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Simulated poaching affects global connectivity and efficiency in social networks of African savanna elephants-An exemplar of how human disturbance impacts group-living species

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Simulated poaching affects global connectivity and efficiency in social networks of African savanna elephants-An exemplar of how human disturbance impacts group-living species

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Selective harvest, such as poaching, impacts group-living animals directly through mortality of individuals with desirable traits, and indirectly by altering the structure of their social networks. Understanding the relationship between disturbance-induced, structural network changes and group performance in wild animals remains an outstanding problem. To address this problem, we evaluated the immediate effect of disturbance on group sociality in African savanna elephants-an example, group-living species threatened by poaching. Drawing on static association data from ten free-ranging groups, we constructed one empirically based, population-wide network and 100 virtual networks; performed a series of experiments 'poaching' the oldest, socially central or random individuals; and quantified the immediate change in the theoretical indices of network connectivity and efficiency of social diffusion. Although the social networks never broke down, targeted elimination of the socially central conspecifics, regardless of age, decreased network connectivity and efficiency. These findings hint at the need to further study resilience by modeling network reorganization and interaction-mediated socioecological learning, empirical data permitting. The main contribution of our work is in quantifying connectivity together with global efficiency in multiple social networks that feature the sociodemographic diversity likely found in wild elephant populations. The basic design of our simulation makes it adaptable for hypothesis testing about the consequences of anthropogenic disturbance or lethal management on social interactions in a variety of group-living species with limited, real-world data.
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RESEARCH ARTICLE
Simulated poaching affects global connectivity
and efficiency in social networks of African
savanna elephants—An exemplar of how
human disturbance impacts group-living
species
Maggie WiśniewskaID
1
*, Ivan Puga-GonzalezID
2,3
, Phyllis Lee
4,5
, Cynthia MossID
4
,
Gareth Russell
1
, Simon GarnierID
1
, Ce
´dric SueurID
6,7
1Department of Biological Sciences, New Jersey Institute of Technology, Newark, New Jersey, United
States of America, 2Institutt for global utvikling og samfunnsplanlegging, Universitetet i Agder, Kristiansand,
Norway, 3Center for Modeling Social Systems at NORCE, Kristiansand, Norway, 4Amboseli Trust for
Elephants, Nairobi, Kenya, 5Faculty of Natural Science, University of Stirling, Stirling, United Kingdom,
6Universite
´de Strasbourg, CNRS, IPHC, UMR 7178, Strasbourg, France, 7Institut Universitaire de France,
Paris, France
*mw298@njit.edu
Abstract
Selective harvest, such as poaching, impacts group-living animals directly through mortality
of individuals with desirable traits, and indirectly by altering the structure of their social net-
works. Understanding the relationship between disturbance-induced, structural network
changes and group performance in wild animals remains an outstanding problem. To
address this problem, we evaluated the immediate effect of disturbance on group sociality in
African savanna elephants—an example, group-living species threatened by poaching.
Drawing on static association data from ten free-ranging groups, we constructed one empiri-
cally based, population-wide network and 100 virtual networks; performed a series of experi-
ments ‘poaching’ the oldest, socially central or random individuals; and quantified the
immediate change in the theoretical indices of network connectivity and efficiency of social
diffusion. Although the social networks never broke down, targeted elimination of the
socially central conspecifics, regardless of age, decreased network connectivity and effi-
ciency. These findings hint at the need to further study resilience by modeling network reor-
ganization and interaction-mediated socioecological learning, empirical data permitting. The
main contribution of our work is in quantifying connectivity together with global efficiency in
multiple social networks that feature the sociodemographic diversity likely found in wild ele-
phant populations. The basic design of our simulation makes it adaptable for hypothesis
testing about the consequences of anthropogenic disturbance or lethal management on
social interactions in a variety of group-living species with limited, real-world data.
PLOS COMPUTATIONAL BIOLOGY
PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1009792 January 18, 2022 1 / 23
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OPEN ACCESS
Citation: Wiśniewska M, Puga-Gonzalez I, Lee P,
Moss C, Russell G, Garnier S, et al. (2022)
Simulated poaching affects global connectivity and
efficiency in social networks of African savanna
elephants—An exemplar of how human
disturbance impacts group-living species. PLoS
Comput Biol 18(1): e1009792. https://doi.org/
10.1371/journal.pcbi.1009792
Editor: Yamir Moreno, University of Zaragoza:
Universidad de Zaragoza, SPAIN
Received: April 5, 2021
Accepted: December 23, 2021
Published: January 18, 2022
Peer Review History: PLOS recognizes the
benefits of transparency in the peer review
process; therefore, we enable the publication of
all of the content of peer review and author
responses alongside final, published articles. The
editorial history of this article is available here:
https://doi.org/10.1371/journal.pcbi.1009792
Copyright: ©2022 Wiśniewska et al. This is an
open access article distributed under the terms of
the Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Author summary
We consider the immediate response of animal groups to human disturbance by using the
African savanna elephant as an example of a group-living species threatened by poaching.
Previous research in one elephant population showed that poaching-induced mortality
reduced social interaction among distantly related elephants, but not among close kin.
Whether this type of resilience indicates that affected populations operate similarly before
and after poaching is an outstanding problem. Understanding this is important because
poaching often targets the largest or most socially and ecologically experienced group
members. Drawing on empirical association data, we simulated poaching in one empiri-
cally based and 100 virtual elephant populations and eliminated the most senior or socia-
ble members. Targeted poaching of sociable conspecifics was more impactful. Although it
did not lead to population breakdown, it hampered theoretical features of intraspecific
associations that in other systems have been linked with social cohesion and the efficiency
of transferring socially valuable information. Our findings suggest that further inquiry
into the relationship between resilience to poaching and group performance is warranted.
In addition, our simulation approach offers a generalizable basis for hypothesis testing in
other social species, wild or captive, subject to exploitation by humans.
