Group size affects social relationships in yellow-bellied marmots (Marmota flaviventris) Adriana A. Maldonado-Chaparro1

Abstract

Demographic variation, such as changes in population size, affects group-living conditions and thus creates new opportunities for individuals to interact socially. To understand how this variation in the social environment affects social structure, we used social network analysis to explore affiliative behaviors of nonpup (i.e., 1 year or older), female, yellow-bellied marmots (Marmota flaviventris). We examined 4 social attributes (outdegree, indegree, closeness centrality, and betweenness centrality) to measure social plasticity in response to group size variation. We found that, in response to increases in group size, individuals established fewer social connections than possible, which suggests that marmots experience constraints on sociality. Similarly, closeness and betweenness centrality decreased as group size increased, suggesting that females are expected to lose influence over other members of the group as group size increases, and there are substantial constraints on marmots transmitting information to others in large groups. Our results also suggest that group-level responses, such as behavioral plasticity, can be explained by individual-level mechanisms that evaluate the costs and benefits of sociality. Interestingly, the mechanistic basis of these group-level responses may, at times, follow patterns expected by chance. We propose that further research is necessary to uncover the mechanisms underlying the individual-level behavioral response. Like group size effects studied in other domains, formally considering group size effects on social structure may shed novel light on the constraints on sociality.

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Behavioral
Ecology
Original Article
Group size aects social relationships in
yellow-bellied marmots (Marmota flaviventris)
Adriana A.Maldonado-Chaparro,a LilahHubbard,a and Daniel T.Blumsteina,b
aDepartment of Ecology and Evolutionary Biology, University of California, 621 Charles E.Young Drive
South, Los Angeles, CA 90095-1606, USA and bThe Rocky Mountain Biological Laboratory, Box 519,
Crested Butte, CO 81224, USA
Received 31 July 2014; revised 21 February 2015; accepted 26 February 2015.
Demographic variation, such as changes in population size, affects group-living conditions and thus creates new opportunities for
individuals to interact socially. To understand how this variation in the social environment affects social structure, we used social
network analysis to explore affiliative behaviors of nonpup (i.e., 1year or older), female, yellow-bellied marmots (Marmota flaviventris).
We examined 4 social attributes (outdegree, indegree, closeness centrality, and betweenness centrality) to measure social plasticity
in response to group size variation. We found that, in response to increases in group size, individuals established fewer social connec-
tions than possible, which suggests that marmots experience constraints on sociality. Similarly, closeness and betweenness central-
ity decreased as group size increased, suggesting that females are expected to lose influence over other members of the group as
group size increases, and there are substantial constraints on marmots transmitting information to others in large groups. Our results
also suggest that group-level responses, such as behavioral plasticity, can be explained by individual-level mechanisms that evaluate
the costs and benefits of sociality. Interestingly, the mechanistic basis of these group-level responses may, at times, follow patterns
expected by chance. We propose that further research is necessary to uncover the mechanisms underlying the individual-level behav-
ioral response. Like group size effects studied in other domains, formally considering group size effects on social structure may shed
novel light on the constraints on sociality.
Key words: centrality, degree, group size effects, social networks, yellow-bellied marmots.
INTRODUCTION
Ecological variation creates demographic opportunities that
allow individuals to aggregate and form social groups (Blumstein
2013). Ecological factors (e.g., food availability and climate) can
aect population characteristics, such as survival and reproduc-
tion, and thus drive variation in social groups and social systems
(Butler 1980; Crockett and Eisenberg 1987). Such population level
eects may increase or decrease with changes in group size and
may create new opportunities for individuals to interact if they
are not otherwise constrained. Therefore, in group-living animals,
sociodemographic variation may aect social structure (Griths
and Magurran 1997; Blumstein 2013; Schradin 2013). We view the
social system as the group of conspecifics that consistently interact
with each other and do so more often with each other than with
individuals of other groups (Kappeler and van Schaik 2002), the
social structure as the pattern of social interactions and the result-
ing relationships among individuals in the social system (Hinde
1976; Kappeler et al. 2013), and social organization as the size,
sexual composition, and cohesion of a social system (Kappeler and
van Schaik 2002; Kappeler etal. 2013).
