NOTICE: This is the author’s version of the following article.
Nakamura M (2000) Is human conversation more efficient than chimpanzee grooming?: comparison of clique sizes. Human Nature
11: 281–297. DOI 10.1007/s12110-000-1014-2© Walter de Gruyter, Inc.

Is Human Conversation More Efficient than Chimpanzee Grooming?
Comparison of Clique Sizes
Michio Nakamura
Kyoto University

ABSTRACT
Clique sizes for chimpanzee (Pan troglodytes) grooming and for human conversation are compared in order to test
Robin Dunbar’s hypothesis that human language is almost three times as efficient a bonding mechanism as primate
grooming. Recalculation of the data provided by Dunbar et al. (1995) reveals that the average clique size for humanconversation is 2.72 whereas that of chimpanzee grooming is shown to be 2.18. The efficiency of human conversation
and actual chimpanzee grooming over Dunbar’s primate grooming model (always one-to-one and a one-way interaction) is 1.27 and 1.25, respectively, when we take role alternation into account. Chimpanzees can obtain about thesame efficiency as humans in terms of quantity of social interactions because their grooming is often mutual andpolyadic.
Key Words: Bonding mechanisms; Chimpanzees (Pan troglodytes); Clique size; Conversation; Efficiency; Grooming.

DUNBAR’S THEORY OF THE EFFICIENCY OFLANGUAGE
Most primate species show social grooming (or allogrooming) behavior (Goosen 1987; Sparks 1967).
The original function of grooming may have been hygienic, in that monkeys remove ectoparasites and otherdebris from each other’s fur or hair (e.g., Tanaka and
Takefushi 1993). However, in most studies, grooming
is interpreted as a behavior showing intimate and relaxed relationships among individuals or as a means ofestablishing such relationships. Consequently, grooming is often considered to be analogous to human conversation (e.g., Goodall 1986; Goosen 1987; Morris1967).
Robin Dunbar, not stopping at a mere analogy, wasthe first to compare grooming and conversation theoretically and quantitatively. He hypothesized that human language evolved as a better bonding mechanism
when our ancestors faced difficulties in bonding
through conventional primate grooming (Dunbar 1996).
He showed that, at least in catarrhine primates, thefrequency of social grooming correlates with group size
(Dunbar 1991) and that group size is a function of neocortical volume (relative to whole brain volume; Dunbar 1992). Larger groups require more complex levelsof association and coalitions because of increased intra-group competition and aggression. He also estimated that the upper limit for social time would be
about 20% of the daytime whereas humans would need
42% if we used conventional primate grooming forbonding, given our group sizes (Dunbar 1993). Therefore, sometime in the course of the evolution of larger

brains, which is also related to the increase in groupsize, our ancestors had to find a more efficient bonding
mechanism than primate grooming. In his hypothesis,
language was the mechanism we acquired. He alsoemphasizes other social aspects of language, such as
the fact that it enables gossiping about other individuals
and thus provides social information on not only those
who are present but also those who are absent.
He supports the above predictions by comparing theefficiencies of human language and primate grooming.
Among nonhuman primate species, chimpanzees (Pantroglodytes) have the largest mean group size at about
53.5; the predicted group size of humans is about 147.8.
Therefore, language should logically be 2.76 (147.8 /53.5) times more efficient than social grooming (Dunbar 1993:690). Here, by “efficiency” he means “thenumber of interactants that can be simultaneously
reached during social interaction” (1993:689–690).
Then, Dunbar et al. (1995) counted clique sizes of human conversational groups in several public settings
and found an upper limit of about four in conversationcliques. He then stated that because “grooming is exclusively a one-to-one interaction” (Dunbar 1993:690)(i.e., one groomer can reach only one groomee at atime), this clique size of four (i.e., one speaker canreach three listeners at a time) matches the efficiency oflanguage predicted from group size. Finally, he suspected that “human groups are three times larger thanthose of chimpanzees precisely because humans canreach three times as many social contacts as chimps fora given amount of social effort” (Dunbar 1996: 122).