Introduction
In group-living animals, from insects to mammals [1,2], interactions among conspecifics with
diverse social roles [35] impact individual survival [69], reproductive success [1012] and
adaptive behaviors [1316]. In species with complex organization characterized by flexible
aggregates of stable social units [1719], the loss of influential group members through natural
or anthropogenic causes can be detrimental to surviving conspecifics [2022] and to entire
populations [23,24]. Unlike natural phenomena, such as fire [25,26], harvest is intrinsically
nonrandom [2729]. For instance, poachers profiting from pet trade prefer to capture imma-
ture individuals as the most economically desirable commodity [30], eliminating gregarious
‘brokers’ who engage in frequent or diverse social interactions [31,32]. As another example,
trophy hunters target individuals with prominent features, such as elephants with big tusks
[33,34], killing the oldest and socioecologically experienced conspecifics [3539].
Animal social network analysis, which quantifies intraspecific relationships as ‘networks of
nonrandomly linked nodes’, is useful in demonstrating how elimination of individuals with
key social roles impacts closely knit animal groups [40,41]. For example, node deletion experi-
ments manipulating empirical association data have revealed that while some disturbed groups
fracture into multiple components [42,43] others stay connected [44]. In biological popula-
tions, elimination of impactful group members through harvest, is much less destabilizing to
persistence of larger social groups compared to small ones [20]. Our current understanding of
whether the relationships in remaining groups, or group fragments, operate as prior to distur-
bance is based on a small number of studies. In an instance of captive zebra finches, group for-
aging ability decreased following repeated social disturbance [45]. In simulated primate
groups, network disturbance led to a decrease in its global connectivity and the efficiency of
social diffusion indices, but did not lead to group fragmentation [46]. These indices depend on
network structure; are based on an assumption that transmissible currency, such as informa-
tion, diffuses through network links [47]; and have been related to cohesion, the transfer of
social currency and robustness to loss of influential conspecifics [4850]. In light of the anthro-
pogenic impact on animal communities [5154], evaluating the relationship between post-
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Simulated poaching affects social networks in African savanna elephants
PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1009792 January 18, 2022 2 / 23
Data Availability Statement: Data and code are
available on the Dryad repository under https://doi.
org/10.5061/dryad.g4f4qrfrz.
Funding: M.W. received funding for this project
through the 2018-2019 STEM Chateaubriand
Fellowship Program. The website for this award is
https://www.chateaubriand-fellowship.org/. The
funders had no role in study design, data collection
and analysis, decision to publish, or preparation of
the manuscript.
Competing interests: The authors have declared
that no competing interests exist.
disturbance social structure and resilience vis-à-vis group performance in natural animal sys-
tems is becoming increasingly important [20,55].
To explore this relationship, we considered the African savanna elephant (Loxodonta afri-
cana)—a group-living species threatened by poaching [5658]. Elephant social organization
consists of several tiers, ranging from transitional clans and bonded groups of distant and
intermediate kin, to matrilineal core units of adults and their immature offspring [59]; or flexi-
ble groups of postdispersal males of varying ages and kinship [36]. While immature elephants
frequently engage in affiliative interactions [60,61], mature individuals are not only well
socially connected but also more experienced about resource distribution and phenology
[62,63], and about social dynamics [6466]. The interactions among individuals with diverse
social roles across social tiers manifests as fission-fusion dynamics in response to changing
sociophysical landscape [19,67]. Poaching—which during the militarized wave of the past
decade eliminated large subsets of populations including mature and immature elephants [68]
—impacts demography [69], resource acquisition [70,71] population genetics [72] and various
social behaviors [73,74] in targeted populations.
Evidence from social network analysis using data spanning periods of low and high poaching
in one free-ranging population revealed that the composition and association patterns within
matrilines were conserved among close but not distant surviving kin. This outcome suggests
clan-level impact of poaching on network structure and resilience, with little detrimental effect
at the bonded group- or core unit-levels [75]. Whether changes in network structure in ele-
phants relate to group functionality is difficult to test directly. However, quantifying network
connectivity together with global efficiency while simulating poaching may shed new light on
the theoretical capacity for dissemination of social currency and the limitation to social resil-
ience in disturbed populations. These insights may eventually inform our understanding about
the mechanisms of group performance, and means of mitigating human-elephant conflict
[76,77] to conserve this economically important but endangered, keystone species [78,79].
We characterized the immediate effect of eliminating the most influential individuals on
the global structure of simulated, social networks. We used a static set of empirical association
data on one free-ranging elephant population from Amboseli National Park (NP) in Kenya
[80] because continuous data featuring network reorganization after poaching, necessary to
parametrize time-varying models, do not yet exist for wild elephants. Initially, we assembled
one, empirically based social network using the Amboseli dataset and conducted a series of
‘poaching’ experiments by either incrementally removing 1) the oldest elephants as presum-
ably the most experienced and prone to poaching, or topologically central individuals with
high betweenness centrality (often referred to as social hubs) as the most sociable network
members [81,82]; or 2) by removing individuals randomly [43,83]. To quantify network-wide
structural changes, we evaluated four theoretical indices: two of which are used to diagnose
network-wide connectivity (i.e., clustering coefficient and modularity, dependent on local
neighborliness or global partitioning, respectively); and the other two are commonly used to
express the efficiency of social diffusion (i.e., diameter and global efficiency, based on the dis-
tance or pervasiveness of diffusion, respectively) [49]. To set these results in the context of a
large-scale variation in demography and social interactions found in real elephant populations,
we generated 100 distinct, virtual populations modeled on demographic trends in empirical
data. To simulate social network formation in these populations, we built a spatiotemporally
nonexplicit, individual-based model with rules informed by empirical associations [59,80].
The steps of assigning social influence, conducting deletion experiments and quantifying dele-
tion effects were as mentioned earlier.
