Self-organised Social Systems Of
Animals
Mini Course Italy Day2 Hour 1
150909
Charlotte K. Hemelrijk,
Theoretical Biology
Centre for Ecological and Evolutionary Studies
University of Groningen
The Netherlands
Complex Social Phenomena
Birds
Fish
Primates
Primate Societies
• Diverse social systems
• Competition
• Dominance hierarchy
Societies: Despotic
Hierarchy: Steep
Egalitarian
Weak
( Vehrencamp, 1983)
Despotic and Egalitarian Primate Societies
Egalitarian
Despotic
Macaques (e.g., Thierry 1985, 1990)
Long-tailed Macaque
Despotic Egalitarian
Hierarchy
Steep Weak
Attack Intensity
Celebes
Sparse
Macaque
Attack Asymmetry
Male Migration
Female choice
etcetera
Each difference: separate mechanism?
This talk: one factor (intensity of aggression)
Virtual Laboratory
(Epstein & Axtel, 1996)
Virtual World Inhabited by Entities
(Hogeweg, 1988)
• Move About and Aggregate
• Perform Dominance Interactions
Social-Spatial Structure
Dominants in Center, Subordinates at Periphery
Vary: Intensity of Aggression
Individual-Oriented Model
* World: Torus, Continuous Space
* Activation: Local and Random
* Agents:
• Group and Compete
• One Sex
* Experiments and Analyses:
•10 Runs for each Intensity of
Aggression (High/Low)
• Averages over 10 Runs
torus
Periodic boundary
Rules
Dominance
SELECT
NEAREST PARTNER
Grouping
OTHERS
YES
NO
Consider
DOMINANCE
INTERACTION
YES
OTHERS
WIN
PERSSPACE?
NO
MOVE ON
OTHER
LOSES
FLEE FROM
OPPONENT
CHASE
OPPONENT
NEARVIEW ?
MOVETO
OTHER
YES
MAXVIEW?
NO
TURN
(SEARCH-ANGLE)
Dominance Acquisition
• Conventional:
Quality of Individual (Ellis, 1994)
• Self-Structuring:
Chance and Self-reinforcing Effects of Winning
and Losing (Chase et al, 1994)
Dominance Interactions
(Hogeweg & Hesper, 1983; Hemelrijk 1998, 1999, 2000)
1. DOM = Capacity to Win
initDom 8
2. Upon Meeting, Conflict
Risk Sensitive
Hemelrijk (1998)
DOMi
3. Prob(i wins from j) ~ DOMi
=
RelDom
+ DOMj
4. Updating
Domi,n+1 := Domi,n ± (Wi,n - RelDom) * StepDom
0 or 1
Damped Positive Feedback
Low
High
0.10
1.0
Behavioural Measurement
* Who Interacts with Whom
* Dominance Hierarchy
• Differentiation
* Spatial Structure
Centrality of Dominants
Measurements
Coefficient of Variation ( CV):
CV  SDDOM .100
AvDOM
30
CV High
CV Low
Dominance Differentiation
Dom-Values
20
10
0
0
100
200
300
400
500
Time
Spatial Centrality of Dominants
3
5
2
2
5
46 3
1
.5
5
1
.5
5 57
42
1
.
5
1
.5 4 5
7
2
4
4 1
4
1
46
7
1
.5
.5
2
.5
3
3
774 4
1 1
6
5 1
.5
3 1
.52
7
5
.5 6 4 6
563
6 1
34
7
5
6
63
5
1
4
6
5
3
6
6
6
6
3
4
7
3
6
64
6
3
547
1
.5 4
6
7
7
4
1
.5
7
3
1
.5
6
4
3
6
6
7
7
7
5
5
5
6
3
1
.
5
5
3
1
.5
4
77
8
1
.5
7
4
4 7
3
3
7
4
5
5
6 7
2
1
.5 2
4
6
76 7
3
1
2
6
1
.53
54
31
7
.