CLIQUE SIZE FOR PRIMATE GROOMING
Dunbar’s view of primate grooming is that it always
occurs on a one-to-one basis and as a one-sided interaction. This view seems to come mainly from observations of baboon grooming, which he studied for a longtime. These characteristics of grooming seem to be truein many primate species. There are many studies ofgrooming throughout primate taxa (for review, see
Goosen 1987), but most authors seem to take it for
granted that grooming is a one-to-one and one-sided
interaction, usually not discussing any other options atall. Some studies, however, have reported that occasionally two participants groom each other simultaneously and that three or more participants engage ingrooming at one time, such as A→B→C or A→B→C.
Cooper and Bernstein (2000) observed 385 triadic episodes, 5 quadratic episodes, and 45 mutual episodes ina total of 5,397 grooming episodes of Macaca assamensis. Sugawara (1984) observed 14 triadic and no
mutual episodes in 184 grooming (lice removal) episodes in Homo sapiens. There are also some descriptions of polyadic and/or mutual grooming for Macaca
fuscata (Furuya 1957), M. mulatta (Boccia 1983; Sade1965), M. nemestrina and radiata (Kaufman and
Rosenblum 1966), Presbytis entellus (McKenna 1978),and Cebus apella (Parr et al. 1997). However, thesestudies only report that such grooming sometimes orrarely occurs, and the authors simply divided them into
dyadic episodes for analysis (for example, A→B→C isdivided into A→B and B→C). Moreover, the above
reports provide no data on frequency.
Unlike baboons or macaques, chimpanzees often
form large grooming clusters (Goodall 1986), and quitea large amount of grooming is polyadic. They alsoquite often engage in mutual grooming (e.g., McGrew
and Tutin 1978; Oberski 1993; Takahata 1990a, 1990b).
When estimating efficiency, Dunbar compared groupsize of chimpanzees with that of humans because
chimpanzees have the largest mean group size among
nonhuman primates. However, he did not compare
human conversation with chimpanzee grooming. Perhaps the data on chimpanzee polyadic grooming were
not available because this kind of grooming is also
often divided into dyadic occurrences in chimpanzee
studies (e.g., Nishida 1988). These characteristics ofchimpanzee grooming are important when we compare
clique sizes. Furthermore, the chimpanzee is geneticallyone of the closest species to humans (Caccone andPowell 1989) and also they show the highest intelligence among nonhuman primates as well as some language ability in laboratory studies (Kojima 1984; Savage-Rumbaugh et al. 1978).
It is difficult to say whether grooming andconversation clique sizes can be directly compared in
the way Dunbar did. And even under the assumptionthat they can, is conversation really three times more
efficient than chimpanzee grooming? In the next section, I will point out a few simple mistakes in Dunbar’s
calculation of the efficiency of conversation in relation
to primate grooming. In the following section, I willcompare clique sizes of chimpanzee grooming, basedon my own data, with the data on human conversationcliques provided in Dunbar et al. 1995.

METHODSThe field observation was conducted on awild chimpanzee (P. t. schweinfurthii) group (M group)in Mahale Mountains National Park, Tanzania, between
July 1996 and May 1997. For detailed information
about the research site, see Nishida 1990. I selected 10
males and 10 females as focal target individuals (Table
1) and followed them as long as possible while recording all of the grooming that occurred around thetarget. This sampling method enabled wider observation than that of ad libitum sampling of various individuals by minimizing the possibility that observations
might be biased toward those individuals who tended tocongregate. Total duration of observation was about
480 hours. In order to record the sizes and patterns ofcliques in large grooming clusters, a micro tape recorder was used to check the time when any individualin the cluster made a change in grooming status (i.e.,
started grooming, stopped grooming, or changed partners). Grooming comprises a series of behavioral elements with other individuals such as stroking hair,picking hair, removing things with hand(s) or lip(s),and scratching (Nakamura et al. 2000). Self-grooming
and leaf grooming were not included in the analysis. A
grooming cluster is defined as a gathering of individuals who exhibit at least one grooming behavior. A cluster begins when one or some individuals begin togroom and ends when no individuals have groomed formore than five minutes. Because some data are incomplete, I only use the 38 sets of complete grooming
clusters that were observed from beginning to end. I
only analyzed clusters that lasted more than 30 minutes
because shorter grooming is often used as a token(Goodall 1986). Total duration of these complete
grooming clusters is about 30 hours.
Dunbar and colleagues (1995) collected their data at
cafeterias and receptions in which conversation would
last for extended periods. Therefore, their data are also
likely free of brief conversations such as greetings
when two persons meet on the street.