Sociodemographic variation may dierently aect a popula-
tion’s or a species’ social organization, mating system, and social
structure. Previous studies have shown that increases in group size
can lead to the formation of complex societies that are character-
ized by a higher degree of morphological dimorphism and social
roles (Bourke 1999), can increase male mating success (Alexander
1974; Hovi et al. 1994), and can also be associated with reduced
ospring survival and declining birth rates after a certain group
size is reached (van Noordwijk and van Schaik 1999). Primate stud-
ies that focused on the relationship between group size and social
structure found that grooming increases with group size, but fur-
ther increases in group size leads to constraints: individuals have
insucient time to allocate to maintaining their social relationships
(Lehmann et al. 2007; Pollard and Blumstein 2008). Such find-
ings suggest that individuals can modify their behavior and conse-
quently alter the social relationships that emerge with changes in
group size. Thus, we aimed to explore how dierences in group
size are associated with variation in individuals’ social attributes
that aect group structure. By doing so, we sought to identify the
Address correspondence to D.T. Blumstein. E-mail: mar mots@ucla.edu.
Behavioral Ecology (2015), 00(00), 1–7. doi:10.1093/beheco/arv034
Behavioral Ecology Advance Access published April 15, 2015

Behavioral Ecology
mechanisms that permit females to behaviorally respond to changes
in their social environment.
The relationships that individuals can establish with other mem-
bers of the group may vary in the face of varying ecological and
social conditions. Such changes in an individual’s behavior as
a function of the conditions they experience are defined as phe-
notypic plasticity (Bradshaw 1965; Stearns 1989; Pigliucci 2001).
Plasticity of behavioral traits is known as behavioral plasticity
(West-Eberhard 1989; Dingemanse and Wolf 2013). Thus, social
plasticity can be defined as the ability of an individual to modify
its social behavior (social interactions and relationships) in response
to the social environment that it experiences (i.e., when found in
dierent sized groups). We suggest that individuals modify their
social behavior as a function of changes in their social environment
through social plasticity. By documenting the nature of these plastic
responses, we can understand how these behavioral changes alter
the overall social structure of the social system and identify poten-
tial constraints on sociality.
Here, we used a population of yellow-bellied marmots (Marmota
flaviventris; herein marmots), a diurnal and facultatively social
rodent, as a study system to investigate variation in social struc-
ture in response to changes in the social environment. The mar-
mot population around the Rocky Mountain Biological Laboratory
(RMBL) oers a great opportunity to address this question,
because females live in matrilines (i.e., kin groups), and the popu-
lation size has dramatically increased over the past decade. This
increase combined with a major population crash in 2011, prob-
ably as a result of warming spring temperatures and consequently
an increase in food availability during the marmots’ active season
(Ozgul et al. 2010), has resulted in substantial variation in group
size. Additionally, it has been suggested that marmots may increase
aliative behavior as group size increases to maintain social cohe-
sion (i.e., the degree to which members of a group are connected to
each other, Maldonado-Chaparro etal. forthcoming). Thus, in this
study, we will concentrate on aliative interactions because they
are often important for both group social cohesion and individual
fitness (Silk 2007b; Silk etal. 2009; Wey and Blumstein 2010, 2012)
and because these interactions also play an important role for dis-
persal decisions (Blumstein etal. 2009).
