Behavioral Ecology
doi:10.1093/beheco/ars122
Original Article
What is a subgroup? How socioecological
factors influence interindividual distance
Filippo Aureli,a,b Colleen M. Schaffner,a,c Norberto Asensio,d and David Lusseaue
de Neuroetología, Universidad Veracruzana, Av. Dr. Castelazo Ayala S/N, Col. Industrial
Animas, Ap 566, Cp 91190, Xalapa, Veracruz, Mexico, bResearch Centre in Evolutionary Anthropology
and Palaeoecology, Liverpool John Moores University, UK, cDepartment of Psychology, University of
Chester, UK, dFaculty of Environment and Resource Studies. Mahidol University, Salaya, Thailand, and
eInstitute of Biological and Environmental Sciences and Marine Alliance Science and Technology for
Scotland, University of Aberdeen, UK
aInstituto
Fission–fusion dynamics derive from spatial adjustments that animals make depending on resource distribution, resulting in
splitting and merging of subgroups. New frameworks propose to classify social systems depending on their degree of fission–
fusion dynamics, but little has been done to quantify such dynamics. Operationally defining subgroup is a building block in such
quantification. We aimed to define subgroup using interindividual distances (IIDs), while examining the relative contribution
of social and ecological factors on the distribution of such distances. We employed a modeling approach using location data
collected with a handheld GPS unit from single individuals belonging to a long-term study community of wild spider monkeys
and determined the minimum distance at which 2 individuals can be considered in different subgroups. Our results strongly
support the crucial role of both social and ecological factors in influencing the way individuals position themselves with respect
to other group members. Our socioecological model explained the observed interactivity and interseasonal variation in IIDs in
a biologically relevant manner. The critical IID to define subgroup fell within the expected range from field observations. This
modeling approach can contribute to the understanding of the factors influencing the evolution of social systems. ­Key words:
fission–fusion, modeling approach, social system, socioecology, spatial distance, subgroup. [Behav Ecol]
Introduction
K
ummer (1971) introduced the term “fusion–fission” to
describe a social system in which group members make
spatial adjustments depending on their activity and resource
distribution, resulting in fissions (i.e., separating from group
members) and fusions (i.e., joining group members after temporary separation) of subgroups. This system was contrasted
with other systems, which were overall considered cohesive.
More recently, subgroup formation has been recognized as a
grouping pattern more widespread than previously thought
(Strier 1989; Sussman and Garber 2007; Aureli et al. 2008),
existing in a variety of forms in several group-living animals
(e.g., African elephants, Loxodonta africana: Wittemyer et al.
2005; Moss and Lee 2011; red deer, Cervus elaphus: Conradt
1998; Bechstein’s bats, Myotis bechsteinii: Kerth et al. 2011;
bottlenose dolphins, Tursiops spp: Connor et al. 2000; Lusseau
et al. 2003; chimpanzees, Pan troglodytes and bonobos, Pan
paniscus: Nishida and Hiraiwa-Hasegawa 1987; Stumpf 2011;
spotted hyenas, Crocuta crocuta: Smith et al. 2008; spectacled parrotlets, Forpus conspicillatus: Wanker 2002; human
hunter-gatherers, Homo sapiens: Marlowe 2005). As a consequence, fission–fusion dynamics do not characterize a single
Address correspondence to F. Aureli. E-mail: [email protected],
[email protected].
Received 4 March 2012; revised 22 June 2012; accepted 23 June
2012.
© The Author 2012. Published by Oxford University Press on behalf of
the International Society for Behavioral Ecology. All rights reserved.
For permissions, please e-mail: [email protected]
social system but refer to the extent of variation in spatial
cohesion and individual membership in subgroups over
time (Aureli et al. 2008). Hence, we can now characterize
any social system by its degree of fission–fusion dynamics.
For example, the degree of fission–fusion dynamics is low
in highly cohesive groups, is intermediate when individuals segregate into subgroups with stable membership, and is
high in systems with frequent formation of subgroups with
flexible membership. Recent work provides new frameworks
in which we can conceptually classify these systems varying
in the degree of fission–fusion dynamics (Aureli et al. 2008;
Sueur et al. 2011). We now need to develop measures that
can help us identify the factors influencing the degree of fission–fusion in social systems.
Aureli et al. (2008) proposed a framework involving 3
dimensions that together capture the degree of fission–fusion
dynamics in a given environment: 1) the temporal variation
in spatial cohesion among group members, 2) the temporal
variation in subgroup size, and 3) the temporal variation
in subgroup composition. We can use data on the distance
between individuals (interindividual distance or IID) to
quantify this first dimension. For the other 2 dimensions, an
operational definition of subgroup is needed, but so far an
overarching definition has been problematic, being more
intuitive than empirically based (Chapman et al. 1993). One
possibility to define subgroups is to determine the minimum
distance at which 2 individuals can be considered in different
subgroups (Ramos-Fernandez 2005). Such a distance should
reflect species-specific characteristics, such as body size and
1309
Aureli et al. • What is a subgroup?
sensory abilities. For example, the distance is likely shorter
for smaller species than for larger ones or when the main
mode of communication is visual rather than auditory (Aureli
et al. 2008).
