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The dynamics of social networks among female
Asian elephants
de Silva et al.
de Silva et al.BMC Ecology 2011, 11:17
http://www.biomedcentral.com/1472-6785/11/17 (27 July 2011)
RESEARCH ARTICLE Open Access
The dynamics of social networks among female
Asian elephants
Shermin de Silva
1,2,5*†
, Ashoka DG Ranjeewa
2,3
and Sergey Kryazhimskiy
4*†
Abstract
Background: Patterns in the association of individuals can shed light on the underlying conditions and processes
that shape societies. Here we characterize patterns of association in a population of wild Asian Elephants at Uda
Walawe National Park in Sri Lanka. We observed 286 individually-identified adult female elephants over 20 months
and examined their social dynamics at three levels of organization: pairs of individuals (dyads), small sets of direct
companions (ego-networks), and the population level (complete networks).
Results: Corroborating previous studies of this and other Asian elephant populations, we find that the sizes of
elephant groups observed in the field on any particular day are typically small and that rates of association are low.
In contrast to earlier studies, our longitudinal observations reveal that individuals form larger social units that can
be remarkably stable across years while associations among such units change across seasons. Association rates
tend to peak in dry seasons as opposed to wet seasons, with some cyclicity at the level of dyads. In addition, we
find that individuals vary substantially in their fidelity to companions. At the ego-network level, we find that
despite these fluctuations, individuals associate with a pool of long-term companions. At the population level,
social networks do not exhibit any clear seasonal structure or hierarchical stratification.
Conclusions: This detailed longitudinal study reveals different social dynamics at different levels of organization.
Taken together, these results demonstrate that low association rates, seemingly small group sizes, and fission-fusion
grouping behavior mask hidden stability in the extensive and fluid social affiliations in this population of Asian
elephants.
Keywords: Elephas maximus, social organization, fission-fusion
Background
Determining the ecological conditions that shape group
formation and social structures is a prerequisite for
understanding social evolution [1-4]. Studies in numer-
ous group-living species that follow individuals longitud-
inally over multiple years find that relationships among
individuals change both quantitatively and qualitatively
over time [5-9]. This is especially true of societies struc-
tured by fission-fusion processes, in which associations
among individuals may change over time scales ranging
from hours to months [10-13]. Patterns in these
dynamics may shed light on the underlying ecological
conditions that drive the behavior of individuals
[2,3,14,15]. In this paper, we examine social dynamics in
a population of Asian elephants.
The longevity and cognitive sophistication of elephants
make them potentially capable of maintaining complex
social relationships [16-19]. The Asian elephant (Elephas
maximus), African savannah elephant (Loxodonta afri-
cana) and African forest elephant, (Loxodonta africana
cyclotis or Loxodonta cyclotis)aretheonlylivingmem-
bers of the proboscidean clade [20-23]. Among adult
African and Asian elephants, females and calves form
the basis of social units. In African savannah elephants,
relatives associate most closely, but multiple social units
associate periodically to form hierarchically stratified
‘multi-tiered’societies with fission-fusion dynamics
[6,24,25]. Relatedness decreases at higher order ‘tiers’
[26]. Much less is known about the social organization
of African forest elephants, but it appears they generally
* Correspondence: shermin@elephantresearch.net; skryazhi@oeb.harvard.edu
†Contributed equally
1
Department of Biology, University of Pennsylvania, Philadelphia, PA 19104,
USA
4
Department of Organismic and Evolutionary Biology, Harvard University,
Cambridge, MA 02138, USA
Full list of author information is available at the end of the article
de Silva et al.BMC Ecology 2011, 11:17
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© 2011 de Silva et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creative commons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in
any medium, pro vided the original work is properly cited.
tend to form smaller social groups than savannah ele-
phants [27,28].
Surprisingly little is known of the social behavior of
Asian elephants in the wild, despite their long history of
co-habitation with people. While it has been commonly
assumed that Asian and African elephants behave simi-
larly [29], independent field studies in India and Sri
Lanka suggest that adult females associate only with
maternal relatives [30,31] and also tend to form smaller
groups than African savannah elephants [30,32]. Early
studies report that Asian elephants form ‘loose’associa-
tions with one another, implying unstable social affilia-
tions [32,33]. A more recent study of Asian elephants at
UdaWalaweandYalaNationalParksinsouthernSri
Lanka found that matrilineal kin in fact associated
together only 18-20% of time, based on observation and
telemetry data, leading to the conclusion that individuals
from different matrilines are unlikely to associate at all,
and that inter-group transfer of females most likely does
not occur [30]. It was proposed that family groups fis-
sion into daughter groups which then become largely
independent of one another [30].
In this paper we investigate how local ecological con-
ditions influence the social dynamics of adult female
Asian elephants by tracking associations within a single
wild population that inhabits a highly seasonal environ-
ment in Sri Lanka. There are at least three distinct tem-
poral patterns of associations that we could potentially
observe: random, cyclic, or stable. In the light of pre-
vious findings [30], we expect to be able to reject the
null hypothesis of random associations. We expect to
observe cyclicity in associations if seasonal resource
abundancegovernsthedegreetowhichindividuals
associate. Alternately, individuals may form stable asso-
ciations that are independent of environmental condi-
tions. We take cross-sectional and longitudinal views to
determine which patterns emerge at different levels of
organization within the society. First, we characterize
how the strength of the relationship between pairs of
individuals changes over time. We then quantify how
close companions of individuals, their putative ‘ego-net-
works,’change over time. Finally, we take a bird’seye
view of the population to examine whether this Asian
elephant society has a tier structure akin to that of Afri-
can elephants.
Results
We identified 286 adult females from September 2006
to December 2008. Key terms used throughout the
paper are given in Table 1. The number of sightings per
identified individual ranged between 1 and 48, with a
median of 9. The number of identified adult females
seen per month tended to peak at the end of dry sea-
sons in 2007 and 2008 (Table 2), just prior to the onset
of the long monsoon, and the rest of the year remained
above 66 individuals per month. On average we identi-
fied 64% of all adult females encountered. The identifi-
cation rate was higher (84%) for groups where at least
one adult female was previously identified, which is
comparable to other similar studies [12]. Group sizes, in
terms of the number of adult females encountered in a
group, ranged widely but the median was between 2 and
3 in all seasons.
Structure at the level of dyads
We measure associations between pairs of individuals
using the Simple Ratio Index or SRI [34-36], which is in
essence a proportion of time two individuals spend
together (see Methods). Summary data are given in
Table 2, the SRI matrices and a measure of uncertainty
of the SRI values are shown in the supplementary mate-
rial (see Additional file 1: Figure S1). We find that asso-
ciations among adult females within all five seasons are
significantly nonrandom (sample sizes as in Table 2 per-
mutation test, P<0.001,seeMethods).TheSRI
matrices are also significantly correlated across seasons
(Table 3). Thus, pairs of individuals that associate in
one season are likely to associate in other seasons and
pairs that do not associate in any one season rarely
associate in any other season. However, SRI matrices
from corresponding seasons across years are not corre-
lated any more or less than matrices from adjacent
seasons.
