Effects Of Cohesiveness On Inter-Sexual Dominance
Relationships And Spatial Structure Among GroupLiving Virtual Entities.
Charlotte K. Hemelrijk
AI Lab, Department of Computer Science,
University of Zürich, Winterthurerstr 190, CH-8057
Zürich, Switzerland, Fax 0041-1-363 00 35, Email:
[email protected].
Abstract. Since male primates are bigger and stronger than females, they are by
default considered dominant. When in a cohesively grouping ape (but not in its
loosely grouping relative), females often appear dominant to males, the static
image of female weakness is maintained and female dominance is attributed to
high, species-specific co-operation among several females against single males.
In this paper, an individual-oriented model is used to produce a parsimonious
alternative: female dominance over males may directly vary with groupcohesiveness without species-specific differences in co-operative tendencies
among females. The model consists of a homogeneous world in which entities
roam. Entities are so constructed as to have merely a tendency to group and
perform dominance interactions. ‘Male’ entities (StrongTypes) are
characterised by a higher initial dominance value and intensity of attack than
‘female’ entities (called WeakTypes). Dominance values change and evolve
due to the self-reinforcing effects of winning and losing contests. In the model,
more rank-overlap between both types arises from a stronger feedback between
dominance and spatial structure in cohesive than in looser groupings. Biological
implications of these phenomena and testable hypotheses for real animals are
discussed.
1 Introduction
High dominance rank is supposed to be associated with many benefits and
accordingly it is thought to be of central importance in primate social behavior (1).
Although many anthropoid primate species live in permanently bi-sexual groups,
hardly any data on male-female dominance relations exist (2). Instead, dominance
relations are usually studied within each sex separately, and females, being often
smaller and of inferior fighting capacity, are considered to be subordinate to males by
default. Although case histories of females being dominant to all or some males in
some groups of certain species are known (3), they are usually disregarded as
abnormal. For those few species in which it is consistently reported that adolescent or
adult males have difficulties in dominating females, an additional assumption is made
that females of these species have a stronger than usual tendency to form large
coalitions against single males (4,5). In this way, the generally accepted image of
weak individual females is maintained because female dominance is attributed to
collective force of larger numbers.
Although it is common to attribute social characteristics to internal qualities, and
the observation of different social characteristics at a group level, automatically leads
to the search for a different individual behaviour, an alternative, more integrative
approach is possible which we will follow here. In this approach, social
characteristics are studied and explained within the context of typicalities of the
species. For instance, Deneubourg and co-authors (6) described a very different
swarming pattern for each of three ant species. Instead of attributing this to internal
differences between the species, they showed, by means of a simulation, that under
the different feeding conditions that are characteristic of the three species, one and the
same set of rules leads to the three characteristic swarming patterns. Thus, the
swarming patterns result from the interactions between the entities and their
environment.
The same, contextual approach will be followed in this paper as regards the
difference in social behaviour in two related chimpanzee species, the common and
pygmy chimpanzee. Female dominance over males manifestly occurs in the pygmy
chimpanzee, male dominance is current in the common chimpanzee (7). Following
the traditional scenario, female dominance in the pygmys is attributed to the
formation of coalitions against males but such coalitions are described also for
common chimpanzees, for instance by de Waal (8). Since both species differ
significantly in cohesiveness of grouping (the pygmy chimpanzees group more
cohesively (7)), we will focus here on explaining the described contrast in female
dominance as a side-effect of the difference in cohesiveness per sé, without assuming
a higher tendency among females to form coalitions against males.
In our approach we discard the fixed image of dominance, because cherishing it
implies the assumption that there is a strong heritable component in dominance rank.
This view is supported by some (9), but it is contradicted by the failure to replicate
former dominance relations in experiments in which individuals are reshuffled
between groups (10).
Instead of being strongly inherited, others, such as Rowell (11) and Chase (12)
consider dominance to be due to chance and the self-reinforcing effects of winning
and losing. Whereas the winner of the first encounter is decided purely by chance,
after winning or losing once, the effects of winning and losing are self-reinforcing.