513
.5
5
1
.5
5
1
.5
1
.5
6 51
5
4
1
5 1
.5
43 3
1
.5 3
7
2
1
2
2
2
3
5
7
5
41
.5 1
2
7 2
4
3
7 25
1
2
5
1
5
1
5
7
1
.5
1
6
4
2
2 1
7
6
6 .5
3
1
2
5
1
.5
1
.5
4
1
5
5
Y
Negative Correlation: Dom-value and
Vector for Being Surrounded
at all Sides
-5
-1
5
-2
5
-3
5
-3
5
-2
5
-1
5
-5
5
X
1
5
3
2
5
3
5
Results
• Demo
Dominance Differentiation
0
.9
0
.8
0
.7
0
.6
CoefficientofVariation
0
.5
0
.4
0
.3
0
.2
40
40
35
35
30
30
25
25
20
20
15
15
10
10
0
.1
0
.0
5
5
0
0
0
50
100
150
200
250
M
ildS
p
e
c
ie
s
Low
300
0
50
100
150
200
250
300
F
ie
rc
eS
p
e
c
ie
s
High
Intensity of Attack
Stronger Differentiation at High Intensity
Asymmetry of Attack?
Symmetry of Attack
(Hemelrijk, 1990: Anim. Behav. 39, J. theor. Biol. 143)
Receiver
Actor
A
B
C
A
B
C
A X
2
1
A X
12
22
SA
Actor B 12
C 22
10
X
21
Receiver
X
B
2
X
21
SB
C
1
10
X
SC
SS
Negative correlation:
Unidirectionality
tKr
Corrected for
ties and N
+
Dominance Differentiation and Symmetry
0
.9
0
.8
-0.1
0
.7
0
.6
Symmetry
CoefficientofVariation
0
.5
0
.4
0
.3
0
.2
40
40
35
35
30
30
25
25
20
20
15
15
10
10
0
.1
0
.0
-0.3
5
5
0
0
0
50
100
150
200
250
M
ildS
p
e
c
ie
s
Low
300
0
50
100
150
200
250
300
F
ie
rc
eS
p
e
c
ie
s
High
Intensity of Attack
-0.5
Low
H
igh
IntensityofA
ttack
Stronger Differentiation, less Symmetry at High Intensity
Cohesion and
Reduction of Aggression
4
6
17.5
4
2
16.5
15.5
Low
3
8
High
14.5
13.5
12.5
11.5
Low
10.5
0
60
120
T
im
eu
n
its
180
Time units
240
FrequencyofAttack
Distance
3
4
3
0
2
6
High
2
2
0
6
0
1
2
0
1
8
0
T
im
e
-U
n
its
Emergent:
Not just internal Characteristic
2
4
0
Spatial Structure
H
ig
hIn
te
n
s
ity
3
5
2
2
5
46 3
.5
5
1
.1
5
5
7
4
2
4
.5 5 1
.5 4 5
721
4
6
4 1
4
1
4
7
.1
5
.5
2
.5
3
36 7 7 4 4
1 1
5 1
.5
3 1
3
1
.
5
2
7
4
5
3
.5 6 4 6
5
6
6
3
7
5
6
6
5
1
4
6 76
5
3
66
6
46
3
4
3
6
6
3
5
4
7
1
.
5
4
1
.5
736
1
.5
6 7 7 44
355
666 31
7
.5 5 7
3
1
.57
4757
8
1
.5
7
4 7
3
374
54
56 7
2
1
.5 2
7
4
67 6 1
36
1
2
1
.5 5 531
7
.
513
1
.5
5
1
.5
1
.5
6 5 .5 3 4
5
4
14
5
1
.
5
3
.5 7
3
2
1
21
372 2
3
5
5
41
.5 2
7 24
3
1
7
5
1
2
1
1
5 25
715
1
.5
6
4
2
2 1
7
6
6 .5
3
1
2
5
1
.5
1
.5
1
5
Y
5
-5
-1
5
-2
5
-3
5
-3
5
-2
5
-1
5
-5
5
1
5
3
2
5
3
5
X
No ‘Centripetal Instinct’ needed
as in Selfish Herd Theory (Hamilton, 1971)
High Intensity of Attack
Distance
FreqAttack
4
6
Dom-values
17.5
40
15.5
30
low
4
2
16.5
35
3
8
14.5
Distance
20
FrequencyofAttack
25
Distance
3
4
13.5
12.5
15
11.5
-
10
+
5
0
0
50
100
150
Time
200
250
60
120
180
240
2
6
2
2
0
6
0
1
2
0
1
8
0
T
im
e
-U
n
its
T
im
eu
n
its
2
4
0
high
300
Dominance Differentiation
+
10.5
0
3
0
+
Spatial Centrality
of Dominants
+
+
+
+
-
Freq Attack
-
Stability of Hierarchy
H
ig
hIn
te
n
s
ity
3
5
2
2
5
46 3
.5
5
1
.1
5
5 5 74 2
.5
1
.5 4 5
721
4
4 1
4
1
46
7
.1
5
.5
2
.5
3
36
774 4
1 1
5 1
.5
3 1
3
1
.
