Download Measuring variation in the frequency of group fission and fusion from

Journal of Mammalogy, 96(4):791–799, 2015
DOI:10.1093/jmammal/gyv084
Measuring variation in the frequency of group fission and fusion from
continuous monitoring of group sizes
Guillaume Body, Robert B. Weladji,* Øystein Holand, and Mauri Nieminen
Department of Biology, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada (GB, RBW)
Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, P.O. Box 5003, N-1432 Ås, Norway (ØH)
Finnish Game and Fisheries Research Institute, Reindeer Research Station, Toivoniementie 246, FI-99910 Kaamanen, Finland (MN)
* Correspondent: [email protected]
The frequency of group fission and fusion is critical for understanding the evolution of sociality, as it measures
group cohesiveness, which can confer a high fitness value on individuals who practice it. Variations in the frequency
of fission and fusion can also reveal an individual’s response to environmental changes. As fission–fusion group
dynamics influence the risk of disease transmission, measuring it accurately may have implications for population
management. Here, we extend a method to assess the frequency of fission and fusion from continuous monitoring
of group composition. The former method was based on the variation in group size (i.e., party/subgroup size)
within which marked individuals were successively recorded. Upon validation of the method here, we propose
a correction, using the coefficient of variation in group size instead of the variation in group size. We performed
our study on an enclosed herd of reindeer, Rangifer tarandus. All reindeer were tracked using Global Positioning
System (GPS) collars and followed by direct observations. GPS collars allowed us to obtain accurate measures of
the frequency of fission and fusion that we used to validate our models. The resulting method best described the
temporal variation in fission and fusion frequency without the confounding effect of the variation in group size.
This method can easily be applied to other populations where some individuals can be recognized and their group
size repeatedly recorded. It will also help in quantifying the 2nd dimension of the fission–fusion group dynamics:
the variation in group size.
Key words: caribou, fission–fusion, self-organization, sociality, ungulates
© 2015 American Society of Mammalogists, www.mammalogy.org
In animal societies, the fission and fusion of groups (also called
parties or subgroups) is increasingly being recognized as an
important component of social structure (Aureli et al. 2008;
Sueur et al. 2011). Fission–fusion group dynamics (FFGD)
were defined in a recent framework as the “extent of variation
in spatial cohesion and individual membership in a group over
time” (Aureli et al. 2008). According to the framework, the
social systems of mammals can be compared along the gradient
of variation and explained by ecological contexts. For example,
Australian snubfin dolphins, Orcaella heinsohni, have large
and cohesive groups with individuals maintaining strong bonds
in contrast to Indo-Pacific humpback dolphins, Sousa chinensi.
This difference in cohesiveness was then explained by a difference in food distribution as snubfin dolphins often feed on large
and concentrated food resources, whereas humpback dolphins
feed on patchy and irregular distribution of fish (Parra et al.
2011). Increased group cohesiveness may have evolved due to
its fitness advantages. Female feral horses indeed have a higher
reproductive success when they form strong social bonds,
which is independent of their kinship (Cameron et al. 2009).
The extent of group cohesiveness has also been linked with the
evolution of cognitive abilities (the social brain hypothesis), as
primate species displaying high levels of FFGD had higher success on inhibition tasks (Amici et al. 2008). Accordingly, the
study of group living is shifting from a cost/benefit approach
of the optimal group size toward the study of group cohesiveness (self-organization theory—Couzin and Laidre 2009) and
individual decisions (Conradt et al. 2009).
The most complex social systems are described by hierarchical organization of social structures. Indeed, elephants
Loxodonta africana (Wittemyer et al. 2009), giraffes Giraffa
camelopardalis (Bercovitch and Berry 2012; VanderWaal et al.
2014), and some primates (reviewed in Grueter et al. 2012)
form multilevel societies where cohesive groups temporarily
join each other and form subcommunities, which themselves
could be grouped into communities. Another level of complexity corresponds to the formation of subgroups, as seen in giant
noctule bats, Nyctalus lasiopterus (Popa-Lisseanu et al. 2008),
791
792
JOURNAL OF MAMMALOGY
and spider monkeys, Ateles geoffroyi (Ramos-Fernández and
Morales 2014), where a social group may split into unstable
subgroups, which are often merging and splitting together.
Subgroups vary in size and composition, while the overall group
is stable in size, composition, and territory occupied. Although
highly complex social systems have been the main focus of
FFGD studies, simpler systems also display FFGD. Kangaroos,
Macropus sp. (Caughley 1964), and many ungulates (e.g.,
chamois Rupicapra pyrenaica—Pépin and Gerard 2008; bison
Bison bison—Fortin et al. 2009) have highly unstable and fluid
groups. Groups often merge, split, and their composition may
vary randomly (Gerard et al. 2002). By contrast, solitary and
territorial species often form very stable groups, and some species previously classified as solitary are now being described
by FFGD (e.g., Raccoon Procyon lotor—Prange et al. 2011).
Therefore, any mammalian species (see Silk et al. 2014 for a
review in birds) can be described as displaying a certain degree
of FFGD (Couzin and Laidre 2009).