Definition of Terms
Clique: Following Dunbar et al. (1995), I define“clique” as the number of individuals taking part in aparticular conversation (or grooming). In other words,
it is a subgroup of individuals who are directly connected through conversation (or grooming) in a larger
gathering of conversation (or grooming). This usage ofclique is different from that in graph theory or network
analysis (Scott 1991).
Actor: In grooming, the one who acts is the “groomer,”while in conversation he or she is the “speaker.” In thisarticle both of these types of individuals are referred toas “actors.”
Recipient: The one who receives the action is a“groomee” in grooming and a “listener” in conversation.
These two types of individuals are referred to as “recipients.”

RESULTS
Average Clique Size for Human Conversation
Dunbar argued that because usual primate grooming
is one-to-one (i.e., clique size is two) whereas cliquesize for human conversation is four, human conversation is three times more efficient than grooming (Dunbar 1996:121). This clique size of four seems to be
derived from the finding that “human clique size
reached an asymptotic value of 3.0–3.5 at a group sizeof about four individuals” (Dunbar et al. 1995). Thismeans that when the number of people present issmaller than four, all the group’s participants usuallyengage in only one clique. However, when group size
exceeds four, it breaks down into two or more cliques.
Therefore, “asymptotic value of 3.0–3.5” only meansthat cliques of larger than four are not likely to occur; itdoes not mean the average size of human conversationcliques is about four. When we compare the efficiencyof grooming with that of conversation, we have to consider the average efficiency of each, not the potential
efficiency. If reality follows what theory requires, human conversation must be three times more efficientthan grooming on average. Recalculations of the datafrom Dunbar et al. (1995) reveal that the average cliquesize for human conversation is 2.72 (Table 2). Thismeans that there are 1.72 recipients for one actor on
average; therefore, human conversation is only 1.72
times more efficient on average than grooming as modeled by Dunbar.

Role Alternation Model
Dunbar does not seem to have taken role alternation
into account. He argues that conversation is three times
more efficient than grooming when conversational
clique size is four. This seems true when we count the
number of arrows representing social interaction in
Figure 1a. There are three recipients of conversationfrom individual A, but only one recipient in Dunbar’s
grooming model. If we only consider this moment, it isthree times more efficient for A to be an actor in conversation than in grooming, as Dunbar mentioned.
However, in reality A cannot perform as an actor all thetime; instead A has to be in the role of recipient whileothers are playing the actor’s role. In Figure lb, role
alternation is taken into account. In grooming, A takes
the actor’s role in the first turn, has to be a recipient in
the second, then can again take an actor’s role in thethird, and so on. In conversation, A can take the actor’srole and direct his conversation toward three other individuals at a time in the first turn, but A has to wait asa recipient during the following three turns.
In grooming with role alternation, A can have twoarrows (i.e., social interaction flows) as an actor andtwo arrows as a recipient; therefore, in total, A can havefour arrows in this certain amount of time. In conversation, A can have six arrows, three as an actor and three
as a recipient. Therefore when we consider the alternation of roles, conversation in the clique size of four isonly 1.5 times more efficient than in Dunbar’s grooming model in which clique size is always two. In Figure
1, I only considered conversation in the clique size offour, but there are of course various sizes of cliques. In
general, to calculate efficiency while considering therole alternation model is precisely the same as calculating the ratio of arrows in a certain moment withequaled numbers of participants in grooming and conversation. When clique size of conversation is n, thenumber of arrows in the conversation is n - 1 (all theparticipants minus one actor), and if these n individuals
groom as in Dunbar’s model, the number of arrows
becomes n/2. Therefore, the efficiency of conservation
over grooming is 2(n - 1)/n.

