24]. Nevertheless, we still lack data on the way
leaders emerge and the viability of the decision-making system
concerning the entire group’s satisfaction. Using a modelling
approach, Rands et al. [12,25] and Conradt et al. [26] showed
that individuals with the highest nutrient requirements can be
more prone to lead the group if there is an advantage to foraging
together. Their studies were however restricted to pairs of
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individuals or to situations in which individuals faced two mutually
exclusive target destinations only.
Here, we use a state-dependent dynamic model [27,28] to
determine how nutrient and social requirements can determine the
synchronization of a group of n individuals, their activity budget,
and the emergence of leaders. This kind of models allows us to
understand how simple rules based on nutrient requirements and
social factors explain synchronization between group members
[27] but also segregation as shown in ungulates [28], where each
individual has some requirements to satisfy (nutrient require-
ments such as protein, energy and water but also other social
requirements and resting). We assume that if there is an advan-
tage to being in a group, then the group members should
synchronize their activities in order to stay cohesive. We assume
that individuals do not know the requirements of their conspecifics
(and further show that such ability may not be necessary for
effective group coordination). Each individual requirement
combines a reserve and a motivation that we call probability to
lead. When the reserve decreases, the probability increases. At one
moment, the individual with the lowest reserve – among its own
needs and in comparison to other individuals – will have the
highest probability to lead (these individual probabilities are
compared at each time step) and will decide for the entire group
on changing activity in order to fulfil its respective reserve
[8,9,12,25,26]. In the next step, when the need of the previous
leader is satisfied, a new leader will emerge and decide for the
whole group. We applied this condition in our model in order to
assess if this simple hypothesis ‘‘leading according to needs and
deciding for all the group’’ is viable and if so, how the leadership
will be distributed among group members less or more
heterogeneous in their needs.
Results
We first tested a group of two individuals, A and B, with two
needs, x1 and x2. We set three conditions: 1) needs are equal
(a1 = a2 = b1 = b2), 2) needs of each individual are different but
their sums are equal between individuals (a1.a2; b1.b2;
a1+a2 = b1+b2) and 3) the sum of needs for individual A are
always superior to the one of individual B (a1+a2.b1+b2). Values
of needs for each tested group of each condition are detailed in
table 1. We tested 10 groups for each condition. Results show
that the decision system is viable, no individual dies, i.e., no
individual has needs not met (reserves go to 0), whatever the
tested condition. When sums of needs are equal between
individuals (conditions 1 and 2), the leadership (proportion of
decisions, i.e., initiations per individual) is equally distributed
between the two individuals (Fig. 1A), even if, at each time step,
one individual is the leader and the other one is the follower
according to the reserves’ difference. This result is similar to the
one of the paper of Rands et al. [25] where individuals are
identical. However, when the sum of needs is superior for one
individual (Fig. 1B), this one becomes the leader of the pairs of
individuals and the other individual becomes a follower almost all
the time (Kolmogorov-Smirnov test, P,0.0001). The leadership
difference between individuals increases with their relative
difference of needs in a logarithmic way (curve estimation test:
R2 = 0.96, P,0.00001; Fig. 1C). This result is similar to the one
of Rands and colleagues [12]: leaders emerge when individual
reserves differ.
In a second step, we used data coming from animals in order to
validate our model and to study emergence of leaders in larger
groups.. According to needs of macaques, animals were divided
into five categories: adult males, adult cycling females, lactating
females, subadults, and juveniles. An individual has five require-
ments to satisfy: water, protein, energy, resting, and socializing
[29–34]. The nutrient requirements of an individual (water,
protein and energy) depend on its body mass whilst social and
resting needs did not [31–34]. We chose to include social activity
in the model because many social species spend time maintaining
their relationships and group cohesion [31–35]. Group composi-
tion (table 2) and individual characteristics (table 3) are based on
data on macaques and are detailed in the method section. We
tested 10 groups of 5, 10 and 20 individuals with same needs
(individuals of the same category and with the same body mass)
and 10 ones with different needs (individuals of both different
categories and different body masses).
Simulations showed that the system – leadership by those in
need – is sustainable in groups of 5, 10 and 20 individuals. All
individual requirements are satisfied at the end of simulations,
whatever the group composition. Moreover, the group activity
Author Summary
Making decisions together to reach a consensus is one of
the most important challenges of any society. In some
communities, however, some leaders have more weight in
the decisions than the other individuals. Similar rules exist
in animal societies. Studies on animal groups have shown
that some individuals are more likely to be leaders because
of their social power or the pertinent information they
possess. This leader may be the dominant one, the oldest
one, but also the one having the highest physiological
need. However, how may other group members have their
needs satisfied if always the same individual decides? To
gain insight into this problem, we build an agent-based
model where group members have to satisfy different
needs but the individual with the lowest reserve decides
when and where to move for all its conspecifics. This
simple rule leads to a viable decision-making system that
satisfies all individuals and suits their requirements.