Social and ecological factors are likely to influence the spatial distribution of group members (Beauchamp et al. 1997;
Danchin et al. 2004) and therefore IIDs and subgroup size.
There is, however, no established method to infer the relative
contribution of these factors on the geometry of subgroups.
Here we develop a modeling approach to infer the relative
contribution of social and ecological factors on IIDs. Such an
approach can further help us understand how these factors
influence the evolution of social systems in different environments and for species with different life history strategies.
model through the integration of the biosocial attraction
model (Equation 3):
Models to explain IIDs
Using observed probability density distributions, instead of
counts, we can further extend Equation 5 to estimate the relative contribution of the 3 elements to the observed IIDs:
Many theoretical and experimental studies have used the biosocial attraction model, or one of its derivatives, to explain
how individuals might cluster (Okubo 1986; Bonabeau et al.
1999; Mogilner et al. 2003). This model assumes that an individual attracts conspecifics within a range of a meters and
repulses them within a range of r meters. That is, the position
of an individual in its habitat is solely governed by 2 social
forces: repulsion from conspecifics at close range and attraction at intermediate range. Because the components of the
model represent intervals between point processes (i.e., the
locations of individuals), they are expected to follow exponential distributions. The absolute contribution of each process is
accounted using 2 scaling parameters, A and R, respectively
(Equation 1). If a > r, then individuals tend to group
f (d ) = Re
−
d
r
− Ae
−
d
a,
(1)
where d is the IID.
The sensorial abilities of the species and the environment
in which it lives constrain the upper limit of a. However,
many behavioral mechanisms have evolved to allow individuals to constrain or expand their attractivity within this range
(McGregor 1993). Additionally, ecological models have also
focused on the way individuals are distributed in their environment. In its simplest form, individuals can be expected to
distribute following a Poisson process (Clark and Evans 1954;
Mitchell and Powell 2004; Dormann et al. 2007). Hence, the
probability of IID should be exponentially distributed as it is
the interval of a Poisson process (Equation 2),
p(d ) = λe −λd (probability density function), (2)
where λ is the mean of the Poisson process governing the spatial distribution of individuals. In its simplest form, which we
assume here, λ is a measure of the heterogeneity in the habitat of the studied animals. It is an integrated measure of the
way important ecological factors, such as food resources and
predation risk, are distributed spatially in such a habitat.
Both social and ecological factors are known to affect the
position of individuals in their environment. We propose
that both past modeling approaches need to be combined in
order to obtain a full picture of the distribution of individuals
in relation to conspecifics. We can extend the biosocial attraction model to account for the additional effect of the ecological landscape on the position of individuals. Such models can
be used to explain IIDs in natural settings. Hence, we can
decompose the probability to observe a given IID into the
proportional contributions of the 1) ecological landscape,
2) attraction to conspecifics, and 3) repulsion of conspecifics.
We can derive the probability density function of the original
x
p(x )biosocial = ∫ f (x )dx
−∞
p(d )biosocial = Aae
d
−
a
(3)
− Rre
−
d
r
(4)
and we can simply add the contribution of the ecological
landscape, the absolute contribution of which is accounted by
the scaling parameter C:
p(d ) = Aae
p(d ) = paae
−
d
a
−
d
a
− Rre
− prre
−
d
r
−
d
r
+ C λe −λd . + (1 − pa − pr )λe −λd . (5)
(6)
We labeled it (Equation 6) the socioecological model. By
eliminating the component for the contribution of the ecological landscape, we obtain the equation for the biosocial
attraction model (Equation 7):
p(d ) = paae
−
d
a
−(1 − pa )re
−
d
r.
(7)
By eliminating the component for the biosocial attraction model from the socioecological model (Equation 6), we
obtain the equation for the ecological model (Equation 8), in
which the distance between individuals is simply influenced
by the ecological landscape:
p(d ) = λe −λd. (8)
If the extended socioecological model is warranted to
explain IID, and consequently the relative position of individuals in their home range, then it should provide a better fit to observed IIDs than the biosocial attraction model
and the ecological model. As a test, we fitted these 3 models
(Equations 6–8) to observed IIDs obtained from a long-term
study community of spider monkeys (Ateles geoffroyi) to determine if it was the case.
Spider monkey as the study system
We aimed to investigate methods to define subgroup
using IIDs, while examining the processes underlying the
distribution of such distances. Spider monkeys have a social
system characterized by a high degree of fission–fusion
dynamics (Symington 1990; Aureli and Schaffner 2008),
in which subgroup size is adjusted depending on food
availability (Chapman et al. 1995; Asensio et al. 2009). They
also engage in a variety of social interactions. For example,
they use embraces to facilitate access to other females’
infants (Schaffner and Aureli 2005; Slater et al. 2007) and
to reduce the likelihood of aggression at fusion (Aureli and
Schaffner 2007). However, spider monkeys’ interactions
are also characterized by risk, underlying some restraint in
interacting with other group members (Rebecchini et al.