Chimpanzee Grooming Cliques
Dunbar’s model of primate grooming (1993,1996)
makes intuitive sense because it seems impossible foran actor to groom multiple recipients simultaneously,
whereas a speaker routinely has multiple listeners.
However, a recipient can be groomed by multiple actors or an individual can play both an actor’s role and arecipient’s role at the same time, as is quite common inchimpanzees.
Figure 2 shows the types of chimpanzee grooming
cliques actually observed. There were 23 patterns, thelargest of which involved seven participants. The frequencies of these cliques are shown below in Table 4.
Chimpanzees often engage in mutual grooming inwhich two participants groom each other simultaneously. For one adult male, the proportion of mutual
grooming accounted for about 30% of all of his
grooming time. In mutual grooming, the number ofarrows (i.e., the number of grooming interactions) is
two even when clique size is two. If the issue is theefficiency of social interaction, mutual grooming is
twice as efficient as normal grooming even though thenumber of participants remains the same.

ComparisonsFirst, let us compare clique sizes in a simple way. A
clique size of two was the most common in chimpanzee
grooming as well as in human conversation; however,cliques with more than three accounted for 15% of thepatterns observed. The largest clique size for chimpanzee grooming (7) was the same as that for human con-versation. The average clique size for chimpanzee
grooming was 2.18 (Table 2), while that for humanconversation was 2.72, as we have seen earlier.
Table 3 compares the efficiency of human conversation with that of grooming in Dunbar’s model while
taking the effect of role alternation into account. Overall, the average number of arrows in human conversation is 1.72, while it is 1.36 in the grooming model.
Thus, human conversation is only 1.27 (1.72 / 1.36)
times more efficient than grooming.
Table 4 compares the efficiency of chimpanzee
grooming with that of Dunbar’s grooming model in thesame way as in Table 3. The average number of arrows
is 1.36 for chimpanzee grooming and 1.09 for Dunbar’s
model. Consequently, chimpanzee grooming is 1.25
(1.36 / 1.09) times more efficient than Dunbar’s model.
Both human conversation and chimpanzee groomingare 1.2-1.3 times more efficient than Dunbar’s model.

DISCUSSION
Most studies of language evolution emphasize its
special features, for example its ability to express abstract meaning or refer to things that are not present byusing complex vocalization and syntax. If we see only
these complex and special features of language, communication of nonhuman primates is far from comparable. However, primitive but very basic features of language seem to be forgotten or taken for granted. Conversation (which is made with language) is without
doubt the most common form of social interaction
among humans. Although much information is usuallycontained in conversation, do we not often talk just for
its own sake? In such conversation, the aspect of conveying information becomes minor, and the bonding ormaintaining of social relationships aspect is considerable. Furthermore, this bonding mechanism exists evenwhen language conveys information. The most common social interaction exhibited by our close relatives
the nonhuman primates is grooming. In this respect
Dunbar’s work is quite valuable. He compared primate
grooming and human conversation from the viewpointthat both have the same function of making social
bonds among individuals in a group.
According to Dunbar, one of the major reasons forthe evolution of language is that language is three times
more efficient than primate grooming as a means ofsocial bonding. However, as I have shown, chimpanzee
grooming has about the same efficiency as human conversation when we consider the quantities of these social interactions. I do not want to argue that chimpanzee
grooming is equivalent to human conversation. It is still
unknown whether the same duration of conversation or
grooming is really comparable solely from the viewpoint of efficiency.
It should be noted that conversation itself is quite
diverse, and thus even the same quantities of conversations do not always have the same efficiency. How can
one compare the efficiency of a serious talk between
two people and a garrulous chatter among many friends