The degree of FFGD can be summarized using 3 axes: the
variation in spatial cohesion, the variation in group size, and the
variation in group composition (Aureli et al. 2008). Differences
in the degree of FFGD are expected among species (e.g., Parra
et al. 2011), among populations (e.g., Kelley et al. 2011), and
even within population through time (e.g., Body et al. 2015).
These differences would reflect differences not only in social
structure but also in population density, food distribution, or
predation risk. Accurately estimating the degree of FFGD may
prove to be valuable for a number of theoretical studies and
management practices, such as the understanding of information spread (Couzin and Laidre 2009), the evolution of cognitive abilities (Shultz and Dunbar 2006; Pérez-Barbería et al.
2007), or the management of disease spread (Proffitt et al.
2012). However, the methods used to quantify these 3 dimensions of the FFGD are far from established, and much effort is
needed to develop these methods. The aim of this article is to
improve an existing method to assess the temporal variation
in the frequency of fission and fusion, which directly influences the variation in group size. Indeed, from an individual
viewpoint, the more frequent fission and fusion events are (i.e.,
groups are unstable), the more variable group sizes will be.
This method has been proposed by Gower et al. (2009) on
elk Cervus elaphus and then used on pronghorn Antilopacra
americana (White et al. 2012) but has not yet been evaluated.
Gower’s method is based on the variation in group size within
which one particular individual is found during a particular
interval of time. Results of these 2 studies showed a strong correlation between this measure of the rate of fission and fusion
and the average group size. Such a variance–mean correlation
is a common pattern as it corresponds to issues of heteroscedasticity (Crawley 2007). As a result, this method merits further reflection to ensure that the variation of the measured
variable (variation in group size) actually reflects a variation
in the rate of fission and fusion and not a variation in average
group size, which would have a different biological interpretation. For instance, an increase of the average group size could
be the consequence of either an increase in population density
or an increase of predation risk. However, we expect increasing population density to increase the rate of fission and fusion
and increasing predation risk to decrease the rate of fission and
fusion.
Consequently, our study has 3 objectives: 1) to improve
Gower’s method by using the coefficient of variation instead
of the group size variation, 2) to validate the modified-Gower’s
method using an accurate record of the frequency of group fission and fusion in a controlled herd, and 3) to perform a sensitivity analysis on the model parameters to provide best practice
advices when using the modified-Gower’s method. To achieve
these objectives, we analyzed the temporal variation in the rate
of group fission and fusion reported in reindeer Rangifer tarandus (Body et al. 2015) during one breeding season. During the
rut, reindeer form harems that include 1 dominant male, with
or without subdominant males, and females. Harems are not
restrained in space and are highly unstable, although female
interharem movements and harem fission are less frequent during the peak rut due to the herding activity of dominant males
(Body et al. 2014a). From direct and indirect observations of
group size, we predicted the variation in the rate of fission and
fusion. To validate the tested methods, we compared their predictions with the temporal variation in the actual frequency of
group fission and fusion.
Materials and Methods
Study herd and GPS methods.—In 2011, we studied a herd
of 45 adult reindeer (34 females and 11 males), free to move
in a 13.4-km2 fenced enclosure (the Sinioivi enclosure of the
Kutuharju Field Reindeer Research Station, Finland), during
39 days in the breeding season (8 September–18 October). We
equipped all individuals except 1 female with GPS collars,
which synchronously recorded their positions every 15 min
(hereafter “recording”). GPS collars weighed about 700 g
(< 2% of reindeer body mass) and had an average positioning error of 13.8 m (Body et al. 2015). On each recording,
we assessed aggregations of individuals based on a chain rule
(Croft et al. 2008) stating that 2 neighbors were in the same
aggregation if they were closer than 89 m (Body et al. 2015).
These aggregations are named “group” based on Lent’s (1965)
definition: “an aggregation of individuals separated by some
distance from other aggregations, showing coordination of
activities, such as travelling together or resting and feeding
together.” This definition, therefore, matches the definition of
“subgroup” or “party” used in other research domains (e.g., in
primatology, see Aureli et al. 2008). Because male movement
may be different from female movement (Ramos-Fernández
and Morales 2014), particularly during the mating season, and
to match previous research (Body et al. 2015), we focused
our study only on females: the smallest group being a group
of 1 female. We identified fission from fusion by comparing
group composition among successive recordings. In the case
of fission, females from one group at time t were recorded in
different groups at time t + 1, and for fusion, females from
different groups at time t were recorded together at time t +
BODY ET AL.—MEASURING FISSION–FUSION FREQUENCY793
1. Every day from 21 September to 17 October, we also located
groups and recorded their composition in the field. We recorded
identities of females that comprised the groups using unique
collar identification numbers (L’Italien et al. 2012). Handling
of animals and data collection were done in agreement with
the Animal Ethics and Care certificate provided by Concordia
University (AREC-2010-WELA and AREC-2011-WELA) and
by the Finnish National Advisory Board on Research Ethics.
Research on live animals also followed American Society of
Mammalogists guidelines (Sikes et al. 2011).
Gower’s method and the modified-Gower’s method.—
Gower et al. (2009) calculated their measure of the rate of fission and fusion from the group size variation as: “the absolute
difference between a given group size and the mean group
size for [the period in focus].” The corresponding statistical
method used in their study (Gower et al. 2009; White et al.