However, a single individual, the one with the highest
needs, becomes the leader in 38% to 95% of cases
according to the heterogeneity of needs in the group.
Table 1. Values of daily requirements (a1, a2, b1, b2) for each
individual, A and B, in each condition (1 to 3) and each group
(1 to 10).
Group 1 2 3 4 5 6 7 8 9 10
Condition 1 a1 500 600 700 800 900 1100 1200 1300 1400 1500
a2 500 600 700 800 900 1100 1200 1300 1400 1500
b1 500 600 700 800 900 1100 1200 1300 1400 1500
b2 500 600 700 800 900 1100 1200 1300 1400 1500
Condition 2 a1 500 600 700 800 900 1100 1200 1300 1400 1500
a2 1500 1400 1300 1200 1100 900 800 700 600 500
b1 1500 1400 1300 1200 1100 900 800 700 600 500
b2 500 600 700 800 900 1100 1200 1300 1400 1500
Condition 3 a1 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450
a2 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450
b1 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
b2 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
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budget is fairly similar to the activity budget of wild primate
groups (27.361.7% of time devoted to moving, 33.861.7% to
foraging, 21.760.7% to resting, and 17.263.1% to socializing).
All individuals could become leaders but the distribution of the
leadership proportion is not the same according to the
requirements’ heterogeneity (equal or different needs; Kruskal-
Wallis test, P,0.001). In groups with similar needs, the
proportion of leadership differs weakly between individuals and
is about 10% per individual. The relation between leader-
ship proportion and rank (i.e., individuals were ranked from the
most frequent leader to the less frequent one) is linear (linear
curve estimation test: R2 = 0.92, F1,8 = 93.05, P,0.00001,
y =20.0006x+0.1339). The leadership is about 14% for the
individual that decides the most and 7.6% for the individual that
decide the least (Fig. 2A). This result corresponds to the equi-
probability of being leader per individual (proportion divided by
the number of individuals per group). On the other hand, the
leadership is not equally distributed in heterogeneous groups. The
relation between the proportion of leadership and individuals is
exponential (exponential curve estimation test: R2=0.83,
F1,8 =38.07, P=0.0002, y=3.5727e
24.602x, Fig. 2B), with one
individual being responsible for 38% to 95% of decisions per group,
while some individuals decide only in 0.0003% to 0.0007% of cases
per group. We obtained the same relationship with groups of 5
(exponential curve estimation test; R2=0.97, F1,3 =12.81,
P,0.00001, y=0.9825x23.207, Fig. 3A) and 20 individuals (expo-
Table 2. Mean, minimum, and maximum number of
individuals per category for n= 10 individuals per group.
Mean±SD Minimum Maximum
Adult male 1.660.7 1 3
Adult cycling female 3.161.3 2 6
Lactating female 1.761.3 0 4
Subadults 1.961.3 0 4
Juveniles 1.860.9 0 3
doi:10.1371/journal.pcbi.1000917.t002
Figure 1. Leadership ratio according to the condition for groups of 2 individuals. Condition 1 (a.): needs are equal (a1= a2= b1= b2).
Condition 2(a.): needs of each individual are different but their sums are equal between individuals (a1.a2; b1.b2; a1+a2= b1+b2). For these two
conditions, the leadership is equally distributed between individuals (Kolmogorov-Smirnov test, P.0.972). Condition 3(b., c.): the sum of needs for
one individual is superior to the one of individual. For Condition 3, the ratio (a1+a2)/(b1+b2) ranged from 1 (Group 1) to 1.45 (Group 10). For this
condition, one individual becomes the leader when its needs are superior to the ones of its conspecifics. Fig. 1c represents the difference of
leadership according to the relative difference of needs between A and B.
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Table 3. Mean individual weight and requirements for each category and each need.