We used social network analyses, which allowed us to statistically
analyze the structure and components of networks that involve
multiple types of interactions (Krause et al. 2009) and to study
direct as well as indirect relationships (Wasserman and Faust 1994;
Croft etal. 2008; Wey etal. 2008). We focused on 4 social network
attributes that describe an individual’s direct interactions and ability
to influence other members of the group and allow us to quantify
variation in an individual’s behavioral response: outdegree, inde-
gree, closeness centrality, and betweenness centrality. Outdegree
quantifies the number of other individuals with whom an indi-
vidual initiates interactions (Wasserman and Faust 1994), whereas
indegree specifies the number of other individuals that direct inter-
actions toward the subject (Wasserman and Faust 1994). Closeness
centrality quantifies connectedness of an individual in terms of its
direct and indirect interactions with every member of the group
(i.e., measures an individual’s influence), and betweenness centrality
indicates the ability of a member to control paths of information
(or disease) between members in a group. We chose these measures
because they permitted us understand group structure (Freeman
1979) and to characterize how extensively individuals are involved
in relationships with other individuals in the network. This permit-
ted us to capture the propensity of an individual to develop social
relationships as well as to quantify changes in the social dynam-
ics of female marmots that may drive biological processes such as
information or disease transmission.
We assumed that 1) changes in the social context oer new
opportunities to interact with potential members of the group,
2)such additional social interactions lead to new relationships that
may aect an individual’s social network, and 3) individuals are
able to optimize the assessment of alternative behavioral trade-os.
Given these assumptions, we hypothesized that females will adjust
their aliative social behavior in response to variation in group size
to balance the cost–benefit trade-os associated with social living.
However, because individuals must also distribute their time and
energy between social interactions and other activities, includ-
ing foraging, resting, and traveling around their home ranges, the
time available for interacting may act to constrain sociality (Dunbar
1992b; Pollard and Blumstein 2008; Blumstein 2013). Therefore,
we also predicted that, as group size increases, individuals will
increase the number of social partners until the cost of group
living (i.e., increased competition over access to resources and
mating opportunities, increased risk of disease, and increased pre-
dation risk) will exceed the benefit (i.e., protection from predators,
increased foraging success, and reduced infanticide probability)
and animals will be unable to engage in additional social relation-
ships. Also, assuming that not all individuals in the group choose to
increase the number of social partners (i.e., increase the number
of direct connections), we expected animals to be less closely con-
nected to other individuals in the group (i.e., lower closeness cen-
trality) and to have less control over information flow (i.e., lower
betweenness centrality).
METHODS
Monitoring social behavior and demography in
yellow-bellied marmots
Since 1962, marmots in and around the RMBL have been regu-
larly livetrapped and observed during the active season (between
mid-April and early September). Using baited live traps, we trapped
100% of the individuals in our population annually. Individuals
were given numbered ear tags the first time they were captured and
were marked with fur dye for identification from afar (Blumstein
et al. 2009). Additionally, we weighed (using a digital scale) and
sexed each individual. Individuals were classified into 3 age catego-
ries: pups (<1year), yearlings (1year old), and adults (≥2yearsold).
For these analyses, behavioral observations were conducted on
an average of 53 females per year over a period of 12 years. We
observed marmots from mid-April to early September, during
hours of peak activity (from 7:00 to 10:00 h in the morning and
16:00 to 19:00 h in the afternoon; Blumstein etal. 2009). Observers
sat quietly and observed marmots from about 20 to 150 m away
(Blumstein etal. 2009) with binoculars and 15–45× spotting scopes.
We recorded all observed social interactions (details in Wey and
Blumstein 2010). For each individual interaction, we recorded the
type (i.e., aliative or agonistic), the initiator and recipient, the
location, and the time of interaction. The number of hours of
observation per year over the study period (2002–2013) averaged
874 h but varied from 302 to 1270 h (Supplementary Table S1).