2011). Therefore, attraction and repulsion characterize
interactions among group members. This is well illustrated
by the relationships between younger and older males (Vick
2008; Schaffner et al. 2012) and by the “push-and-pull”
1310
grappling sessions, which are prolonged exchanges between
2 individuals of facial greeting, face touching, embraces, tail
wrapping, pectoral sniffing, and genital contact, involving
several approaches and retreats (van Roosemalen and Klein
1988; Aureli and Schaffner 2008). Thus, spider monkeys are
an ideal model species to define subgroup and to test models
to explain IIDs.
The study spider monkeys live in an environment with
marked wet and dry seasons (Janzen 1986) that lead to pronounced variation in the way resources are distributed in the
monkeys’ habitat (Chapman 1988; Asensio et al. 2009). We
could derive the following predictions from our socioecological model. If the socioecological model is biologically
relevant, we would expect λ to be greater during the wet season (where resource availability is more homogeneous) than
during the dry season (prediction 1a). A more homogeneous
and more productive habitat should decrease within-group
competition and therefore we would expect pa to be larger
during the wet season (prediction 1b).
Like other animals, spider monkeys are likely to spatially
distribute themselves in different ways depending on the
activity in which they engage. For example, individuals compete, directly and indirectly, for resources during foraging
activities, so they should increase IID. In contrast, individuals
seek others during resting in order to reduce predation risk
and engage in social activities (e.g., grooming) and therefore
reduce IID. Thus, the behavioral context in which individuals
engage should influence the range and contribution of both
social forces. We, therefore, predicted pa to be larger during
resting (prediction 2a) and r to be larger during foraging
(prediction 2b).
MATERIALS AND METHODS
Study site and subjects
The study was carried out at the Santa Rosa Sector of the Area
de Conservación Guanacaste, Costa Rica (10º50ʹN, 85º38ʹW).
The Santa Rosa sector comprises 10800 ha of tropical dry
forest from the foothills of volcanic mountains down to the
Pacific coastal plain (300–0 m elevation), characterized by a
severe dry season between December and May and a wet season during the rest of the year when most of the annual rainfall occurs (900–2500 mm) (Janzen 1986). We investigated
1 community (i.e., a social group) of spider monkeys (Ateles
geoffroyi) that varied from 25 to 32 individuals (6 adult and
subadult males, 15–17 adult and subadult females, 2–5 juveniles, and 4–8 infants) during the study period due to birth,
immigration, and disappearance. The monkeys were well
habituated to being followed by researchers and were individually recognized by variations in pelage color, body size,
and shape. All adult and subadult individuals (i.e., the sexually mature individuals) were the subjects of the study, given
that juveniles and infants always travelled with their mothers.
Data collection and analysis
We collected data from August 2007 until June 2008 during
full-day follows of spider monkeys of the study community
or balanced observations between mornings and afternoons
when full-day follows were not possible. Scans were made at
predetermined times recording the geographical coordinates of the location of each monkey by taking a waypoint
with a handheld GPS (Garmin GPSMAP 76CSX) standing
directly underneath the monkey (spider monkeys are highly
arboreal: Campbell et al. 2005). We collected data based on
Ramos-Fernandez’s (2005) procedure only when the monkeys were stationary while resting or foraging. If the monkeys
Behavioral Ecology
started to travel before the scan was completed, the scan
was aborted. Scan data were collected by 1 researcher, and
another researcher stayed with the monkeys in view in order
to monitor whether the monkeys started to travel. At the
beginning of each scan, the main activity of the monkeys in
view was recorded as resting or foraging and the location of
each monkey in view was recorded along with the monkey ID.
Then, the researcher searched for other monkeys by walking
30 m away from about the center of the sampled monkey locations and slowly completing a circle of 30-m radius around
such a center with the help of the GPS unit, while scanning
for monkeys within his visual range. A pilot study revealed
that in most parts of the study community’s home range, the
visual range was 30–50 m. Therefore, the researcher could
find monkeys that were from his position to the center of the
sampled monkey locations and from his position to at least
60 m away from the center. Once a monkey was found, the
researcher identified it and then recorded its location with
the GPS unit while standing directly underneath it. Then,
he returned to the position he left and continued until the
30-m circle was completed. At this point, the researcher made
another circle with a 75-m radius from the center following
the same procedure. Although some monkeys may have been
missed, the procedure facilitated the collection of location
data on the majority of monkeys within a circle with at least a
100-m radius during each scan.
The monkey locations collected during 108 scan samples
(52 during the dry season and 56 during the wet season) were
used to calculate IIDs with the distance-between-points tools
(within layer) of Hawth Tools for ArcGIS 9.2 (Beyer 2004).
