Social Networks
North-Holland
293
11 (1989) 293-314
SOCIOMETRICS OF MA CA CA MULA TTA IV:
NETWORK ANALYSIS OF SOCIAL STRUCTURE
OF A PRE-FISSION GROUP *
B. Diane CHEPKO-SADE
The North Country Institute for Natural Philosophv
Karl P. REITZ
Chapman
College
Donald
Northwestern
Stone SADE
University;
The North Country Inmtute
for Natural Philosophy
Cluster analysis is applied to the grooming network of a group of free-ranging
rhesus monkeys
undergoing
group fission to examine the social structure of the pre-fission
group. A matrix of
grooming interactions
was compiled from detailed field notes collected over a 6-month period,
during the mating season of 1972. The group underwent
fission at the beginning
of the 1973
mating season. The network analyses, based on an algorithm
developed
by Mizoguchi
and
Shimura (1980) and adapted by Karl Reitz for application
to social structures (Reitz 1982, 1988)
are designed to detect natural hierarchically
arranged clusters of individuals
within a group. The
resulting sociograms provide measures of the cohesiveness of a group as a whole, and show how
smaller clusters of close grooming partners are grouped into larger clusters within the group based
on less frequent grooming interactions.
The results of the network analyses are discussed in light
of behavioral and demographic
observations
of the group’s structure over the study period, and
are found to compare well with the observer’s intuitive understanding
of the social structure of the
group as described in Chepko-Sade
and Sade (1979).
* This work has been supported
by a research grant to B. Diane Chepko-Sade
from the Harry
Frank Guggenheim
Foundation
through The North Country Institute for Natural Philosophy,
Inc.. The North Country Institute for Natural Philosophy, Inc., Northwestern
University, and The
College of Environmental
Science and Forestry, SUNY Syracuse have provided research facilities.
The collection of behavioral and demographic
data at Cayo Santiago was funded by grants from
the NSF to Donald Stone Sade. The Caribbean Primate Research Center was supported by grants
from NIH to the University of Puerto Rico. Errors in the analysis and interpretation
of data are
the responsibility
of the authors.
0378-8733/89/$3.50
0 1989, Elsevier Science Publishers
B.V. (North-Holland)
294
B. D. Chepko-Sade
et al. / So&metrics
of Maraca mulutta IV
1. Introduction
1.1. Rhesus monkey social organization
Free-ranging
rhesus monkeys, both on Cayo Santiago (Sade 1980, Sade
in the wild in Pakistan (Pearl 1982) live in groups
composed
of adult males, adult females and young ranging from
newborns to sub-adults of both sexes. The adult sex ratio tends to be
skewed toward females, frequently with two or more females per male.
Males born in the group generally leave the group they are born in
(referred
to in this paper as the “natal” group) as subadults,
and
subsequently join other social groups. They are replaced by emigrating
males from other groups. Females remain in their natal groups for life,
and are seen to change groups only in the infrequent
event of group
fission. Female philopatry in rhesus monkeys results in the concentration of matrilineal relatives within social groups. When relationships
between matrilineal relatives are known, the kin group can be depicted
as a matrilineal
genealogy, connected
by lines from mother to offspring, so that the relationship
between any two individuals
in the
matrilineage can easily be traced (Figure 1).
Social groups on Cayo Santiago contained as many as 23 matrilineal
genealogies of females in 1969, but only 6 or less by 1972 (from Sade et
al. 1985). This is because: (1) large groups (with large numbers of
genealogies)
were removed between 1969 and 1972; (2) fissioning
groups divide primarily between genealogies, so that group fission leads
et al. 1985) and
Fig. 1. Genealogies
of Group F, 1973. The six genealogies of Group F are represented
by tree
diagrams,
with birth year indicated at the top, and a line connecting
each individual
with its
mother. The genealogies are arranged in order of dominance
rank, from highest (top) to lowest
(bottom).
Females are represented
as circles, males as triangles. Only individuals
born in the
group and present during 1973 are represented.
Females who are deceased but whose presence is
necessary to link descendant
members to the genealogy are filled in with black. Non-natal
males
are not shown. Symbols representing
individuals
who were members of Group M in 1973 are
stippled; those representing
members of the main body of group F are clear. The three highest
ranking genealogies (Genealogies
065, 004 and AC) remained intact in Group F, while the lowest
ranking genealogy (Genealogy 022) moved in its entirety to Group M. Two genealogy were split
by the group division: Genealogy 073, and Genealogy 076, both middle-ranking
large genealogies,
split along family lines, with each family independently
joining one or the other group. Only one
family, that of KD in Genealogy 076, was divided between the two groups. KD’s eldest daughter
(YL) plus offspring joined a different group from that joined by her sisters ZM. Kl and N2 and
their offspring. (Redrawn with permission from Chepko-Sade
and Sade, 1979.)