2012) was a linear mixed model with the individual identity
as the random term, the measure of the group size variation
during the studied interval as the response variable, and time
intervals, among others related to their specific questions, as
explanatory variables. The methods we implemented were
not exactly the method described in these articles: we adapted
the Gower’s method (see next paragraph) to better suit our
data set and some biology principles. These adaptations do
not correspond to the main change we implemented as they
should not influence the outcome of Gower’s method. Then,
we modified the response variable used in Gower’s method
(see 2nd paragraph below) to create the “modified-Gower’s
method” and we compared the Gower’s and the modifiedGower’s methods.
For our purpose, we adapted Gower’s method in 3 ways.
First, to enhance the temporal variability, we calculated group
size variation on sliding windows instead of time intervals.
These windows are referred to as “the period in focus.” The
influence of the chosen window length was then evaluated
in a sensitivity analysis (see below). Second, when applying
the method, we only used the group sizes related to each individual’s standpoint, and not to the population data set, which
means that each individual had its own average group size for
the period in focus. This approach matches individual exposure
to group size more closely than using the average group size at
the population level (Vander Wal et al. 2013) and is in line with
the individual-based observation of group size (i.e., the typical group size—Jarman 1974). Gower’s method already takes
into account this aspect by including the individual identity as a
random term. The advantage of our version is the separation of
interindividual variations in average group size from the interindividual variations in the rate of group fission and fusion.
This is accomplished by controlling interindividual variations
in average group size prior to analyses and by isolating interindividual differences in group size variation in the random
term. Third, we used time as a continuous explanatory variable,
instead of a categorical variable, and consequently, we used a
generalized additive mixed model (GAMM) with the individual identity as random factor (i.e., intercept only), instead of a
linear mixed model, as it provided a better fit of the temporal
variability. These adaptations applied to both Gower’s method
and the modified-Gower’s method.
The modified-Gower’s method only differed from Gower’s
method on the response variable. Instead of the group size
variation, we calculated the coefficient of variation (i.e.,
CV = SD / X ) using the same data (i.e., the group sizes
recorded per individual during the sliding window). The main
advantage of using the coefficient of variation is its independence from the average group size, in contrast to the variation
in group size as previously calculated by Gower et al. (2009).
This modification would, therefore, allow us to differentiate a
variation in the rate of group fission and fusion from a variation
in average group size. We compared the actual variation in the
frequency of fission and fusion (see paragraph below) to the
variation of the predictions obtained from both methods when
applied to testing data sets (see below).
Validation analysis and comparison of the Gower’s and the
modified-Gower’s methods.—We applied the Gower’s and the
modified-Gower’s methods on 2 different data sets to evaluate their performance in predicting the frequency of fission and
fusion. Data set A included GPS-based group size data and thus
was very precise. In contrast, data set B included group size
data from daily field observation and thus was more realistic
(Fig. 1). Each data set was formed by 3 sub–data sets: 1) the
actual variation in average group size, 2) the actual variation
in frequency of fission and fusion, and the testing sub–data
set based on 3) the observed group compositions (Fig. 1). We
applied the Gower’s method and the modified-Gower’s method
on the observed group composition sub–data sets to obtain 2
sets of predictions in temporal variations of the fission and
fusion frequency, for each data set (Fig. 1). Then, we compared these 2 predictions with the actual variation in average
group size and with the actual variation in fission and fusion
frequency, for each data set A and B separately (Fig. 1). Data
sets A and B differed in data frequencies; window lengths and
periods analyzed but have similar number of data per window.
The actual variations of the average group size and the actual
variations of the frequency of fission and fusion were based on
the GPS data as it provided the most accurate data. Average
group sizes were calculated for each individual using the GPS
data at the frequency given by the data set (A or B). The frequencies of fission and fusion were evaluated from the 15-min
GPS data set as previously described (see “Study Herd and GPS
Methods”), but frequencies of fission and fusion were reported
per hour, i.e., it corresponded to the number of these events
occurring during the period in focus divided by the window
length in hour. We fitted a GAMM on each of these 4 sub–data
sets, with the time as an explanatory variable and the individual’s identity as a random variable. The smoothing parameter of
the GAMM depended on the data set.
Data set A is entirely based on GPS data on a 4-h frequency
and it uses a window length of 12 h. We used the entire study
period for this data set (39 days) and each GAMM used a smoothing parameter (k) equal to 8 (in agreement with previous analyses—Body et al. 2014a). We used a 4-h frequency to increase
the independence among successive group compositions and to
794
JOURNAL OF MAMMALOGY
Fig. 1.—Organization of data sets A and B as described in “Materials and Methods.” Actual variation in group size and in the frequency of fission
and fusion are obtained from GPS data; the testing sub–data sets are the individual-based group size obtained from the GPS data (data set A) or
from field observations (data set B). The frequency of fission and fusion is estimated by the Gower’s method and the modified-Gower’s (m-G’s)
method from each testing data set. Predictions from each model corresponding to the actual and estimated temporal variations in the frequency of
fission and fusion are compared, on each data set, based on 3 criteria. Continuous-line boxes correspond to actual data or their derived predictions,
while dashed-line boxes are estimations of the frequency of fission and fusion.
accelerate analyses, as higher data frequency did not improve
the results (see “Results”). We used a window length of 12 h to
match the number of data per window of data set B.