5
2
7
4
5
3
.5 6 4 6
6
36
76
5
653
1
45 6 3
6
5
4
76
366
6 46
635 4 7
1
.5 4
1
.5
736
1
.5
657 7 44
355
666 31
77
.5 5 7
3
1
.57
4
7
8
1
.5
76 7
4
4 7
3
374
55
2
1
.5 2
4
67 6 7
3
1
2
6
1
.535 4
1
7
.5
51
513
.5
531
.
.5
1
.5
6 51
5
4
1
5 1
.5 4 3 3
.5 3
7
2
1
21
2
3
5
772 24
5
41
.5 2
3
17 2 5
5
1
2
1
1
5
715
1
.5
6
4
2
2 1
7
.
5
6
6
3
1
2
5
1
.5
Positive Feedback
1
.5
4
1
5
Y
5
-5
-1
5
-2
5
-3
5
-3
5
-2
5
-1
5
-5
5
X
1
5
3
2
5
3
5
between Spatial Structure
and Hierarchy
Test by weakening
spatial structure
Make group less compact
Rules
Dominance
Grouping
SELECT
NEAREST PARTNER
OTHERS
YES
NO
YES
DOMINANCE
INTERACTION
OTHERS
WIN
NEARVIEW ?
PERSSPACE?
NO
MOVE ON
OTHER
LOSES
MOVETO
OTHER
FLEE FROM
OPPONENT
YES
MAXVIEW?
NO
TURN
(SEARCH-ANGLE):
180° or 45°
CHASE
OPPONENT
Grouping:
?
?
Loose groups
(Equal Aggression Frequency, Hemelrijk, 1999)
0
.8
1.0
0
.7
0.8
0
.6
0
.5
0
.4
CentralityofDominants
C.V.Dom-values
0.6
0.4
0.2
0.0
C
ohes
iv
eLoos
e
0
.3
0
.2
0
.1
0
.0
-0
.1
C
o
h
e
siveL
o
o
se
Self-Organisation
via Spatial Constraints
Real Macaques
Model
Despotic and Egalitarian
More Intense Attack associated with:
•
•
•
•
Symmetry of Attack
Cohesion
Freq of Attack
Rank-Related
Behaviour
• Centrality of Dominants
•
•
•
•
Same
Same
Same
Same
(Thierry, 1985, 1990;
Caldecott, 1986;
de Waal & Luttrell, 1989)
• Indications in space
and grooming
One Trait Only ?
Study interconnection of traits in real animals
2.2
Primate Groups
• Bi-sexual
– Males bigger than females (1.5 * size
females)
– Males intenser in their fights (more biting)
than females
• In model represent sexes by difference in
– initDom (like body size, physiology)
– StepDom (Intensity of fighting)
Dominance Interactions
(Hogeweg & Hesper, 1983; Hemelrijk 1999,2000)
1. DOM = Capacity to Win
VirtualMales: 16(32)
VirtualFemales: 8(16)
2. Upon Meeting
Risk Sensitive
Conflict
Hemelrijk 1998
DOMi
3. Prob(i wins from j) ~ DOMi + DOMj = RelDom
4. Updating
Domi:= Domi + (wi - RelDom) * StepDom
0 or 1
Damped Positive Feedback
Low
High
VirtualMales: 0.10
1.0
VirtualFems: 80% of Males
Inter-sexual Dominance
H
ig
hIn
te
n
s
ity
L
o
w
4
0
4
0
3
6
Fe
m
M
a
le
3
2
High Intensity
• Greater Female Dominance
• Lower Lowest Males
3
0
2
8
Dom-values
Dom-values
2
4
2
0
1
6
1
2
2
0
1
0
8
4
0
0
6
0
1
2
0
T
im
e
-U
n
its
1
8
0
2
4
0
0
0
6
0
1
2
0
1
8
0
2
4
0
Tim
e
-U
n
its
Support in despotic societies
• GreaterFemale Dominance: Coalitionary Tendency (Thierry 1990)
• More Male migration (Caldecott, 1986)
Integrative Model
(Grouping and Competition among Agents)
Egalitarian Society
Intensity of Aggression
•
•
•
•
Cohesion
Frequency of Attack
Symmetry
Spatial-Social Structure
– Grooming
Despotic Society
• Female Dominance
(Hemelrijk et al 2008)
– Female Choice
– Male Migration
Inter-sexual dominance?