B. D. Chepko-Sade
et al. / Sociometrics
of Macaca mulatta IV
295
to a regular reduction in number of genealogies per group (Chepko-Sade
and Sade 1979); and (3) as the population
was under study for more
years, the depth (number of generations) and size of known genealogies
increased,
so that each genealogy
included
more remotely
related
individuals (e.g. first and second cousins, great aunts and uncles) as
Q-
073
,
0
_291A
”
A
I
A
076
022
3
-“’
13v.:
..
296
B. D. Chepko-Sade
et al. / Sociometrm
of Macaca mulutta IV
data accumulated. This is not to say that there were not more remotely
related relatives in groups present in earlier years, but rather that our
knowledge of the history of the population
only allowed us to report
such relationships after the population had been under study for three
or more monkey generations.
1.2. Genealogies as behavioral subunits
It became clear early in the study of the colony that genealogical
relationships
between individuals had an important
bearing on social
relationships between individuals. Closely related individuals tended to
groom one another and sit or lie in contact with one another more than
less closely related animals (Sade 1965, 1966). Dominance
rank of
females is determined by the dominance rank of their mothers: young
females take their place in the adult dominance hierarchy immediately
below their mothers and above all of their older sisters. This pattern of
acquisition
of adult dominance
rank has been found to be highly
predictable and stable for rhesus monkeys (Sade 1972a, 1980) Japanese
macaques (Kawai 1958) and baboons (Walters 1980).
As long as known genealogies are small and restricted
to a few
generations, the genealogy can often be seen as a behavioral subunit of
the group as a whole: relatives tend to move together, groom each other
more than non-relatives,
collectively rank either above or below other
genealogies as a group, and remain together in one or the other of the
new groups formed by group division. However, as more generations
are known for a genealogy, the genealogy begins to behave less as a
behavioral unit. For instance, the 3-5 generation genealogies involved
in group fissions were more frequently split between daughter groups
than 2-3 generation genealogies involved fissions (Chepko-Sade
and
Sade 1979).
When genealogies did divide between two of the groups formed by
group fission, two patterns of intragenealogical
splitting were observed
(Chepko-Sade
and Sade 1979). The first, referred to here as an “eldest
daughter split”, was when the eldest daughter of the matriarch of the
genealogy, along with her children, joined a different new group from
that joined by her mother and sisters. A variation on this pattern is
when the eldest daughter’s eldest daughter
and her family join a
different group from that joined by her mother and sisters-not
infre-
B.D. Chepko-Sade et al. / Sociometrics of Maraca mulatta IV
291
quently that joined by her grandmother and aunts (for more detailed
discussion see Chepko-Sade and Sade 1979).
The second pattern of intragenealogical fission observed involved the
dispersal of the matriarch’s daughters’ families to the new groups
independently of one another, as if the behavioral subunits were now
the families of the daughters rather than the whole genealogy as we
knew it. Genealogies in which this occurred were 4-5 generations deep
and the behavioral subunits were 2-3 generations deep. In both cases,
the matriarch of these genealogies was dead, so that the oldest living
members of the genealogy were the daughters of the matriach.
1.3. Social structure of Group F prior to group fission (I 971- 72)
Group fission in rhesus monkeys is a fairly lengthy process, frequently
taking one to two years to complete. The Group F division is described
in some detail in Chepko-Sade and Sade (1979). Its main points are
summarized below.
During the mating season of 1971, Group F was the third largest
group on Cayo Santiago, with 106 members. The group was fairly
spread out spatially as its members fed and rested, but generally moved
as a unit from one place to another, especially when they were being
chased by a larger group. Whereas adult males and females and natal
young were usually seen together, there was a group of young non-natal
males who never interacted with the adult males and females of the
group except aggressively, and who were almost always seen together,
at a little distance from the rest of the group. These males were called
“ peripheral males”.
In November of 1971, Group A, then the largest on the island, was
removed from Cayo Santiago, leaving Group F the second largest
group. In late November and December of 1971, a subgroup of adult
males, females and young began to be seen separate from the rest of
Group F. This group, called the “splinter group” or “022’s group”, was
frequently seen separate from the rest of Group F during the remainder
of 1971, but with the onset of the birth season of 1972 became
reintegrated with the rest of Group F. At the beginning of the mating
season of 1972, the splinter group was again seen separate from the rest
of Group F, though its composition had changed somewhat, due to
deaths of certain key individuals (see Chepko-Sade and Sade 1979). In
addition, there was a dramatic change in the status of the peripheral
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of Macaca
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males of 1971. Never seen to mate during the 1971 mating season, they
mated with many females during the 1972 mating season. They were
also seen frequently among other members of the group, and not only
at the periphery. At the same time, younger males had been joining
Group F from other groups (especially those who had previously been
members of Groups A and K, which had recently been removed).
These new immigrants formed a new peripheral male group attached to
Group F.
