Individual analyses of Lévy walk in semi-free ranging Tonkean macaques (Macaca tonkeana).

Individual Analyses of Le´vy Walk in Semi-Free Ranging
Tonkean Macaques (Macaca tonkeana)
Ce´dric Sueur1,2,3*, Le´a Briard1,2,3, Odile Petit1,2,3
1Unit of Social Ecology, Free University of Brussels, Brussels, Belgium, 2Centre National de la Recherche Scientifique, De´partement Ecologie, Physiologie et Ethologie,
Strasbourg, France, 3Universite´ de Strasbourg, Institut Pluridisciplinaire Hubert Curien, Strasbourg, France
Abstract
Animals adapt their movement patterns to their environment in order to maximize their efficiency when searching for food.
The Le´vy walk and the Brownian walk are two types of random movement found in different species. Studies have shown
that these random movements can switch from a Brownian to a Le´vy walk according to the size distribution of food
patches. However no study to date has analysed how characteristics such as sex, age, dominance or body mass affect the
movement patterns of an individual. In this study we used the maximum likelihood method to examine the nature of the
distribution of step lengths and waiting times and assessed how these distributions are influenced by the age and the sex of
group members in a semi free-ranging group of ten Tonkean macaques. Individuals highly differed in their activity budget
and in their movement patterns. We found an effect of age and sex of individuals on the power distribution of their step
lengths and of their waiting times. The males and old individuals displayed a higher proportion of longer trajectories than
females and young ones. As regards waiting times, females and old individuals displayed higher rates of long stationary
periods than males and young individuals. These movement patterns resembling random walks can probably be explained
by the animals moving from one location to other known locations. The power distribution of step lengths might be due to
a power distribution of food patches in the enclosure while the power distribution of waiting times might be due to the
power distribution of the patch sizes.
Citation: Sueur C, Briard L, Petit O (2011) Individual Analyses of Le´vy Walk in Semi-Free Ranging Tonkean Macaques (Macaca tonkeana). PLoS ONE 6(10): e26788.
doi:10.1371/journal.pone.0026788
Editor: Sharon Gursky-Doyen, Texas A&M University, United States of America
Received July 27, 2011; Accepted October 3, 2011; Published October 26, 2011
Copyright: � 2011 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 the Japan Society for the Promotion of Science (PE10062). 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@iphc.cnrs.fr
Introduction
All animals have to adapt their activity and movements patterns
to their environment in order to maximize their nutrient intakes and
therefore their fitness [1–4]. How the heterogeneity of resource
distribution and how it affects individual foraging decisions is of
great interest in ecology [5,6] but also in decision sciences [2,7] and
physics [8,9]. Indeed, several species seem to behave like particles
suspended in a fluid: they move in their environment according to
Brownian motion [6,10–12]. Authors have suggested that the use of
these random walks should increase the probability of the subject to
find food or a reproductive partner [10–15].
Le´vy walks are a special class of random walks in which
movement displacements (step lengths) and stationary periods
(waiting times) are not constant but follow a probability
distribution with a power-law tail [6,16]. The opposite is seen in
the Brownian walk, where the probability of showing a certain step
length is constant, and its distribution follows an exponential law
[11,13,17]. The topic continues to be discussed and questioned
[5,10,17–19], but the main hypothesis is that the Le´vy walk is used
by animals as an optimal strategy when they are seeking resources
without information about the heterogeneous environment with
low density food patches in which they live. Previous studies have
reported Le´vy walks in social amoebas [20], zooplankton [10],
jackals [16], albatrosses [6] and primates [19,21]. However, few
studies have assessed whether individual characteristics, such as
body mass, age or sex could influence movement patterns. One
study alone showed that Le´vy walks differed between male and
female spider monkeys (Ateles geoffroyi) [21]. Authors suggested that
this difference was due to a different space-use strategy, with males
ranging over wider areas than females in order to control the
boundaries of their home range. Studying on an individual level
rather than a population level is an interesting possibility to further
develop our understanding of the emergence of random walks in
animals. Here, we assess whether individuals from a semi free-
ranging group of Tonkean macaques (Macaca tonkeana) show
different movement patterns and whether these differences depend
on socio-demographic variables.