Requirement
weight (kg) protein (g.day21) energy (KJ.day-1) water (ml.day21) social time (minutes.day21) resting time (minutes.day21)
Adult males 15.1861.34 38.5563.40 53136889 1269.086212.34 100650.41 87.50655.71
Females 9.6262.39 24.4466.07 31916792 762.246189.20 112.73619.89 50.91633.52
Lactating females 9.8561.04 30.0662.63 605961191 1447.236284.50 86.67630.688 106.67637.41
Subadults 4.4360.66 11.2761.67 14716219 351.40652.35 170.53630.09 30628.72
Juveniles 3.3361.43 8.4663.63 11056474 264.006113.32 176.67614.14 80.83633.80
doi:10.1371/journal.pcbi.1000917.t003
Figure 2. Mean leadership proportion or ratio (solid line) according to individuals with (a) equal needs and (b) different needs in
groups of 10 individuals. Individuals are ranked from the individual with the highest leadership proportion to the one with the lowest leadership
proportion. The upper and lower dotted lines indicate respectively the maximum and minimum leadership proportions for each rank. The leadership
proportion is different between individuals whatever the condition.
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nential curve estimation test; R2=0.96, F1,18 =498.95, P,0.00001,
y=11.48x24.86, Fig. 3B).
We compared this unequally distributed leadership to the
requirements of individuals in order to understand how so many
differences can emerge in heterogeneous groups. We calculated the
relative difference in requirements (corresponding to the highest
probability to lead) between each leader and other individuals. The
relationship between the leadership and this difference in
requirements follows a sigmoid curve (y~1{ 1
1z x
s
� �n
0
B@
1
CA with a
threshold S of 1.37 and a minimal n value of 30; curve estimation
test: R2= 0.71, F1,108 = 269.72, P,0.00001; Fig. 4A). The n value
represents the sensitivity of the process. The higher the n value is, the
more sensitive the process is (quick and sudden transition between
the two states). In our context, this means that one individual
becomes the most frequent and prominent leader of a group as soon
as one of its requirements exceed about 137% of those of one of
its conspecifics. This transition between equally distributed
leadership and one exclusive leader is highly non-linear, given the
n value we observed. The same sigmoid law is observed between the
proportion of leadership and the body mass of individuals (sigmoid
curve estimation test: R2= 0.66, F1,108 = 205.73, P,0.00001;
Fig. 4B). When the mass of an individual is more than 170%
(S=1.7, n= 30) of those of its conspecifics, this individual is the
main group leader. Except for lactating females, requirements and
then leadership are related to body mass in about 60% of cases. The
rest of the decisions concern resting and socializing and are not
related to mass. We obtain similar results for groups of 5 (sigmoid
curve estimation test: R2=0.71, F1,53 = 111.52, P,0.00001,
y~0:96{ 0:96
1z x
1:33
� �30
0
B@
1
CA, Fig. 5A) and 20 individuals (sigmoid
curve estimation test: R2= 0.16, F1,218 = 42.13, P,0.00001,
y~0:96{ 0:96
1z x
1:40
� �30
0
B@
1
CA, Fig. 5B). For 8 out of 10 groups of
20 individuals, 4.662.2 group members were never leader. They
were satisfied by following their conspecifics.
Discussion
Leading by those highest in need resembles the results obtained by
Rands et al. [25], where the individual with the lower reserve
spontaneously becomes the leader. Moreover, a recent study by
Conradt et al. [26] showed that a small minority of individuals with
strong needs are more prone to lead the group than a larger majority of
individuals with few needs. However, it is the first time that a threshold
[2,18,36] has been demonstrated concerning the emergence of
leadership. The decision-making system implies high differences in
leadership proportion whilst relatively small differences are observed in
the requirements of individuals. The threshold we obtained in this
study is probably dependent on 1) the group structure of primates (one
or a small number of males compared to the other categories) [35] and
2) to the physiology of primates [31–34]. Indeed, in primates, and
especially in macaques, a sexual dimorphism exists and males may
reach a mass 150 to 200% superior to the one of females.
Several authors suggested that dominant individuals are the
only leaders in several species [9–12,14,22,23]. The dominance is
however strongly correlated to the body mass and then to the
nutrient requirements of animals [10]. This indirect effect of
dominance on leadership, through the needs and then the
probability to initiate a movement, needs to be taken into account
in subsequent studies testing dominance effects. For instance, two
field studies in baboons showed that the main leader – the
individual initiating most of movements – was the dominant male.
However this male is also certainly the biggest individual in the
group. In the study of Stueckle and Zinner [36], the four males of
the group, bigger than females, are the ones initiating the most of
movements (Fig. 6). Moreover, the distribution of leadership also
follows an exponential as the one in the study model. We may
suggest that the slope of this exponential distribution of leadership
will be less or more important according to the group composition.
This slope would be around 0 when the group is homogeneous
and increases with group heterogeneity.