We hypothesized that elimination of the most influential individuals, defined according to
their age category or network position (i.e., betweenness centrality) would affect global
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network connectedness and efficiency. Specifically, we predicted that relative to random dele-
tions, targeted removal of the most central or mature individuals would result in a decrease in
global clustering coefficient and efficiency, and an increase in the diameter and modularity.
We also anticipated a worsening in these outcomes as a function of the proportion of deleted
individuals, resulting in an eventual network breakdown. This set of findings would be an indi-
cation of increased subgrouping at the population level, fewer interactions with intermediately
and distantly related social partners and fewer pathways for timely and fault-tolerant transfer
of social currency.
Although it was not parameterized to reflect the rate of ‘poaching’ events in absolute time
and cannot be used to inform response to poaching after network reorganization, our work
offers a novel perspective on the immediate response to disturbance in a large number of
sociodemographically diverse populations with experience of poaching-like stress. Keeping in
mind the limitations of our approach, we interpret our findings in the context of a common
behavioral repertoire in wild elephant populations and offer insights about how our findings
may help view natural populations subject to poaching. Finally, we consider the utility of our
simulation approach as a generalizable tool for testing hypotheses about the disturbance of
social dynamics in other species that facilitate ecosystem functioning or impact human welfare
[84,85].
Materials and methods
We performed a series of deletion experiments after constructing one empirically based, social
network derived from association data in a free-ranging elephant population; and 100 virtual
networks mimicking the empirically based network. Details of these experiments and underly-
ing assumptions are described below.
To gather baseline information about demography and social interactions characterizing
elephant sociality, we considered two association datasets from Amboseli NP originally pub-
lished elsewhere [80]. We assume that these datasets, collected at vantage points where differ-
ent social units converge, capture a range of social processes including events that required
group cohesion and transfer of information (e.g., conflict avoidance in a multigroup gathering
at a waterhole requires learning and recall about which conspecifics to affiliate with and whom
to avoid [86]).
Inferring population-wide social interactions and assembling one social
network based on empirical association data
Originally, the authors inferred proximity-based associations at two social tiers: 1) between
pairs of individuals within 10 core units or groups (within core group—WCG); and 2) between
64 core groups (between core group–BCG). During each WCG sampling event, the individuals
were considered to be in the same group and therefore associating when no more than 100 m
separated the most distant member from her nearest neighbor [80]. During the BCG data sam-
pling, interacting groups were defined as aggregations of elephants where no single member
was farther from her nearest neighbor than the visually estimated diameter of the core group
at its widest point. Each core group was defined on the basis of its anticipated membership
and activity synchrony and treated as a single social entity, or a node, without between-indi-
vidual associations being recorded.
Our goal, unlike in the original study, was to examine social dynamics between individuals
from different groups, for instance, individuals iG and aB from core groups G and B respec-
tively. To derive a proxy of associations occurring between individuals from different core
groups, we assembled a dyadic association matrix by combining the WCG data and a subset of
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the BCG data [87]. Although the original BCG dataset included 64 groups, we only focused on
10 groups for which both WCG and BCG data were available (labeled AA, CB, DB, EA, EB,
FB, JAYA, GB, OA, and PC). To reflect the typical, multi-tier structure of an elephant society
[59], we aggregated the 10 core groups into eight bond groups [i.e., B1 (core group AA, includ-
ing 10 individuals); B2 (FB, 6); B3 (EA, 9 and EB, 10); B4 (DB, 4); B5 (CB, 6 and OA, 10); B6
(GB, 11); B7 (PC, 9); and B8 (JAYA, 8)] and three clan groups [i.e., K1 (bond groups B1, B2,
B3 and B4); K2 (B5, B6 and B7); and K3 (B8)] using information about genetically determined
relatedness indices (which can be found in the original publication) and long-term, behavioral
associations inferred by the authors [80]. For the purpose of this paper all members of the core
group were considered as close kin. The members of the same bond or clan were considered as
intermediately and distantly related kin respectively.
To represent associations within each core group in the population, we used the WCG
association data and calculated the dyadic association indices (AIs) according to equation 1:
AI
iG, jG
= x
iG, jG
/ (n
G
—d
iG, jG
). In this equation, x
iG, jG
is the number of times individuals iG
and jG were seen together in their core group G; d
iG, jG
is the number of times neither individ-
ual was seen; and n
G
is the total number of times group G was observed [87].
Because group composition per each WCG sampling event was not reported in the original
publication, we were unable to directly account for the dependence of the associations between
individuals i and j as a function of their respective associations with individual k. To overcome
this data limitation, we derived a proxy of individual gregariousness by calculating a fraction
of all sightings when an individual i from core group G was seen interacting with its core
group conspecifics j and/or k. To that end, we used equation 2: f
iG
=(AI
iG, jG
, AI
iG, kG
) / # of
dyads. In this equation, f
iG
falls in the interval {0,1}. This process was repeated for every indi-
vidual in its core group (e.g., f
iG
, f
kG
, f
aB
, f
cB
, etc.) and served as a basis to next estimate social
dynamics at the population level which we achieved using equations 3 and 4 detailed below.
To calculate the fraction of all sightings when core group G was seen with group B, we used
equation 3: f
G,B
= n
G,B
/ (n
G
+ n
B
+ n
G,B
). Here, n
G,B
indicates the number of times groups G
and B were seen together; n
G
indicates the number of times group G was seen without group
B; and n
B
indicates the number of times group B was seen without group G. Thus, the denomi-
nator is the total number of times groups G and B were seen individually or together. This pro-
cess was repeated for every pair of groups in the population.
Next, to estimate a symmetric and weighted proxy matrix of dyadic AIs between any pair of
individuals from two different core groups, for instance, individuals iG and aB from groups G
and B respectively, we used equation 4: p(iG, aB) = f
iG
×f
aB
×f
G,B
.
Finally, we used the resulting matrix of AIs to construct a population-wide social network
and used it in deletion experiments described in the following sections.