Primates are known to use high-level cognitive processes in their
foraging and movement decisions [7]. It would therefore be logical
to consider that primates would not walk ‘‘randomly’’ (i.e. in an
unpredictable way) in their environment. However, their physio-
logical differences might affect how they will move, the distance
traveled and the time they spend foraging, and therefore influence
the distribution of their step lengths or waiting times. Differences
between individuals had already been shown in several species,
namely in diet and activity budget [22–30]. Resting tends to
increase with age whilst moving decreases [22,29]. In many cases,
adult females spend more time foraging than adult males, but the
opposite case can also be seen. This result mainly depends on the
sexual dimorphism existing between the two genders, with adult
males foraging more than females when the dimorphism increases
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[22,23,31]. In the same way, and due to their small body mass,
young individuals spend less time foraging than adult ones. Finally,
young individuals socialize, and particularly play more than adult
individuals [32]. All these results showed that socio-demographic
characteristics have a significant impact on how individuals adapt
their activity to their environment.
We studied activity budget and movement patterns of ten
Tonkean macaques living in a park containing grass, trees and
bushes. Despite these semi-free ranging conditions, animals spend
more than a third of their time foraging and searching for food
(pellets provided within the indoor housing, as well as natural
fruits, leaves and buds in their captive environment; see [33]).
They also adjust their behaviour according to variation in
environmental constraints throughout the day and in the course
of a year [33,34]. We first studied whether animals displayed
differences in their activity budget, as already shown in several
other primate species. We then used the maximum likelihood
method to analyse the distribution of step lengths and waiting
times for each individual [10,19,35]. This is considered to be the
most efficient method when testing for the presence of Le´vy walk
in animals. We expected animals to display differences according
to their age and their sex. For the distribution of step lengths, given
the fact that young individuals play more (short movements) but
forage less (long movements) than adults, we suggested that the tail
of the power function would be longer in adults than in young
individuals, i.e. that adults would walk less but would cover longer
distances than juveniles. Given the sexual dimorphism between
male and female Tonkean macaques, we suggested that males
would forage more than females, and that the tail of the power
function would be also longer for males. As adults rest more but
play less than young individuals, we expected a longer tail of
waiting time distribution in adults than in young individuals. We
did not expect to see any difference in waiting time distribution
between different genders.
Materials and Methods
Ethics Statement
This study involved the observation of animals without animal
handling or invasive experiments carried out on studied subjects.
The body masses of individuals were scored during a health check,
performed during the observation period. We declare that our
study was approved by our institution and carried out in full
accordance with the ethical guidelines set out by this institution
(certificate number: 67–339, French Republic, Bas-Rhin County
Hall, French veterinary services). Our experiments comply with
European animal welfare legislation. Please see the section below
(Subjects and environment) for amelioration of animal welfare. The
work being carried out during this study is in accordance with the
weatherall report and all efforts were made to ensure the welfare of
the animals and minimize suffering.
Subjects and environment
The study group was bred under semi free-ranging conditions at
the Strasbourg University Centre of Primatology. At the time of
the study (November 2005 to March 2006), the group consisted of
10 individuals: one adult male (over five years old), five adult
females (over four years old) and four juveniles (aged one to three
years). This group composition is comparable to that of wild
groups [33,36–38]. Wild Tonkean macaques are typically found in
the primary and secondary rainforests of Sulawesi (Indonesia) and
are mainly frugivorous [36,38]. The Tonkean macaques in this
study had complete access to 0.32 ha (maximal length = 80 m;
maximal width = 60 m) of wooded parkland as well as indoor
housing within the enclosure. The indoor housing (20 m2) is made
of cement and tiling, and animals were able to climb on it. The
enclosure area was made up of various slopes and uneven ground.