Influenced by:
•
•
•
•
•
•
Intensity of aggression
Frequency of aggression
Cohesion of group
Attraction between sexes
% males in group
Sexual dimorphism
Intensity of Aggression
(Hemelrijk 1999)
The sexes
H
ig
hIn
te
n
s
ity
L
o
w
High
Intensity
Low
4
0
4
0
3
6
Fe
m
M
a
le
3
2
3
0
2
8
Males
2
0
1
6
1
2
8
4
0
0
Females
6
0
1
2
0
1
8
0
T
im
e
-U
n
its
MM
MM
FF
FF
2
4
0
Dom-values
Dom-values
2
4
2
0
1
0
0
0
6
0
1
2
0
Tim
e
-U
n
its
Rel H Pos F = 0 /16
1
8
0
2
4
0
F
M
M
F
M
F
F
M
Female dominance
4
2
1
1
__
8
Rel FemDom =
FemDom/ MaxFemDom =
8 /16 = 0.5
More intense Aggression,
More female Dominance Due to Stronger Differentiation
Also due to higher frequency of aggression →
Frequency of Aggression,
Food Distribution and Group Cohesion
Hemelrijk, Wantia, Daetwyler (2003)
• DomWorld with Food
and Feeding Behaviour
– Food Trees
• # = 36 Trees
• Degree of clumping
(High, Medium, Low)
• Regrowth exponential
• InitEnergy = 20,
MaxEnergy = 50 units
Low
Medium
– Feeding behaviour
• Energy > 35, statiated:
grouping and competing
• Hunger: if Energy < 35
Prob of SearchFood
increases
• Digestion 0.5 units per
time-unit
High
Clumping of Food Sources
medium
high
0.470
0.465
0.460
0.455
0.450
0.445
0.440
0.435
CV Dominance
Hierarchical
Differentiation
low
0.430
0.425
Low
Medium
High
Clumping of Food
Steeper Hierarchy and Clearer Spatial Structure
Density Effect on Hierarchical Differentiation
Hierarchy
Measure of
Female Co-dominance
# Males below Female
1+2 = 3
Mann Whitney U-value
U := S of # Males below Females
2
0 +
____
U = 5 Umax = 9
RelHPos =0.55
2.8
2.6
More Female Dominance
due to Cohesion (due to
Food Clumping)
2.4
2.2
2.0
1.8
Medium
1.6
1.4
High
1.2
1.0
0.8
0.4
Low Clumping
0.2
0.0
Fema
Female Dominance
depends on Environment!
0.6
-0.2
0
50
100
150
200
Time Units
250
300
Empirical Relevance of greater
dominance of females to males?
• Receipt of
– less aggression by males
– Less ‚rapes‘
– More tolerance by males
• Alternative to exchange
Male ‚Tolerance‘
Females are attractive
during Tumescence
Males compete for Females
• Monopolise
• ‘Friendly Strategy’: Food for
Sex, e.g. chimpanzees
Male Reproductive Strategy
(Tutin, 1979)
Males
• Male ‘tolerance’ to females at food sources
Males share food with same Female
• with whom they mate more often ?
• to whom they bear more offspring ?
No Statistical Evidence
(Hemelrijk et al. 1992;Hemelrijk, Meier, Martin 1999)
Why are males ‘tolerant’ to tumescent females ?
Sexual Attraction
DominanceWorld
High Intensity
(Despotic)
Low Intensity
(Egalitarian)
Sexual Attraction
?