The testing sub–data set of data set B is based on daily field
observation of group composition (see “Study Herd and GPS
Methods”). Occasionally individual females were recorded
multiple times within a day. We retained these records in data
set B as they are rare and thus not expected to influence the
analysis. To match the data frequency of the testing sub–data
set, we used a data frequency of 1 day for the actual variation in
average group size and in the frequency of fission and fusion.
We used a 3-day window length because it provided the largest
number of data (i.e., windows that included at least 2 records
of group size observed in the field, for each individual) for the
shortest window length. A shorter window length provided a
better fit of the data (see result of the sensitivity analysis) and
best matched the temporal variations. As the period analyzed
was 27 days long, the smoothing parameters of the GAMMs
were reduced to k = 6 (proportional to the period analyzed).
To facilitate the application of the modified-Gower’s method,
we provide the R script (Supporting Information S1) and the
testing sub–data set of data set B (i.e., the group compositions
based on field observation; Supporting Information S2) for an
example of application.
For data sets A and B, we compared the predictions obtained
from the Gower’s and the modified-Gower’s method with the
actual variations in average group size and in frequency of
fission and fusion based on 3 criteria: a visual observation of
temporal variation patterns, the Pearson correlation coefficient,
and the sum of square errors (SSEs). As predicted values from
the Gower’s and modified-Gower’s methods do not have the
same units as the fitted values for the average group size and
for the fission and fusion frequencies, we scaled (centered and
reduced) each prediction and fitted value before calculating the
SSE, which is used as a goodness-of-fit measure.
Sensitivity analysis.—We performed the modified-Gower’s
method on a range of data frequencies and window lengths
based on the GPS data. We rarefied data frequencies to 2, 4, 8,
12, 24, 36, and 48 h and enlarged window lengths to 4, 8, 12,
24, 48, 72, 96, 120, 144, 168, 192, 216, and 240 h (i.e., from
4 h to 10 days), with all possible combinations having at least
2 records per window. To compare results based on these different arrangements, each fitted model was then used to predict
a single time frame of 4-h intervals covering the whole study
period. Then, we compared these predictions with the fitted values of the frequency of fission and fusion obtained on the data
set A based on the Pearson correlation and the SSE (with scaled
values).
BODY ET AL.—MEASURING FISSION–FUSION FREQUENCY795
We ran a generalized linear model (GLM) to assess the effect
of data frequency and window length on the Pearson correlation coefficient as well as on the SSE. We included in the models the interaction between the data frequency and the window
length to verify whether the number of data per window was a
good criterion to improve the Pearson correlation and to reduce
the SSE. We fitted a logistic model for the Pearson correlation
model, as it is limited by the interval [0,1] and a linear model
(i.e., with a Gaussian error structure) for the SSE model.
Using a data frequency of 4 h and a window length of 12 h
(as for data set A), we performed a sensitivity analysis on the
number of females followed. We used 33 (i.e., the maximal),
30, 25, 20, 15, 10, 5, and 2 randomly chosen females, with 10
different subsamples for each subsample size (except for 33
females that was the full data set). Again, we calculated the
Pearson correlation and the SSE (with scaled values) between
the predictions made by these models and the actual variation
in frequency of fission and fusion. Then, we performed a GLM
to explain the variation of the Pearson correlation coefficients
(logistic model) and the variation of the SSE (Gaussian error
structure) by the number of females followed. All analyses
were performed with R 3.0.3 (R Core Team 2014).
Results
Methods comparison and validation.—Slightly different results
were obtained from the GPS records (data set A; Fig. 2) and
from the records based on direct observation of the group compositions (data set B; Fig. 3). In both cases, the actual average
group size increased until the peak rut week, then decreased
(Figs. 2a and 3a). The actual frequency of fission and fusion
showed the opposite pattern, decreasing until the beginning of
the peak rut, and then increasing (Figs. 2b and 3b).
Results from data set A support the prediction that the
modified-Gower’s method better fits the temporal variation of the frequency of fission and fusion than the Gower’s
method. Predictions from the modified-Gower’s method were
more strongly correlated with the actual variation of the frequency of fission and fusion and had a lower SSE than predictions from the Gower’s method (Gower’s method: r = 0.43,
P < 0.001, SSE = 262, Fig. 2c; modified-Gower’s method:
r = 0.94, P < 0.001, SSE = 27, Fig. 2d). In addition, predictions from the modified-Gower’s method were negatively correlated to the actual variation in average group size (r = −0.69,
P < 0.001), which matched the negative correlation between
the actual variation in frequency of fission and fusion and the
actual variation in average group size (r = −0.63, P < 0.001).
Predictions from Gower’s method were positively correlated to
the average group size (r = 0.25, P < 0.001). Visual observation
also revealed a high similarity between the temporal variation
predicted by the modified-Gower’s method (Fig. 2d) and the
temporal variation in frequency of fission and fusion (Fig. 2b),
while the temporal variation predicted by the Gower’s method
was different (Fig. 2c).