Quantifying the social environment
The social context of yellow-bellied marmots can be hierarchically
described. Marmots physically live in colony sites, a geographic
Page 2 of 7

Maldonado-Chaparro etal. • Group size eects on social structure
area that may contain one or more social groups that are found in
patches of suitable habitat. Social groups are a subset of 2 or more
individuals that live in close proximity in space and time and thus
are more associated among themselves than with other individuals
in the colony site. Not all individuals in a social group are observed
to interact above ground and thus animals in a social group may
or may not interact to form social networks. Thus, group size may
dier from social network size, which we defined as the set of indi-
viduals within a social group that were seen to behaviorally interact
with other members of the group during the study period. Asocial
network can be defined based on observations of aliative interac-
tions, agonistic interactions, orboth.
We focused on individuals found in 4 geographically distinct
areas (colony sites): Bench-River, Gothic Town, Marmot Meadow,
and Picnic that are patchily distributed between 2700 and 3100
m.a.s.l. Our Marmot Meadow and Picnic sites are located in higher
elevations (i.e., up valley) than our other 2 sites (i.e., down valley).
Within each colony site, we identified social groups based on the
marmot’s space-use overlap (Smith JE, Strelio CC, Blumstein DT,
unpublished data). To do this, we focused on nonpup (i.e., 1 year
or older) female and male marmots seen or trapped at least 5 times
in a year. Then we used Socprog (Whitehead 2009) to calculate
the simple ratio index (SRI, Cairns and Schwager 1987) from live-
trapping and observation data for each pair of marmots. We then
used the estimated SRI to identify the number and identity of the
individuals that belonged to a particular social group (i.e., mod-
ule) using the random walk algorithm on Map Equation (Rosvall
and Bergstrom 2008; Rosvall et al. 2009). For the purpose of this
study, we defined the social environment as the female group size
(the number of nonpup females present in a social group) because
we were interested in female sociality. Therefore, after identifying
the members of each social group, we removed all males from the
social group analysis to obtain the female group sizes. Between
2002 and 2013, we identified 86 social groups composed of 2 or
more nonpup females. Nonpup female group sizes varied from 2 to
18 individuals for the years under study (Supplementary Table S2).
Quantifying individual social attributes
We focused on aliative interactions (i.e., sit in body contact, sit in
proximity, grooming, and social play) recorded during the entire
active season to construct the aliative social matrix and the cor-
responding social network for each social group in each colony site
for each year from 2002 to 2013 (Figure1). Social networks con-
sisted of nodes (female marmots ≥1 year old) connected by directed
edges (i.e., observed aliative interactions between individuals). We
calculated the 4 social attributes for each nonpup female individual
in each social network (i.e., the connected components of the social
group). Outdegree was computed as the number of connections ini-
tiated by an individual (Wasserman and Faust 1994). Indegree was
the number of connections received by an individual (Wasserman
and Faust 1994). Closeness centrality was calculated by taking the
reciprocal of the sum of the shortest paths between the focal and
other individuals (or the sum of the reciprocals) (Wasserman and
Faust 1994; Wey etal. 2008; Wey and Blumstein 2012). Betweenness
centrality was the proportion of shortest path lengths between pairs
of other group members in which the focal individual was a point
on the path (Wasserman and Faust 1994; Wey etal. 2008; Wey and
Blumstein 2012). Outdegree and indegree were calculated using
directed, unweighted networks, whereas closeness and betweenness
centralities were calculated using undirected, unweighted networks.
All measurements were normalized to facilitate comparison
across networks of dierent sizes; thus, all of our measurements
ranged from 0 to 1.Indegree and outdegree were each divided by
n − 1 (the maximum number of possible connections), where n was
the total number of nodes in the network. For closeness, we multi-
plied the raw closeness by n − 1, where n was the number of nodes
in the graph, whereas for betweenness, we used 2× B/(n × n − 3×
2002 2004 2006
2008 2010 2012
Figure1
Examples of female (nonpup) yellow-bellied marmot (Marmota flaviventris) social networks in Marmot Meadow observed over dierent years. These networks
dier in size and structure. Gray nodes: yearling and adult females; solid lines: undirected aliative interactions.