For instance, Chase has shown by means of experiments that after losing, a monkey is
more likely to lose again even when it encounters a much smaller opponent whom it
would have defeated easily under other circumstances. This points to a strong psychophysiological, experience-based component in dominance rank.
Furthermore, how dominance may be subject to self-organisation, because
characteristics of dominance hierarchy and spatial structure (specifically the central
location of dominants) are mutually reinforcing has been shown by means of an
individual-oriented model (13,14).
Taking the last-mentioned approach, we are now going to study the effects of
cohesiveness on rank-overlap between both sexes by means of an individual-oriented
model. Since primate species are described to differ in their intensity of attack (15),
we study virtual entities of different species-specific intensities of attack. The present
model deals with dominance interactions among grouping entities and was originally
inspired by a model designed by Hogeweg (13). It consists of a homogeneous world
with entities that are merely aggregating and that, upon meeting each other, perform
dominance interactions, if risks are low (14,16-18). The superior fighting capacity of
males compared to females is represented by a higher intensity of aggression
(following findings on primates by Bernstein 19) and by a higher initial rank value in
so-called ‘StrongType’ entities, higher than in ‘female’ inspired entities called
‘WeakTypes’. Within each type of entity, individuals are completely identical at the
beginning of each run. The outcome of the model will be used to produce testable
hypotheses for real primates.
2 Methods
In this section, a description of the model and behavioural measures is given.
2.1 The Model
The model is individual-oriented and event-driven (see 20). It is written in objectPascal, Borland Pascal 7.0 and consists of a ‘world’ (toroid) with its interacting
agents, its visualisation and special entities that collect and analyse data on what
happens in the ‘world’ (cf. the ‘recorders’ and ‘reporters’ of Hogeweg, 1988). The
‘world’ consists of a space of 200 by 200 units. At the start of each run entities
occupy random locations within a predefined subspace of 30 by 30 units. Since the
space of the world is continuous, agents are able to move in any direction. They have
an angle of vision of 120 degrees and their maximum perception distance (MaxView)
is 50 units. Activities of agents are regulated by a timing regime, as follows. Each
entity draws a random waiting time from a uniform distribution. The entity with the
shortest waiting time is activated first. The lapse of waiting time is usually the same
for all entities, but if a dominance interaction occurs within NearView of an agent, its
waiting time is reduced, thus increasing the probability that the agent will be
activated. Agents group and perform dominance interactions according to a set of
rules described below (figure 1).
2.1.1 Grouping rules
Usually, two opposing forces affecting group structure are postulated: on the one hand
animals are attracted to one another because participation in a group provides safety;
on the other, aggregation implies competition for resources, and this drives
individuals apart (e.g., 21).
The forces leading to aggregation and spacing are realised in the model by a set of
rules that are graphically displayed in Figure 1 (see 14).
Select Nearest Partner
Others
Yes
No
Yes
No
DOMINANCE
INTERACTION
Move On
OTHERS
Ego Wins
Goto
Opponent
PERSSPACE?
Others
Ego Loses
Flee From
Opponent
NEARVIEW?
Move To
Other
MAXVIEW?
No
Yes
TURN (Search Angle
At Random To Right
Or Left)
Fig. 1. Flow chart for the behavioural rules of the entities
2.1.2. Dominance interactions
Dominance interactions are competitive interactions over resources that are not
specified in this model, but are presumed to include, food, mates and spatial location.
Competitive interactions are only initiated if the perceived risks of defeat are low (i.e.
so-called risk sensitive system (14). Interactions between agents are modelled after
Hogeweg (22) and Hemelrijk (14), as follows:
− Each entity has a variable DOM (representing the capacity to win a hierarchical
interaction).