Such IIDs could range from 0 to about 200 m. Although monkeys could move during the time a scan was completed, IID
data were calculated only when such movements were small
because the scan was aborted if the monkeys started to travel.
The data set for the analyses included 3288 IIDs.
In order to assess whether there was a marked change in
its frequency of occurrence as IID increased, as we would
expect if subgroups were spatially well delimited, we fitted a segmented regression (package segmented: Muggeo
2008) to the IID frequency distribution. To do so, we binned
the IID data (using 50 bins) and estimated the density of IID
(piid) for each bin. This analysis not only gives a simple assessment of changes in the occurrence of IIDs as the distance
between individuals increased but also provides an approximate means to assess subgroup definition, which we then
compared with the definition of the threshold at which the
process was inferred to operate using the model approach
(a in Equation 6).
Fitting models and assessing sensitivity to sampling errors
Both our models are mixtures of exponential distributions.
Simulation studies suggest that it is more appropriate to fit
such models using the untransformed cumulative frequency
distribution (cfd) instead of the probability frequency distribution (pfd) itself. It is a more robust approach to binning issues, such as the definition of bin size, and provides
more accuracy to contrast models of long-tailed distribution
(Clauset et al. 2009). Although it would have been simpler
to fit this model using log-transformed pfd data, we used the
untransformed cfd to ensure greater accuracies in the fit of
our models. To ease fitting, we fitted β ( = 1 / λ) instead of λ.
In addition, deriving the likelihood function to fit a mixture
of exponential distributions to data is not straightforward.
Such mixture likelihood functions tend to have multiple maximum likelihoods (ML), and parameter estimation is therefore difficult and sometimes does not result in an appropriate
fit. Therefore, after considering expectation maximization
1311
Aureli et al. • What is a subgroup?
approaches to fitting our models to the data, we decided to
approximate the ML using a least-squares approach. We used
a robust, weighted iterative nonlinear regression technique,
using the Levenberg–Marquardt algorithm at each iteration, implemented in nlinfit in Matlab (version 7.7.0.R2008B
Natick, Massachusetts: The MathWorks Inc., 2008). Such
iterative approaches provide robust approximation of ML
(Green 1984). We repeated the fitting process 100 times with
varying starting values, and the model fit presented here was
not sensitive to these varying starting values. We used Akaike
information criteria (AICc) to select the best fitting models
(Burnham and Anderson 1998).
We used Monte Carlo approaches to test the robustness
of our results to the potential biases introduced by sampling
heterogeneity and GPS accuracy (Manly 1997). Scan samples
were jackknifed (removed 1 at a time, exhaustively) to assess
potential influence of some samples on parameter estimates.
Second, the GPS fixes error was propagated on each data
point by considering each point as having an added error
corresponding to the GPS unit error. The Garmin GPS 76Cx
has a 2dRMS accuracy of about 5 m. For each data point, we
generated 1000 simulated data points each drawn from a
normal distribution, with a mean corresponding to the data
point and a standard deviation of 2.5 m. Models were refitted to these 1000 simulated data sets. We could then infer the
effect of propagating the GPS error on the model parameter
estimates.
RESULTS
Overall, the socioecological model explained the observed
IID probability distribution better than the biosocial
attraction model (Table 1; Figure 1). The ecological model
performed especially poorly (Table 1). For all tests, there was
no support to retain either the biosocial attraction model
or the ecological model as explanatory models, given the
difference in AIC observed (Tables 1–3).
Our results were robust to potential biases from sampling
heterogeneity (SE in Tables 1–3) and GPS accuracy measurement error (Table 4). The observed IID cfd varied with season and activity. The socioecological model could capture this
variation, whereas the biosocial attraction model could not as
there were no biologically relevant changes (i.e., depending
on season and activity) in the parameters for the latter model
(Tables 2 and 3). The influence of the environment changed
between seasons. Variability in resource availability, as perceived through the individuals (β, the inverse of λ; Table 2),
was lower during the wet season than it was during the dry
season (prediction 1a). The proportional contribution of
attraction (pa) was greater during the wet season (prediction
1b). The observed IID cfd variation between activities was
explained by the range of repulsion (r) as expected (prediction 2b), with the range being greater while foraging (Table 3;
Figure 3). However, prediction 2a was not supported as pa was
not larger during resting than during foraging (Table 3).
We used the segmented regression with variety of binning
intervals to determine how the probability to observe given
IIDs changed as IID increases. The following results were
robust to varying bin size. The break point was estimated
to be 36.1 m (SE:1.85) from this segmented regression
(R2 = 0.94; Figure 4). Before this point, IID density declined
with a slope of −0.00112 (F1,34 = 288.6, P < 0.0001, 95%CI:
[−0.0013; −0.00093]), and beyond it piid declined with a slope
of −0.00004 (F1,34 = 264.1, P < 0.0001, 95%CI: [−0.000056;
−0.000016]). This break point is consistent with the break
point defined by the socioecological model as the range of
attraction (a) was 36.7 m (Table 1).