The distribution of vegetation was also heterogeneous, with three
layers (grass, trees and bushes) that were unevenly distributed
throughout the enclosure. Within the park, animals moved
cohesively during 50% of movements, in sub-groups in 20% of
movements, and alone in 30% of movements [39]. They used the
park in a heterogeneous way according to ecological conditions
(topology and vegetation; [33]). Despite the ad libitum provision of
commercial primate pellets and water within the indoor housing,
animals were seen to spend 36.3% of their time foraging and
searching for other food than the pellets provided (leaves, buds and
fruits) outside the indoor enclosure (see [33] for details). Fresh fruit
and vegetables were provided at the same location once a week,
one hour after the end of the observation session. Thus, the
behaviour of the animals was unlikely to be affected by this event.
Animals were used to human presence in their enclosure.
Scoring of variables
Observations occurred from November 18th, 2005 to March
23rd, 2006, for four hours per day, from 9:00 to 13:00 or from
13:00 to 17:00.
Every 10 minutes, an observer noted the position of each
animal in the enclosure on a map (scale: 1/550; precision: one
meter) and recorded each animal’s activity, using the instanta-
neous sampling method [40]. The measurement of 77 landmarks
enabled us to create a precise grid of the park with 1 m2 cells. The
activities we were interested in (listed below) were defined
according to the same criteria used in previous studies for
Tonkean macaques [33,36,38]:
N Moving: locomotion including walking, running, climbing
and jumping;
N Foraging: reaching for, picking, manipulating, masticating, or
placing food in mouth, as well as manipulating the contents of
a cheek pouch (if an individual masticated whilst walking, we
considered it to be moving);
N Resting: Body stationary, usually sitting or lying down;
N Social activities: playing, grooming, sexual and aggressive
behaviour.
We only retained scans where the position and the activity of all
individuals could be noted. At the end of the study, we had
Table 1. Individual characteristics of Tonkean macaques.
ID Age Body mass (kg) Dominance rank Sex
Ga 11 14.8 1 M
Je 12 12.7 2 F
La 10 9.6 3 F
Ne 8 9.4 4 F
Ol 7 9 5 F
Pa 6 8.2 6 F
Sh 4 7 7 M
Ta 2 6.5 8 M
Ul 2 6.1 9 M
Uj 2 4.5 10 F
doi:10.1371/journal.pone.0026788.t001
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obtained a total of 24 days of observation, 558 scans and 5580
recordings of individual positions within the enclosure.
We established the dominance relationships through the scoring
of spontaneous agonistic interactions and drinking competition
around a single source of orange juice. Individuals were then
ranked in a matrix of agonistic interactions and the linearity of this
ranking was checked using Matman software (h9=0.75,
p = 0.0006; [41]).
Data analysis
Parameters. We estimated the activity budget of each
individual by determining the percentage of observations of each
activity (number of scans spent in one activity divided by the total
number of scans).
A step was defined as an interval in which either or both
coordinates in two consecutive samples differed. The maps on
which we scored spatial positions were used to directly calculate
the length L of a step in meters for each individual. Waiting times
were calculated for each individual using the number of samples in
which an individual had not changed position. We did not
consider the turning angle distributions in the current paper, as
turning angles do not give any clear information relating to the
hypotheses. Indeed, we were unable to predict how age or sex
could influence turning angles of individuals.
Analyses. Individual characteristics are given in Table 1. As
body mass and dominance rank are highly correlated to age of
individuals (body mass: rs = 0.98, N= 10, p,0.00001; dominance
rank: rs =20.98, N= 10, p,0.00001), we performed correlation
analyses with activity budget and movement patterns using age.
Dominance rank is also correlated to body mass (rs = 1.00, N= 10,
p,0.00001). We found no difference according to age between
males and females (U=7.00, Nmales = 4, Nfemales = 6, p = 0.352,
mmales = 3[2;9], mfemales = 7 [5;10]).