Quantifying social influence in empirically based social network
To identify influential network members serving as social centers or intermediaries of social
interactions [88], we quantified each individual’s betweenness and degree centrality scores
[82]. Given that these metrics were highly correlated—a findings that is unsurprising and
could be addressed by finding ‘cutpoint potential’ identifying highly important network mem-
bers, we used betweenness centrality going forward because it is particularly suitable for ques-
tions about global connectivity and efficiency of social diffusion in a society with fission-fusion
dynamics [50,89,90]. From this point onward we often refer to individuals with high between-
ness centrality scores as the most central individual. To include age as a form of social influ-
ence due to presumed disparity in socioecological experience between mature versus
immature individuals, we considered four age categories. They included young adults, prime
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Simulated poaching affects social networks in African savanna elephants
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adults, mature adults and the matriarchs (or the oldest or most dominant females in the core
group) [91]. Betweenness centrality and age category were not correlated. Their definitions are
detailed in Table 1.
Conducting deletions using empirically based social network
To assess how disturbance affects global structure in the empirically based, elephant social net-
work, and to determine the level of stress that would bring about network fragmentation, we
carried out a sequence of targeted deletions by selecting 20 percent of the oldest or most cen-
tral network members (two ‘deletion metric’) and deleting them in a random sequence in
increments of four percent. By eliminating up to 20 percent of members, we attempted to
Table 1. Definitions of social influence metrics (i.e., betweenness centrality or age category) network level indices (weighted (W) diameter, global efficiency and
modularity, as well as unweighted clustering coefficient) along with formulas we used to calculate them; and the expected outcomes per deletion proportion ranging
from 0 to 0.2 in increments of 0.04. and type (i.e., targeted or random). The impact of deletions on each network level index was measured after incremental deletion of
the most socially influential individuals while targeting individuals with high betweennesscentrality or age category, or when individuals were deleted at random. Our
expectations are expressed with a greater- or less-than sign (>or <). For instance, we predicted that relative to random deletion, targeted deletion of seniors would result
in lower clustering coefficient values; and that higher deletion proportions would also result in lower clustering coefficient values. (1). Our procedure assumes that the
higher the weight of a link between two individuals (or nodes), the shorter the distance between them. To reflect this relationship, we define the length of a link as the
inverse of its weight. Using the inverse of the weights of the links connecting all pairs of nodes, we calculated all shortest paths in the network [50,97]. (2). Social transfer is
a theoretical expression of the efficiency of passing of transmissible currency, such as information, assumed to be diffusing across network links [47].
Individual level deletion
metric
Definition
Betweenness centrality The number of shortest paths1 passing through an individua (or a node) l. High value indicates high social interconnectedness and thus
important theoretical role that a node has in the exchange of social currency, such as information [98,99].
• betweenness centrality = # of shortest paths
(1)
through a node
Age category A segment of the population within a specified range of ages, including: 1) young adults (individuals >12 and <20 years old); 2) prime
adults (20–35); 3) mature adults (>35); 4) the matriarchs (the oldest or most dominant females in the core group)) used when categorical
consideration of age is desired, or when data on absolute age are not available; in the empirically based population the age ranges were
based on year of birth; in the virtual populations, the age range distribution was modeled to parallel the empirical distribution of ages
[80,91].
Network level index Predictions
Clustering coefficient The ration between the number of closed triplets and the total theoretical number of open and closed triplets, which
can be thought of as the total possible number of links in the network (uses transitivity function in igraph R package).
A closed triplet is a set of links between three nodes connected by three links, and an open triplet is a set of links
between three nodes connected by two links. High values have been associated with high group cohesion, little
subgrouping, and resilience against disturbance-induced breakdown [41,50].
• transitivity = total # of closed triplets in a network / # of open and closed triplets in a network
deletion
proportion:
0>0.4
deletion type:
random >targeted
Diameter W The path with the maximum weight among the shortest paths
(1)
across all dyads. High values have been associated
with low degree of cohesion potentially impeding rapid transmission of information [41,43,82].
• diameter weighted = max (shortest path)
0<0.4
random <targeted
Global efficiency W The average social transfer
(2)
over all pairs of nodes. High values have been associated with high probability of social
diffusion in a group and thus important theoretical role in efficient transmission of information [97,100]. To
calculate this this index, we first calculate the distance between nodes i and j as the sum of the link lengths over the
shortest path connecting them. Next, we calculate the efficiency in social transfer between nodes i and j which we
assume to be inversely proportional to the shortest path length. When there is no path linking i and j, the distance
between them = + 1, and the efficiency in the social transfer between them = 0.
• n = # of nodes in a network
• distance per dyad ij = (the link lengths over the shortest path
(1)
between nodes i and j)
• efficiency of social transfer per dyad ij = 1 / distance per dyad ij
• global efficiency weighted = (1 / (n (n—1))(efficiency of social transfer per dyad ij)
0>0.4
random >targeted
Modularity W The density of links within modules in a weighted network relative to the density of links between modules (using
cluster leading eigenvector function in igraph R package). High value indicates low group cohesion with cohesive
subgroups, and susceptibility to breakdown after disturbance [101103]. The formula of modularity below applies to
a case where all nodes in a network belong to the same module. For a case when some nodes in a network belong to
module A and others to module B is detailed in the following resources [102].
• modularity = (# of links over all dyad in a weighted network—expected # of links over all dyad in a weighted
network where the links are placed randomly but the # of links per a node is constant)
0<0.4
random <targeted
https://doi.org/10.1371/journal.pcbi.1009792.t001
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mimic the varying degree of poaching stress likely imposed on wild populations [92]. In addi-
tion, we were motivated by evidence that many synthetic, biological systems [93] are organized
around several, highly connected nodes, important for network development and stability
[94]. We compared the effect of targeted deletions against a null model (two ‘deletion types’)
by also deleting 20 percent of network members randomly in increments of four percent (five
‘deletion proportions’). Each deletion proportion was repeated 100 times per both deletion
types (i.e., targeted and random) and both metrics (i.e., betweenness centrality and age cate-
gory) [46].