Results from data set B are less clear. Gower’s method provided a stronger correlation between its predictions and the
Fig. 2.—Data set A: Temporal variability of a) the actual average group
size (individual-based) and b) the actual frequency of fission and fusion
(FF). Predictions of the temporal variation in the frequency of fission
and fusion are presented according to c) the Gower’s method and d) the
modified-Gower’s method. The temporal variations are presented with
their 95% CI. The gray vertical bar represents the peak rut week.
actual variation in frequency of fission and fusion and a lower
SSE than the modified-Gower’s method (Gower’s method:
r = 0.84, P < 0.001, SSE = 8.3; modified-Gower’s method:
r = 0.73, P < 0.001, SSE = 13.5). As for the data set A, Gower’s
method predictions were positively, but not significantly, correlated with the average group size (r = 0.29, P = 0.14), while
the predictions from the modified-Gower’s method were
negatively correlated with the average group size (r = −0.53,
P = 0.005). By comparison, the actual variation in average
group size and in frequency in fission and fusion were not significantly correlated in the data set B (r = −0.10, P = 0.61).
Visual observations of the temporal variations showed a better
fit when predicted by the modified-Gower’s method than by
the Gower’s method: the modified-Gower’s method predictions
decreased then increased (Fig. 3d), which correctly matched
the main temporal variation in frequency of fission and fusion
(Fig. 3b), while the predictions from the Gower’s method only
display a straight increase (Fig. 3c).
Sensitivity analysis.—None of the parameters used in the
modified-Gower’s method statistically influenced the Pearson
correlation between the predicted and the actual frequency of
fission and fusion (data frequency: P = 0.11, window length:
P = 0.09, interaction: P = 0.18, and number of females followed: P = 0.07). However, visual inspection of the graphs
suggested that we obtained the highest Pearson correlation for
high data frequency and short window length (Figs. 4a and 4b)
796
JOURNAL OF MAMMALOGY
and that decreasing the number of data per window increased
the Pearson correlation (Fig. 4c). Increasing the number of
females followed gradually increased the Pearson correlation
and reduced its variability among subsamples (Fig. 4d).
Model parameters that best fit the variation in the frequency
of fission and fusion, and thus minimized the SSE, were similar to those that maximized the Pearson correlation and were
statistically significant. The SSE decreased when the data were
more frequent for short window length (P < 0.001; Fig. 4e).
Decreasing the window length for frequent data reduced the
SSE (P < 0.001; Fig. 4f), and decreasing the number of data per
window reduced the SSE (P < 0.001; Fig. 4g). Increasing the
number of females followed gradually decreased the SSE and
reduced its variability among subsamples (P < 0.001; Fig. 4h).
Discussion
Fig. 3.—Data set B: Temporal variability of a) the actual average
group size (individual-based) and b) the actual frequency of fission and fusion (FF). Predictions of the temporal variation in the
frequency of fission and fusion are presented according to c) the
Gower’s method and d) the modified-Gower’s method. The temporal
variations are presented with their 95% CI. The gray vertical bar represents the peak rut week.
In this article, we suggested and evaluated a method to assess
the temporal variation in group size experienced by individuals.
Furthermore, we showed that the suggested method accurately
described the variation in the frequency of fission and fusion.
As we illustrated here with the difference between the Gower’s
method and the modified-Gower’s method, to avoid erroneous
interpretations, it is critical that methods used to quantify patterns be evaluated and validated, prior to testing process.
The main change from the Gower’s method to the modifiedGower’s method is the mathematical independence between
the predicted variation in the frequency of fission and fusion
and the variation in average group size. The relative variations of these 2 parameters of the population could help us to
Fig. 4.—Variation of a–d) the Pearson correlation and e–h) the sum of square error (SSE) between the actual and predicted frequency of fission
and fusion according to the variation in a and e) the data frequency, b and f) the window length, c and g) the number of data per window, and d and
h) the number of females followed. Points are actual Pearson correlation coefficients or SSE and lines are the predictions from the models. The
darkness of points and lines are correlated in panels a and e to the window length (lightest: window length = 4 h; darkest: window length = 240 h)
and in panels b, c, f, and g to the data frequency (lightest: data every 48 h; darkest: data every 2 h).
BODY ET AL.—MEASURING FISSION–FUSION FREQUENCY797
distinguish at least 2 situations. While being just an example,
this distinction requires further validation. Increasing population density increases the number of groups and the average
group size (Caughley 1964; Beauchamp 2011), and increasing
the density of groups increases the frequency of fusion (Pépin
and Gerard 2008), while increasing group size increases group
fission probability (Body et al. 2015). Therefore, when both the
frequency of fission and fusion and the average group size are
increasing, it may represent an increase in population density
(situation 1). In contrast, opposite trends in these variables, i.e.,
an increase in the average group size combined with a decrease
in the frequency of fission and fusion, likely represent changes
in individual’s behavior (situation 2), such as the increase of
group cohesiveness in our study population (Body et al. 2015).
Indeed, decreasing fission probability increased the average
group size and reduced the opportunities for group fusion,
as fewer groups were present in the environment (Body et al.
