Theory of Forager Networks: Simulation, Comparative Data and
Evolution of Human Cohesion and Cooperation
AAA Session on Kinship
San Francisco, Nov 2012
Doug White and Tolga Oztan
Irvine Social Science Gateway (SDSC)
Kinsources, Project Simpa (French NSF)
Theory of Forager Networks: Simulation, Comparative Data and
Evolution of Human Cohesion and Cooperation
**double starred slides begin new topics
• Cohesion, cycles & cooperative ties in network structures
• Kinship history, networks and the bicomponent (!Kung)
• Evolution of cooperation, network density & kin behavior: Joking,
Avoidances and a density packing threshold
• Simulation: Boorman/Levitt 1980 & Helbing 2012
• Succinct Summary for forager evolution
• Beyond foragers: the Densification of human society and what we
know about egalitarian behavior and network bullying in schools.
**Moody and White 2003
structural cohesion as a measurement concept
Idea: implement Menger’s 1927 theorem as a pair of isomorphic measurements:
Maximal subnetwork with no less than a (min) k-node separator  (easy proof)
min here = max below
Maximal k-cohesive subnetwork with a minimum number k of node-independent paths
between any x, y pairs of nodes  (hard) isomorphic with above
http://www.math.unm.edu/~loring/links/graph_s05/Menger.pdf proof
Theorem proven in 2005 by Ron Aharoni for infinite graphs
http://www.math.haifa.ac.il/berger/menger_2nd_submition.pdf
Hard part to develop an algorithm (slow – now fast computation)
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Cohesion: History
•
The 1927 Menger theorem proves the equivalence of a largest k-connected set of nodes in a
network (with k or more node-independent paths between them, none with a common
intermediary) and a a largest k-separable set of nodes in the same network that cannot be
separated without removal of at least k nodes. (Similarly for pairs of nodes.) Synonyms today are kcohesive sets (or pairs) or stru-cohesion. This is considered one of the core theorems and insights
of GT (graph theory)
•
“Structural cohesion” still defined after 1927 by a laundry list, not GT.
•
The 2001 White-Harary article proves that GT gives a useful measure of cohesive subgroups in
networks. The algorithm for stru-cohesion is thought to be NP hard.
The 2003 Moody-White article implemented an algorithm in SAS computing stru-cohesion. It showed
that for 10 randomly chosen AddHealth high school studies of friendship networks stru-coheion (kconnectivity outperforms all other network measures tested for prediction of student
questionnaire responses measuring “attachment to school.” Stru-coehison is a major predictor in
the Powell, White, Koput & Owen-Smith (2005) study of the Biotech Industry.
Predictions of key properties of subgroups of kinship networks hypothesized to be more demonstrably
cohesive and “cooperative” have since been found to yield significant results (100,000 marriage
networks in Medieval Florence 1200-1500, Turkish Nomads, farming communities in Austria and
Costa Rica, etc.).
The computationally hard 2003 MW algorithm is programmed by iGraph's Csárdi in 2009.
iGraph’s Csárdi 2012 discovers an O(<n2) cohesive.blocking algorithm.
(Tolga Oztan)
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Kinship Data as a DAG (Dir Asym Graph):
Basic kin-net kinship networks: Nodes are parents, edges are gendered individuals
Married individuals are a single node but link up to separate parents
Kin-net graphs constructed from standard
genealogies or GED files, using PAJEK or a
number of other programs.
Femal
e edge
Male
edge
This type of graph allows us to study
cohesion in kinship networks. It has no
k-components with k > 2, hierarchically
embedded
Marries
her MBS
Coefficients of biological relatedness ri,j
and pairwise cohesion ki,j can be coded
in matrices or graphs with individuals as
edges
FaFaSiDaSo
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Some Forager Datasets (Oztan)
•
!Kin
These and 21 others examined as well in their demographicenvironmental and network contexts.
All but two have
Joking and/or Avoidance relatives.
Joking is cooperative; Avoidance reduces conflict.
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**Kinship: History, Networks, Cohesion
Evolutionary (Galton* contra:Tylor; Driver*)
Processual & Genealogy* (Rivers*)
Structure & Link Behavior* (Radcliffe-Brown*)
Functional (Malinowski, Murdock*)
Structural-Algebraic (Lévi-Strauss*, Weil*)
Critical (Schneider* Kinship not simply biological)
Empirical Formalism-Cognition (Read*, Leaf*)
Networks (Graph theoretic, Link behavior, Network

cohesion, Bicomponents-- White*, Harary, Houseman*,
Hamberger*, Oztan*) Statistics (Bayes)
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Hypothesis: bicomponent (yellow) nodes are more likely “cooperators” (among the
questions being explored by Oztan for his PhD)
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!Kung band-wise kinship p-graph
solid lines male, dashed lines female, arrows point to parents
(Oztan) Research questions, e.g.: How do usufruct rights in
resource clusters map onto kin ties, marriage and movement
between groups, and band memberships?