Firstly, we used Spearman rank correlation tests to correlate age
with the absolute frequency of observations per activity per
individual. We then tested the effect on activity using a Mann-
Whitney test.
We checked for the predominance of either a Le´vy walk (power
distribution, y = a*xm) or a Brownian walk (exponential distribu-
tion, y = a.ex*l) in animals. This was achieved via the maximum
likelihood method [10,35]. The maximum likelihood method
(MLE) involves calculating the exponent of the distribution (i.e.
power and exponential in the case of the current study) in order to
calculate the distribution log likelihood. Log likelihoods for the
exponential distribution and the power distribution can then be
compared for step lengths and waiting times using the Akaike
Information Criterion (AIC). One AIC is calculated for each
hypothesis (Brownian or Le´vy) and we retained the hypothesis with
the lowest AIC.
For the step length distribution, we first calculated the maximum
likelihood estimate of the power law exponent as follows:
mMLE~1zn
Xn
i~1
ln
xi
xmin
!{1
ð1Þ
Where n is the total number of step lengths, xmin is the minimum step
length included in the analysis (in the current study, the minimum
measured step length equals one meter). Considering the maximum
likelihood estimate, we can now calculate the log likelihood for the
Figure 1. Percentage of observations for each activity (a. resting, b. socializing, c. foraging and d. moving) according to the ages of
individuals.
doi:10.1371/journal.pone.0026788.g001
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power law as:
Lpow~n ln mMLE{1ð Þ{lnxminð Þ{mMLE
Xn
i~1
lnxi
xmin
ð2Þ
The maximum estimate of the exponential law exponent was then
calculated as:
lMLE~n
Xn
i~1
xi{xminð Þ
!{1
ð3Þ
And the log likelihood of the exponential distribution calculated as:
Lexp~nlnlMLE{lMLE
Xn
i~1
xi{xminð Þ ð4Þ
Concerning the waiting times distribution, as the waiting time data
are discrete, we changed the equation (5) with the following
corrected formula [19]:
mMLE~1zn
Xn
i~1
ln
xi
xmin{0:5
" #{1
ð5Þ
We also changed the equation 3 to:
lMLE~
n
Pn
i~1
xi
~ 1
x
ð6Þ
In the current study, the minimum waiting time was 5 minutes. The
log likelihoods for the waiting time distributions are calculated are
calculated via equation 2 for the Le´vy walk (power law) and via
equation 4 for the Brownian walk (exponential law).
Using these measures, we then calculated the AIC of the two
distributions (power and exponential) for both step length and
waiting time:
AICi~{2Liz2Ki ð7Þ
where Ki is the number of free parameters in the model i (in the
current study, the exponent is the only parameter for both the
power and the exponential distribution). We then calculated an
Akaike weight vi for each model i (Brownian and Le´vy):
vi~
exp AICi{AICmin2
� �
Pp
j~1
exp
AICj{AICmin
2
� � ð8Þ
This Akaike weight is dichotomised as scores of 0 for the
unsuccessful model (highest AIC) and 1 for the successful model
(lowest AIC) when comparing two models. In the current study,
we checked which distribution i scored 1 in order to characterize
the walk of animals as i (Brownian or Le´vy).
A Kolmogorov-Smirnov test was used to test the uniformity of
distributions for maximum step lengths and maximum waiting
time (xmax). We then correlated the estimates for exponents and log
likelihood to age using Spearman rank correlation tests. Mann-
Whitney tests were used to assess whether the estimates and log
likelihoods differed between males and females.
The significance level was set at 0.05. We used the exact
significance method for small sampling size. All tests were two-
tailed. We carried out the analyses using SPSS 10.0 (SPSS Inc.,
Chicago, IL, USA). Values are presented as median and inter-
quartiles.
Table 2. Statistical and descriptive values of differences of
activities between males and females.