Discussion
This is the first time theoretically derived models of
aggregation dynamics are tested against detailed observations
of one of their key characteristics, that is, IID. Our results
strongly support the hypothesis that both social and
ecological factors play a crucial role in influencing the way
individuals position themselves in their environment with
respect to other group members. More importantly, we
show that we can use a modeling approach to estimate the
relative contribution of the various socioecological processes
constraining the behavioral decisions individuals make to
succeed in a given socioecological landscape. The classical
biosocial attraction model could not capture the observed
interactivity and interseasonal variation in IID. In contrast,
our socioecological model could capture this variation and
explain it in a biologically relevant manner. The observed
differences in the fitted models were in broad agreement
with our predictions based on the socioecology of the
study species.
The range of attraction varied according to season and
activity, albeit not significantly, and could be approximated to
range between 35 and 70 m. This falls within expected range
from field observations. The monkeys live in a forest where
visual detection of conspecifics beyond such a range would
be difficult. This range of attraction supports the operational
definition of subgroup used in previous studies of the same
community based on a chain rule (Ramos-Fernandez 2005),
according to which individuals were considered in the same
subgroup if they were at a distance ≤50 m from at least 1 other
subgroup member (Asensio et al. 2009). As a consequence,
fission occurs when 1 or more individuals from the followed
subgroup are not observed at a distance ≤50 m from at least
1 current subgroup member for more than 30 min. Fusion
occurs when 1 or more individuals not belonging to the followed subgroup come to a distance ≤50 m from any member
of the followed subgroup. Comparative data are needed to
evaluate whether the range of attraction for the operational
definition of subgroup (e.g., 35–70 m in our case) is related
to ecological factors or species characteristics such as body
size, prevailing sensory system, and degree of fission–fusion
dynamics.
There was consistency in the critical IID to define subgroup
between the model and the segmented regression methods.
The break point obtained by the latter method is consistent
with the break point defined by the socioecological model
(i.e., range of attraction: Table 1), confirming researchers’
intuitions. The segmented regression approach is possibly
easier to apply because it is based on simple linear regression.
Thus, it may be more attractive to field workers in order to
obtain an empirical definition of subgroup for their study
species in a given environment. However, the more comprehensive model approach is preferable because the shape of
the IID distribution may not be only affected by the attraction
component, as shown in our results. The collection of the IID
data used in this study was time consuming. However, once a
definition of subgroup is established, subsequent studies of
the same group can be carried out using the same definition.
In addition, similar analytical methods can be applied to telemetric data that can ease the sampling process.
Additional analyses revealed that our results were robust to
potential biases from sampling heterogeneity and GPS accuracy
measurement error. The analysis on the effect of main activity
on IID was limited to variation between resting and foraging.
The definition of subgroup obtained in this way is usually accurate when the research focuses on behaviors, such as grooming
or competition, that take place mostly during these activities.
However, if the definition needs to be more comprehensive,
1312
Behavioral Ecology
Table 1
Estimates of the parameters for the 3 competing models for the whole data set
pa
a
pr
r
β
AIC
Socioecological model (±SE) [CI]
Biosocial attraction model (±SE)
0.0004 (±0.00002) [0.0003–0.0006]
36.7 (±0.55) [33.56–39.92]
0.033 (±0.0007) [0.028–0.039]
4.03 (±0.044) [3.79–4.28]
7.61 (±0.13) [6.87–8.35]
−1340
0.50 (±0.002)
23.1 (±0.238)
Ecological model (±SE)
23.0 (±0.237)
1.44 (±0.011)
−384
−1083
pa: proportional contribution of attraction; pr: proportional contribution of repulsion; a: range of attraction; r: range of repulsion (both in
meters), β is the inverse of λ, the mean of the spatial Poisson process explaining the distribution of individuals; SE: jackknifed standard errors; CI:
the estimated 95% confidence intervals for each parameters (only shown for socioecological models).
Table 2 Estimates of the parameters for the 2 prevailing models during the wet (based on 1654 IIDs) and dry (based on 1634 IIDs) seasons
Socioecological model
Biosocial attraction model
Wet season
paa
a
pr
r
βa
AIC
Dry season
Wet season
Dry season
Estimate (CI)
SE
Estimate (CI)
SE
Estimate
SE
Estimate
SE
0.0004 (0.0003–0.0006)
40.0 (34.53–45.43)
0.031 (0.022–0.041)
4.41 (3.93–4.88)
7.28 (6.14–8.43)
−1069
0.00001
1.57
0.0014
0.090
0.264
0.0001 (0.00004–0.0002)
59.74 (42.81–76.67)
0.032 (0.028–0.037)
3.11 (2.80–3.43)
9.83 (8.71–10.95)
−1166
<0.0001
1.755
0.0013
0.116
0.205
0.50
26.755
0.0001
0.439
0.0027
19.27
0.0001
0.381
26.754
0.440
0.060
0.0046
−919
−917
Details of the ecological model are not shown here because there was no support for it during model selection (AICecological, wet season = −322 and
AICecological, dry season = −331). See Table 1 for abbreviations.
a Confidence intervals do not overlap between the 2 seasons.