By the following mating season, the splinter group was consistently
separate from Group F according
to both spatial and behavioral
criteria, and was accorded the status of a new separate group, Group
M. By this time, however, its composition
had again changed: Four
matriarchs of genealogies (065, 004, 076 and 022) and two mothers of
large families (DL and K) had died, and these deaths appeared to
result in their immediate families showing less cohesion than while they
were alive. Perhaps as a result of these deaths, four females who had
previously been seen only with the portion of the group that continued
to be called Group F joined Group M in the mating season of 1973:
WX and 299 of genealogy 076 had joined group M, as had OT and her
family from genealogy 073 (see Figure 1). W, eldest daughter of 022,
also joined Group M, although she had been with the main group in
1971 and 1972.
1.4. In search of a sociogram
The social changes in Group F between 1971 and 1973 are of great
interest from the point of view of rhesus monkey social organization.
Observations
of the differing tendency for small versus large genealogies to divide have led us to hypothesize
specific changes in the
patterns of affiliation within the genealogy over time (Chepko-Sade
and Sade 1979). Similarly, changes in the social statuses of individual
males as they become older and accumulate
tenure in the group
indicate that there is a pattern to the flow of males into and out of a
group over time (Chepko-Sade
1982). Until recently, however, these
hypotheses were untestable because social organization
could only be
discussed in highly subjective terms. Most observers would agree that a
given genealogy was “socially cohesive”, or “socially fragmented”,
or
that a given male was “central”
or “peripheral”,
but these classifications are a matter of degree, and can change over time. The periph-
B. D. Chepko-Sade et al. / Sociometrlcs of Macaw mulatta IV
299
era1 males of 1971 had become more central by 1972-at least to that
part of Group F that would become Group M in 1973. What was
needed was an algorithm that would allow us to characterize
the entire
group objectively and repeatably, not only as to degree of cohesion but
also identifying its component parts in a way that would enable one to
compare one group with another as well as track changes in a single
group over time.
Fig. 2. Early attempt to construct
a sociogram of Group F. Sociogram based on the grooming
network of Group F for March and April of 1973, using animals 3 years old and older. Males are
underlined;
females are not. Members who joined Group M in August of that year are stippled.
Individuals
who remained in Group F are clear. The algorithm
used to obtain the sociogram
allowed only one central individual
[centrality
being measured
by the number of three-step
grooming linkages directed toward the individual as described by Sade (1972, and present issue)],
surrounded
by those individuals
that groomed that individual,
surrounded
by individuals
that
groomed them, etc. This algorithm always produced
a series of concentric
semicircles, with the
single central animal as the center. Because the algorithm made provision for only one center, any
subgroups present would be superimposed
upon one another, and hence indistinguishable.
300
B. D. Chepko-Sade
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mulattu
I V
The social relations among a small group of individuals (2-10) can
easily be described and characterized
by a simple two-dimensional
drawing indicating links and lack of links between individuals (whether
“links” are defined as choices, friendship or grooming behavior) and a
reader can easily understand
such a diagrammatic
representation
(e.g.
Freeman, 1979). However, Group F contained 126 members at the end
of the mating season of 1972. Preliminary attempts to display grooming
relationships
diagrammatically
(Figure 2) resulted in such an elaborate
spider web pattern that no one but the drawer could interpret it at all.
An algorithm was needed that would cluster individuals according to
the frequency of their interactions
with one another, with the size and
number of clusters being determined
by the data rather than by the
algorithm or by a priori assumptions.
1.5. Reitz’s network analysis
The network analysis developed by Karl Reitz (Reitz 1988) is designed
to detect natural hierarchically
arranged clusters of individuals within a
social group, using measures of social distance between pairs of individuals within the group. It is adapted from an algorithm developed by
Mizoguchi and Shimura (1980) for detecting clusters within a scatter of
points in two-dimensional
space using measures of the physical distances between the points. Reitz’s model identifies subgroups within
the group with no a priori decision being made regarding the number
of clusters or the size of clusters to be found. Furthermore,
the analysis
allows one to compare groups of different sizes (unlike many cluster
analyses) and so is appropriate
for detecting changes in the structure of
a group over time even if the size of the group fluctuates, as it does for
most social groups, due to births, deaths, emigrations
and immigrations. One could also apply the analysis to several social groups in a
population
at a given time to determine mathematically
which of the
groups are more highly integrated
and which are more fragmented.
Observers are generally able to detect such changes, but are unable to
quantify their impressions in terms of measurable parameters.
Reitz’s
method showed promise of providing a non-subjective
tool for measuring group structure and solidarity. The purpose of this paper is to see if
the method could indeed provide such measures.
B. D. Chepko-Sade
et al. / Sociometrics
of MacucandurruIV
301
2. Materials and methods
A history of the Cayo Santiago rhesus monkey colony is given in Sade
et al. (1985). During the study period the genealogies in Group F were
known to a depth of 3-4 generations.