only by their durations? Chimpanzee grooming also
seems to be diverse, and it looks quite different whenchimps groom in a large grooming cluster and when
they groom one-to-one, often face-to-face. Thus perhaps we will have to consider not only quantitative
efficiency but also qualitative aspects of the social interactions.
Chimpanzee grooming was shown to be as efficientas human conversation precisely because they do notalways groom like the monkeys in Dunbar’s model, but
often mutually and polyadically. These characteristics
of chimpanzee grooming also make their grooming
cliques quite diverse, as we have seen in Figure 2. It is
not clear whether mutual and polyadic grooming reallyoccurs less often in other primates than in chimpanzees
because there are very limited descriptions of mutual
grooming and polyadic grooming for species other thanchimpanzees. However, in most of these descriptions(Boccia 1983; Furuya 1957; Kaufman and Rosenblum
1966; McKenna 1978; Sparks 1967), primates are said
to groom mutually or polyadically only sometimes orrarely. The scarcity of this kind of description may
imply that these occurrences themselves are rare. Perhaps other species have the potential to groom in thesame way as chimpanzees but simply do not have tobecause their group size is usually smaller than that ofchimpanzees. It is also possible that some set of cognitive abilities is required to be an actor and a recipient ofdifferent interactions at the same time, which might
prevent monkeys from grooming in the way chimpanzees do. Chimpanzees are also known to use grooming
in quite complex and various ways such as trading forfood (de Waal 1997), using deceptive tactics (Nishida1998), and in many other social situations (e.g., Goodall 1986). The “cultural” diversity in chimpanzee
grooming (McGrew and Turin 1978; Nakamura et al.
2000) implies that their grooming is more socially determined than that of other primates. Perhaps the various patterns of cliques are also related to this kind ofcomplex use of grooming.
One would think that primate grooming and humanconversation are intrinsically different because, forexample, chimpanzees can groom each other simultaneously whereas humans cannot do so in conversation.
This is nearly true for English-speaking people (Sacks
et al. 1978) and perhaps for Japanese as well. In thesecultures, the speakers must alternate in a way quite
similar to the way in which the monkeys in Dunbar’s
model behave in grooming. When simultaneous
speeches occur, they are usually taken as mistakes inconversation and one or both speakers stop talking.
However, it is not correct to assume that this characteristic is universal among humans because somehunter-gatherer people often talk simultaneously forquite a long time (e.g., the |Gui Bushman, Sugawara
1998; the Baka Pygmy, Kimura 1995). These simultaneous speeches are sometimes agonistic, as they usually
are in our heated debates, but they are often cooperative
or parallel (Sugawara 1998). Chorus or co-singing may
be another example of simultaneous vocalization. Chorus is not strictly conversation, but it surely helpsbonding among the participants. We have to be cautious about the fact that both grooming and conversation can potentially be mutual or alternating. If we include these kinds of communication, the efficiency ofhuman conversations would become greater. However,no such data are available thus far. At this point, dataon clique sizes of both primate grooming and conversation are very limited. In this paper I only presented thedata from one population of chimpanzees. Comparisonsamong many primate species and also among different
human cultures are needed.
Grooming and conversation both have an aspect thatfunctions as a group bonding mechanism. However,these are not the only mechanisms, nor are they incompatible. For example, in bonobos (Pan paniscus),
female estrus is prolonged (Furuichi 1992) and sexual
behavior has some aspects of a group bonding mechanism apart from its reproductive function (de Waal
1989; Kano 1992). The original function of grooming
may have been to remove ectoparasites (e.g., Tanaka
and Takefushi 1993), while that of language (or vocal
communication) may have been to convey some information to a remote individual. However, they now bothseem to be used as bonding mechanisms as well. Groupbonding mechanisms do not have to have evolved only
for their own sake. As for humans, we can think ofvarious bonding mechanisms, such as conversation,
sexual or nonsexual contact, co-feeding, exchange ofgoods, eye contact, and facial expressions. We will
have to explore the possibility that the group bonding
mechanism may be a mosaic of many elements of behavior, not only grooming or conversation.