A simple correlation analysiscapturesonlyverycoarse
features of data and misses more subtle patterns. We
therefore examine the social dynamics of the Uda
Walawe population in more detail using other methods.
In order to maximize the signal to noise ratio in the
data, we restrict the subsequent analyses to 51 core indi-
viduals, i.e., those that were present in all seasons and
were seen at least 30 times during the study period. We
plot the SRI values for each pair of individuals as a
function of time to determine whether such temporal
SRI trajectories follow any of the three natural patterns
that we expect a priori (see Methods for details): stable,
which are signified by a flat trajectory (type A), tempor-
ary, signified by a single-peak trajectory (type B), or cyc-
lic, signified by a trajectory with multiple peaks (type C).
We find that out of the 478 dyads that associated in at
least one season, 6 dyads (1.3%) formed by 9 (17.6%)
individuals maintain bonds with strength at or above 0.3
in all seasons (Table 4; also see Additional file 2: Figure
S2). Thus, approximately 18% of the females engage in
at least one relationship that is relatively strong com-
pared to the majority of ties. Although these relation-
ships still fluctuate over time, we consider them to be
instances of type A trajectories. Using K-means cluster-
ing, we find that the remaining 472 dyads have one of
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six distinct SRI trajectories, (Table 4, Figure 1; also see
Additional file 3: Figure S3). 433 (90.6%) of dyadic rela-
tionships (the five most abundant trajectory types) have
SRI trajectories of type B, with a single peak in one of
the five seasons. All of 51 examined individuals partici-
pate in such relationships. Moreover, for 292 dyads
(61.1%), the SRI peaks in either the transitional or dry
seasons. Finally, 39 (8.2%) of dyadic relationships formed
by 32 (62.7%) individuals have the SRI trajectories of
type C with peaks in the two dry seasons. This suggests
cyclicity in associations among some individuals that a
statistical test of correlation across seasons does not
pick up. Interestingly, even though single peaks (type B)
occur in wet seasons, we do not detect a typical trajec-
tory with peaks in both wet seasons.
So far we have been concerned with how the strength of
association among dyads changes over time. Yet an indi-
vidual may uniformly increase or decrease the absolute
amount of time she spends with others without
changing the rank order of her preferred companions.
We now ask whether the identities of her preferred
companions change over time, irrespectively of the tie
strength (see Methods for details). We find that a typical
individual partitions her time approximately equally
among her long-term companions, i.e., those that are
present in her top-five for five seasons (21.1% of her
time), and her short-term companions, i.e., those that
are present in her top-five for one season (31.0% of her
time, Figure 2; Wilcoxon signed-rank test, W= 480, N
= 51, not significant). This is different from an expecta-
tion under the null hypothesis that individuals randomly
reshuffle their companions every season (Figure 2). The
observed fraction of long-term companions is signifi-
cantly higher than the fraction expected under this null
hypothesis (observed: 31.0%, expected: 0.01%; P<
0.001). Interestingly, individuals have a significantly
smaller fraction of medium-term companions, i.e., those
that are present in top-five for four seasons, than either
short-term companions (Wilcoxon signed-rank test, W
=322.5,N= 51, P< 0.05) or long-term companions
(Wilcoxon signed-rank test, W= 215.5, N= 51, P<
0.001), resulting in a U-shaped distribution of compa-
nionship preferences (Figure 2).
We also observe individual variation in social behavior
at the level of dyads. 8 females (15.7%) maintained 4 to
5 of their top-five companions for all five seasons, while
16 females (31.4%) completely changed their top-five
companions over the course of the study (Figure 3).
Moreover, individuals vary by as much as factor of 4 in
the number individuals they associate with on average
Table 1 Glossary of terms
Term Definition
Group A set of individuals observed in the field moving, resting, or interacting non-aggressively within an approximately 500 m radius of one
another.
Cluster A set of individuals that repeatedly associate together such that they form a distinct unit which is revealed by an objective analytical
clustering method.
Ego-
network
The set of individuals that the central individual, called ‘ego’, is directly connected to.
Social unit A general term describing sets of socially affiliated individuals. Social units can form at different levels. For example, an individual’s ego-
network, a social unit at one level, may be embedded in a larger network, constituting a social unit of a higher level.
Table 2 Data summary
2007 2008
Jan -
Apr
May -
Sept
Oct -
Dec
May -
Sept
Oct -
Dec
Season Label T1 D1 W1 D2 W2
No. of
individuals
161 201 170 165 154
Observation days 48 68 44 62 37
Mean group
size
1
3 3 2.8 3 2.9
Max. group size
1
12 13 12 17 10
Mean SRI 0.015 0.011 0.012 0.011 0.013
SD SRI 0.092 0.071 0.07 0.062 0.08
% Non-zero SRI 4.5 4.4 5.3 5.8 4.4
Mean non-zero
SRI
0.34 0.25 0.23 0.19 0.29
Number of
clusters
2
24 24 18 18 15
Mean cluster
size
2
6.7 8.3 9.4 9.2 10.3
Max cluster size
2
29 29 44 44 23
1
Group size here refers to the number of adult females in a group after data
aggregation (see Methods).
3
Clusters are obtained using the Girvan-Newman
algorithm with the SRI threshold equal to zero (see Methods). Distributions of
group sizes and cluster sizes are shown in Figure 6.
Table 3 Correlation between matched SRI matrices
Comparison RN
T1 vs. D1 0.60 130
T1 vs. W1 0.61 117
D1 vs. W1 0.67 144
D1 vs. D2 0.66 143
D2 vs. W2 0.70 125
W1 vs. W2 0.72 122
Rdenotes the Pearson correlation coefficient. Ndenotes the number of
individuals common to both seasons. All Rvalues are highly significant
(Mantel test, P< 0.001).
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within a season and in the average strength of their ties
(Figure 4). We also observe that those individuals who
associate with many individuals (i.e., those that have
many non-zero SRI values) typically have weak ties to
their associates (mean non-zero SRI is low), whereas
those who maintain few associates have strong ties to
them (Figure 4, negative correlation, R
2
= 0.29, P< 0.01;
for data by season rather than averages see also Addi-
tional file 4: Figure S4). Since the association index
reflects the amount of time two individuals spend
together, this negative correlation suggests a trade-off
between the number of associates that an individual can
maintain and the amount of time she can spend with
each of those associates.
Table 4 Temporal SRI trajectories for the core individuals
Trajectory type Peak season(s) Number of dyads
(percent)
Number of individuals (percent)
A N/A 6 (1.3) 9 (17.6)
B-1 D2 108 (22.6) 39 (76.5)
B-2 D1 99 (20.7) 39 (76.5)
B-3 T1 85 (17.8) 43 (84.3)
B-4 W2 71 (14.9) 43 (84.3)
B-5 W1 70 (14.6) 44 (86.3)
C D1 and D2 39 (8.2) 32 (62.7)
The total number of potential dyads is 1275, of which 478 (37.5%) had a nonzero SRI value in at least one season. ‘Trajectory type’denotes the K-means curve
type that best describes the SRI trajectory of the dyad (see Methods), with corresponding plots shown in Figure 1. ‘Peak season’refers to the time period in
which association strength is greatest. ‘Number of dyads’shows the number of dyads whose SRI trajectory has the respective type (percentages are calculated
with respect to 478 dyads with at least one non-zero SRI). ‘Number of individuals’indicates the number of individuals forming the respective dyads (percentages
are calculated with respect to 51 core individuals).