2015). The opposite scenarios could also happen: a decrease
of group cohesiveness could increase the frequency of both fission and fusion, while decreasing the average group size and
a reduction in density could decrease the average group size
and the frequency of fission and fusion. The latter scenario may
explain the decrease in elk average group size in open habitat in
response to fine-scale predation risk (Creel and Winnie 2005).
The elk population density in open habitat is likely to decrease
in the presence of wolves, as elk antipredator behavior consists of finding refuge under cover of wooded areas (Creel et al.
2005). Analyzing the frequency of fission and fusion in this
population independent of average group size may strengthen
this explanation.
As shown by our study, Gower’s method led to erroneous
conclusions, as the estimated variation in the frequency of fission and fusion was also influenced by the variation in average
group size. Therefore, we advise that previous studies using
Gower’s method (Gower et al. 2009; White et al. 2012) be
updated with the modified-Gower’s method to verify their findings. We recommend using the shortest possible sliding window, given that windows should include at least 2 records per
individual. We also showed that it was not necessary to increase
the frequency of data to improve the fit of statistics. However,
the frequency of data should match the temporal scale of the
biological question. In our system, we were looking at the
temporal variation in the rate of fission and fusion during the
breeding season. Therefore, daily records were more appropriate than, for instance, weekly records, as it would have provided too few data. Researchers should also invest more time
obtaining regular records of a subsample of females rather than
obtaining irregular records of a large number of females. If the
number of females followed is sufficiently large, a valuable
addition would be to bootstrap the analysis and obtain confidence intervals or to study variations among individuals in their
experience of group size variations.
The modified-Gower’s method performed well on daily fieldbased group composition records. It can, therefore, be applied
to studied natural populations where group size records include
some recognizable individuals, as the modified-Gower’s method
is based on individual variation in group size. Populations studied using radiocollared individuals are perfect candidates for
the modified-Gower’s method, as it is relatively easy to repeatedly and regularly observe the group size in which these individuals are present. The modified-Gower method can also be
applied to populations studied through transect counts where
some individuals are tagged, although observation of each individual may be less regular.
The variation in group size due to fission and fusion is a
pattern representing group stability, not a process. Processes
underlying change in this pattern could be assessed following
self-organization principles (Couzin and Krause 2003) and
should be studied at the individual or group level. The influence
of both external variables (e.g., population density and landscape—Pays et al. 2012) and internal variables (e.g., fear of
predation, sociality, and mating tactics—see Sueur et al. 2011)
should be investigated by analyzing fission or fusion probability of groups or individuals. For instance, the decrease in frequency of fission and fusion during the rut of reindeer was first
linked to an increase of group cohesiveness (Body et al. 2015),
which was then explained by males herding females back into
the group (Body et al. 2014a). In spider monkeys, individuals
were splitting less often and were merging more often when the
group sex-ratio was biased toward their own gender. Therefore,
this process at the individual level can explain the observed
pattern of sexual segregation in this species (Ramos-Fernández
and Morales 2014).
Fission–fusion group dynamics is often understood as an
adaptive behavior with respect to variation in food distribution. This interpretation suggests that fission–fusion societies
evolved from stable groups to better adjust the level of intragroup feeding competition. An alternative explanation would
be that group cohesiveness evolved from highly unstable
groups. Null models assuming independence of movement
among individuals indeed produce a high degree of FFGD due
to similar space use (Ramos-Fernández et al. 2006; Holdo and
Roach 2013). Group cohesion is also increased by the presence of uninformed individuals who will copy the behaviors
of their neighbors (Conradt et al. 2009; Pillot et al. 2011). The
fitness benefit provided by social integration (kinship recognition, friendship, or stable dominance hierarchies—Cameron
et al. 2009) may then increase the structuring of societies into
cliques (stable units) and the evolution of multilevel societies.
At any point in this evolution of cohesiveness, the evolution of
territoriality also decreases FFGD as it prevents individuals (or
social groups) from merging with each other. Group cohesiveness is, therefore, a good alternative measure to group size in
assessing species social complexity (Shultz and Dunbar 2006),
and measuring it in species that are not highly social is fundamental to better understand the early steps of the evolution of
sociality.
The modified-Gower’s method provides one way to quantify the 2nd dimension of FFGD. We identified 2 other promising methods to assess this dimension depending on the kind
of data available: the method described in Fortin et al. (2009)
should be applied on GPS data, while the mathematical
798
JOURNAL OF MAMMALOGY
model described in Juanico (2009) could provide a solution
when group sizes are recorded but individuals are not identified. For a complete assessment of the framework proposed
by Aureli et al. (2008), the 2 other axes should be evaluated
as well. The 1st dimension, the variation in spatial cohesion,
could be measured by interindividual distances (e.g., Aureli
et al. 2012; King et al. 2012; Ramos-Fernández and Morales
2014), although we personally prefer to use the distance to
the nearest neighbor. It is a more efficient metric for defining groups (Croft et al. 2008; Body et al. 2014a), an easier
metric to measure in field conditions, and it is theoretically
independent of group size. The 3rd dimension, the variation
in group composition, could be measured by metrics from
social network analysis (Croft et al. 2008; Ramos-Fernández
and Morales 2014). Simultaneously quantifying the 3 axes
of FFGD will be a great challenge for the coming years, and
we hope that the modified-Gower’s method will be a good
starting point.