The non-linear differences in leadership among group members
eventually emerge from two simple rules: individuals need to
remain cohesive and the individual with the lowest reserve at one
moment decides for the group [2,3,24–26]. Mechanisms of
coordination and cohesion do not need complex signalling or
Figure 3. Mean leadership proportion or ratio (solid line) according to individual in groups of (a) 5 and (b) 20 individuals having
different needs. Individuals are ranking from the individual with the higher leadership proportion to the one with the lower leadership proportion.
The up and down dotted lines indicate respectively the maximum and minimum leadership proportions for each rank.
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complex cognitive ability [2,3,13,24]. The emergence of a unique
leader may also occur when decisions are not necessarily imposed
on other group members but because other individuals do not
express the necessity to move or to make a decision. An individual
becomes a leader because its conspecifics decide to follow it [8,9].
This outcome may make important contributions to our
understanding of decision making in animal and human societies.
Materials and Methods
Models’parameters
The model was developed in Netlogo 3.15 [37]. The model and
model’s procedures can be found in the supplementary material
‘‘Dataset S1’’. One time-step in the simulation represents one
minute. We defined the probability to lead a for the requirement
A and the individual i as:
P(a)i~(daily requirement in A - reserve in A)=
(daily requirement in A)
The probability to lead for the individual i is:
Pi~max P(a)i,:::,P(n)ið Þ
In this way, the probability to lead can vary between 1 (highest
Figure 4. Relation between the leadership proportion and (a) the difference in needs and (b) the difference in mass for each
individual and the other group members in groups of 10 individuals. These functions are both sigmoid. N = 110. Each point represents
characteristics of one individual in each group (ten groups with different needs and one with equal needs are represented).
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probability to lead, weakest reserve) and 0 (weakest probability to
lead, highest reserve). Each reserve is bounded by a maximum
above which each group member cannot gain further reserves and
a minimum at which each group member is assumed to die if it is
reached. At each timestep (equal to one minute), each reserve of
each individual decreases (i.e., expenditure) depending on the
individual category and the current activity. This reserve decrease
will increase the individual probability to lead. In order to fulfil this
reserve, the individual should have to carry out the corresponding
activity (i.e., intake). This gain may be done by becoming a leader
or by following the leader. We implement optimal foraging
decisions in the model: when an individual decides to forage, it will
forage until its reserve has been fulfilled. After the end of each
activity period, the individual with the highest probability to lead
Pi becomes the new leader. Individuals have a walking speed of
0.4m.s21.
The group environment is two-dimensional environment of
96696 connected cells. Each cell represent one meter. Each cell
has four immediate neighbours and the sides of the arena were
joined to form a torus. The number of areas where animals fulfil
their reserves is two for the first model with two individuals having
two needs and four for the model from 5 to 20 individuals having
Figure 5. Relation between the leadership proportion and the differences in need in groups of (a) 5 and (b) 20 individuals. These
functions are both sigmoid. Each point represents characteristics of one individual in each group (ten groups with different needs and one with equal
needs are represented).
doi:10.1371/journal.pcbi.1000917.g005
Figure 6. Number of initiations per individual in a group of baboons studied by Stueckle and Zinner [36]. Black squares represent
females, white squares represent males. The distribution of initiations follows an exponential curve as (black line) determined by the study model
(curve estimation test: R2 = 0.99, P,0.00001, y = 22.73e20.219x).
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five needs (see details below). At the start of a simulation,
individuals are at the same distance of each area (i.e., at the middle
of the torus). According to the distribution of areas inside the torus,
groups have a travel distance between two areas ranging from a
minimum of 25 meters to a maximum of 75 meters. This range
fits with travel distances in primate species of similar body mass
and similar group size [4,38–41]. Positions of areas were fixed in
our model but this does not affect results since variability among
needs – what is the highest need and the weakest one – is much
more important between individuals and groups. This means that
the areas corresponding for instance to the two highest needs for
an individual are not always the closest ones. There is no
intragroup competition in this model: all individuals can occupy
the same area. We run 1000 simulations for each group. A
simulation stops when one reserve of one individual reaches 0 or
after 90 days.
Model with two individuals having two needs
The two individuals have two needs and thus two daily
requirements. Values of these requirements for each condition
and each individual are described in table 1. We tested ten different
groups for each condition. Expenditures of each reserve are
0.0760.035 units.min21. Intakes are 10 units.min21. The environ-
ment is composed of two areas, one for each requirement.
Individuals have to move to the respective area to fulfil each reserve.