After each deletion proportion, in each deletion type and metric, we quantified four theo-
retical indices diagnostic of social network connectivity and efficiency of social diffusion. These
indices included the clustering coefficient and weighted forms of the diameter, global efficiency
and modularity. Weighted variants of these indices are informative when individuals associate
differently with different conspecifics, which has been reported in elephants (e.g., young adults
may associate more frequently with close rather than distant kin) [65]. Given the importance of
fission-fusion dynamics in elephant populations occurring through interactions among imme-
diate and distant kin [95], we quantified the clustering coefficient and weighted modularity
before and after removal of socially influential or oldest elephants. By characterizing the number
and weight of links within (i.e., clustering coefficient) and across (i.e., modularity) disparate
subgroups or modules, we simultaneously compared the change in network connectivity at the
social unit and population levels. By measuring weighted diameter and global efficiency, we
aimed to illustrate the potential rapidness (i.e., diameter) and pervasiveness (i.e., global effi-
ciency) of social diffusion. Evaluating these indices in the context of the empirically based, social
network allowed us to identify if social interactions with capacity for timely diffusion of social
currency change after poaching-like disturbance. The definitions of these indices and our pre-
dictions regarding their change after deletions are detailed in Table 1 [50].
We assessed the mean value of each index as a function of each deletion condition (e.g., tar-
geted deletion of four percent of the most mature conspecifics). Because each deletion condi-
tion was repeated 100 times—a process theoretically unlimited in its sample size, instead of
using a comparison of means informed by a biological distribution, we quantified the differ-
ence in the effect size between means of targeted and random deletions using Hedge’s g test
[96]. We expressed the differences in the mean values between all corresponding conditions
using the 95 percent confidence intervals.
Virtual data—characterizing composition and association properties in
virtual populations
To evaluate the impact of poaching-like disturbance on global network structure in the context
of sociodemographic diversity likely seen in wild elephant communities, we generated 100 virtual
populations. These populations were modeled on the composition of the 10 core groups
described before [80]. Each virtual population consisted of females in the previously detailed age
categories (Table 1) and four social tiers, namely core (or closely related kin), bond (or interme-
diately related kin), clan (or distantly related kin) and non-kin clan groups (S1 Table) [59].
Evaluation of the AI ranges in the empirically based network according to age category and
kinship revealed the following patterns. 1) Individuals of any age category were most likely to
associate within their core group. They were also more likely to associate with kin from the
same bond group than from other bond groups; then with individuals from their clan; and
lastly with non-kin [104]. 2) In a core group, individuals of any age category were slightly
more likely to associate with conspecifics from older age categories (Fig 1A). Since these pat-
terns are generally consistent with the dynamics described in many elephant populations
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(genetic relatedness—[104,105]; multilevel structure—[80]; spatial proximity—[65,106]), we
used the AI ranges seen in the empirically based network as a model for social network assem-
bly in the virtual populations (Fig 1B).
Simulating virtual social networks
To simulate social networks in the 100 virtual populations described in the previous section,
we used a spatiotemporally nonexplicit, individual-based model at two levels—between dyads
Fig 1. The distribution of association indices in (A) the empirically based versus (B) virtual populations, as a function of age
category and kinship of the associating individuals. Age categories are abbreviated using the following symbols: Y—young
adult; P—prime adult; M—mature adult; G–the matriarch. During each random deletion, the same proportion of individuals
as in targeted deletions was removed randomly. After every deletion proportion, we recalculated the following network level
indices: clustering coefficient, as well as weighted diameter, global efficiency and modularity (Table 1). As in the empirically
based portion of our study, we used the Hedge’s g test to quantify the difference in the effect size between the means of all
network indices across 1) the deletion proportion spectrum, 2) deletion type and 3) deletion metric [96].
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within the same core group and between core groups. The probability of association between
two individuals—according to their kinship and age category, were drawn from a triangular
distribution (Fig 1B).
We used a triangular distribution because we do not know the true distribution of AIs in
the empirical population. Given the per age category and kinship AI minima and maxima
observed in empirically based population, we set the lower and upper bounds of the triangle as
the lowest and highest probabilities of association observed and the peak equal to the median
value. At each time step, each dyad in the population had the opportunity to associate. Once
all dyadic associations had been determined, the total number of observed associations per
each dyad was updated and the time step was terminated (Fig 2).
Because the empirical association data were collected over four years, we did not know how
many interactions would be required to simulated networks reflecting the structure of empiri-
cally based network. For that reason, we used the time step approach by observing how the
global structure of simulated social networks changed at different stages of the development,
and when it would reach a plateau. To do so, we stopped the simulation at 100, 200, 300, 400
or 500 time steps (S1 Fig). Finally, we noted the age category and quantified betweenness of
every individual in each of the 500 time step virtual networks.
To compare their structure, we present graphs of the empirically based network and an
example of a similarly sized virtual network according to age category and betweenness cen-
trality of all network members (Fig 3). They appear similar in age category makeup and WGS
associations. The empirically based network has fewer BCG associations than the virtual net-
work. In addition, compared to the virtual networks, the empirically based network had the
nodes with high betweenness centrality concentrated within specific core units.
Conducting deletions using virtual social networks
To measure if the disappearance of the most socially influential individuals changed the con-
nectivity and efficiency in the 500 time step virtual networks, we performed a series of targeted
and random deletions. Individuals were deleted in four percent increments, ranging from zero
to 20 percent. In targeted deletions, 20 percent of individuals selected for removal had the
highest betweenness centrality or belonged to the oldest age category. During each random
deletion, the same proportion of individuals as in the targeted deletions was removed ran-
domly. After every deletion proportion, we recalculated the following network level indices:
clustering coefficient, as well as weighted diameter, global efficiency and modularity (Table 1).