The fieldwork was supported by a grant from the International Scientific Research Program (07041138 to T. Nishida)of the Monbusho (Japanese Ministry of Education, Science,Sports, and Culture). I would like to express my thanks to the
Tanzania Commission for Science and Technology(COSTECH), Serengeti Wildlife Research Institute (SWRI),
Tanzania National Parks (TANAPA), Mahale Mountains
Wildlife Research Centre (MMWRC), and Mahale Mountains
National Park (MMNP) for permission to do the research.
Thanks are also due to K. Kawanaka, S. Uehara, H. Sasaki, W.
C. McGrew, L. F. Marchant, R. Kitopeni, M. B. Kasagula, M.
Matumula, and K. Athumani for cooperation in the field. I also
express gratitude to F. Fukuda, T. Nemoto, and H. Kayunbo
for their help in various ways in Tanzania; T. Nishida and G.
Yamakoshi for comments on an early version of the manuscript; and all the members of the Laboratory of Human Evolution Studies, Kyoto University for useful comments andsuggestions. Michio Nakamura is a research fellow at Japan
Monkey Centre. He received his Master of Science degreefrom Kyoto University in 1996. He is carrying out research on
the grooming behavior of chimpanzees at Mahale, Tanzania,
for his doctorate.

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Table 1. Information on 20 Focal Individuals
Names
MALES
KalundeNsaba
FananaHanby
DoguraBonobo
Alofu
CarterSinsi
Darwin
FEMALES
Gwekulo
FatumaIkochaNkonboPinky
Christina
Abi
Serena
Maggy
Ai
a
b

Year of Birtha

Rank/Status

1963?
1973
1978?
1980
1981?
1981
1982
1985
1985?
1988

2
1
3
5
4
8
5
adolescentadolescentjuvenile

1962?
1963?
1965?
1970?
1972?
1975?
1982
1987
1987
1988

cyclinglactatinglactatingcycling
cyclinglactatingcycling
cycling (adolescent)adolescentjuvenile

Kinb

Hours of Total Observationmo,ys,ys
mo,yb
ys

so,da
so, da
so
so
mo,ys
ob
mo,ob,ys

29.55
15.67
30.85
20.74
31.10
13.72
25.50
24.63
13.82
33.19
25.84
22.80
26.18
28.03
26.84
23.22
23.75
21.30
22.40
20.95

? indicates estimated year of birth.
mo = mother, ob = older brother, yb = younger brother, ys = younger sister, so = son, da = daughter.

Table 2. Distribution of Clique Sizes for Human Conversation and Chimpanzee Grooming

Clique
Size
2
3
4
5
6
7
Averageclique sizecaHumanaSample 3
Sample 4

Sample 1

Sample 2

237
98
57
22
0
0

231
93
44
16
3
1

25
27
20
7
2
2

77
66
22
5
2
0

2.67

2.63

3.28

2.77

Total

Overall %ChimpbOverall %

570
284
143
50
7
3

53.93
26.87
13.53
4.73
0.66
0.28

84.36
13.88
1.34
0.34
0.02
0.05

2.72

2.18

Source: Dunbar et al. 1995. They use 4 samples from different public settings.
Source: Author’s data.
cCalculated as ∑(k × Pk), where k = clique size and Pk = proportion of appearance of k-size clique.
bTable 3. Efficiency of Human Conversation Compared with Dunbar’s Grooming Model
Clique Size

Frequency (%)aNumber of Arrowsb
HumancDunbar’s Modeld
1
1
2
1.5
3
2
4
2.5
5
3
6
3.5

Efficiencye
1.00
1.33
1.50
1.60
1.67
1.71

2
53.93
3
26.87
4
13.53
5
4.73
6
0.66
7
0.28
Average number of
1.72
1.36
1.27
arrowsfaSource: Dunbar et al. 1995b
An arrow means a social interaction.
c
For humans, the number of arrows is n - 1 when clique size is n.
d
Calculated as the total participants at equal number to clique size of humans. Therefore, the number of arrows is n/2
when clique size is n for humans.
e
The number of arrows for humans divided by the number of arrows for Dunbar’s Model.
fCalculated as ∑(Nk × Fk /100), where Nk = the number of arrows when clique size is k, and Fk = Frequency (%) ofappearance of k-size clique.