The group was observed for
approximately
8 hours each weekday and 33.5 hours on Saturdays and
Sundays. Field notes consisted of longhand narrative records of all
dominance
interactions,
grooming, mating behavior, and other social
interactions
recorded at the time they occurred. See Sade (1965) for a
definition of grooming bouts. A grooming matrix including all adults
and young l-year-old or older was compiled for the study period. The
present study applies Reitz’s cluster analysis to a single matrix of
grooming interactions
recorded among the 126 monkeys present in
Group F during the 1972 mating season (1 July 1972 to 31 December
1972).
2.1. Analysis
The algorithms
used to compile the sociograms
are based on an
intuitive definition of social group, in which social group is defined by
social ties that reflect both a hierarchical component (leadership) and a
symmetric component
(closeness).
Leadership is defined here as an
individual
attribute
or a ranking of the individuals
in the social
network. Closeness is an attribute of dyads and is often thought of as
symmetric.
Leadership could be defined as the number of times an individual is
chosen by others as a recipient of grooming or, alternatively,
as the
number of individuals who chose a given individual. A more complex,
but perhaps more telling, measure of leadership
or status might be
based on the sum of the individuals who groom an animal plus the
individuals
who groom those individuals.
This recursive method of
calculating a centrality index for individuals in a group can be carried
back for any number of links (see Sade 1972b, Sade et al. 1988, and
Sade 1989, this issue). However, leadership
need not be based on
information
contained
in the grooming matrix to be analysed, but
could be input into the program based on any other criteria chosen by
the researcher. For example, in the present case, dominance rank based
on the outcomes of aggressive encounters between individuals could be
302
B. D. Chepko-Sade
e-1al. / Sociometrrcs of Macuca mulutta IV
used (but see Sade et al. (1988) on the lack of a simple relationship
between dominance and centrality in male rhesus monkeys).
In the present study, separate analyses were run using two different
criteria for leadership. In the first two analyses, the number of times an
individual is chosen as a recipient of a grooming episode was used. In
the case that two individuals are tied in terms of first-order
interactions, this tie is broken by examining
if one individual
has more
incoming second-order connections than the second. In the third analysis, the number of individuals who chose an individual as a recipient of
grooming was used as the criterion for leadership.
Closeness between members of each dyad is based on the number of
grooming interactions
between each pair of individuals relative to the
level of grooming among individuals in the group as a whole. It is
determined
by creating a symmetrized
double-normalized
version of
the raw grooming matrix. The effect of double normalization
is to
make ties between those who chose or are chosen only a few times
stronger than similar choices between individuals
who chose or are
chosen frequently.
This ensures that in the process of drawing
boundaries, ties between individuals who have few ties are less likely to
be cut than those between individuals who have many ties. The double
normalization
is done so that each row and each column sums to the
number of individuals in the network, so that the average value of all
the cells in the matrix is one. This has the advantage that the number of
ties can be added across sets of individuals and then compared with the
expected number.
After double normalization,
matrices are made symmetrical.
Since
grooming matrices are not ordinarily symmetrical,
they are here made
symmetrical by summing the interactions in which i grooms j with the
interactions in which j grooms i, so that
g:j =
s;,= k,
+ g,,L
where G = {gi, } is the raw data matrix and G’ = {g:, } is the symmetrized matrix. Making the matrix symmetrical
eliminates information
regarding directionality
of interactions but retains information
regarding the relative strength of ties.
Given these two measures of leadership
and closeness,
the algorithms proceed as follows. For each individual, a given number of
closest neighbors is determined. This given number is arbitrary, and an
B. D. Chepko-Sade
et al. / Soclotnetrtcs
of Macaca mulatta IV
303
optimal number must be determined
experimentally.
We found that
when one was used the group broke down into many small unconnected family groups. The results obtained when the two and three
closest neighbors were used are described below.
The next step involves choosing from among a given individual and
its neighbors the one with the highest rank in terms of “leadership”.
If
the one chosen is other than the given individual then the tie between
the given individual and the chosen one is considered “unbreakable”
in
all subsequent steps. If the given individual is the one chosen then he or
she is at the top of a hierarchy. When this is done for each individual in
the network the result is a set of hierarchical
tree-like structures. The
individual at the top of a tree is of higher rank than any of the other
members of the tree. A link in the tree indicates a “close” tie between
the individuals linked. The higher individual in such a link is the one
with the higher rank.
The final step in the algorithm involves collecting these tree structures into meaningful subcollections.
Two subcollections
(starting with
the individual tree structures) are combined if the average tie between
the two subcollections
is greater than one (the average expected level of
grooming) and is the largest such average of all those between pairs of
subcollections.
This combining
of subcollections
continues
until the
average connection
between any two subcollections
is less than one.
The final result is a data-determined
set of clusters, where each cluster
consists of a collection of hierarchical
structures. The method is not
dependent on size or density of the network, and structures obtained
for different groups or for the same group at different times can be
meaningfully
compared. The number of clusters is an important measure of the degree to which the network is fragmented. If it is large, the
group is highly fragmented;
if small, the group is fairly cohesive.