Table 3 Estimates of the parameters for the 2 prevailing models for data collected when individuals were foraging (based on 805 IIDs) and resting
(based on 2483 IIDs)
Socioecological model
Biosocial attraction model
Foraging
pa
a
pra
ra
β
AIC
Resting
Foraging
Resting
Estimate (CI)
SE
Estimate (CI)
SE
Estimate
SE
Estimate
0.0002 (0.0001–0.0003)
59.85 (49.04–70.67)
0.020 (0.016–0.024)
5.17 (4.84–5.51)
9.73 (8.52–10.93)
−1097
0.00002
8.87
0.0013
0.196
0.793
0.0003 (0.0002–0.0004)
42.09 (34.74–49.44)
0.034 (0.027–0.041)
3.63 (3.38–3.89)
8.03 (7.02–9.05)
−1093
0.00001
1.568
0.0008
0.074
0.179
0.0013
28.8
0.0001
1.095
0.0023
20.76
.0001
0.296
0.032
0.0091
0.033
0.0029
−919
SE
−905
Details of the ecological model are not shown here because there was no support for it during model selection (AICecological, foraging = −306 and
AICecological, resting = −324). See Table 1 for abbreviations.
a Confidence intervals do not overlap between the 2 activity states.
Table 4
Monte Carlo simulation results in order to understand the
propagation of GPS error and the sensitivity of the socioecological
model to this error
pa
a
pr
r
β
Estimated bias
CI
0.00001
−0.3423
−0.0013
0.1329
0.0197
0.0004–0.0005
34.61–38.38
0.030–0.035
4.00–4.33
7.25–8.04
Estimate bias is the difference between the mean parameters for the
1000 models and the estimated parameter. CI is the 95% confidence
interval for 1000 resampled data sets accounting for the accuracy of
the GPS unit. See Table 1 for other abbreviations.
IID data should be collected during simultaneous follows of
individuals using focal animal sampling instead of scan sampling unless the observation conditions permit collecting IID
data of individuals during other activities such as travelling.
Our findings support previous studies showing that
the observed grouping pattern of spider monkeys can be
derived from ecological models of individual movement
(Ramos-Fernandez et al. 2006) that include the influence of
conspecifics. Indeed, although the proportional contribution of
social attraction in the socioecological model is small (Table 1),
the model based only on the ecological landscape performed
poorly in explaining the observed IIDs. This means that sociality plays a small but key role in spider monkey grouping. Thus,
our findings point to a rich decision-making process in which
individuals have to trade off between maintaining contact with
1313
Aureli et al. • What is a subgroup?
Figure 1 Observed cumulative probability distribution of IIDs for the whole data set and fitted biosocial attraction and socioecological models (Table 1).
Plot is on a semilog scale to present the differences between the 2 models, but models were fitted on an untransformed scale.
Figure 2 Semilog plot of observed cumulative probability distribution of IIDs for the wet and dry seasons (Table 2).
a small proportion of “preferred” community members, while
avoiding others, at least temporarily (Ramos-Fernández et al.
2009), and between minimizing travel costs while maximizing
resource acquisition (Asensio et al. 2009). These monkeys use
social interactions to deal with such issues (Aureli and Schaffner
2007; Amici et al. 2009a, 2009b), which would result from individuals evolving under the pressure of such decision-making
mechanisms.
In conclusion, the modeling approach offers an avenue
to test the relative contributions of social and ecological factors on the way individuals interact. It is also instrumental in
operationally defining subgroup, which is a building block in
quantifying the degree of fission–fusion dynamics. Whereas
our specific results are only relevant to the study group of spider monkeys, the 3 models can be directly used with data from
other groups and species. Indeed, there is the need to carry
1314
Behavioral Ecology
Figure 3 Semilog plot of observed cumulative probability distribution of IIDs for foraging and resting (Table 3).
FUNDING
This study was financially supported by The British Academy,
the Leakey Foundation, the North of England Zoological
Society and the Scottish Funding Council (Marine Alliance
Science and Technology for Scotland pooling initiative).
We thank Elvin Murillo and Cara Murphy for support during data
collection, Daniel Stahl for helpful input at an early stage of the study
and the staff from Santa Rosa sector of ACG, especially Roger Blanco
and Maria Marta Chavarria for continuous support to our long-term
project.
References
Figure 4 Density of IID (m) aggregated in 50 bins. The black dot above the
x axis represents the estimated break point from the segmented
regression (the bar is the standard error of the estimate).
out similar analyses over a number of species with contrasting
social systems and populations of the same species exposed to
different ecological factors. Results may vary depending on the
group ecology, degree of fission–fusion dynamics, and other
species-specific characteristics, but the fitted parameters from
the models can be compared directly across groups and species.