Unlike in the empirically based network derived using association indices in the [0,1] range, in
the virtual networks, constrained by the simulation design, we used the number of interactions
as expression of associations. This numeric difference is the reason for the dissimilar range
between the empirically based and virtual outputs for the diameter weighted index. However,
given that the AI indices of the empirically based network and virtual networks follow within
the same range, we also expect that the resulting diameter weighted values from both network
types can be compared qualitatively (Fig 2). As previously, we used the Hedge’s g test to quan-
tify the difference in the effect size between the means of all network indices across 1) the dele-
tion proportion spectrum, 2) deletion type and 3) deletion metric [96].
Motivated by a preliminary assessment indicating a high degree of resilience to fragmenta-
tion after the deletion of the oldest or most central members, we explored if virtual networks
would break down when subject to prior elimination of relatively weak associations [107].
Here we wanted to determine if weak associations, likely formed among individuals with high
betweenness centrality, could also be explained by age category. During this process, we
manipulated the 500 time steps networks by filtering out the ‘weakest links.’ To do so, we
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divided the value of each link in the association matrix by the highest link value and eliminated
the links with values up to three percent of the highest link in increments of one percent. After
each elimination without replacement, we carried out the deletions and quantification of the
outcomes as described above. This perspective is relevant to understanding various forms of
poaching. Removal of weak links resembles indiscriminate poaching events when, instead of
seniors with prominent tusks, less conspicuous individuals in younger age classes are also
eliminated, potentially resulting in lover group cohesion. This form of poaching, by renegade
militias seeking profit at all costs, was relatively common during the most recent phase of
poaching (ca. 2009–2016) [68,108,109].
Software used
The social network quantification and analysis of both the empirically based and virtual data
were performed using the R statistical software, version 3.2. (R Core Team 2017). Visualization
of the social networks was performed in Gephi software, version 0.9.2 [111].
Results
Empirically based network
Contrary to our expectations, the results of targeted deletions in the empirically based portion
of our study revealed disparities in almost all network indices between age category and
betweenness centrality (S2 Table) and an overall unexpected level of resilience against
disturbance.
The effect size statistics estimating the mean difference between age category-targeted and
random deletions at each deletion proportion revealed no change in clustering coefficient, as
well as weighted diameter, global efficiency and modularity (Fig 4 and S2 Table). Overall, the
removal of the oldest elephants in simulated populations appears less damaging to the network
connectivity and efficiency than we expected.
In contrast, the effect size statistics comparing the differences between targeted and random
elimination of individuals with highest betweenness centrality, as a function of deletion pro-
portion, showed an expected decrease in clustering coefficient and weighted global efficiency,
as well as an increase in weighted diameter (Fig 4 and S2 Table). Weighted modularity revealed
no change relative to random deletions (Fig 4 and S2 Table). This set of results indicates that
the loss of the most central conspecifics impedes connectivity and efficiency in the empirically
based network and, even more interestingly, that age is not strictly associated with this
impediment.
Virtual networks
The results in the virtual portion of this study were in part similar to those from the empirically
based portion (S1 Fig). When age category was the focus of deletions, the effect size statistics
comparing means of targeted and random deletions in the 500 time step virtual networks
revealed an increase in clustering coefficient and weighted global efficiency. There was no
Fig 2. Flow chart summarizing the process of simulating social networks among virtual elephant populations. At
initialization, the probabilities of association within and between groups are set according to kinship and age category (Fig
1B). At the beginning of each time step, the set probability of association within each group or between each set of groups,
and between each dyad, is compared to a randomly generated number (RDN) between {0,1}. If this probability is greater
than RDN, the association is set to occur. If this probability is lower than RDN, the association does not occur, and the time
step is terminated. At the end of each time step the number of times a specific dyad has formed across all previous time steps
is updated (i.e., increased by one if the association had occurred, or remained the same otherwise).
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Fig 3. Social network graphs of the empirically based population with color partitioning according to a core group, considered from the
perspective of either (A) age category or (B) betweenness centrality; and a comparable example of a virtual population with the partitioning
according to a core group, and either (C) age category or (D) betweenness centrality. The nodes are ranked by size where the largest nodes indicate
oldest age or highest betweenness centrality. The links are color coded to match the nodes they originate from and ranked according to their relative
weight. The thickness scheme depicting the weight of each link ranges from thin (low) to thick (high weight). The links with weight less than 5
percent were filtered out for visual clarity.
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change in mean weighted modularity or diameter between targeted and random deletions (Fig
5and S3 Table). Contrary to our expectation, these results suggest that removal of older indi-
viduals improved connectivity networks but without improving their efficiency.
When targeted deletions were performed according to betweenness centrality, the cluster-
ing coefficient and weighted global efficiency decreased, while weighted modularity and diam-
eter increased. The effect size statistics for these indices were large across most time steps and
deletion proportions. As we expected, these results point to a decrease in connectivity and effi-
ciency in virtual elephant networks and importance of individuals with high betweenness cen-
trality in shaping these network features (Fig 5 and S3 Table).
Elimination of the weakest association links with values ranging from one to three percent
of the highest link in 500 time step networks led to multiple events of breakdown into at least
two modules (S4 Table). Given their ‘premature’ disruption, we excluded these networks from
the subsequent deletions. In the remaining filtered networks, targeted deletions of individuals
with the highest betweenness centrality, more so than age category, caused more
Fig 4. Graphs representing results (mean plus 95% confidence interval) of 100 deletions per each combination of deletion proportion (i.e.,
0–20%) and type (i.e., random vs. targeted) in the empirically based network. The deletions were either targeted according to age category
(black series) or betweenness centrality (blue series); or were random (grey and teal series represent random deletions without considering
individual traits conducted as control conditions to age- or betweenness centrality-targeted experiments, respectively). The network indices
evaluated included clustering coefficient as well as weighted modularity, diameter and global efficiency. For a cross-species context, the minima
of y-axis ranges per clustering coefficient as well as weighted modularity and global efficiency are plotted to express the minima from a similar,
theoretical treatment in an egalitarian primate society [46]. The weighted diameter index depends on group size, thus the pertinent y-axis is not
expressed in a cross-species context. For results of Hedge’s g test expressing the differencein the effect size between the means of each network
index between targeted versus random deletions along the deletion proportion axis and per deletion type, refer to S2 Table.