Model with five to 20 individuals with five needs
According to data in macaques, the daily protein requirement is
estimated to 2.54g.day21.kg21, daily energy requirement to
351.7Kcal.day21.kg21, and daily water requirement to
0.24ml.KJ21, except for lactating females for which these
requirements are higher than the ones of non lactating females
(about 125% for proteins and 200% for energy and water of
requirements of non lactating females) [31–34]. Social and resting
times are not dependent on body mass. Individual expenditure per
need and activity is described in table 4. Details about individual
intake rate per need are in table 5.
The environment is composed of four areas: one area for
foraging for proteins, one area for foraging for energy, one
waterhole, and one resting site [42]. When individuals need
energy, proteins, or water, they have to move toward the
respective areas. Until the group is in a specific activity among
the five ones (eating proteins, eating energy, drinking water,
resting or socializing), each individual gains a certain amount of
the requirement according to its category (table 5). Concerning
resting, individuals need to go to the resting site for the night (at
the 720th time-step and for 720 time-steps), but during the day
they can rest in any area. The same rule applies to socializing.
Concerning resting and socializing activity, we fixed a minimal
period of 5 minutes for doing these activities.
Statistics
Differences in leadership between individuals were tested using
a Kolmogorov-Smirnov test for groups of 2 individuals and a
Kruskall-Wallis test for groups from 5 to 20 individuals. The
relations between the proportion of leadership and differences in
needs or mass were determined through a curve estimation test.
We compared observed curves to exponential, linear and sigmoid
ones. Only theoretical curves best fitting with observed data are
indicate in results. Analyses were performed in SPSS 10.00. a was
set at 0.05. Means were 6 S.E.M.
Supporting Information
Dataset S1 This file contains the model used for this publication
and its related files. The file ‘‘modele beta min.nlogo’’ is the model
used for this publication. Algorithms can be seen in the
‘‘procedures’’ window. ‘‘attributes.txt’’ file is used to implement
individual characteristics in the model. Row 1 corresponds to the
identity of agents. Row 2 represents the body mass. Row 3 is the
daily protein requirement. Row 4 is the daily energy requirement.
Table 4. Individual expenditure per activity for each need.
Expenditure
protein (g.min21.kg21) energy (KJ.min21.kg21) water (ml.min21.kg21) social time (min.min21) resting time (min.min21)
Foraging 0.002760.0013 0.2960.15 0.0760.035 social time requirement/720 resting time requirement/720
Walking 0.2460.10 0.057560.023
Socializing 0.2960.15 0.0760.035
Resting 0.1060.05 0.02560.012
doi:10.1371/journal.pcbi.1000917.t004
Table 5. Mean individual intake rate categories for each need.
Intake
protein (g.min21) energy (KJ.min21) water (ml.min21) social time (min.min21) resting time (min.min21)
Males 0.21760.108 41.9623.1 50625 1.060.5 1.060.5
Females 0.21760.108 38.9618.7
Lactating females 0.21760.108 38.2620.2
Subadults 0.20260.101 28.4615.2
Juveniles 0.12660.63 23.7611.2
doi:10.1371/journal.pcbi.1000917.t005
Non-Linear Emergence of Leaders
PLoS Computational Biology | www.ploscompbiol.org 8 September 2010 | Volume 6 | Issue 9 | e1000917

Row 5 is the protein intake rate. Row 6 is the energy intake rate.
Row 7 is the daily water requirement. Row 8 is the daily social
time requirement. Row 9 is the daily resting time requirement.
Row 10 is the category of individuals (male, female, etc.).
‘‘Links.txt’’ file is used to implement social relationships of
individuals in the model. This variable is not used and analyzed
in this study. ‘‘activitybudget.doc’’ file is used to score group
activity budget per day. ‘‘highestvalue.doc file’’ is used to score
which individual has the highest motivation at the end of the day
and what is this motivation. ‘‘idleaderfrequency.doc’’ is used to
score the frequency of leadership per individual during all the
simulation.
Found at: doi:10.1371/journal.pcbi.1000917.s001 (0.35 MB ZIP)
Acknowledgments
We would like to thank Sean Rands and two anonymous reviewers for their
helpful comments.
Author Contributions
Conceived and designed the experiments: CS JLD IDC. Performed the
experiments: CS. Analyzed the data: CS IDC. Contributed reagents/
materials/analysis tools: CS JLD OP IDC. Wrote the paper: CS JLD OP
IDC.
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Non-Linear Emergence of Leaders
PLoS Computational Biology | www.ploscompbiol.org 9 September 2010 | Volume 6 | Issue 9 | e1000917