− After meeting one another in their PerSpace, entities ‘decide’ whether or not to
attack following the Risk-Sensitive system. Here, the probability to attack
decreases according to the potential risk of defeat as follows. Upon meeting
another agent and observing its DOM-value, an entity may predict it will win or
lose on the basis of a ‘mental’ battle, which follows the rules of a dominance
interaction as described below. If ego loses the mental interaction, it will refrain
from action (thus displaying ‘non-aggressive’ proximity). If it wins the mental
battle, it will start a ‘real’ dominance interaction.
− If an actual dominance interaction takes place, then entities display and observe
each other’s DOM. Subsequent winning and losing is determined by chance and
values of DOM as follows :
DOM i

 1 DOM + DOM > RND(0,1)
wi =
(1)
i
j

else
 0
Here wi is the outcome of a dominance interaction initiated by agent i (1=winning,
0=losing). In other words, if the relative dominance value of the interacting agents
is larger than a random number (drawn from a uniform distribution), then agent i
wins, else it loses. Thus, the probability of winning is larger for whoever is higher
in rank, and this is proportional to the relative DOM-value with its partner.
− Updating of the dominance values is done by increasing the dominance value of
the winner and decreasing that of the loser:


DOMi
 *STEPDOM
DOMi : = DOMi +  wi −


+
DOM
DOM

i
j


DOMi
 *STEPDOM
DOM j: = DOM j −  wi −


DOM
+
DOM

i
j
(2)
The consequence of this system is that it functions as a damped positive feedback:
a victory of the higher ranking agent reinforces their relative DOM-values only
slightly, whereas success of the lower ranking agent gives rise to a relatively large
change in DOM. (To keep DOM-values positive, their minimum value is,
arbitrarily, put at 0.01.) The change in Dom-values is multiplied by STEPDOM,
i.e. as a scaling factor that varies between 0 and 1 and represents intensity of
aggression. High values imply a large change in DOM-value when updating it,
and thus indicate that single interactions may strongly influence the future
outcome of conflicts. Conversely, low STEPDOM-values represent low impact.
− Winning includes chasing the opponent over one unit distance and then turning
randomly 45 degrees to right or left in order to reduce the chance of repeated
interactions between the same opponents. The loser responds by fleeing under a
small random angle over a predefined FleeingDistance.
From now on, the initiation of a dominance interaction is for short referred to as
‘attack’.
2.2 Experimental set-up and Data collection
Here, the same parameter setting (n=8, persSpace=2, nearView=24,
FleeingDistance=2 units) is used as in a former study (23).
The present study is confined to a population size of ten entities consisting of two
types that differ in fighting capacity. Reflecting the physiologically superior fighting
abilities of males (e.g. muscle structure) compared to females, StrongTypes start with
a higher winning tendency than WeakTypes (i.e. of 20 versus 10) and display a
higher intensity of aggression. I have experimented with three different StepDom
values (i.e. 1.0, 0.5 and 0.25 for StrongTypes). StepDom values for WeakTypes were
always 80% of those of StrongTypes (respectively 0.8, 0.4, 0.20).
Varying the SearchAngle (i.e. 45, 90 and 180 degrees) produces three degrees of
cohesiveness of grouping. For each combination of Stepdom and Searchangle, 5 runs
are conducted, resulting in a total of 5 * 3 * 3 = 45 runs.
During a run, every change in spatial position and in heading direction of each
entity is recorded. After every time step (consisting of 160 activation), the distance
between agents is calculated. Dominance interactions are continuously monitored by
recording: 1) the identity of the attacker and its opponent; 2) the winner/loser; 3) the
updated DOM-values of the entities.
2.3 Measurements
At intervals of two time steps (320 activation), the degree of rank differentiation and
the overlap between the dominance hierarchies of StrongTypes and WeakTypes are
measured as follows.
Rank differentiation is measured by the coefficient of variation (standard deviation
divided by the mean) of Dom-values (24). For each run the average value is
calculated. Higher values indicate larger rank distances among entities.
At the start of each run, all StrongTypes are dominant over each WeakTypes, but
during run-time some WeakTypes may become dominant over (some or all)
StrongTypes. The degree of dominance of WeakTypes over StrongTypes is estimated
by the Mann Whitney U- statistic (25). At the beginning of the run U-values are zero.