Pattern B−1
0
0.2
0.4
Pattern B−2
SRI
Pattern B−3
0
0.2
0.4
Pattern B−4
Pattern B−5
T1 D1 W1 D2 W2
0
0.2
0.4
Pattern C
Season
T1 D1 W1 D2 W2
Figure 1 Typical temporal SRI trajectories. Typical trajectories are
based on K-means clustering of dyadic association vectors, as
described in Methods. Light gray curves represent SRI trajectories for
specific dyads, heavy black curves show the mean profile for each K-
means cluster. Patterns B-1 through B-5 represent associations that
peak in a single season (see text). Pattern C represents cyclic
associations that peak in dry seasons. Pattern A is shown in
Additional file 2: Figure S2. The numbers of individuals and dyads
that have each type of the SRI trajectories are given in Table 4.
Number of seasons
spent with an associate
Fraction of companion slots
12345
0
0.1
0.2
0.3
0.7 Expected
Observed
Figure 2 Allocation of an individual’s companion slots to her
associates. The histogram shows the fraction of an individual’s
companion slots that she allocates to spend with her m-term
associates, where mis shown on the x-axis (see Methods for
details). Black bars represent the observed mean values, and error
bars indicate ± 1 standard error (N= 51). Gray bars represent the
distribution expected if individuals chose their companions
randomly every season.
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Ego-network structure
We now expand our view beyond dyads to look at mul-
tiple direct associates of an individual simultaneously in
a larger sample of 88 residents, i.e., individuals that were
observed in every season (see Methods). We represent
SRI matrices as weighted social network graphs [37,38],
where nodes correspond to individuals, edges connect
those who have been associated within a season, and
edge weights correspond to the SRI values (Figure 5).
An ego-network is then a social network that consists
only of the subject, or ‘ego,’and the nodes to which she
is directly connected, i.e. individuals with whom she was
associated at least once (Table 1). For each resident, we
compute five ego-network measures, defined in Table 5.
Average values of ego-network measures over all resi-
dents are called ego-network statistics.
All ego-network statistics except ‘Density’tend to have
lower values in wet seasons than in dry seasons (Table
5), indicating that ego-networks are larger in dry seasons
than in wet seasons. The measure ‘Density’is marginally
lower in dry seasons, implying that the ego-networks are
less interconnected in dry seasons than in wet seasons.
Because ego-network measures for different individuals
are non-independent, we cannot directly test for differ-
ences between the distributions of ego-network mea-
sures in different seasons. Instead, we test for
differences in the bootstrap distributions of ego-network
statistics [39]. The bootstrap means of ego-network sta-
tistics are reported in Table 5. Bootstrap distributions
for all ego-network statistics differ significantly between
seasons. We note however that these distributions for
all statistics in all seasons are systematically shifted with
respect to the observed values (Table 5). This suggests
that the bootstrap method we used produces biased dis-
tributions of ego-network statistics, but we are not
aware of a better method for statistical comparison. We
therefore must be cautious with the interpretation of
Table 5.
The ego-network measures are sensitive to the num-
ber and arrangement of companions but ignore their
identities. However, visualizations of ego-networks
demonstrate that while a subject’s direct companions do
change over time, she has a few that are almost always
present; even those that are not present continuously
may have been companions in previous seasons (Figure
5). Thus, individuals maintain long-term relationships
with others even though they may be apart for one or
several seasons and have low SRI values.
Population-level structure
We now step out further and examine global relation-
ships among the entire study population within each
season using the Girvan-Newman method for finding
community structure, as described in the Methods. To
avoid confusion with sociological definitions of commu-
nities, here we refer to the subnetworks found by this
Number of associates retained in
top five for 5 seasons
Fraction of individuals
012345
0
0.1
0.2
0.3
0.4
Figure 3 Turnover of an individual’s closest associates.Bars
show the fraction of individuals that retain a given number of
associates in their top-five (see Methods and Results). Value zero in
the x-axis implies that the identities of an individual’s top-five
associates have completely changed over five seasons; value 5
implies that her top-five associates have not changed over this
period. For example, approximately 20% of individuals retained two
associates over all five seasons.
R2 = 0.29
P < 0.01
Mean number of associates
Mean non−zero SRI
0 5 10 15 20
0
0.1
0.2
0.3
0.4
0.5
Figure 4 Mean SRI of an individual versus the number of her
associates. Each point shows the number of associates of an
individual averaged over 5 seasons and the SRI value of the
individual averaged over all of her associates and all seasons (see
text for details). Data for each season as opposed to averages over
all seasons are shown in Additional file 4: Figure S4.
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301
471 KAL
KAM
KAN
RAM
RHL
TAM
TAN
TUL
TUS
301
457
471
KAL
KAM
KAN
RAM
RHL
TAM
TAN TUL
TUS
TAN
457
471
KAL
KAM KAN
RAG
RAM
RHL
TAM
TUL
TUS
301
457
471
KAL
KAM
KAN
RAG
RAM
RHL
TAM
TAN
TUL
TUS
457 471 KAL
KAM
KAN
301
RAG
RAM
RHL
TAM
TAN
TUL
TUS
T1
D1
W2
W1
D2
PopulationResidentsEgo
Figure 5 Social networks by season. Nodes represent adult females and the thickness of edges corresponds to the SRI value. Isolates appear
in the upper left corner of each network. Each row corresponds to a season and each column to a type of network. ‘Ego’shows the ego-
networks of selected subjects, who are indicated by black circles with colored borders. Node colors correspond to each Ego’s Girvan-Newman
cluster assignments in T1. These colors are maintained through all seasons to allow comparison across seasons (actual cluster designations in
other seasons are not shown). In subsequent seasons, individuals colored gray are those who did not appear as Ego’s companions in any
preceding season covered by this study, although they may have associated prior to January 2007. Labeled nodes indicate those who associated
with the subject in nearly every season. By the fifth season, networks clearly consist primarily of individuals who previously associated with the
subject, even if not all were present in every season. ‘Residents’shows all residents. One can track the coherence of each cluster over time.
Some clusters from T1 maintain their integrity (e.g. brown) whereas others do not (e.g. light blue); associations among clusters also change over
time, most notably the large pink and dark green clusters. Clusters are connected via just a few bridging individuals. ‘Population’shows the full
social network for each season with sample sizes reported in Table 2. Social networks constructed from real data have distinct structure, whereas
those constructed from randomized data do not (see Additional file 5: Figure S5).
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algorithm simply as ‘clusters.’These clusters represent
one or more social units, i.e. sets of individuals that
have more ties to one another than to those outside of
the set (Table 1). Results are presented in Figures 6, 7
and 8.