Page 3 of 7

Behavioral Ecology
n + 2), where B is the raw betweenness and n is the number of
nodes in the graph (Freeman 1979). The unit of analysis was an
individual studied in a given year. All our calculations were con-
ducted in the iGraph package v.0.7.1 (Csardi and Nepusz 2006) in
R software v.3.1.1 (R Core Team 2014).
Statistical analysis
To explore the potential relationship between group size and social
structure, we performed a series of regression analyses that allowed
us to identify group size eects. We used a reaction norm approach
(Pigliucci 2001) to isolate the eect of group size on standardized
network parameters. A simple linear reaction norm graph (i.e.,
straight line) contains 2 main characteristics: slope and elevation
(Pigliucci 2001); however, more complex relations can be explained
through nonlinear reaction norms (Koons etal. 2009). The slope
quantifies the population’s phenotypic plasticity, measured as the
change in phenotypic expression with respect to environmental
variation (Pigliucci 2001), and the elevation quantifies the aver-
age phenotypic response (Pigliucci 2001; Nussey etal. 2007). This
approach allowed us to ask if social plasticity was a mechanism that
explained variation in an individual’s social attributes.
To describe the behavioral response pattern for each of our
dependent variables, outdegree, indegree, closeness centrality, and
betweenness centrality, we fitted a set of candidate mixed eect
models that included linear and nonlinear relationships and per-
formed a model selection analysis (Table 1). In each model, the
dependent variable was modeled as a function of the year-spe-
cific social environment (i.e., female group size). We also included
age category as a factor to control for known behavioral dier-
ences between yearlings and adults (Wey and Blumstein 2010;
Maldonado-Chaparro et al. forthcoming). Additionally, and to
account for repeated measures on individuals, we included female
identity and year as random eects. The error structure of the
models varied for each of the dependent variables. Outdegree
and indegree were based on proportion data and therefore we fit-
ted a binomial model (logit link) (Noutdegree = 384; Nindegree= 384).
Closeness and betweenness centrality were arcsine square-root
transformed and we fitted a Gaussian model (identity link)
(Ncloseness = 395). Betweenness centrality contained 80% of zeros.
Thus, we focused only on the subset of our data where betweenness
was greater than 0 (N = 143). We identified the best model sup-
ported by the data by using the Akaike information criterion cor-
rected for small samples. For Gaussian models, we evaluated the
significance of fixed eects using the Satterthwaite’s approxima-
tion for degrees of freedom in the lmerTest package (Kuznetsova
etal. 2014). All of our models were analyzed using the lme4 pack-
age (Bates etal. 2013) and the gamm4 package (Wood and Scheipl
2013) in R software (R Core Team 2014).
Finally, we assessed if the observed pattern in each of our social
attributes diered from the pattern expected from social attri-
butes estimated for random networks. To do this, for each of our
observed social networks, we generated an equivalent Erdös–Rényi
(E–R) random graph using the same number of n nodes. The prob-
ability (P) in E–R graphs can vary between 0 and 1, where 0 rep-
resents an empty graph and 1 represents a complete graph. Thus,
we defined P as 0.5 to allow for the maximum uncertainty of a ran-
dom graph (Takahashi etal. 2012). Then, we calculated the node-
based indegree, outdegree, betweenness, and closeness in all of our
E–R networks. We used the values obtained through the equivalent
E–R graphs to create a data set that contained values expected by
chance. We then used these random values as the response variable
and fitted the best models that were selected for the observed val-
ues of outdegree, indegree, closeness, and betweenness. Finally, we
built the 95% confidence intervals of the regression lines for the
observed and the random data sets and determined if the confi-
dence intervals overlapped. If they overlapped, the observed group
size eect was expected by chance.