Later on they may become positive.
Bidirectionality of attack is calculated as a τKr-correlation between an actor and
receiver matrix of attack (26). This statistic measures the correlation between the
corresponding rows of two social interaction matrices. The method reckons with the
statistical dependency due to recurrent observations of the same individual. The
measure of Unidirectionality of attack corresponds to the sign-changed τKr-value.
The clustering together of entities of the same type is measured as a τKr-correlation
between a matrix of mean distance among entities and a ‘hypothesis’-matrix. The
‘hypothesis’-matrix reflects Type-segregation because cells belonging to entities of
the same type are filled with the number 1 and cells of different types are filled with
zeros. Segregation is thus reflected by a positive correlation.
The degree with which dominants occupy the centre is measured by the spatial
directions of others around ego. Using circular statistics (27) the centrality of each
individual is calculated for each scan by drawing a unit circle around it and projecting
the direction of other group members (as seen by ego) as points on the circumference
of this circle. Connecting these points with the origin produces vectors. The length of
the mean vector represents the degree in which the position of group members relative
to ego is clumped; longer mean vectors reflect more clustering in one direction and
indicate lower centrality (i.e. lower ‘encirclement’). Thus, greater centrality of higher
ranking entities is reflected in a stronger positive correlation between rank and
encirclement.
To exclude a possible bias brought about by transient values, the correlations for
centrality of dominants, for unidirectionality and between social behaviour and rank
of the partner, are calculated on data collected after time-step 200.
3. Results
3.1 Cohesiveness of groups.
Cohesiveness of grouping decreases at lower values of SearchAngle, because
entities return to others later. This is in line with former findings based on a discrete,
lattice-based world (16,17). Different degrees of cohesiveness will be referred to as
high (SearchAngle=180°), medium (SearchAngle=90°) and low cohesiveness or loose
groupings (SearchAngle=45°). Looser grouping diminishes the frequency of
interaction. StepDom affects mean distance much less than SearchAngle and only
affects distance for the most cohesive grouping (i.e. via route 1, described below).
Cohesiveness
B
A
High
0.9
C. V. Dom-values
RankOverlap
H
Ste
M
pD
om
L
L
M
H
h
Co
iv
es
en
e
ss
0.8
0.7
1.0
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.6
0.5
0.4
0.3
0
28 56 84 112 140 168 196 224 252
0.3
0.3
0
Time Steps
E
Ste
pD
om
L
28 56 84 112 140 168 196 224 252
Time Steps
High Cohesiveness
Loose Grouping
30
35
26
30
22
H
M
0
Time Steps
40
M
M H ss S
tep L
L
ne
e
Do
siv
m
he
Co
L
M
C
H
e
oh
s
n
ive
e
ss
Dom-Values
Centrality
H
28 56 84 112 140 168 196 224 252
C
Unidirectionality
D
Loose
Medium
1.0
25
18
20
15
14
10
10
5
6
0
-5
-20
2
40
100
160
Time-Steps
220
280
0
60
120
180
240
Time-Steps
Fig. 2. Means and standard errors are calculated over 5 runs. H = high, M = medium, L = low.
A. Standard error above and below the mean U-statistic (measuring dominance of Weak- over
StrongType) for different degrees of cohesiveness and StepDom-values. B. Mean Rankdifferentiation measured by the coefficient of variation of Dom-values for different conditions.
Lines of increasing boldness correspond to increasing StepDom-values. C. Differentiation of
Dom-values for Strong and WeakType entities with StepDom = 1. Typical case as observed in
one run of highly cohesive and loosely grouping VirtualSpecies. Grey: WeakTypes, black:
StrongTypes. Bottom left: Standard error above and below the mean of D. centrality measure
between Dom-value and Encirclement and E. the measure for unidirectionality.