Activity
Resting Socializing Foraging Moving
Statistics Mann-Whitney U 11.00 9.00 5.00 9.50
P-value 0.914 0.610 0.171 0.610
Males
(N = 4)
Median 60 165 205 43
Lower inter-quartile 46 73 187 36
Upper inter-quartile 167 192 217 48
Females
(N = 6)
Median 59 149 227 46
Lower inter-quartile 48 108 202 37
Upper inter-quartile 83 173 256 54
The descriptive values are the number of observations in each activity.
doi:10.1371/journal.pone.0026788.t002
Table 3. Information concerning the maximum likelihood estimates for power and exponential distributions of step lengths.
n mmle Lpow lmle Lexp AICpow AICexp vpow vexp
Ne´re´is 92 1,63 2279,91 60858 240256553,5 562 80513109 1 0
Shan 176 1,57 2587,90 221584 2278972090 1178 557944181 1 0
Gaetan 125 1,56 2421,54 120375 2115919663 845 231839327 1 0
Tao 143 1,63 2435,45 116259 294516899,1 873 189033800 1 0
Ulysse 164 1,62 2509,10 163836 2163670195 1020 327340392 1 0
Jeanne 96 1,74 2255,27 46656 222673783,9 513 45347569,9 1 0
Patsy 139 1,56 2470,69 162352 2189625468 943 379250939 1 0
Olga 137 1,64 2410,36 111792 291220679,5 823 182441361 1 0
Ujung 144 1,66 2419,88 116064 293545904,7 842 187091811 1 0
Lady 98 1,63 2297,93 63798 241531413,8 598 83062829,6 1 0
doi:10.1371/journal.pone.0026788.t003
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Results
Activity budget
Analyses showed that age is correlated with resting (rs =0.80,
N=10, p=0.005, fig. 1a) and socializing (rs=20.78, N=10,
p=0.008, fig. 1b) activities but not with foraging (rs =0.12, N=10,
p=0.748, fig. 1c) and moving activities (rs= 0.52, N=10, p=0.121,
fig. 1c). The younger the individuals were, the less they were observed
to rest and the more they were observed to socialize. More
specifically, young individuals played together. Whatever the activity,
no difference was observed between males and females (Table 2).
Distribution of step lengths
Information concerning the maximum likelihood estimates of
both exponential and power distributions for each individual are
given in Table 3. The Akaike weight for the power distribution
equalled 1 for each individual (AICpow is the lowest AIC) meaning
that all individuals seemed to follow a Le´vy walk rather than a
Brownian one (see Fig. 2 for a graphical representation).
We then performed analyses on the power estimates for the step
length distributions.
Age is correlated to the log likelihood of the power law Lpow (rs=0.67,
N=10, p=0.034) but not to the exponent mMLE (rs=0.18, N=10,
p=0.623). The dominant male (with the highest body mass) displays
the longest tailed distribution of step lengths. Indeed, his maximum step
length was 71 meters (non-uniform distribution with other group
members: Z=1.98, p=0.001) whilst maximum step lengths in other
group members ranged from 42 to 51 meters (mmaximum=47[46.5;48],
uniform distribution: Z=1.00, p=0.270). The log likelihood of the
power law Lpow differed between males and females (U=2.00,
Nmales=4, Nfemales =6, p=0.033, mmales=2472 [2528; 2425],
mfemales=2354[2432; 2273]) whereas the exponent mMLE did not
(U=4.00, Nmales=4, Nfemales =6, p=0.088, mmales=1.59 [1.56;1.63],
mfemales=1.64[1.61;1.68]) even if a tendency is visible.
Waiting time distributions
Information concerning the maximum likelihood estimates of
both exponential and power distributions for each individual are
given in Table 4. The Akaike weight for the power distribution
equalled 1 for each individual (AICpow is the lowest AIC) meaning
that all individuals seemed to follow a Le´vy walk more than a
Brownian one (see Fig. 3 for a graphical representation).