RESULTS
We constructed 86 nonpup female social networks based on
observed aliative interactions (some of the individuals in smaller
spatially defined groups were not observed to interact). The
observed networks had an average of 4.5 (±SD=3.0) female mar-
mots. As expected, our measures were somewhat correlated (i.e.,
indegree vs. outdegree, see Supplementary Figure S1), but we ana-
lyzed them independently because each one may reflect a dierent
social process.
Our regression analyses revealed that group size was always sig-
nificantly associated with an individual’s social attributes, whereas
age category was only sometimes significantly associated with an
individual’s social attributes. More precisely, outdegree and inde-
gree declined nonlinearly with group size. For each additional
member of the group, the probability that a female added an addi-
tional social partner initially decreased at an average of −0.339
(standard error [SE]=0.04; P<0.001) and then, for groups larger
than 10, increased at an average of 0.026 (SE =0.007; P<0.001)
social partners per additional individual (Figure 2a). Yearlings did
not significantly dier from adults in their average response (0.432;
SE= 0.251; P = 0.086). Our outdegree model explained 30.75%
of the variance.
Table1
Set of candidate models fitted for each of the 4 network
measures (outdegree, indegree, closeness centrality, and
betweenness centrality) calculated for members of the
female social networks in yellow-bellied marmot (Marmota
flaviventris)
Model df AICc
Outdegree
Age category 5 511.80
Group size + age category 6 429.36
Group size + group size2 + age category 7 418.22
s(Group size) 7 431.44
Indegree
Age category 5 507.41
Group size + age category 6 395.65
Group size + group size2 + age category 7 390.01
s(Group size) 7 397.71
Closeness centrality
Age category 5 383.19
Group size + age category 6194.81
Group size1 + group size2 + age category 7 145.28
s(Group size) 7 415.39
Betweenness centrality
Age category 5 105.69
Group size + age category 6 89.32
Group size1 + group size2 + age category 7 51.53
s(Group size) 7 61.71
The model in bold represents the selected model based on the Akaike
information criteria (AICc). Superscript 2 indicates squared group size
and subscripts 1 and 2 indicate the slope for group size below and above
the estimated breakpoint, respectively. s indicates the smooth function. df,
degrees of freedom.
Page 4 of 7

Maldonado-Chaparro etal. • Group size eects on social structure
Likewise, the probability that an individual received more social
interactions decreased at an average of −0.393 (SE = 0.044;
P < 0.001) and then, for groups larger than 10, increased at an
average of 0.023 (SE= 0.008; P =0.003) social partners per addi-
tional individual (Figure2b). Yearlings were more likely to receive
more ties as group size increased than adults (0.710; SE=0.264;
P=0.007). Our indegree model explained 39.77% of the variance.
Closeness centrality significantly decreased at a rate of −0.129
(SE = 0.009; P< 0.001) per additional individual. The slope sig-
nificantly changed from a steep to gradual decrease around a group
size of 8 individuals. After this break point, closeness centrality did
not significantly change (−0.009; SE=0.007; P<0.001) as a func-
tion of increased group size (Figure2c). Yearlings were significantly
closer to other members of the group than adults (0.107 ± 0.030;
P=0.007). The closeness model explained 55.51% of the variance.
Finally, betweenness centrality decreased quickly at small group
sizes (−0.950 ± 0.127; P< 0.001; Figure2d) and then it decreased
at lower rates for larger groups (>5 individuals) (−0.03 ± 0.008;
P<0.001; Figure2d). Yearling and adults did not significantly dif-
fer in their betweenness (0.014 ± 0.043; P = 0.747). Our between-
ness model explained 74.33% of the variance.
The observed reaction norms for our social attributes indegree,
outdegree, and closeness diered from that expected by chance
(Figure2a–c). In other words, compared to a random process, mar-
mots were significantly more social at small group sizes. However,
as group size increased, marmots were significantly less likely to
initiate or receive connections or to have more central positions
than expected by chance. For betweenness, there were significant
deviations from random for groups smaller than 8 but not for larger
groups (Figure2d). In other words, for small group sizes, between-
ness centrality decreased at a significantly faster rate than expected
by chance, but this trend disappeared as group size increased.