First, we note that the social network formed by indi-
viduals in this population is extensive and well-con-
nected (Figure 5). Moreover, in all seasons, a typical
cluster detected by the Girvan-Newman algorithm is 2
to 3 times larger than a typical group encountered by
observers in the field (Figure 6 and Table 2). These find-
ings are unexpected in the light of previous studies
which have suggested that Asian elephants do not dis-
play extensive social affiliations [30,33].
Next, we examine how the structure of the social net-
work changes over time. For each season, we plot the
network structure curves (Figures 7 and 8; see Methods
for detailed explanation), which show how ties of var-
ious strengths are distributed in a manner that is easier
to digest than the social network diagrams depicted in
Figure 5 (the effect of the thresholding procedure on
the T1 network is illustrated in Additional file 5: Figure
S5). A network generated from randomized data shows
no distinct clusters (see Additional file 6: Figure S6). As
a result, the corresponding network structure curve
remains flat until the SRI threshold reaches the mean
tie strength in the network, at which point the curve
rapidly declines to zero (Figure 8). In contrast, the net-
work structure curves for real data have a distinct peak.
This is probably a consequence of the fact that both
extremely weak ties and extremely strong ties can be
influenced by sampling effects, but intermediate values
clearly distinguish core social units. Although all seasons
have 10-20 well-defined clusters at the SRI threshold of
zero, network structure curves for each season behave
differently at subsequent SRI threshold values. In parti-
cular,theslopeofthecurvechangesonlyonce(from
positive to negative) in seasons D1, D2 and W2, but
changes twice (from zero to positive and from positive
to negative) in seasons T1 and W1 (Figure 8). This sug-
gests that the network structures in each season are dif-
ferent (also visible in Figure 5). Although the network
structure curves are different across seasons, there
appear to be no patterns characteristic of dry or wet
seasons per se. Visual inspection of networks shows
that, while many clusters maintain their integrity across
seasons, some individuals transfer between clusters, and
the connections among clusters change (Figure 5).
Discussion
We have presented the first detailed quantitative charac-
terization of social organization in an Asian elephant
population, at multiple levels of organization and across
ecological timescales. We asked whether associations are
random, stable, or cyclic. We find that the answer
depends on the timescale and level of organization.
Most ties are weak (SRI values below 0.3) compared
those of African savannah elephants where typical asso-
ciation rates are above 0.6 [6,13,25]. Despite the overall
weakness of ties, most individuals have a few strong ties
(SRI values exceeding 0.3) as well as a few consistent
ties (maintained over several seasons) with some of their
associates. Individuals do not mix randomly within the
population, nor are they always with the same compa-
nions,butrathertheyshuffleamongstasubsetofpre-
ferred companions. All individuals engage in temporary
associations, especially during dry seasons. Some also
associate to a greater degree in dry seasons, forming
cyclic associations. This cyclicity is evident at the level
of dyadic associations (Figure 1), but not at the ego-net-
work or population levels.
Our results suggest a view of Asian elephant social
structure that is different from what has been described
in the literature before. Earlier studies reported small
group sizes typically consisting of less than five adult
Table 5 Ego-network statistics
Size Ties Pairs Density 2-Step Reach
T1 Mean 8.6 30.7 51 0.77 23.2
SD 6.1 32.4 63.9 0.23 16
BM
1
7.1 23.6 35.4 0.82 16.7
D1 Mean 12.6 55.5 100.4 0.7 41.1
SD 7.5 48.9 114.7 0.21 23.8
BM
1
10.2 40.3 68.3 0.74 30.7
W1 Mean 11.4 45.2 74.1 0.71 36
SD 5.5 34.6 71.9 0.2 19.5
BM
1
8.7 29.7 45.2 0.76 23.7
D2 Mean 12.9 63.7 106.9 0.72 40.6
SD 7.8 66.9 127.3 0.19 24.3
BM
1
10.4 46 73.6 0.74 30.2
W2 Mean 7.5 19.8 31.9 0.75 20.7
SD 3.8 18 35.3 0.22 10.9
BM
1
6 14 20.7 0.79 14.1
1
BM is the mean of the bootstrap distribution
’Size’is the number of the subject’s (ego’s) direct companions, i.e., those
individuals seen in a group with her at least once. ‘Ties’is the number of ties
between a subject’s direct companions. ‘Pairs’is the number of potential ties
in the ego-network, i.e., the number of ties that would exist if all of subject’s
direct companions were also each other’s direct companions. ‘Density’is the
ratio of actual to potential connections in the ego-network (Ties/Pairs),
indicating how well-connected companions are to each other. ‘2-Step Reach’
is the number of individuals within two degrees of separation from the
subject, i.e., the number of friends and friends of friends. For each season, the
first column shows the ego-network statistic, i.e., the mean of the distribution
of ego-network measures across 88 residents; the second column shows the
standard deviation of this distribution, and the third column shows the
expected value of the ego-network statistic derived from 1000 bootstrap
samples. Bootstrap distributions were generated as described in Methods. The
bootstrap distributions for the Size, Ties, Pairs and 2-Step Reach statistics are
shifted towards lower values with respect to the actual values in all seasons,
and the bootstrap distribution of the Density statistic is shifted towards higher
values in all seasons. All bootstrap distributions are significantly different from
each other across seasons (Wilcoxon rank sum test, P< 0.001).
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females [30,33], a number comparable to the group sizes
observed in this study. The number of individuals with
the same mitochondrial haplotype ranged from 3 to 12
[30], which could be taken as matrilineal family sizes.
However, families and observer-defined groups are only
relevant structural units insofar as they relate to actual
social units, expressed through the animals’behavior.
The latter are revealed by a quantitative analysis of
long-term association data rather than genetics [6,26]. It
took up to two years to obtain repeated observations of
all members of some social units in this study (Figure 5
and unpublished data from 2005-2006). In this paper,
we used the Girvan-Newman procedure to detect such
social units and found that they are in fact much larger
than either the group or family sizes reported in pre-
vious studies (Table 2, Figures 5 and 6). Such units are
more stable across years than individuals’immediate
companions. Informal photographic records suggest that
some of the individuals in this study have associated
since at least 2001 (unpublished data), which supports
the existence of long-term stable associations. Since
Asian elephants are capable of communicating both che-
mically [29,40] and acoustically [41,42] at distances
humans find difficult to observe, they may be aware of
the their associates’locations even when the latter are
beyond the visual range of human observers. Indeed,
vision is not the preferred mode of perception for ele-
phants, as we see individuals track precise paths taken
by others using scent even when both parties are plainly
visible to humans. Moreover, outside protected areas,
elephants are largely nocturnal (personal observations).