We then performed analyses on the power estimates for the
waiting time distributions.
Age is correlated to the log likelihood of the power law Lpow
(rs =20.88, N= 10, p = 0.001) but not to the exponent mMLE
(rs =20.44, N=10, p = 0.208). The exponent mMLE of the power
law differed between males and females (U= 1.00, Nmales = 4,
Nfemales = 6, p = 0.019, mmales =289 [2103; 283], mfemales =
2109[2123; 2100]) whereas the log likelihood Lpow did not, even
if a tendency is visible (U= 3.00, Nmales = 4, Nfemales = 6,
p = 0.055males = 2 [1.98;2.23], mfemales = 1.89[1.77;1.94]). Maxi-
mum waiting times ranged from 60 to 90 and the median is 90
[81.25;90]. The distribution of maximum waiting time is not
uniform between individuals (Z= 2.00, p = 0.01).
Discussion
This is the first study to examine the possible effects of socio-
demographic variables on the individual distributions of step
lengths and waiting times. The results are as we expected.
Individuals differed in their activity budget and in their movement
patterns. We found an effect of age and sex of individuals on the
power distribution of their step lengths and of their waiting times.
The Le´vy walk has been described as an optimal strategy for
food research efficiency or reproduction in several species [11,13].
This link between the Le´vy walk and optimality can be applied
when the forager lives in a heterogeneous environment with low-
density food patches and has no information concerning the
location of food supplies [6,11]. For instance, marine predators
switch between Le´vy and Brownian movement as they move
through different types of habitat, the Brownian walk being
associated with the presence of abundant prey [11]. More
questions arise about the significance of Le´vy walks when this
so-called ‘‘random’’ movement - implying that it is ‘‘unpredict-
able’’- is found in species which possess high cognitive skills and a
mental map of their environment, such as the primates in the
current study [17,19,42]. In this context, the criteria justifying a
Le´vy walk are no longer applicable, even if some authors [21] have
suggested that a Le´vy walk may favour the ripening of fruit or
leaves before the next visit to the patch in question. In animals that
are informed about their environment and have a cognitive map of
where they are living, the hypothesis of a random walk is no longer
sustainable. Finding a walk which ressembles a Brownian or Le´vy
walk is therefore due to the distance distribution between the
Figure 2. Distribution (mean frequency) of step lengths (meters). (a.) Normal distribution. The bold line is the mean frequency among all
group members. The upper thin line is the maximum observed in the group. The lower thin line is the minimum observed in the group. (b.) Log-log
distribution. The continuous line is the best-fitting power curve. The dotted line is the best-fitting exponential curve.
doi:10.1371/journal.pone.0026788.g002
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different spots (food patches, waterhole, resting sites) the animals
visit. For instance, Ramos-Ferna´ndez, Boyer and colleagues
explain that the Le´vy walk found in spider monkeys was directly
dependent on the environment in which animals lived. They built
a model in which the monkeys follow mental maps and chose to
move according to a maximum efficiency criterion in a spatially
disordered environment containing trees with a heterogeneous size
distribution. They showed that moving the tree size frequency
distribution could result in different random walks such as the
Le´vy walk [18,42,43]. Schreier and Grove could not distinguish
whether another species of primates, the hamadryas baboon (Papio
hamadryas), displayed Brownian or Le´vy walks. They also attributed
their findings to the distribution of food patches in the baboon
environment [19]. In the current study, we were able to identify
whether Tonkean macaques displayed a Le´vy walk. It is interesting
to note that the subjects still displayed a Le´vy walk in a semi-free
ranging environment where food was given ad libitum. These
movement patterns resembling random walks can probably be
explained by the animals moving from one location to other
known locations. The power distribution of step lengths might be
due to a power distribution of food patches in the enclosure whilst
the power distribution of waiting times might be due to the power
distribution of the patch sizes. For instance, animals spend a
higher quantity of time in their indoor housing where pellets and
water are ad libitum.