Acknowledgments
We thank J. Siitari and H. Törmänen of the Finnish Game and
Fisheries Research Station for the management of GPS collars data and individuals’ data and M. Tervonen of the Finnish
Reindeer Herder’s Association for the management of reindeers in Finland. We thank S. Engelhardt, N. Melnycky, and
H. Gjøstein who helped with data collection and 2 anonymous
referees for valuable comments on an early version of this manuscript as well as Q. Gray and E. Anderson for language correction. We also acknowledge the financial support of the Natural
Sciences and Engineering Research Council of Canada to
RBW, the Research Council of Norway to ØH, and the Quebec
Centre for Biodiversity Sciences to GB.
Supporting Information
The Supporting Information documents are linked to this
manuscript and are available at Journal of Mammalogy online
(jmammal.oxfordjournals.org). The materials consist of data
provided by the author that are published to benefit the reader.
The posted materials are not copyedited. The contents of all
supporting data are the sole responsibility of the authors.
Questions or messages regarding errors should be addressed
to the author.
Supporting Information S1.—R script for the modifiedGower method.
Supporting Information S2.—Testing sub–data set of data set
B with group compositions based on field observations.
Literature Cited
Amici, F., F. Aureli, and J. Call. 2008. Fission-fusion dynamics,
behavioral flexibility, and inhibitory control in primates. Current
Biology 18:1415–1419.
Aureli, F., C. M. Schaffner, N. Asensio, and D. Lusseau. 2012.
What is a subgroup? How socioecological factors influence interindividual distance. Behavioral Ecology 23:1308–1315.
Aureli, F., et al. 2008. Fission-fusion dynamics: new research frameworks. Current Anthropology 49:627–654.
Beauchamp, G. 2011. Functional relationship between group size
and population density in Northwest Atlantic seabirds. Marine
Ecology Progress Series 435:225–233.
Bercovitch, F. B., and P. S. M. Berry. 2012. Herd composition,
kinship and fission–fusion social dynamics among wild giraffe.
African Journal of Ecology 51:206–216.
Body, G., R. B. Weladji, Ø. Holand, and M. Nieminen. 2014a.
Highly competitive reindeer males control female behavior during
the rut. PLoS One 9:e95618.
Body, G., R. B. Weladji, Ø. Holand, and M. Nieminen.
2015. Fission-fusion group dynamics in reindeer reveal an
increase of cohesiveness at the beginning of the peak rut. Acta
Ethologica 18:101–110. doi:10.1007/s10211-014-0190-8.
Cameron, E. Z., T. H. Setsaas, and W. L. Linklater. 2009. Social
bonds between unrelated females increase reproductive success
in feral horses. Proceedings of the National Academy of Sciences
106:13850–13853.
Caughley, G. 1964. Social organization and daily activity of the
red kangaroo and the grey kangaroo. Journal of Mammalogy
45:429–436.
Conradt, L., J. Krause, I. D. Couzin, and T. J. Roper. 2009.
“Leading according to need” in self-organizing groups. American
Naturalist 173:304–312.
Couzin, I. D., and J. Krause. 2003. Self-organization and collective behavior in vertebrates. Advances in the Study of Behavior
32:1–75.
Couzin, I. D., and M. E. Laidre. 2009. Fission–fusion populations.
Current Biology 19:633–635.
Crawley, M. J. 2007. The R book. John Wiley & Sons Ltd.,
Chichester, United Kingdom.
Creel, S., and J. A. Winnie. 2005. Responses of elk herd size to
fine-scale spatial and temporal variation in the risk of predation by
wolves. Animal Behaviour 69:1181–1189.
Creel, S., J. A. Winnie, B. Maxwell, K. Hamlin, and M. Creel.
2005. Elk alter habitat selection as an antipredator response to
wolves. Ecology 86:3387–3397.
Croft, D. P., R. James, and J. Krause. 2008. Exploring animal
social networks. Princeton University Press, Princeton, New Jersey.
Fortin, D., M.-E. Fortin, H. L. Beyer, T. Duchesne, S. Courant,
and K. Dancose. 2009. Group-size-mediated habitat selection
and group fusion-fission dynamics of bison under predation risk.
Ecology 90:2480–2490.
Gerard, J.-F., E. Bideau, M.-L. Maublanc, P. Loisel, and
C. Marchal. 2002. Herd size in large herbivores: encoded in the
individual or emergent? Biological Bulletin 202:275–282.
Gower, C. N., R. A. Garrott, P. J. White, S. Cherry, and N.
G. Yoccoz. 2009. Elk group size and wolf predation: a flexible
strategy when faced with variable risk. Pp. 401–422 in The ecology of large mammals in central Yellowstone: sixteen years of integrated field studies (R. A. Garrott, P. J. White, and F. G. R. Watson,
eds.). Academic Press, San Diego, California.
Grueter, C. C., B. Chapais, and D. Zinner. 2012. Evolution of
multilevel social systems in nonhuman primates and humans.
International Journal of Primatology 33:1002–1037.