‘Groups’of Asian elephants are not unlike those formed
by African elephants [13]. As with other animal societies
that exhibit fission-fusion dynamics, such as that of
chimpanzees [43,44], the social organization of a highly
mobile species like Asian elephants is not fully evident
Frequency
T1
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Cluster size
01020
0
20
40
60
D1
0 5 10 15 20
01020
Group size
W1
0 5 10 15 20
Cluster rank
01020
D2
0 5 10 15 20
01020
W2
0 5 10 15 20
01020
Figure 6 Group- and cluster-size distributions by season. Top row shows the group size distributions. Inverted triangles show the mean
group sizes (see Table 2). Bottom row shows the size of Girvan-Newman clusters ranked by size. The horizontal dashed lines show the mean
cluster size (see Table 2).
cd
ab
cd
ab
cd
a
bc
d
ab
Number of clusters
SRI threshold
10
0
1
2
3
4
Number of clusters
SRI threshold
10
0
1
2
3
4
Figure 7 Schematic social networks and corresponding
network structure curves. Top and bottom panels show two
networks that have identical topology, but different distributions of
tie strengths. The network in the top panel has a homogeneous
distribution of tie strengths while the network in the bottom panel
shows a heterogeneous distribution. Edge widths indicate tie
strength. The Girvan-Newman clustering algorithm detects highly
interconnected subunits regardless of edge weights, and so, at the
SRI threshold of 0 both networks have the same number of clusters
(a). By removing ties with the SRI values below successive
thresholds and re-running the clustering algorithm, the underlying
differences in the networks are easily visualized in the network
structure curve on the right (b-d).
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without systematic and prolonged observations, particu-
larly in areas where visibility is restricted. Long-term
observations of other Asian elephant populations would
be extremely useful to corroborate this finding.
Previous authors also concluded that associations
among different families were highly unlikely as associa-
tions even among family members appeared infrequent
[30]. However, these conclusions were drawn from
extremely small sample sizes (for instance, only 1
mtDNA haplotype from Uda Walawe and few repeat
observations). Our results suggest otherwise. While the
association rate of 18-20% reported in a previous study
[30]isroughlyanalogoustothemedianSRIvalueof
found in our study (Table 2, Figure 6), we do find reli-
able SRI values that range as high as 1 (see Additional
file 1: Figure S1). Moreover, there is at least some trans-
fer of individuals between social units across seasons
(Figure 5). However, the population-level social network
structure does not appear to exhibit any clear seasonal
patterns (Figure 8). It is not clear whether individuals
form hierarchical social ‘tiers’, such as those observed in
African savannah elephants, which form higher-order
associations among multiple families in wet seasons
[6,24,25,45]. Among savannah elephants, relatedness
decreases at higher-order tiers of association, where
associations are weaker than 0.6 [13,26,46], and are
mediated by intra- and inter-group dominance interac-
tions [47,48]. The network structure curve for Asian ele-
phants peaks near an SRI threshold of 0.3 (Figure 8).
Although there is no consistent social stratification in
this Asian elephant population, it is possible that the
clusters prior to the peak have a lower degree of related-
ness than the clusters that follow it. A detailed genetic
study of this population examining the hypothesis
above, with larger sample sizes than previously obtained,
would also be illuminating and is planned in the future.
There is much variation in individuals’long-term fide-
lity to companions (Figures 3 and 4). For instance,
Kamala (KAM) and Kanthi (KAN) were two mature
females who appeared close to the same age and were
nearly always together (Figure 5). The so-called ‘K’unit
(Kamala, Kanthi, Karin, Kavitha and Kalyani) almost
always contained every member whenever it was seen
although they also interacted with others to form a lar-
ger cluster. On the other hand, individuals like ‘471,’
also part of a large cluster, had few stable companions
(Figure 5). The social placement of a few other females
remained unresolved despite numerous repeat observa-
tions. The fitness consequences of these different social
strategies remain to be seen. Moreover, while it is widely
assumed that Asian elephants, like African elephants,
form strongly bonded family groups centered around
matriarchs [29,40], the apparent variation and fluidity in
social preferences shown in this study would seem to
question such a characterization.
It is intriguing that social dynamics differ depending
on the level of analysis - the bottom-most (dyadic) and
top-most (population) levels of organization exhibit a
greater degree of instability than the intermediate level
(social units and long-term ego-networks). Uncovering
the ecological basis for observed patterns would require
separate investigations and hypotheses at each level. Pre-
ferences for one another shown by some pairs of indivi-
duals might depend on reproductive state (e.g. those
with similarly-aged calves), while social units may differ
in their strategies depending on whether they are seaso-
nal inhabitants of the park or residents. For instance,
killer whales of the same species exhibit different social
strategies depending on whether they are resident or
T1 rand
0
10
20
30
40
50
0
0.05
0.10
0.15
0.20
T1
D1
Number of clusters
0
10
20
30
40
50
Fraction of ties
0
0.05
0.10
0.15
0.20
W1
D2
0 0.2 0.4 0.6
0
10
20
30
40
50
0
0.05
0.10
0.15
0.20
W2
SRI threshold
0 0.2 0.4 0.6
Figure 8 Network-structure curves and SRI distributions by
season. Black curves show the number of Girvan-Newman clusters
in the thresholded network (left y-axis). Gray bars show the fraction
of dyads with the given SRI value (right y-axis). Red dots show the
points at which the network-structure curves display slope changes
at the significance level of 0.05 or below with the window size w=
0.2 (see Methods; exact P-values for this and other window sizes are
shown in Additional file 8: Figure S7). While the majority of ties are
weaker than 0.2 in both real and randomized data, the distribution
has a long tail in real data but not in randomized data. Randomized
network shows no ties above a threshold of 0.5, and a nearly level
network structure curve up to this threshold with no significant
slope changes. In contrast, observed networks for each season show
peaked curves with significant changes in slope. Q
max
remains
above 0.6 for real data while for randomized data it peaks and falls
sharply (see Additional file 9: Figure S8).
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transient, in accordance with the associated feeding
ecology [5].
Our analyses are based on association index data, cal-
culated from observations of individuals in the field.
There are at least two sources of uncertainty associated
with this type of data. First, we expect that some varia-
tion comes from the fact that we observe different sets
of individuals in different seasons. Our observation area
is largely constrained by the road network inside Uda
Walawe National Park. While we expect to have a reli-
able observation record for individuals whose range
strongly overlaps with this area, we also observe indivi-
duals that presumably move into this area only periodi-
cally [49]. Such individuals, being farther away from the
centers of their home ranges, might exhibit different
behavioral and social patterns than individuals residing
more centrally, thus introducing additional noise in our
data. The second source of variation stems simply from
relatively low counts of events in some seasons for some
individuals. To minimize the first type of noise, we have
constrained most of our analyses to the so-called resi-
dent individuals, i.e. those that we have consistently
observed every season. To minimize the second type of
noise, we have constrained some of the analyses even
further, to individuals that have been seen at least 30
times. Nevertheless, we can extrapolate the conclusions
drawn from these analyses to less sampled individuals in
the population, since such individuals are not ostensibly
differentfromthosesampledthoroughly.Onedoes
however need to keep in mind that we describe the
behavior of individuals that are close to the center of
their home range.
One of our surprising findings is that the elephants at
UWNP tend to form a greater proportion of strong ties
in dry seasons than in wet seasons. This suggests that
aggregation may be more advantageous in the former,
perhaps for accessing and protecting scarce resources.