Table 4. Efficiency of Chimpanzee Grooming Compared with Dunbar’s Model of Grooming
Clique Typea

Clique Size

Frequency (%)

Number of Arrowsb
ChimpcDunbar’s Modeld
1
1
2
1
2
1.5
3
1.5
3
1.5
2
1.5
3
2
4
2
3
2
4
2
3
2
4
2
3
2
4
2.5
4
2.5
4
2.5
4
2.5
4
2.5
5
2.5
5
2.5
5
3
6
3.5
7
3.5

Efficiencye

2-1
2
69.44
1.00
2-2
2
14.92
2.00
3-1
3
7.40
1.33
3-2
3
2.39
2.00
3-3
3
0.10
2.00
3-4
3
3.98
1.33
4-1
4
0.52
1.50
4-2
4
0.08
2.00
4-3
4
0.13
1.50
4-4
4
0.09
2.00
4-5
4
0.39
1.50
4-6
4
0.03
2.00
4-7
4
0.10
1.50
5-1
5
0.03
1.60
5-2
5
0.05
1.60
5-3
5
0.05
1.60
5-4
5
0.02
1.60
5-5
5
0.08
1.60
5-6
5
0.09
2.00
5-7
5
0.01
2.00
6-1
6
0.02
1.67
7-1
7
0.02
1.71
7-2
7
0.03
2.00
Average number
1.36
1.09
1.25
of arrowsfa
See Figure 2.
b
An arrow means a social interaction flow.
c
For chimps, the number of arrows is counted directly from Figure 2.
dCalculated as the total participants at equal number to clique size of chimps. Therefore
number of arrows is n/2 when clique size is n for chimps.
e
The number of arrows for chimps divided by the number of arrows for Dunbar’s Model.
fCalculated as ∑(Nk × Fk /100), where Nk = the number of arrows when clique type is k, and Fk = Frequency (%) ofappearance of k-type clique.

a. Without
Role Alternation

A

B

b.

With Role Alternation

A

B

A

B

A

B

A

B

C

D

C

D

C

D

C

D

Grooming

A's perspective

Actor to B.

Actor to B.

Recipient of B.

Actor to C.

Recipient of C.

A

B

A

B

A

B

A

B

A

B

C

D

C

D

C

D

C

D

C

D

Conversation

A's perspective

Actor to B, C, D.

Ratio of Arrows
for Individual A

1:3

Actor to B, C, D.

Recipient of B.

Recipient of C.

Recipient of D.

4:6 = 2:3

Figure 1.

Two models of efficiency of human conversation and primate grooming, ideally supposing that conversation clique sizes are always four andgrooming cliques are always dyadic and one-sided as in Dunbar's model. Circled letters indicate individuals and black arrows indicate social
interaction (grooming or conversation) flows. In 1b, the flow of time is indicated with large arrows. One box indicates a certain period of timeafter which role alternation takes place.

Not Including
IncludingNumber of
MutualGrooming
MutualGrooming
Participants
2-1

CircleNot Including
Mutual Grooming

Number ofParticipants

2-2IncludingMutual Grooming

5-1

2

5
5-2
3-1

3-2

3-3

3
5-3
3-4

4-1

4-2

4-3

4-4

5-4

5-5

5-6

5-7

4

4-5

4-6

6-1
4-7

6
7-1

7-2

7

Figure 2. All types of chimpanzee grooming cliques observed. Circles indicate individuals and arrows indicate direction of grooming.