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fragmentation than random deletions. Finally, although the weakest links were rather evenly
distributed between individuals of various intermediate age categories, they occurred more
often among individuals from different clans (S2 Fig) indicating an important role in network
connectivity.
Discussion
In this study, we addressed a timely question about the response of animal groups to human
disturbance by simulating poaching in one empirically based and 100 virtual African savanna
elephant populations. After targeted removal of socially influential individuals, according to
their age category or position in a social network (i.e., betweenness centrality), we character-
ized network indices associated with cohesion and transfer of information in animal groups in
Fig 5. Graphs representing results (mean plus 95% confidence interval) of 100 deletions per each combination of deletion proportion (i.e., 0–20%) and
type (i.e., random vs. targeted) in an example virtual network that is comparable in size to the empirically based social network (see Figs 3and 4for
detail). The deletions were either targeted according to age category (black series) or betweenness centrality (blue series); or were random (grey and teal series
represent random deletions without considering individual traits conducted as control conditions to age- or betweenness centrality-targeted experiments,
respectively). The network indices evaluated included clustering coefficient as wellas weighted modularity, diameter and global efficiency. For a cross-species
context, the minima of y-axis ranges per clustering coefficient as well as weighted modularity and global efficiency are plotted to express the minima from a
similar, theoretical treatment in an egalitarian primate society [46]. The weighted diameter index depends on group size, thus the pertinent y-axis is not
expressed in a cross-species context. For results of Hedge’s g test expressing the difference in the effect size between the means of each network index between
targeted versus random deletions along the deletion proportion axis and per deletion type, refer to S3 Table.
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the empirically based and virtual networks. We anticipated that targeted disturbance in both
network types would 1) perturb theoretical indices of network connectivity and the efficiency of
social diffusion immediately after disturbance and 2) increase as a function of deletion propor-
tion (i.e., 0–0.2) leading to network breakdown. The results of manipulating the empirically
based and virtually networks were qualitatively similar, and we summarize and discuss them
together.
Contrary to our expectations, targeted deletions according to age category resulted in
improved connectivity in the empirically based and virtual networks. This outcome, however,
instead of pointing to social influence of seniors, revealed their peripheral roles in contributing
to network connectivity relative to younger conspecifics. Elimination of individuals with high
betweenness centrality led to an anticipated decrease in indices expressing connectivity and
efficiency of social diffusion in the empirically base and virtual networks. Unlike age category,
betweenness centrality, in both network types, proved to be an indicator of social influence in
the context of strong links among close kin as well as weak links among distant kin. Finally,
regardless of the deletion metric (i.e., age category or betweenness centrality), the simulated
networks did not break down even when subject to relatively high degree of ‘poaching’ (i.e.,
0.2 deletion proportion), leaving the question of a theoretical breaking point outstanding.
The disparities between age category- and betweenness centrality-specific deletions are con-
sistent with intraspecific behaviors in species with multilevel sociality, established dominance
hierarchy and high degree of tolerance towards subordinate group members [112]. For
instance, in real elephant populations, immature individuals are rather indiscriminate in their
affiliations and likely to engage with multiple conspecifics of different ages and kinship
[60,61,113]. Frequent bouts of social engagement may afford them some social skills without
direct engagement of senior kin and fosters cohesion between distinct subgroups [31,75]. In
contrast, similarly to mature individuals in other group-living species [114,115], senior ele-
phants may be more selective about their social partners and less sociable [80]. Their value as
social intermediaries contributing to network connectivity and efficiency may for that reason
be comparable to their immature conspecifics [36,75], regardless of the wealth of socioecologi-
cal experience seniors likely possess and display during social activities (e.g., such as group
antipredator defense led by the matriarch—[116]).
This type of organization, where network stability is mediated by different categories of indi-
viduals, exemplifies a decentralized system, likely persisting to buffer destabilizing effects of pro-
longed fission or stochastic events such as disease-induced die-off [117] or poaching. The notion
of network decentralization, reflected in our results, parallels the findings by Goldenberg and col-
laborators who proposed that the redundancy between social roles of mature elephants, prior to
poaching, and their surviving offspring is a potential mechanism of network resilience against
breakdown [75]. The empirically based and virtual networks in our research were also resilient to
removal of the socially influential group members. Given the seemingly greater flexibility and
interconnectedness in elephant populations, relative to other closely knit social species [46], find-
ing the hypothetical limitations to social resilience may require evaluating more intensive but still
biologically meaningful ‘poaching’ disturbance than considered in our work [118].
Although our assessment of the effects of disturbance on social organization and resilience
does not account for the dynamic and indirect responses to poaching (e.g., network reorgani-
zation or avoidance of poaching hotspots), or the dependence of interactions among multiple
conspecifics, it is a valuable first step in systems with limited real-world data. Having access to
information about the proportion and type of missing group members may 1) offer basic but
meaningful insights about why some poached elephant populations take exceptionally long to
recover from member loss [119], while others recover much quicker [120] and 2) help reason
about the fate of recovering populations.
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Our ideas may also be transferable to management of other group-living, keystone species
if baseline understanding of their reactions to the disturbance of interest is available [121
125]. For instance, applied without consideration for social interactions, trophy hunting of
pride lions may intensify infanticide by immigrant males [23,28,123] and displace distressed
females to hunt in fringe habitats exacerbating conflict with humans [124,126]. Prior to mak-
ing decisions about lethal management or translocations of ‘problem’ individuals, wildlife
managers may be well served by simulating relevant disturbance on focal populations, quanti-
fying social network effects and adjusting management decisions for better outcomes [41,127].