This hypothesis remains to be tested with additional
seasons of data and behavioral studies. While direct
behavioral evidence of resource defense among adult
females is rare, we have observed competition over
water and mud, dominance interactions when unfamiliar
individuals or social units meet, as well as the vocal and
physical displacement of one social unit by another [41].
Resource monopolization may more often take the form
of competitive exclusion rather than confrontation, in
which acoustic and chemical signals facilitate social
cohesion as well as avoidance despite the seeming fluid-
ity of associations. Herbivores must balance intraspecific
resource competition against potential anti-predator
benefits [3,50,51]. Among artiodactyles, gregariousness
is an anti-predator adaptation seen in species inhabiting
open environments [52]. African savannah elephants
likewise may be more gregarious than Asian elephants
because they typically inhabit more open environments,
and also encounter predators other than humans
[53-55]. Interestingly, in drier regions of Sri Lanka just a
few kilometers east of the study site, elephants are
reported to aggregate in wet seasons rather than dry
seasons [56], a similarity to African savannah elephants
that could be ecologically driven. Similar longitudinal
studies in other Asian elephant populations, especially
thoseinIndia,wherethereislikelytobegreatervaria-
tion in habitat quality and home range sizes [57] would
be of great interest. More data are also needed on Afri-
can elephants occupying various habitats including
desert and forest environments, the latter being more
similar to those of many Asian populations. It is possible
that societies in general and elephant societies in parti-
cular are more flexible and responsive to environmental
pressures than generally conceded.
Conclusions
Associations among female Asian elephants can be char-
acterized as fission-fusion. Patterns of association differ
across levels of organization and ecological timescales.
Individuals are found by observers in small groups
whose composition changes on the timescale of days.
However, most individuals belong to relatively large
social units which can be revealed by quantitative analy-
sis of longitudinal data. Such units generally maintain
their cohesiveness over longer timescales, although there
is some transfer of individuals between units. Social
units may fission or fuse without discernible seasonal
patterns or clear hierarchical stratification into social
‘tiers’at the level of the population. Individuals vary
highly in the number of stable companions they main-
tain over time, and some repeatedly associate in dry sea-
sons. Their companions tend to form a pool of long-
term associates. Interesting future directions include
examining the relatedness among social units, the ecolo-
gical basis of observed dynamics at each level of organi-
zation, and the fitness consequences of the seemingly
different social strategies employed by individuals.
Methods
Study site
Uda Walawe National Park (UWNP), Sri Lanka, is
located between latitudes 6° 25’-6°34’N and longi-
tudes 80° 46’- 81° 00’E, at an average altitude of 118 m
above sea level. It encompasses 308 km
2
around the
catchment of the Uda Walawe reservoir. The study area
comprises approximately 1/3 of this area, which includes
tall grassland, dense scrub, riparian forest, secondary
forest, a permanent river, seasonal streams, and other
water sources. It has a highly predictable pattern of rain-
fall with two monsoons per year, which occur in March
through April and in October through December
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[58,59]. There appear to be no non-human predators of
elephants at this location. The Sri Lankan subspecies of
Asian lion (Panthera leo sinhaleyus) was extinct prior to
the colonization of the island by humans [60]. The leo-
pard (Panthera pardus cotiya)isthecurrenttopland
predator in Uda Walawe, but there is no evidence that
it hunts elephants. The only other large predator is the
freshwater crocodile (Crocodylus palustris), but preda-
tion on elephants has not been documented. The great-
est threat to elephants both historically and currently is
human activity, but disturbance within the park is mini-
mal. Tourism has also led to the elephant population
becoming well-habituated to people in vehicles.
Data collection
The data presented here span 259 field days (twenty
months) from years 2007 and 2008, two or three days per
week on average except between January and April 2008,
when UWNP was temporarily closed due to political
unrest. We typically entered the park between 0600-0700
h (sunrise), remaining continuously inside until 1730-1830
h (sunset). Driving routes were varied such that all accessi-
ble parts of the park were covered in a week. Locations
where animals were closest to the road were marked on a
hand-held GPS unit. Temperature, humidity and wind
were recorded at least three times per day with a Kestrel™
pocket weather station. Rainfall (mm.) was recorded daily
using a standard U.S. Weather Bureau rain gauge.
Individuals were identified photographically and catalo-
gued for two years preceding the study period. All indivi-
duals were given numbers; the most frequently seen were
also given names. A previous study of Asian elephants
considered individuals within 100 m of one another to be
associated [30] whereas studies of African elephants have
usedadistanceofupto500mtodefineaggregations
[6,25,61]. We considered all individuals within visual
range of the observer and up to 500 m of one another
who moved, rested, shared resources (mud, mineral
wells, trees) to be a single aggregation, or group. Occa-
sionally individuals showed affiliative vocal or tactile
behavior such as growling and bodily rubbing [41] but
such interactions were uncommon and not required for
individuals to be considered part of the same group. Mul-
tiple groups occasionally shared water without interac-
tion. The term ‘group’here carries no implication of
social history or permanence(seealsoTable1).Indivi-
duals from multiple groups which initially co-occurred in
space or even passed through one another, were not
counted as associated unless they actively moved
together. It was possible to spend several hours with a
single group. We recorded identities of known indivi-
duals and counted the number of individuals in five size-
based age classes [49]. Unidentified individuals were
counted, but excluded from analyses.
We examined only relationships among adult females,
as most sub-adults and juveniles were not identified
individually. The strength of one individual’sbondwith
another individual over the course of a season was
quantified in terms of their association index. We used
the Simple Ratio Index or SRI [6,35,36,62], which is a
symmetricmeasurethatshowstheproportionoftime
two individuals spent with each other. Before computing
the SRI, we performed data aggregation which consisted
of (a) partitioning the data into day-long sampling inter-
vals; (b) identifying individuals that associated with each
other in a given sampling interval by merging those
groups that shared at least one identified individual; all
individuals within such groups were then, by definition,
‘associated’; and (c) excluding individuals that were
observed only once in a season and only alone. Step (b)
was performed in order to exclude potentially non-inde-
pendent observations of the same group within the
same sampling period. After data aggregation, we com-
pute the association index for each pair of individuals A
and B as SRI = X
AB
/(X
t
-X
n
)whereX
AB
is the number
of times individuals A and B were observed together, X
t
is the total number of observations, and X
n
is the num-
ber of observations in which neither A nor B were
observed [62]. We also compute a measure of uncer-
tainty of the SRI value for each dyad (see Additional file
7: Supplementary Text).
Association data were partitioned according to season.
Months that had a total rainfall higher than the two
year monthly average of 120 cm were designated as
‘wet’months and those that had less were designated as
‘dry’, consistent with the monsoon cycle [59]. May-Sep-
tember constitute the ‘Dry season’and October-Decem-
ber constitute the ‘Wet season’according to this
classification. January-April, with two wet months fol-
lowed by two dry months, were considered a ‘Transi-
tional’period rather than divided into dry and wet
periods since two month periods provided insufficient
data for analysis. We refer to seasons as T1, D1, W1,
D2 and W2 (Table 2).