3.2 Rank-overlap and other social-spatial consequences.
In line with expectancies, WeakTypes dominate more over StrongTypes at higher
levels of cohesiveness (Figure 2). This holds at all intensities of attack. Furthermore,
the degree of rank-overlap between both Types also increases with higher intensity of
attack (Figure 2). This can be explained, because both high intensity and cohesiveness
cause larger rank-differentiation (Figure 2B). Thus, ranks among both Types, Strong
and Weak, diverge more, so that their hierarchies of both types overlap faster (Figure
2C).
The stronger hierarchical differentiation in medium and highly cohesive groups
arises from a complex interplay with spatial structure. This interplay can be described
as if following three sub-routes (Figure 3).
First, while the hierarchy differentiates in the course of time the entities space out.
This is due to the stronger role diversification that accompanies rank differentiation:
some entities become permanent losers and by fleeing again and again from others
they move further and further away from their group members. In this way the group
spaces out. Spacing out causes the frequency of aggression to decline. This naturally
implies a smaller number of opportunities for rank-reversal, and thus a more stable
hierarchy. The stability of the hierarchy, in turn, maintains its differentiation. A more
differentiated hierarchy is more stable (Figure 3, route I).
Second, differentiation of the hierarchy also increases unidirectionality of attack
and this enhances its stability, which in turn supports its differentiation (Figure 3,
route II).
Third, strong hierarchical differentiation and stability cause, and are maintained by,
a spatial structure with dominants in the centre and subordinates at the periphery.
Spatial centrality of dominants emerges because entities of similar rank have equal
chances of being defeated by or defeating each other. Since they are also treated in a
similar way by other group-members, they will remain on approximately the same
location. Lower-ranking entities are chased away by more group-members and
therefore end up at the periphery. In turn, spatial structure also maintains the stability
and differentiation of the hierarchy, because entities mainly interact with partners that
are close in rank. It follows that if a rank-reversal occurs, it will not be a dramatic one
M e a n D ista n c e
+
I
+F re q u e n c y o f A tta c k
R a n k D if fe r e n tia tio n
+
+
II
+-
U n id ir e c tio n a lity
III
S p a tia l C e n tra lity
o f D o m in a n ts
+
+
S ta b ility o f R a n k s
(Figure 3, route III).
Fig. 3. Summary of interrelations of different variables. Numbers indicate processes leading to
increased rank differentiation described in the text.
Although these three routes are interconnected, significant correlations for these
effects are mainly found at medium and high values for cohesiveness and intensity of
attack (see stronger average spatial centrality (Figure 2D) and average
unidirectionality (Figure 2E) found at these conditions).
Cohesive groups differ from loose groups in two respects, the average distance and
total frequency of attack. To keep the total frequency of attack under control we run a
loose group proportionally longer than a highly cohesive group (i.e. ten times). The
hierarchical differentiation, spatial centrality and unidirectionality of attack appear
weaker, after the same frequency of interactions, than in a strongly cohesive group
(Figure 4) and the three routes of social-spatial structuring (based on correlations over
periods lengthened proportionally to contain the same mean frequency of attack as in
cohesive groups) are non-significant. Yet, unexpectedly, dominance of WeakTypes
over Strong ones is similar after the same frequency of attack in highly cohesive
groups! This may be due to lower sexual segregation than in cohesive groups (Figure
4), which may lead to relatively higher frequencies of interactions between the sexs.
As a consequence, StrongTypes may be ‘pulling up’ WeakTypes and WeakTypes
‘pulling down’ Dom-values of StrongTypes, dissolving the rank-differences between
them. These details will be tested in a subsequent study.
0.8
Centrality of Dominants
0.8
0.6
0.4
0.2
0.0
High
Low
0.5
0.7
0.6
Undirectionality
Rank-differentiation
1.0
0.5
0.4
0.3
0.2
0.1
High
Cohesiveness
0.1
High
Low
Cohesiveness
Spatial Segregation
0.06
8
6
(U)
0.2
0.0
Low
10
Rank-overlap
0.3
0.0
-0.1
Cohesiveness
4
2
0
0.4
High
Cohesiveness
Low
0.02
-0.02
-0.06
-0.10
-0.14
-0.18
High
Low
Cohesiveness
Fig. 4. Comparison of social spatial measures (mean plus/minus S. E.) between highly cohesive
and loose groups controlled for the total frequency of attack.