3. Results
3.1. Three nearest grooming partners
Exclusions
There were 126 animals one year old or older in Group F during the
mating season of 1972. Of these, 20 were excluded from the network
because they either groomed or were groomed by fewer than two
304
B. D. Chepko-Sade
et al. / Sociometrrcs
of Maraca mulattrr IV
-
1972
MATING
SERSON
GROOMING
BEHAUlOR
Fig. 3. Subclusters
based on three nearest grooming partners,
leadership
based on number of
grooming interactions
received. The members of genealogies 065 and 004 all appear in one cluster
(Cluster 1) with the exception of high-ranking
adult males 7P and WK, who are in Clusters 2 and
3, respectively. The members of Genealogies 073 and 022 are dispersed among three clusters each,
in small family groups. AC’s genealogy shows an eldest daughter split between Clusters 2 and 5,
with AC and most of the genealogy in Cluster 5, while eldest daughter DL and her family are in
Cluster 2. Genealogy 076 shows a variation of an eldest daughter split: YL, the eldest daughter of
076’s eldest daughter (KD, deceased) is in Cluster 5 with her offspring while the rest of the
genealogy is in Cluster 3. The lines of the eventual split are not clearly seen in this sociogram, as
AC’s family (which joined Group F) is clustered together in Cluster 5 with part of Genealogy 022,
which joined Group M. Also, W. 305 and 85, also of Genealogy 022 (group M) are clustered in
Cluster 1 with Genealogies
065 and 004, which remained in Group F. Late (1973) joiners of
Group M, W and 305 of Genealogy 022, and 299 and WX of Genealogy 076. are clustered with
later Group F members, but OT and her family of Genealogy 073 are clustered in Cluster 6 with
other later Group M members, though she was not noted as a member of the splinter group until
the mating season of 1973. Peripheral males 2E, 4E. F4, 6E. 2C, Ll and 257 are clustered with the
later Group M members, but none are clustered with later Group F members.
B. D. Chepko-Sade et al. / Sociometrics of Macacu mulatto IV
GROOMING
BEHAVIOR 1972 MATING
(2 NEIGHBORS)
305
SEASON
/
Fig. 4. Subclusters
based on two nearest grooming
partners,
leadership
based on number of
grooming interactions
received. Genealogies 065 and 004 are again both completely contained in
Cluster 1, while Genealogy AC is divided between Clusters 2 and 4 in an eldest daughter split.
Genealogies 073 and 076 are divided into family groups distributed
among three and four clusters,
respectively,
and Genealogy
022 is all contained
in Cluster 6. Clusters 1, 2, 3 and 4, with the
exception of four individuals, remained in Group F when the group fissioned in 1973. Two of the
exceptions are WX and 299, who joined Group M late in the mating season of 1973. All members
of Clusters 5, 6 and 7 joined Group M. OT’s family and W and her daughter,
305, were not
recognized by the observer as members of the splinter group in the mating season of 1972, though
they did join group M in 1973. The cluster analysis places them with the splinter group a year
earlier, in the fall of 1972.
partners. Of those excluded, 14 had joined the group just that year and
were very peripheral members. Four had been in the group earlier as
peripheral members but had vacillated in their membership in Group F
during the 1972 mating season. The other two members were natal
males of Group F. One left Group F early in the study period and the
other, yearling 462. had few grooming partners besides his mother.
1972 MATING
3 Closest
Neighbors,
SFASON
GROOMING
Leadership
BEHAVIOR
according
to # of Groomers
B. D. Chepko-Sade et al. / Sociometrics of Maraca mulatta IV
307
Group structure
The rest of the Group F is divided into six clusters (Figure 3). Two
genealogies are contained within a single cluster; one shows an eldest
daughter split, one shows a double eldest daughter split, and two are
dispersed in family groups.
Lines of fission
All of the members of Clusters 1 and 2 remained in Group F after the
F-M fission except females 85, 305 and W (DS, also indicated as a
member of Group M, actually left Group F before the fission was
complete, but had been a member of the splinter group before he left).
Female 85 was at no time considered to be a member of the main part
of Group F, and it is not clear why the algorithm placed her in cluster
1. Her closest grooming partners were 52, 293 and JI, who are in
Clusters 5 and 6. Perhaps since her main grooming partners were in
different clusters, and she had fewer casual ties with other members of
either Cluster 5 or 6, she was placed in Cluster 1 where she had casual
ties with a number of individuals. Female W and her daughter, 305,
were during 1971 and 1972 considered
members of the main group.
They rejoined the rest of their genealogy in Group M late in 1973, after
vacillating between the two groups for a while. All of Cluster 3 also
remained with Group F, except female 299 and female WX and her
children, who joined Group M late in 1973, but were not seen with the
Fig. 5. Subclusters
based on three nearest grooming partners.
leadership
based on number of
groomers per individual. Genealogies 065 and 004 are again completely contained in Cluster 1, as
in Figures 4 and 5, but are joined by W and her daughter, 305, of Genealogy 022, as in Figure 3.