Data analysis
To reduce variance in our data that arises from differ-
ences in the identities of individuals observed in differ-
ent seasons, we constrain some of the analyses below to
the set of 88 individuals that were observed in all sea-
sons (either more than once or in association with other
individuals). We refer to these individuals as ‘residents’.
To further reduce noise in the data due to low number
of sightings, we constrain some of the analyses to the 51
residentsthatwereobservedatleast30timesthrough-
out the entire study period. We refer to these indivi-
dualsasthe‘core individuals’.Theuncertaintyinthe
estimates of association indices for such individuals is
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generally below 10% for all seasons (see Additional file
1: Figure S1).
Dyadic structure
To test the data against the null hypothesis that associa-
tions within a season are random, we permute the sea-
sonally partitioned datasets so that the number of
sightings for each individual and the distribution of
group sizes within the season are preserved. We use the
‘fill’rather than the ‘swap’method to generate 1000 per-
mutations per season [63-65], with the average SRI
value as the test statistic. To speed up computations, we
partition the dry seasons into two overlapping three-
month periods (May-July and July-September). We use
some of the random datasets generated by this proce-
dure in other analyses.
We examine the stability of associations among pairs
of individuals across seasons in a few different ways.
First, we test for correlations between matched SRI
matrices across pairs of seasons using the Mantel test
[63,66,67]. As not all individuals are seen in all seasons,
by ‘matched’matrices we mean that for each pair of sea-
sons we test correlations only across the subset of indi-
viduals seen in both seasons. We used 10,000
permutations per test, with the Pearson product-
moment correlation coefficient as the test statistic. This
is the most basic way to test whether associations across
seasons deviate from random [68].
Second, we track the SRI for each pair of individuals
as a function of time and assess, using K-means cluster-
ing, whether such temporal SRI trajectories fall into dis-
tinct types. Three temporal patterns are natural to
expect.Ifassociationsarestable,weexpecttoseeaflat
SRI trajectory (type A). If associations are temporary, we
expect to see an SRI trajectory with a single peak at a
particular season (type B). If associations are cyclic, we
expect to see an SRI trajectory with more than one
peak, in corresponding seasons across years (type C). In
order to minimize noise in the data due to rarely
observed individuals, we limit this analysis to the 51
core individuals (see above) that can potentially form
1275 dyads. We exclude those dyads that have never
associated during the study period, yielding 478 dyads
with at least one non-zero SRI value within the study
period. We use the correlation distance between SRI tra-
jectories as the metric for K-means clustering because in
this analysis we are interested in similarities in the shape
of temporal SRI trajectories rather than in their absolute
values. The number of clusters, K, that is most appropri-
ate for the data, is chosen using the Bayesian Informa-
tion Criterion (BIC) where each K-means cluster is
assumed to be generated by a Gaussian distribution
[69]. We perform the K-means clustering procedure 100
times for each value of Kbetween 2 and 15, starting
with a random initial condition, and choose Kat which
the expected BIC is maximized as the optimal K.After
determining the appropriate value of K,weruntheK-
means clustering algorithm 1000 times with different
initial condition and pick the partition of the SRI trajec-
tories into clusters that minimizes the sum of distances
between the SRI trajectories and the cluster centroids to
which they belong. In order to avoid confusion with the
population-level clustering procedure below, K-means
clusters are henceforth characterized by their centroids
and are referred to as ‘typical SRI trajectories’.
To investigate whether an individual’s preferred com-
panionschangeovertimeirrespectiveofthestrengthof
the ties, we determine the top-nassociates of each core
individual within each season. Top-nassociates of a core
individual iin the given season are defined as the ncore
individuals (other than i) who have the highest SRI values
with respect to individual iin that season. Then, in each
season, a core individual i, by definition, allocates n’com-
panion slots’of time to spend with her top-nassociates.
Thus, the total number of companion slots available to
each individual in 5 seasons is 5n. If individual jis pre-
sent in the individual i’stop-nover mseasons (1 ≤m≤
5), we say that associate j’occupies’mcompanion slots
of individual i, or that individual iallocates mof her
companion slots to individual j. We then call individual j
’an m-term associate’of individual i.Ifm= 1, individual j
is a short-term associate of individual i,whileifm=5,
individual jis a long-term associate of individual i,with
obvious gradations in between. We arbitrarily set n=5.
To illustrate these concepts, consider two individuals A
and B. If B’s SRI index with respect to individual A is
ranked 3
rd
,2
nd
,6
th
,5
th
,and9
th
in seasons 1 through 5
respectively, then B is in A’s top-5 associates for 3 out of
5 seasons and therefore occupies 3 companion slots.
Thus, individual B is a 3-term associate of individual A.
Now, if k
i
(m) is the number of individual i’sm-term
associates, then f
i
(m)=k
i
(m)m/5nis the fraction of
companion slots that individual iallocates to all of her
m-term associates (note that
5
m
=1
ki(m)m=5
n
because
each individual has a total of exactly 5ncompanion
slots). Then the average fraction of companion slots that
individuals allocate to their m-term companions is
¯
f(m)= 1
N
N
i
=1
fi(m
)
,whereN= 51 is the total number
of core individuals.
¯
f
indicates the extent to which indi-
viduals prefer to associate with the same companions
over many seasons or to change companions from sea-
son to season.
To quantify individual variation in social behavior, we
count, for each of the 51 core individuals, the number
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of associates that are present in her top-nfor the whole
observation period for n= 5. This number ranges from
0ton=5.
Ego-network structure
We represent the SRI matrices as weighted social-net-
work graphs [37,38], where nodes represent individuals,
edges connect those individuals who were associated
within a season, and edge weights correspond to the SRI
values. An ego-network is a social network that consists
only of the subject, called ‘ego,’and the nodes to which
she is directly connected. For each of the 88 residents,
wecomputefiveego-networkmeasures with intuitive
biological interpretations: Size, Ties, Pairs, Density, and
2-Step Reach (defined in Table 5). We then compute
the corresponding ego-network statistics, i.e. the average
values of ego-network measures over all residents. As
ego-network measures for different individuals are non-
independent, we test for differences in ego-network sta-
tistics between seasons using a bootstrap procedure in
which association data for each season are re-sampled
1000 times with replacement [39].
Population structure
In order to investigate how the social network structure
of the whole population changes over time, we construct
‘network structure curves’(Figure 7) for each season
using the following procedure. First, using the full SRI
matrix for each season, we construct the social network
graph for the whole population (i.e., we include non-
resident individuals in this analysis). We then identify
social clusters within the network using the Girvan-
Newman algorithm for community detection [70]. This
algorithm recursively fragments the network into sub-
networks by successively removing the edges with the
highest between-ness [37]. For each resulting subdivi-
sion of the network, the so-called ‘modularity quotient,’
Q, is computed. The modularity quotient takes values
between 0 and 1, where 0 implies that the number of
ties within a cluster does not exceed a random expecta-
tion, and values above 0.3 indicate potentially meaning-
ful subdivisions [71-74]. We label the maximum
modularity for a given social network as Q
max
and take
the partition or partitions that yield this maximum value
to be the most appropriate way of subdividing the net-
work. The term ‘cluster’refers then to the set of indivi-
duals belonging to the same subnetwork in an optimal
subdivision.