DISCUSSION
Specific attributes of yellow-bellied marmot social relationships
are correlated with group size: marmots were less likely to add or
receive new social partners as group size increased, and their close-
ness and betweenness centralities decreased with increases in group
size. Thus, our results show that marmots are behaviorally flex-
ible and can adjust their social behavior to variation in their social
environment. Moreover, many of the identified patterns of behav-
ioral plasticity diered from those expected by chance, suggesting
that there are individual-level mechanisms that allow marmots to
balance the costs and benefits of maintaining social relationships.
This suggests that the flow of information and/or disease may be
1.00
ab
cd
0.75
Outdegree
1.6
1.2
0.8
0.4
Closseness
0.0
0.5
1.0
1.5
2.0
Betweenness
0.50
0.25
0.00
1.00
0.75
Indegree
0.50
0.25
0.00
246810
Group size
12 14 16 18
246810
Group size
357911 13 15 17
Group size
12 14 16 18
246810
Group size
12 14 16 18
Figure2
Results of the generalized linear mixed models explaining the variation in the 4 network measures in response to changes in female marmot groups. Black
solid lines illustrate the regression line fitted with the observed network attributes. The confidence intervals are denoted as a gray shaded polygon. Dark gray
dashed lines illustrate the regression line fitted with the social attributes calculated from Erdös–Rényi random networks (P= 0.5). Confidence intervals are
denoted as a light gray shaded polygon. (a) Fitted line of the outdegree response and raw data, (b) fitted line of the indegree response and raw data, (c) fitted
line of the closeness response and raw data, and (d) fitted line of the betweenness response and raw data. Circles: aggregated values of each of the raw social
network measures.
Page 5 of 7

Behavioral Ecology
aected by the behavioral decisions made by individuals within a
group. Our results also indicated that age is a potentially important
factor that influences sociality. Yearlings are more interactive (i.e.,
they had a higher indegree and closeness) than adults, a finding
that supports previous research that showed that younger individu-
als are more sociable and have a potentially important role in main-
taining social cohesion (Wey and Blumstein 2010).
Although our observed patterns supported the existence of
behaviorally plastic responses, the comparisons between the
observed and the random patterns suggested that when there were
nonsignificant dierences, some elements of the emergent prop-
erties of social behavior at the group level may be explained by
alternative mechanisms that follow random processes. For example,
in house mice (Mus domesticus), and in red foxes (Vulpes vulpes), ran-
dom processes explain aspects of their spatial and social behavior
(Giuggioli etal. 2011; Perony etal. 2012). We know, however, that
animals often interact nonrandomly with group members (Kurvers
etal. 2014). Thus, significant dierences between the emergent pat-
terns of behavioral plasticity and the random expectations suggest
the existence of behavioral rules that govern social interactions.
The ability of marmots to behaviorally respond to changes in
their social environment may imply that individuals are able to
evaluate the costs and benefits of socially interacting under dier-
ent circumstances and avoid the costs of increased sociality. Our
analyses show that at small group sizes, individuals apparently work
to increase social interactions. Interestingly, as group sizes increases,
individuals either behave randomly or seem to avoid participating
in more social interactions. This may be a mechanism to avoid the
costs of increased sociality.
The rate of decline in the likelihood of making new social partners
as group size increased suggests that sociality in female yellow-bel-
lied marmots may entail net costs, such as increases in within-group
competition, spread of parasites, or possibly reproductive suppres-
sion (Alexander 1974; Krause and Ruxton 2002; Silk 2007a). For
example, in long-tailed macaques (Macaca fascicularis), intraspecific
competition may reduce individual food intake and therefore increas-
ing group size creates more costs than benefits (van Schaik and van
Noordwijk 1986). Alternatively, individuals may choose to selectively
interact with few individuals in the group, implying the existence
of social preferences among members of a group (Lehmann and
Boesch 2009) that may reduce the cost of group living. In marmots,
such preferences may emerge as a result of the kinship structure
that influences the aliative networks (Wey and Blumstein 2010).