As another example, the use of social network analysis in captive animal populations is already
helping researchers characterize the dynamics of harmful agonistic interactions, such as tail
biting in newly mixed groups of domestic pigs [128]. These data may help parametrize simu-
lated disturbance to social network structure in captive systems by taking into account traits
such as genetic relatedness in group composition and its link to aggression and health of ani-
mal subjects. Insights from this type of assessment may, in turn, improve animal welfare and
safety of farm workers [129,130].
In summary, our work confirms previous findings that although elimination of the most
central network members in elephant populations decreases network connectivity at the popu-
lation level, it does not lead to network fragmentation—at least in networks with the structure
and at the level of simulated disturbance tested in this research. Uniquely, however, our
research shows that poaching-like stress in a large number of virtual elephant populations
impedes the theoretical efficiency of social diffusion. A follow-up question about the relation-
ship between the structural network changes and population performance will require simulat-
ing a dynamic process that accounts for network reorganization after poaching. In addition, to
tease apart an individual’s importance due to network position versus age-specific experience
will require a method that accounts for interaction-mediated information transfer. Still, our
simulation approach can be easily altered to test basic hypotheses about disturbance of social
interactions in wild and captive systems.
Supporting information
S1 Table. The composition of 100 virtual population according to kinship. Detailed here
are the number of clan, bond and core groups, as well as individuals per population; the num-
ber of bond and core groups, and individuals per clan; the number of core groups per group;
and the number of individuals per bond and core groups. The distribution of age categories
within each core group was the following: young adults (mean = 2 individuals, min = 1,
max = 5); prime adults (mean = 2, min = 0, max = 7); mature adults (mean = 1, min = 0,
max = 3); and matriarchs (mean = 1, min = 1, max = 1). The composition of the empirically
based population is included as a reference (i.e., = 10 core groups including a total of n = 83
individuals) [80,91].
(DOCX)
S2 Table. Results of Hedge’s g test expressing the effect size difference between mean val-
ues of clustering coefficient as well as the weighted forms of modularity, diameter and
global efficiency indices. These statistics express the difference between targeted and random
deletions in empirically based networks, along the deletion proportion axis, with deletions per-
formed according to either age category or betweenness centrality [96]. Bold values indicate
medium (|0.5|) and large (|0.8|) effect size.
(DOCX)
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S3 Table. Results of Hedge’s g test expressing the effect size difference between targeted
and random deletions in virtual populations. The effect size differences, calculated as the
Hedge’s g test, are presented as mean values for each network index in targeted and random
deletions in the virtual networks, in the 500 network time step and deletion proportion incre-
ments. The deletions were performed according to age category or betweenness centrality
[96]. Bold values indicate medium (|0.5|) and large (|0.8|) effect size.
(DOCX)
S4 Table. The summary of the percentages of filtered, virtual networks that broke down
into two or more modules as a result of the deletions performed according to age category
or betweenness centrality. The filtering process was carried out before the onset of the dele-
tions by dividing the value of each link in the association matrix by the highest link value and
eliminating the links with values up to three percent of the highest link in increments of one
percent [107]. Only 500-time step networks were considered in these experiments.
(DOCX)
S1 Fig. The distribution of values for the clustering coefficient, as well as weighted diame-
ter, global efficiency and modularity, expressed as a function of the number of simulation
time steps. The 500-time step cut-off was based on when the density of existing interactions
among network members started to reach a plateau (~ 75% median density) [82]. The values
embedded (red text) are approximated equivalents from the empirically based network prior
to the beginning of the deletion experiments (Fig 4). The values for the diameter weighted can
only be compare qualitatively (Figs 4and 5). Unlike the empirically based network using asso-
ciation indexes in the [0,1] range, the virtual networks used the number of interactions as
expression of associations. This was a consequence of the virtual network simulation process.
(DOCX)
S2 Fig. The percentage of the weakest associations filtered out from the 500-time step, vir-
tual networks prior to deletion experiments. These associations represent links with values
up to three percent of the highest link. Here, these links are presented according to age class in
a dyad (Y = young adult; P = prime adult; M = mature adult; G = matriarch) and one of four
social tiers. For the summary of filtering experiments showing percentages of filtered,
500-time step, virtual networks that broke down into two or more modules as a result of the
deletions performed according to age category or betweenness centrality, refer to S4 Table.
(DOCX)
Acknowledgments
Empirical data were provided by the Amboseli Trust for Elephants.
Author Contributions
Conceptualization: Maggie Wiśniewska, Simon Garnier, Ce
´dric Sueur.
Data curation: Maggie Wiśniewska.
Formal analysis: Maggie Wiśniewska, Ivan Puga-Gonzalez.
Funding acquisition: Maggie Wiśniewska.
Investigation: Maggie Wiśniewska, Ivan Puga-Gonzalez, Ce
´dric Sueur.
Methodology: Maggie Wiśniewska, Ivan Puga-Gonzalez, Ce
´dric Sueur.
Project administration: Maggie Wiśniewska.
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Resources: Phyllis Lee, Cynthia Moss.
Supervision: Gareth Russell, Simon Garnier, Ce
´dric Sueur.
Visualization: Maggie Wiśniewska, Ivan Puga-Gonzalez.
Writing – original draft: Maggie Wiśniewska.
Writing – review & editing: Maggie Wiśniewska, Phyllis Lee, Gareth Russell, Simon Garnier,
Ce
´dric Sueur.
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... Indeed, it has been shown in elephants or primates that these individuals attract attention of other individuals and are recognised as knowledge repository [33,100]. This could have a direct positive impact on survival of the herd as shown in elephants [101]. ...
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