4. Discussion
4.1 The model
Effects of cohesiveness are similar to those of intensity of aggression (for group
size 8, see 14,18): both result in a steeper hierarchy and consequently more rankoverlap develops between types.
In more cohesive groups the initial two rank classes to which StrongTypes and
WeakTypes belong, clearly dissolve faster due to more frequent encounters. This
effect was also described by Hogeweg and co-authors (22,28) in a model on
‘BumbleBees’. The Bumble colony consisted of a Queen with a high initial rank and
many Workers with a low initial Dom-value. Dissolution of the rank differences was
correlated with speed of nest growth. In a slow-growing colony, workers had much
time to interact with the Queen and consequently, relatively many workers transfer to
the ‘elite’ rank category of the Queen. In a fast-growing colony, workers are more
occupied with rearing young and so are left with fewer opportunities for interaction.
Due to the rareness of interactions, the hierarchy among workers remains weak and
labile, so that only few Workers transfer to the ‘elite’ category. Thus, ranks of
Workers and the Queen are kept apart more distinctly.
4.2 Biological Implications
Increased cohesiveness not only obscures rank-categories belonging to different
types, but also enhances spatial centrality of dominants. In the model, such spatial
structure emerges although entities do not prefer a central, or some other, spatial
location. Therefore, the model presents us with a parsimonious alternative to the
selfish herd theory (29) in which it is assumed that individuals evolved a ‘centripetal
instinct’, because it is safer to be surrounded by others as a protection against possibly
approaching predators.
In confirmation of the model, a preference for spatial centrality has so far not been
discovered in real animals, not even in the very elegant fish experiments carried out
by Krause (30). What is clear, however, is that upon perceiving signals of a predator,
fish tighten their shoals. In a shoal consisting of small and large fishes, increased
cohesiveness leads to size assortment, with large fishes in the centre and small ones at
the periphery (31). Again this is in line with our model: Because large fishes were
dominant over small ones, size-assortative shoaling is exactly what is expected to
occur, and there is no need for an assumption of a certain preference for any location.
This model represents only the barest essentials of group-living and dominance
interactions. It bears no resemblance to highly intelligent and complex apes. Yet, the
essential characteristics of this model may hold for any group-living species that
performs dominance interactions. Supposedly, it is a general rule that cohesiveness
entails more rank-overlap among types. Thus, these results confirm the hypothesis
that initially inspired this study: the fact that female dominance is relatively stronger
in pygmy chimpanzees than in common ones may, at least partly, be a due to their
stronger cohesiveness of grouping. Thus it is unnecessary to invoke additional
differences among species in co-operative tendencies among females against males.
However, the model does not preclude that coalitions among females contribute to
female dominance. However, even if future study confirms a relatively higher
frequency of female coalitions among pygmy chimpanzees than common ones, even
then it is not clear whether these coalitions are caused by or the result of female
dominance: after all, higher female rank, arising from stronger cohesiveness, may
allow females to co-operate more intensely against males than in those cases in which
females rank lower.
Cohesiveness of groupings varies not only between species (e.g. see, 32), but also
within species according to environmental conditions. Chimpanzees, for instance,
group more cohesively in less seasonal areas (33). It would therefore be interesting to
compare the degree of rank-overlap between both sexes for different environments.
Thus, these individual-oriented models produce new hypotheses for studying
social-ecological processes and their consequences and direct our research into a more
situated context-based, realistic approach.
Acknowledgements
I am grateful to Rolf Pfeifer for continuous support, to René te Boekhorst for
comments on the figures and to Jaap Hemelijk for correcting the English. This work is
supported by the Swiss National Science Foundation by a grant from the Kommission
zur Förderung des akademischen Nachwuchses der Universität Zürich.
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