Furthermore, restricting the number of individuals one interacts with
may also be an adaptation to minimize the spread of contact-trans-
mitted diseases and parasites by reducing the frequency of direct
contact with potentially infected individuals (i.e., decreasing infection
risk). This may be the case in yellow-bellied marmots, where parasite
load does not always increase with group size (Lopez et al. 2013),
thus suggesting that social species may have acquired an adaptation
to prevent the spread of parasites in large groups (Bordes etal. 2007).
Therefore, as group size increases, the trade-o between the bene-
fits and costs of sociality may determine the number, strength, and
nature of the social relationships among group members.
The decay in closeness values suggests that there may be an
inevitable loss of control over other members of the group as group
size increases. Therefore, females in larger groups have less influ-
ence over other individuals in their group. This has implications for
dominance relationships in larger groups. As individuals lose con-
trol, a single individual may not be able to exert dominance over
others. This might have practical demographic consequences if this
means that formerly dominant individuals are unable to suppress
reproduction of other females. Additionally, most animals have no
calculable betweenness, perhaps because females within a group
occupy more peripheral positions in the network. By contrast, mar-
mots with betweenness centrality values greater than 0 may serve as
links between individuals that are not directly connected, or between
subgroups within a social group, as has been described in bottlenose
dolphin (Tursiops spp.) networks (Lusseau and Newman 2004).
Taken together, our results paint a rather simple picture of female
marmot sociality, which in some ways is similar to male marmot soci-
ality (Olson and Blumstein 2010). The lack of social complexity may
be a product of proximate mechanisms such as temporal and cog-
nitive constraints that limit the number of social relationships that
an individual can maintain (Dunbar 1992b; Lehmann et al. 2007;
Pollard and Blumstein 2008; Sueur et al. 2011; Blumstein 2013),
thus aecting the social structure. Individuals must distribute their
time among various activities (foraging, vigilance, travel, etc.), mean-
ing that individuals are limited in the time that they may allocate to
social activities (Mitani 1989; Dunbar et al. 2009). Alternatively, the
neocortex size limits the amount of information that an individual
can process, which therefore limits the number of social relation-
ships that an individual can monitor (Dunbar 1992a; Lehmann etal.
2007). Therefore, individuals in a group are seemingly limited in the
number of social relationships that they can maintain.
Sociality is a key factor that aects the survival and reproduc-
tion of social species. We have shown that animals seemingly adjust
the specific nature of their social relationships according to changes
in their social environment. Such behavioral plasticity may alter
the interaction between behavior and sociodemography, which in
turn can aect population dynamics (Calhoun 1952). As popula-
tions fluctuate both naturally and as a result of human impacts, it is
important to understand the eects of these fluctuations on social-
ity in order to have a better insight of the role of sociality on the
relationship between temporal environmental variation and popu-
lation dynamics. Our statistical approach (i.e., reaction norms) to
study behavioral plasticity can be widely applied to social species
and, by doing so, may shed novel light on constraints on sociality.
SUPPLEMENTARY MATERIAL
Supplementary material can be found at http://www.beheco.
oxfordjournals.org/
FUNDING
A.M.-C. was supported by a Fulbright Fellowship. D.T.B. was
supported by the UCLA Academic Senate and Division of Life
Sciences, National Geographic Society, and National Science
Foundation (NSF-IDBR-0754247 and NSF-DEB-1119660 to
D.T.B.; and NSF-DBI 0242960, 0731346 to the Rocky Mountain
Biological Laboratory).
We thank all the marmoteers who helped collect data. The comments of
J. Fowler and several anonymous reviewers helped us improve previous
versions.
Handling editor: Alison Bell
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