Holdo, R. M., and R. R. Roach. 2013. Inferring animal population
distributions from individual tracking data: theoretical insights and
potential pitfalls. Journal of Animal Ecology 82:175–181.
Jarman, P. 1974. The social organisation of antelope in relation to
their ecology. Behaviour 48:215–267.
BODY ET AL.—MEASURING FISSION–FUSION FREQUENCY799
Juanico, D. E. O. 2009. Herding tendency as an aggregating factor in a binary mixture of social entities. Ecological Modelling
220:3521–3526.
Kelley, J. L., L. J. Morrell, C. Inskip, J. Krause, and D. P. Croft.
2011. Predation risk shapes social networks in fission-fusion populations. PLoS One 6:e24280.
King, A. J., et al. 2012. Selfish-herd behaviour of sheep under
threat. Current Biology 22:561–562.
Lent, P. 1965. Rutting behaviour in a barren-ground caribou population. Animal Behaviour 13:259–264.
L’italien, L., R. B. Weladji, Ø. Holand, K. H. Røed, M. Nieminen,
and S. D. Côté. 2012. Mating group size and stability in reindeer
Rangifer tarandus: the effects of male characteristics, sex ratio and
male age structure. Ethology 118:783–792.
Parra, G. J., P. J. Corkeron, and P. Arnold. 2011. Grouping and
fission–fusion dynamics in Australian snubfin and Indo-Pacific
humpback dolphins. Animal Behaviour 82:1423–1433.
Pays, O., D. Fortin, J. Gassani, and J. Duchesne. 2012. Group
dynamics and landscape features constrain the exploration of herds
in fusion-fission societies: the case of European roe deer. PLoS
One 7:e34678.
Pépin, D., and J.-F. Gerard. 2008. Group dynamics and local population density dependence of group size in the Pyrenean chamois,
Rupicapra pyrenaica. Animal Behaviour 75:361–369.
Pérez-Barbería, F. J., S. Shultz, and R. I. M. Dunbar. 2007.
Evidence for coevolution of sociality and relative brain size in
three orders of mammals. Evolution 61:2811–2821.
Pillot, M.-H., J. Gautrais, P. Arrufat, I. D. Couzin, R. Bon,
and J.-L. Deneubourg. 2011. Scalable rules for coherent group
motion in a gregarious vertebrate. PLoS One 6:e14487.
Popa-Lisseanu, A. G., F. Bontadina, O. Mora, and C. Ibanez.
2008. Highly structured fission-fusion societies in an aerial-hawking, carnivorous bat. Animal Behaviour 75:471–482.
Prange, S., S. D. Gehrt, and S. Hauver. 2011. Frequency and
duration of contacts between free-ranging raccoons: uncovering a
hidden social system. Journal of Mammalogy 92:1331–1342.
Proffitt, K. M., J. A. Gude, J. Shamhart, and F. King. 2012.
Variations in elk aggregation patterns across a range of elk population sizes at Wall Creek, Montana. Journal of Wildlife Management
76:847–856.
R Core Team. 2014. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna,
Austria. http://R-project.org/. Accessed 26 September 2014.
Ramos-Fernández, G., D. Boyer, and V. P. Gómez. 2006. A complex social structure with fission–fusion properties can emerge from
a simple foraging model. Behavioral Ecology and Sociobiology
60:536–549.
Ramos-Fernández, G., and J. M. Morales. 2014. Unraveling fission-fusion dynamics: how subgroup properties and dyadic interactions influence individual decisions. Behavioral Ecology and
Sociobiology 68:1225–1235.
Shultz, S., and R. I. M. Dunbar. 2006. Both social and ecological factors predict ungulate brain size. Proceedings of the Royal
Society of London, B. Biological Sciences 273:207–215.
Sikes, R. S., W. L. Gannon, and the Animal Care and Use
Committee of the American Society of Mammalogists. 2011.
Guidelines of the American Society of Mammalogists for the use
of wild mammals in research. Journal of Mammalogy 92:235–253.
Silk, M. J., D. P. Croft, T. Tregenza, and S. Bearhop. 2014.
The importance of fission–fusion social group dynamics in birds.
International Journal of Avian Science 156:701–715.
Sueur, C., et al. 2011. Collective decision-making and fissionfusion dynamics: a conceptual framework. Oikos 120:1608–1617.
VanderWaal, K. L., H. Wang, B. McCowan, H. Fushing, and L.
A. Isbell. 2014. Multilevel social organization and space use in reticulated giraffe (Giraffa camelopardalis). Behavioral Ecology 25:17–26.
Vander Wal, E., F. M. Van Beest, and R. K. Brook. 2013. Densitydependent effects on group size are sex-specific in a gregarious
ungulate. PLoS One 8:e53777.
White, P. J., C. N. Gower, T. L. Davis, J. W. Sheldon, and J.
R. White. 2012. Group dynamics of Yellowstone pronghorn.
Journal of Mammalogy 93:1129–1138.
Wittemyer, G., et al. 2009. Where sociality and relatedness
diverge: the genetic basis for hierarchical social organization in
African elephants. Proceedings of the Royal Society of London,
B. Biological Sciences 276:3513–3521.
Submitted 25 August 2014. Accepted 17 March 2015.
Associate Editor was Loren D. Hayes.