The use of these models across a wide range of species will then
provide a tool for standardized comparisons of the influence of
social and ecological factors on the spatial distribution of individuals and will therefore increase our understanding of the
socioecological contributions to the evolution of social systems.
Amici F, Call J, Aureli F. 2009a. Variation in withholding of information in three monkey species. Proc R Soc Lond B Biol Sci.
276:3311–3318.
Amici F, Aureli F, Visalberghi E, Call J. 2009b. Spider monkeys
(Ateles geoffroyi) and capuchin monkeys (Cebus apella) follow gaze
around barriers: evidence for perspective taking? J Comp Psychol.
123:368–374.
Asensio N, Korstjens AH, Aureli F. 2009. Fissioning minimizes ranging costs in spider monkeys: a multi-level approach. Behav Ecol
Sociobiol. 63:649–659.
Aureli F, Schaffner CM. 2007. Aggression and conflict management
at fusion in spider monkeys. Biol Lett. 3:147–149.
Aureli F, Schaffner CM. 2008. Social interactions, social relationships
and the social system of spider monkeys. In: Campbell CJ, editor.
Spider monkeys: behavior, ecology and evolution of the genus
Ateles. Cambridge: Cambridge University Press. p. 236–265.
Aureli F, Schaffner CM, Boesch C, Bearder SK, Call J, Chapman
CA, Connor RC, Di Fiore A, Dunbar RIM, Henzi SP, et al. 2008.
Fission-fusion dynamics: new research frameworks. Curr Anthropol.
48:627–654.
Beauchamp G, Belisle M, Giraldeau L. 1997. Influence of conspecific attraction on the spatial distribution of learning foragers in a
patchy habitat. J Anim Ecol. 66:671–682.
Beyer HL. 2004. Hawth’s analysis tools for ArcGIS [computer program].
Available from: http://www.spatialecology.com/htools.
Bonabeau E, Dagorn L, Freon P. 1999. Scaling in animal group-size
distributions. Proc Natl Acad Sci USA. 96:4472–4477.
Aureli et al. • What is a subgroup?
Burnham KP, Anderson DR. 1998. Model selection and inference: a
practical information-theoretic approach. New York: Springer.
Campbell CJ, Aureli F, Chapman CA, Ramos-Fernandez G, Matthews
K, Russo SE, Suarez SA, Vick LG. 2005. Terrestrial behavior of
Ateles. Int J Primatol. 26:1039–1051.
Chapman CA. 1988. Patterns of foraging and range use by three species of neotropical primates. Primates. 29:177–194.
Chapman CA, Wrangham RW, Chapman LJ. 1995. Ecological constraints on group size: an analysis of spider monkeys and chimpanzee subgroups. Behav Ecol Sociobiol. 36:59–70.
Chapman CA, White FJ, Wrangham RW. 1993. Defining subgroup
size in fission-fusion societies. Folia Primatol. 61:31–34.
Clark PJ, Evans FC. 1954. Distance to nearest neighbor as a measure
of spatial relationships in populations. Ecology. 35: 445–453.
Clauset A, Shalizi C, Newman MEJ. 2009. Power-law distributions in
empirical data. SIAM Rev. 5:661–703.
Connor RC, Wells RS, Mann J, Read AJ. 2000. The bottlenose dolphin.
In: Mann J, Connor RC, Tyack PL, Whitehead H, editors. Cetacean
societies. Chicago (IL): University of Chicago Press. p. 91–125.
Conradt L. 1998. Measuring the degree of sexual segregation in
group-living animals. J Anim Ecol. 67:217–226.
Danchin E, Giraldeau LA, Valone TJ, Wagner RH. 2004. Public
information: from nosy neighbors to cultural evolution. Science.
305:487–491.
Dormann CF, McPherson JM, Araujo MB, Bivand R, Bolliger J,
Gudrun C, Davies RG, Hirzel A, Jetz W, Kissling WD, et al. 2007.
Methods to account for spatial autocorrelation in the analysis of
species distributional data: a review. Ecography. 30:609–628.
Green PJ. 1984. Iteratively reweighted least squares for maximum
likelihood estimation, and some robust and resistant alternatives. J
R Stat Soc B (Methodological). 46:149–192.
Janzen DH. 1986. Guanacaste national park: ecological and cultural
restoration. San Jose (Costa Rica): UNED.
Kerth G, Perony N, Schweitzer F. 2011. Bats are able to maintain long-term social relationships despite the high fission–
fusion dynamics of their groups. Proc R Soc Lond B Biol Sci.
278:2761–2767.
Kummer H. 1971. Primate societies: group techniques of ecological
adaptation. Chicago (IL): Aldine.
Lusseau D, Schneider K, Boisseau OJ, Haase P, Slooten E, Dawson SM.
2003. The bottlenose dolphin community of doubtful sound features a large proportion of long-lasting associations - can geographic
isolation explain this unique trait? Behav Ecol Sociobiol 54:396–405.
Manly BFJ. 1997. Randomization, bootstrap, and Monte Carlo methods in biology. New York: Chapman & Hall.