The original Girvan-Newman algorithm was designed
to find community structure in unweighted networks.
To accounts for edge weights, we add one more step.
We apply the Girvan-Newman procedure to a social
network that consists only of ties with strength above a
particular threshold, and record the number of clusters
in the resulting network (Figure 7). If multiple subdivi-
sions of the network at a given threshold yield identical
Q
max
values, we record the average number or clusters
(e.g. if either 14 or 15 clusters have an equivalent Q
max
at a threshold of 0.1, we record 14.5 clusters). We per-
form this procedure iteratively for different SRI thresh-
olds, incrementing by 0.02: 0, 0.02, 0.04, ..., 1. We then
plot the average number of clusters against the SRI
threshold. We call the resulting plot the ‘network struc-
ture curve,’as it shows the structure of the network at a
glance, being a lower-dimensionalvisualrepresentation
than social network graphs (Figure 7).
In order to test whether network structure curves
have significantly different shapes in different seasons
we modify the method used by Wittemyer et al. [6]. For
each SRI threshold value, we compare the distributions
of increments of the network structure curve within a
window wbefore and after this value, using the Mann-
Whitney test. We then find points in the curve where
these distributions are different from each other at the
significance level 0.05. The points with significant P-
values are consistent when we vary the size of window
wbetween 0.1 and 0.3 (see Additional file 8: Figure S7
and Additional file 9: Figure S8).
Implementation and ethical statement
Permutations of associations, observed group sizes, and
corresponding significance tests within and across time
partitions were implemented in the OCaml program-
ming language; code is available upon request. Network
visualizations were generated in NetDraw using a graph-
theoretic layout with node repulsion [38]. All other sta-
tistical procedures and analyses were performed on
Matlab v. 7.0, and R v. 2.7. This work was carried out in
compliance with requirements of the Institutional Ani-
mal Care and Use Committee of the University of Penn-
sylvania, protocol number 801295.
Additional material
Additional File 1: Figure_S1.pdf. Association index matrices and
matrices of uncertainty by season. SRI matrices (left column) and the
matrices of uncertainty measure based on expression [S1] in the
supplementary text (right column). See additional File 7 for
supplementary text. x- and y- axes represent individuals, ordered by the
total number of sightings across the whole study period. Red squares
show the individuals with 30 or more sightings.
Additional File 2: Figure_S2.pdf. Temporal SRI trajectories of type A.
Type A trajectories are relationships that are maintained at SRI values
above 0.3 in all seasons, and hence exemplify stable associations.
Additional File 3: Figure_S3.pdf. Determining the optimal number
of clusters for clustering temporal SRI trajectories. Bayesian
Information Criterion (BIC) as a function of the number of clusters, K, into
which the temporal SRI trajectories are partitioned by the K-means
algorithm. Light gray curves represent 100 K-means clustering runs with
random initial conditions. Thick black curve represents the mean over
de Silva et al.BMC Ecology 2011, 11:17
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Page 13 of 15
these runs. The mean BIC curve peaks at K = 6 indicating that there are
6 typical shapes of temporal SRI trajectories.
Additional File 4: Figure_S4.pdf. Trade-off between the number of
associates and the strength of association by season. Each point
shows the number of associates of a core individual (abscissa) and the
average non-zero SRI value for that individual (ordinate). Data is
displayed for each season separately (averages across seasons are shown
in Figure 4 in the main text).
Additional File 5: Figure_S5.pdf. Girvan-Newman clusters for season
T1 at various SRI thresholds. This figure is analogous to the schematic
shown in Figure 7 in the main text. Corresponding network structure
curves are shown in Figure 8 of the main text. Individuals that do not
have ties at or above the threshold value are removed for the sake of
clarity. Arrows indicate groups enlarged in the last two panels. Cluster
colors correspond to Figure 5 in the main text. Maximum separation of
groups occurs in this season at SRI values above 0.4. Beyond the SRI
threshold of 0.6 most of these clusters also degenerate.
Additional File 6: Figure_S6.pdf. Social network for randomized T1
data. An example of a social network generated by the randomization
procedure described in the methods. The network is relatively
homogenous, without distinct clusters.
Additional File 7: Supplementary_Text.doc. Description of the
procedure to estimate uncertainty in the estimate of an association
index.
Additional File 8: Figure_S7.pdf. Maximum modularity Q
max
as a
function of the SRI threshold. Data for each of the seasonal data sets
correspond to the network structure curves shown in Figure 8 in the
main text (see Methods in the main text for details).
Additional File 9: Figure_S8.pdf. Detecting differences in the shape
of network structure curves.P-value for the Mann-Whitney test of the
comparison between the distribution of the network structure curve
increments within window wbefore each SRI threshold with the
corresponding distribution within the window wafter that threshold are
shown. Different colors correspond to different window sizes, as
indicated. Dashed line shows the critical P-value of 0.05.
Acknowledgements
SdS wishes to thank Drs. Dorothy Cheney, Robert Seyfarth, Marc Schmidt,
David White, and Arthur Dunham for comments on the manuscript and
research design. The authors thank two anonymous referees for their
constructive comments on the manuscript, Dr. Devaka Weerakoon for advice
in conducting this study, and the Department of Wildlife Conservation, Sri
Lanka for granting permission to work in Uda Walawe National Park. This
research was partially supported by funding from the Binns-Williams Fund in
the University of Pennsylvania graduate group in Ecology and Evolution, a
Doctoral Dissertation Completion grant from the University of Pennsylvania,
an Integrative Graduate Education and Research Traineeship grant from the
National Science Foundation (NSF-IGERT 0504487), and an Animal Behavior
Society student research award to SdS as well as a grant from the US Fish &
Wildlife Wildlife Asian Elephant Conservation Fund (grant no. 98210-7-G167)
to SdS and ADGR.
Author details
1
Department of Biology, University of Pennsylvania, Philadelphia, PA 19104,
USA.
2
Uda Walawe Elephant Research Project, 1/657 Thanamalwila Road,
Uda Walawe, Sri Lanka.
3
Faculty of Natural Sciences, Open University of Sri
Lanka, Nawala Road, Nugegoda, Sri Lanka.
4
Department of Organismic and
Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA.
5
Elephant, Forest and Environment Conservation Trust, 215 A 3/7 Park Road,
Colombo 5, Sri Lanka.
Authors’contributions
SdS conceived of the study, supervised fieldwork, collected field data,
developed analytical methods, conducted data analyses, and wrote the
paper. ADGR participated in planning, running the study, collecting and
entering field data. SK developed and implemented analytical methods,
performed statistical data analyses, and wrote the manuscript. All authors
read and approved the final manuscript.
Received: 23 March 2011 Accepted: 27 July 2011
Published: 27 July 2011
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doi:10.1186/1472-6785-11-17
Cite this article as: de Silva et al.: The dynamics of social networks
among female Asian elephants. BMC Ecology 2011 11:17.
de Silva et al.BMC Ecology 2011, 11:17
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