Male ‘Tolerance’
as side-effect ?
Add attraction of males to females
Male Attraction to Females
Rules
Dominance
Grouping
SELECT
NEAREST PARTNER
OTHERS
YES
NO
FEMALE ?
YES
DOMINANCE
INTERACTION
NEARVIEW ?
NO
YES
MOVETO
HER
NO
MOVE ON
OTHERS
WIN
OTHER
LOSES
FLEE FROM
OPPONENT
GOTO
OPPONENT
PERSSPACE?
MOVETO
OTHER
YES
MAXVIEW?
NO
TURN
SEARCH-ANGLE
meanDomValue
High Aggression-Intensity:
Attraction versus No Attraction
F
e
m
a
le
s
2
0
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1
1
1
0
9
8
7
6
5
0
M
a
le
s
A
ttra
c
tio
n
N
oA
ttra
c
tio
n
6
0
1
2
0
1
8
0
T
im
eU
n
its
2
4
0
2
0
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1
1
1
0
9
8
7
6
5
-2
0
N
oA
ttra
c
tio
n
A
ttra
c
tio
n
4
0
1
0
0
1
6
0
2
2
0
T
im
eu
n
its
Attraction equalizes dominance of both sexes
2
8
0
Sexual Attraction and Female
Dominance to Males (Hemelrijk et al 2003)
Sexual attractiveness:
synchronous or
asynchronous (interval
5, 13, 52)
8
Synchronous Asyn 13
7
6
Asyn 5
5
4
3
Asyn 52
No Attraction
2
Fem dom to males
Relative Female Dominance
S of # of males ranking below
each female
1
0
time units
More female co-dominance during attractive period
Similar for synchronous and asynchronous attraction
Cause?
Group Cohesion?
Distance
C
o
h
e
sio
n
1
4
1
2
1
0
8
6
4
2
0
A
ttra
ctio
n
N
oA
ttra
ctio
n
Cohesion
Centrality of Dominants
Hierarchical Development
Same
50
Asynchronous: Interval of 5, 13, 52
40
30
20
10
# M-F interactions
#MF interactions
Interactions between sexes
0
Attr
M to 1F 5
M to 1F 52
No no
NoAttr
Syn
Asyn5
Asyn13
Asyn52
M to F
M to 1F 13
Attraction
More Interactions Between the Sexes
• Higher Chance for Incidental Victories
• Stronger Increase
Greater Female Dominance
Interactions among males
Asynchronous
40
30
20
10
# MM interactions
#MM interactions
50
0
no Attr
No
No
Attr
Syn
Syn
M to F
Attraction
M
to 1F 55
Asyn
Asyn5
to 1F 52
Asyn
Asyn13
13 MAsyn
Asyn52
52
M to 1F 13
More interactions among males
Males meet near single attractive female !
Stronger Hierarchical
Differentiation among Males
0.7
Asyn 13
0.6
Asyn 52
0.5
Asyn 5
0.4
Synchronous
Asyn 5
CV Males
0.3
no Attraction
0.2
0.1
time units
if females are attractive asynchronously 
smaller dominance differences between the sexes
Female Attractiveness
(Hemelrijk, Wantia, Dätwyler, 2003)
Results in More Female Dominance to
Males
• During Synchronous Attractiveness by:
– More Interactions between Sexes
• Asynchronous Attractiveness by:
– More Interactions and Hierarchical
Differentiation among Males
Female Dominance and
Attraction Increases
Male ‚Tolerance‘
Neutral Proximity
Initiated by Males
to Females
Looks like
Males Initiate to Females
Male ‚tolerance‘
14
Neutral Prox
12
Attraction
10
But is nothing else than
‘Risk avoidance’
to Females
8
6
4
No Attraction
2
0
60
120
Time Units
180
240
Alternative for ‚Male Tolerance‘
and ‚Sexual Exchange‘ !
No individual exchange (Hemelijk, Meier, Martin, 1999)
Male Attraction
to Females
Summary
Interactions
• Between Sexes
• Among Males
Female Co-Dominance with Males
Male
Neutral Proximity
to Females
Alternative to ‚Tolerance‘
‚Friendship‘
Empirical data?