Genealogy AC is divided in an eldest daughter split (between Clusters 2 and 6) as in Figures 4 and
5. Genealogy 073 is dispersed into family groups as in Figures 4 and 5, but those parts that joined
the splinter group are not clustered with other splinter group members as they are in Figure 4.
Genealogy 076 is mostly contained in a single cluster, as in Figure 3, with the exceptions of YL
and her daughter, 438, and 310 who are clustered with 022’s genealogy. Figure 4, however, breaks
genealogy 076 up into family groups, similar to those that dispersed independently
in the group
fission. Genealogy 022 is all in a single cluster (6) except for W and her daughter, 305, who are in
Cluster 1. Late joiners, W and 305 of Genealogy 022, and 299 and WX of Genealogy
076, are
placed with Group F as in Figure 3, but OT and her family are clustered with later Group M
members. AC and her family are clustered with later Group M members, as in Figure 3, though
they were never seen to associate with the splinter group. This is probably because of a mating
consortship
between AC and E2 which involved a large number of grooming interactions
in a
short period of time, but apparently enough to pull AC and most of her family into Cluster 6 with
most of Genealogy 022, who were frequent companions
and grooming partners with E2, both
during the mating season and outside of it.
splinter group previously. The members of clusters, 4, 5 and 6 all joined
Group M except for the members of AC’s genealogy in cluster 5 who
remained with Group F. AC was never considered
a splinter group
member, and it is surprising that she should appear clustered with later
Group M members. The only strong link between AC and this group is
between AC and E2. AC is E2’s third closest grooming
partner,
apparently the result of mating activity between E2 and AC during this
period. E2 also had strong ties with members of JI’s family, both
during the mating season and outside of the mating season. It is
noteworthy that female OT and her family are clustered with members
of the splinter group at this time, since OT was not recognized as a
member of Group M until the mating season of 1973 (Chepko-Sade
1977. Chepko-Sade and Sade 1979).
Non-natal males are distributed amongst the clusters, and there is no
all-male subcluster as there is in Figure 4. Although some of the males
that joined the group as recently as the 1972 mating season are
included in the clusters, all but one (257) of the new immigrants
included are fully adult. A disproportionality
large number of non-natal
males (15 of 20) are attached to those clusters that later formed Group
M (Clusters 4, 5 and 6) as compared to the number of non-natal males
attached to the clusters that remained in Group F (Clusters 1, 2, and 3).
Many of these are those males that were classified as peripheral males
during the mating season of 1971. There was also a peripheral
male
subgroup attached to Group F during the 1972 mating season as there
was during the 1971 mating season, but most of these are more recent
joiners than the previous peripheral male group. This new peripheral
male group was composed of those males who were excluded from the
analysis because they had too few grooming partners.
3.2. Two neurest grooming partners
Cluster analysis using the two nearest grooming partners produced
similar results to those using the three nearest grooming partners, but
there were some interesting differences,
noted below. Individuals
excluded from the sociogram were the same as those excluded using three
nearest grooming partners, since the criterion for exclusion was the
same.
B. D. Chepko-Sade
et ul. / Sociometrics
of Macaca mulutta IV
309
Group structure
The sociogram produced using the two nearest grooming partners as a
measure of closeness is composed of seven clusters as opposed to six
clusters found when using three nearest grooming partners (see Figure
4). The additional cluster is a group of former (1971) peripheral males
which in the cluster analysis based on three closest neighbors
are
placed in two of the heterosexual
clusters that became part of Group
M. Two genealogies are contained in a single cluster; one shows an
eldest daughter split, two are divided into family groups, and one is
intact in a single cluster with the exception of a single female who is in
a different cluster.
Lines of fission
Individuals in Clusters 1, 2, 3 and 4 remained in Group F after the
fission, with only four exceptions. Two of these exceptions are 299 and
WX, who were late joiners to Group M and were never seen with the
splinter group before the fall of 1973. The other two exceptions are E2
and 293, who are clustered with AC’s family, apparently
the result of
mating activity. All of the individuals in Clusters 5, 6 and 7 joined
Group M. Females 8J and W are clustered with their genealogy in
Cluster 7 rather than with the top-ranking
genealogies as in Figure 3.
Males
The younger and more peripheral members of the 1971 peripheral male
group are here clustered together in an all-male cluster, while older
members of that group (E2, GJ, D2 and F8) are in clusters with
females and young. The 1972 peripheral male group was excluded from
the sociogram, as above.