Even if movement patterns depend directly on the environment,
animals should still display differences in step length or waiting
times distribution, since they do not have the same nutrient or
social requirements [44]. Previous studies on different species had
already found differences in activities according to the sex or age of
individuals [22,25,29–31,45]. In this study, we found that age has
an influence on the time individuals will spend resting or
socializing. Young individuals rested less but socialized more than
older individuals. We predicted that individual differences also
have a direct impact on the movement patterns of individuals. We
consequently found an effect of age and sex on the distribution of
step lengths and waiting times in the Tonkean macaques we
studied. The males and old individuals displayed a higher
proportion of longer trajectories than females and young ones.
As regards waiting times, females and old individuals displayed
higher rates of long stationary periods than males and young
individuals. The difference between males and females has already
been described in spider monkeys, and authors suggested that the
specific activities of males such as controlling group home range
boundaries might lead to this difference [21] because the sexual
dimorphism in spider monkeys is not very high. In the current
Figure 3. Distribution (mean frequency) of waiting times (minutes). (a.) Normal distribution. The bold line is the mean frequency among all
group members. The upper thin line is the maximum observed in the group. The lower thin line is the minimum observed in the group. (b.) Log-log
distribution. The continuous line is the best-fitting power curve. The dotted line is the best-fitting exponential curve.
doi:10.1371/journal.pone.0026788.g003
Table 4. Information concerning the maximum likelihood estimates for the power and exponential distributions of waiting times.
n umle lpow lmle lexp AICpow AICexp wpow wexp
Ne´re´is 35 1,58 2114,32 0,03 2156,16 231 314 1 0
Shan 57 2,28 287,46 0,07 2201,57 177 405 1 0
Gaetan 57 2,06 2107,10 0,06 2218,53 216 439 1 0
Tao 51 2,11 291,23 0,05 2198,54 184 399 1 0
Ulysse 39 1,95 281,75 0,05 2158,11 165 318 1 0
Jeanne 52 1,85 2121,45 0,04 2213,19 245 428 1 0
Patsy 47 1,93 2100,99 0,05 2188,00 204 378 1 0
Olga 50 1,96 2104,42 0,05 2197,29 211 397 1 0
Ujung 46 1,94 297,87 0,05 2184,55 198 371 1 0
Lady 54 1,84 2127,74 0,05 2218,56 257 439 1 0
doi:10.1371/journal.pone.0026788.t004
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study, macaques displayed great differences in body mass
according to their age and to their sex. In addition to their social
difference (group members need to socialize when they are
juveniles), this physiological difference (in terms of physiological
needs per day) directly results in different patterns of movements.
The maximum step length of the dominant male - the individual
with the highest body mass - also seems to be different to that
observed in its conspecifics. One can suggest that the dominant
male shows the longest trajectories because it is the top-ranking
individual and as such, probably expects the rest to follow him,
whereas other individuals would negotiate about the direction to
take. However, we showed that Tonkean macaques displayed an
equally-shared consensus where everybody, irrelevant of social
status, can initiate a movement and be followed by the entire
group [34,39].
The Le´vy walk has been described as an optimal strategy for
individuals searching for food, but has always been studied without
taking the characteristics of each individual into account. This
study is the first to thoroughly analyse the influence of socio-
demographic variables on the movement patterns of individuals.
In spite of the semi-free ranging conditions, we found clear
differences between individuals and we have suggested different
explanations for these results. The next step would be to
investigate the influence of individual variables on movement
patterns in other species - i.e. from solitary to social - in order to
better understand how the Le´vy walk emerges and to confirm its
evolutionary significance.
Acknowledgments
The authors would like to thank Marie Pele´, Paul Salze and Julie Duboscq
for their help for collecting data.
Author Contributions
Conceived and designed the experiments: CS OP. Performed the
experiments: CS. Analyzed the data: CS LB. Contributed reagents/
materials/analysis tools: CS. Wrote the paper: CS OP.
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