Marlowe FW. 2005. Hunter-gatherers and human evolution. Evol
Anthropol. 14:54–67.
McGregor PK. 1993. Signalling in territorial systems: a context for
individual identification, ranging and eavesdropping. Philos Trans
R Soc B. 340: 237–244.
Mitchell MS, Powell RA. 2004. A mechanistic home range model
for optimal use of spatially distributed resources. Ecol Model.
177:209–232.
Mogilner A, Edelstein-Keshet L, Bent L, Spiros A. 2003. Mutual interactions, potentials, and individual distance in a social aggregation.
J Math Biol. 47:353–389.
Moss CJ, Lee PC. 2011. Female social dynamics: fidelity and flexibility.
In: Moss CJ, Croze H, Lee PC, editors. The Amboseli elephants:
a long-term perspective on a long-lived species. Chicago (IL):
University of Chicago Press. p. 205–223.
1315
Nishida T, Hiraiwa-Hasegawa M. 1987. Chimpanzees and bonobos:
cooperative relationships among males. In: Smuts BB, Cheney
DL, Seyfarth RM, Wrangham RW, Struhsaker TT, editors.
Primate societies. Chicago (IL): University of Chicago Press. p.
165–177.
Okubo A. 1986. Dynamical aspects of animal grouping: swarms,
schools, flocks, and herds. Adv Biophys. 22:1–94.
Ramos-Fernandez G. 2005. Vocal communication in a fission–fusion
society: do spider monkeys stay in touch with close associates? Int J
Primatol. 26:1077–1092.
Ramos-Fernandez G, Boyer D, Vian G. 2006. A complex social structure with fission-fusion properties can emerge from a simple foraging model. Behav Ecol Sociobiol. 60:536–549.
Ramos-Fernández G, Boyer D, Aureli F, Vick LG. 2009. Association
networks in spider monkeys (Ateles geoffroyi). Behav Ecol Sociobiol.
63:999–1013.
Rebecchini L, Schaffner CM, Aureli F. 2011. Risk is a component of
social relationships in spider monkeys. Ethology. 117:691–699.
Schaffner CM, Aureli F. 2005. Embraces and grooming in captive spider monkeys. Int J Primatol. 26:1093–106.
Schaffner CM, Slater KY, Aureli F. 2012. Age related variation in
male-male relationships in wild spider monkeys (Ateles geoffroyi
yucatanensis). Primates. 53:49–56.
Slater KY, Schaffner CM, Aureli F. 2007. Embraces for infant handling
in spider monkeys: evidence for a biological market? Anim Behav.
74:455–461.
Smith JE, Kolowski JM, Graham KE, Dawes SE, Holekamp KE. 2008.
Social and ecological determinants of fission–fusion dynamics in
the spotted hyaena. Anim Behav. 76:619–636.
Strier KB. 1989. Effects of patch size on feeding associations in
muriquis (Brachyteles arachnoides). Folia Primatol. 52:70–77.
Stumpf RM. 2011. Chimpanzees and bonobos: inter- and intra-species
diversity. In: Campbell CJ, Fuentes A, MacKinnon KC, Bearder SK,
Stumpf RM, editors. Primates in perspectives. 2nd ed. Oxford:
Oxford University Press. p. 340–356.
Sueur C, King AJ, Conradt L, Kerth G, Lusseau D, Mettke-Hofmann
C, Schaffner CM, Williams L, Zinner D, Aureli F. 2011. Collective
decision-making and fission-fusion dynamics: a conceptual framework. Oikos. 120:1608–1617.
Sussman RW, Garber PA. 2007. Cooperation and competition in primate social interactions. In: Campbell CJ, Fuentes A, MacKinnon
KC, Panger M, Bearder SK, editors. Primates in perspective.
Oxford: Oxford University Press. p. 636–651.
Symington MM. 1990. Fission-fusion social organization in Ateles and
Pan. Int J Primatol. 11:47–61.
van Roosemalen MGM, Klein LL. 1988. The spider monkeys,
genus Ateles. In: Mittermeier RA, Rylands AB, Coimbra-Filho AF,
da Fonseca GAB, editors. Ecology and behavior of neotropical primates. Washington (DC): World Wildlife Fund. p. 455–537.
Vick LG. 2008. Immaturity in spider monkeys: a risky business. In:
Campbell CJ, editor. Spider monkeys: behavior ecology and evolution of the genus Ateles. Cambridge: Cambridge University Press.
p. 288–328.
Wanker R. 2002. Social system and acoustic communication of spectacled parrotlets (Forpus conspicillatus): research in captivity and in
the wild. In: Mette-Hofman C, Ganzlosser U, editors. Bird research
and breeding. Furth (Germany): Filander. p. 83–108.
Wittemyer G, Douglas-Hamilton I, Getz WM. 2005. The socioecology
of elephants: analysis of the processes creating multitiered social
structures. Anim Behav. 69:1357–1371.