Table
1
Leadership
of
criterion
subclusters
No. of
nearest
neighbors
No. of
subclusters
No. of
clusters
Size
Times groomed
Times groomed
No. of groomers
3
2
3
30
41
32
6
I
6
l- 9
l- 6
l-11
310
B. D. Chepko-Sade et 01. / Sociometrics
of Mucaca
mulattcr IV
3.3. Analyses using three nearest grooming partners
grooming partners
versus two nearest
Network analysis based on two nearest neighbor links results in a
larger number of subclusters with shorter hierarchical chains than does
network analysis based on the three nearest neighbor links (see Table
1). Arrangement
of subclusters into cluster is also somewhat different,
and in this case results in a larger number of clusters, though in
analyses for other time periods (to be published elsewhere) occasionally
resulted in fewer clusters. The analyses based on two nearest neighbor
links appears to result in a picture of group structure that more closely
accords with the observer’s impressions, apparently because the inclusion of a third link sometimes results in equating some weaker ties with
stronger ties between individuals (see, for example, the difference
in
cluster assignments of 85 and AC for Figure 3 versus Figure 4).
3.4. Leadership criterion: leadership based on number of groomers rather
than number of times an individual is groomed
The arrangement
of individuals in the subclusters (tree diagrams) is
determined by the leadership criterion. For any given tree structure, the
animal with the highest leadership score will appear at the top of the
tree, while animals with lower leadership scores are attached below. In
the above sociograms, leadership is based on the raw column marginals-the number of grooming interactions
received by each individual.
This results in an equal leadership
score for an individual
who is
groomed
45 times by one animal and another
individual
who is
groomed nine times by each of five different animals. A better measure
of leadership
might be the number of animals who groomed
an
individual rather than the number of times the individual was groomed.
Cluster analysis was therefore repeated on the above matrices using the
number of individuals who groomed an individual as the measure of
leadership
rather than the number
of times each individual
was
groomed. For these analyses, closeness was calculated using the three
closest grooming partners (as in Figure 3).
Since the hierarchical tree structures (subclusters) are created before
they are combined into the larger clusters, a change in the criterion for
leadership often results in tree structures of different sizes and compositions from those formed previously. These changes may result in
B. D. Chepko-Sade
et al. / So&metrics
of Macaca mulatta IV
311
animals ending up in different
clusters than before, depending
on
whether the criterion of greater than average grooming between subclusters is met or not.
The analysis using number of groomers as the criterion for leadership resulted in more subclusters
of smaller size than that using
numbers of times an individual
was groomed
as the criterion
for
leadership. This could affect the number of clusters, though that was
unchanged
for this data set. There are also some differences
in the
arrangements
of animals into clusters.
4. Discussion
The sociograms generated by the cluster analysis programs here do
produce a picture of Group F that is consistent with the observer’s
intuitive impressions
of group structure.
Individuals
who were seen
spatially
separated
from the rest of the group in 1971 and who
eventually left the group as Group M do tend to cluster together and
fall into different clusters than do members of the main group. The
peripheral males tend to be either clustered together or excluded from
the network entirely. This is consistent with the observation
that the
peripheral males formed a subgroup which moved as a unit at some
distance from the main group, with little affiliative
behavior
seen
between members except during the birth season.
Generally, the clustering of individuals using two closest neighbors
and number of times groomed fits better with the description of group
structure in Chepko-Sade
and Sade (1979) and with the observer’s
subjective impressions
of group structure
than either of the results
using three closest neighbors
(see figure captions
for specific differences). This is probably because when the third nearest neighbor is
included, weaker relationships
are treated as the equivalent of stronger
relationships,
causing a distortion of group structure. There are only
small differences between the analyses using the different criteria for
leadership defined here (number of times groomed versus three of the
groomers) (Figure 3 versus Figure 5).
Although the clusters and subclusters found by the algorithm tend to
fit well with previous subjective descriptions of the group’s structure, it
is possible that an even better fit could be obtained using a different
criterion for leadership. Whereas either the number of groomers or the
312
B. D. Chepko-Sade
et rrl. / Socmnetrics
of Mucacrr
mulatta
IV
number of times groomed are reasonably
simple measures of leadership, there are more sophisticated
measures of leadership or centrality
available. Sade (1972b, and 1989, this issue) has shown that a centrality
index based on the number of three-step grooming interactions directed
toward an individual is correlated with dominance
rank for females,
and for the dominant male of a group, though not for other males in
the group. Three-step
centrality
scores differed
substantially
from
one-step centrality
scores. This implies that the chuin of directed
grooming links holds important information
about leadership which is
overlooked when only the in-degree of grooming is measured.
Similarly, it seems that occasionally there is distortion of the grooming network due to casual grooming. While there was a procedure for
retaining grooming by individuals who give and receive little grooming,
in the row and column normalization
procedure, there is no procedure
for the elimination of casual grooming. This problem could be solved
by truncation of the original data matrix to eliminate casual grooming
encounters
(e.g. include only grooming interactions
that represented
12.5% or more of the grooming either given or received by an animal).
These and other alternative measures for leadership and closeness will
be explored in future analyses now in preparation.
5. Summary
Sociograms
based on cluster analysis of the grooming
network of
Group F during the mating season one year prior to group fission
yields clusters that correspond to the subgroups described for the group
in Chepko-Sade
and Sade (1979). Subclusters are composed of family
groups and groups of sub-adult males frequently seen together. Sociograms using two different
criteria for closeness and two different
criteria for leadership were tried. Generally, sociograms produced using
the two closest grooming partners fit better with other measures of
group structure and the observer’s intuitive understanding
of the group
than sociograms produced using the three closest grooming partners.
This is probably due to the fact that relationships
with third-closest
grooming partners are frequently much more distant than those with
first- and second-closest
grooming partners.
Overall, the algorithms presented here provide a very sensitive method
of describing social structure for large and complex social groups, and
B.D. Chepko-Sade
et al. / Sociometrics
of Macaca mulatta IV
should prove valuable in describing and comparing
change over time as well as in detecting similarities
between different groups.
313
groups as they
and differences
References
Chepko-Sade,
B.D.
1974 “Division of Group F at Cayo Santiago.” Amerrcan Journal of Physical Anthropology 41:
472.
Chepko-Sade,
B.D.
1977 “Patterns
of group splitting within matrilineal kinship groups. A study of social group
University
of Puerto Rico, Rio
structure
in Macaca mulatta.” Masters Dissertation,
Piedras, Puerto Rico.
Chepko-Sade,
B.D.
Northwestern
1982 “Role of males in group fission in Macaca mulatta.” PhD Dissertation,
University, Evanston, IL.
Chepko-Sade,
B.D. and T.J. Olivier
1979 “Coefficient
of genetic relationship
and the probability
of intrageneaological
fission in
Maraca mulatta.” Behavioral Ecology and Sociobiology 5: 263-278.
Chepko-Sade,
B.D. and D.S. Sade
1979 “Patterns
of group splitting within matrilineal kinship groups: A study of social group
structure in Macaca mulatta (Cercopitiecidae:
Primates).” Behavtoral Ecology and Sociobiology 5: 67-86.
Cheverud, J.M., B.D. Chepko-Sade,
M.M. Dow and D.S. Sade
1988 “Group
selection
models with trait-groups
based on social interaction
networks.”
Journal of Physical Anthropology 77: 427-433.
Freeman, L.
1978/79
“Centrality
in social networks: Conceptual clarification.”
Social Nefworks I: 215-239.
Kawai, M.
1958 “On the system of social ranks in a natural troop of Japanese monkeys. 1. Basic rank
and dependent rank.” Primates I-2: 111-130.
Mizoguchi, R. and M. Shimura
1980 “A nonparametric
algorithm for detecting clusters using hierarchical
structure.”
IEEE
Transactions on Pattern Analysis and Machine Intelligence, Vol. PAM-2, No. 4.
Pearl, M.C.
1982 “Networks
of social relations among Himalayan
rhesus monkeys.”
Unpublished
doctoral dissertation,
Yale University.
Reitz, K.P.
1982 “Social groups: A network approach.”
Doctoral dissertation,
University of California,
Irvine.
Reitz, K.P.
1988 “Social groups in a monastery.”
Social Nefworks 10: 343-357.
Sade, D.S.
1965 “Some aspects of parent-offspring
and sibling relations in a group of rhesus monkeys,
with a discussion of grooming.”
American Journal of Physical Anthropology 23: l-l 8.
Sade, D.S.
1966 “Ontogeny
of social relations
in a group of free-ranging
rhesus monkeys (Macaca
mulatta Zimmerman).”
Unpublished
doctoral
dissertation,
University
of California,
314
B. D. Chepko-Sude
et al. / Sociometrics
of Macactr mulutta IV
Berkeley.
Sade, D.S.
1972a “A longitudinal
study of rhesus monkeys.”
In R. Tuttle (ed.), The Functronul rend
Ecolutronary Biology OJ Primates. Chicago: Aldine-Atherton.
Sade. D.S.
1972b “Sociometrics
of Maraca mulrrtta. I. Linkages and cliques in grooming matrices.” Folra
Primatologica 18: 196-223.
Sade, D.S.
1980 “Population
biology of free-ranging
rhesus monkeys on Cayo Santiago, Puerto Rico.” In
M.N. Cohen, R.S. Malpass and H.G. Klein (eds.), Btosocial Mechanisms of Populutron
Regulatton. New Haven, CT: Yale University Press.
Sade, D.S.
1989 “Sociometrics
of Mucaca mu&a
III: N-path centrality
in grooming networks.”
Soctul
Networks II: 273-292, this issue.
Sade, D.S.. B.D. Chepko-Sade,
J.M. Schneider, S.S. Roberts and J.T. Richtsmeier
1985 Basic Demographic Observations on Free-Ranging Rhesus Monkeys. New Haven, CT:
Human Relations Area Files.
Sade, D.S., M. Altmann, J. Loy, G. Hausfater and J.A. Breuggeman
1988 “Sociometrics
of Macacu mulatta. II. Decoupling
centrality
and dominance
in rhesus
monkey social networks.” American Journal of Ph.ysical Anthropolom
77: 409-425.
Walters. J.
1980 “Interventions
and the development
of dominance
relationships
in female baboons.”
Folio Primutologiccr 34: 61-89.