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Basic kinship networks are bicomponents with egalitarian structure
(conducive to low bullying). Incoming-arrow to parents, outgoing from
children, dotted line for daughter to parents, solid lines son to parents
No tri- or higher k-component:
!Kung san (Kalahari desert)
Degree centralities are also distributed:
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Using graph theory cycles to measure cohesion between
sides as a possible predictor of cooperation in a foraging
society (!Kung – result is similar if females form the sides,
men the links)
e – n + 1 = No. of cycles 128 – 118 + 1 = only 11! - 5/11 are not sided, probability=n.s.
Tho this looks like two-sided marriages sides are random. For these (!Kung) foragers
Within generations its joking relatives across-sides that generate
dyadic 11
cooperation
This is the band-level pattern of !Kung Marriages (crosssided = Joking and Avoidances)
!Kung Marriages have too little density of
offspring to form many cohesive cycles 12
Pul Eliyan Sidedness (P-graph) in-laws are cooperative, siblings competitive over
inheritance of land and irrigation resources passed to son or daughter; gender
ambiguity in sides. This is not random; 146-103+1=44 cycles with 8 “errors” (p=.002).
But this network is almost perfectly 2-sided for marriages of those with common
ancestors (this can be seen visually).
(Foragers are not dense enough to have this level of cohesive sidedness)
Can you spot the “wrong marriage”?
Sidedness cohesion entails cooperation because brothers-in-law cooperate and Joke:
77 red lines within generations for cooperative ties
13 between sides
But !Kung Joking and Avoidances and local “sides” are
ordered purely by the ego role-pattern
ego
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Evidence of Forager Cooperation 1: Binford
2001
Lewis Binford showed that for recent forager groups, as for Pleistocene
archaeological findings, environmental variables are the primary shapers of
variation in social and ethnographic features. It is only at or above the
packing threshold that the many various forms of social organizational
complexity appear.
Ethnographic surveys of foragers uniformly show, rather than dominance hierarchies, reverse dominance hierarchies, where persons who attempt to
dominate others, or their groups, are punished by a variety of means that
prevent domination, including killing or exclusion (Boehm 2012). Prestigious
leaders emerge out of generosity and trust. In a game-theoretic framework, it is
reputation and indirect reciprocity, Nowak’s fourth mechanism (Alexander
1987), not his first (Prisoner's dilemma), that Boehm and Binford see as
the engines of forager cooperation, alongside selection (which Boehm
affirms, Binford denies). Foragers have no up-down cycles of cooperation and
defection with a game-theoretic basis in the Prisoner’s Dilemma of a minimax
optimum temptation to defect from a formerly cooperative partner, except under
catastrophic environmental conditions.
We will soon look at forager kinship behavior.
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Forager Cooperation 2: Binford 2001
Binford identified “unpacked” foragers as people living below a threshold at
which “residential group mobility is … a viable strategy for insuring subsistence
security from naturally distributed food resources” (estimated at 9.1 persons per
100 km2). These migratory “nonpacked” foragers have self-similar patterns of
behavior when comparing archaic and more contemporary time periods, i.e., as
between archaeological findings and ethnographies written over the past 400
years.
Claire Porter and Frank Marlowe note, “It is frequently suggested that human
foragers occupy ‘marginal’ habitats that are poor for human subsistence
because the more productive habitats they used to occupy have been taken
over by more powerful agriculturalists. This would make ethnographically
described foragers a biased sample of the foragers who existed before
agriculture and thus poor analogs of earlier foragers.”
Porter and Marlow tested that assertion “using global remote sensing data to
estimate habitat productivity for a representative sample of societies worldwide,
as well as a warm-climate subsample more relevant for earlier periods of human
evolution.”
Their results show that “foraging societies worldwide do not inhabit significantly
more marginal habitats than agriculturalists” (White, Gosti, Oztan & Snarey).
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Forager Cooperation 3: Cohesion
Within the networks of nonpacked foragers cooperation is based on indirect
reciprocity and easily emulated reputations. Children are taken by their family
members to learn the skills of more distant kin. Differentiation is present and valued
rather than competitive. Sharing among near and distant kin is everpresent.
What is unique about human kinship is the absence of dominance hierarchies
based on gender, compared to our closest relatives, Old World Apes (male
dominance, transmitted to sons, who remain in the community while daughters
migrate out) and New World monkeys (female dominance hierarchies, transmitted
to daughters, who remain in the community, while sons migrate out to mate).
Humans evolved to recognize mating pairs within the band or community, to
recognize fathers and father’s kin as well as the kin of mothers.
This forms a basis for social cohesion among human foragers that differs from
other primates. It's not simply a matter of sharing. Eskimos share, for example,
but sharing is also greater for some than for others (Pryor and Graburn 1980 “The
Myth of Reciprocity”).
Our hypothesis (White, Oztan) is that to the extent that differences in cohesion can
be recognized and measured in forager societies, the more cohesive subgroups
will also exhibit greater cooperation within the community. People are free to leave
a community but those who leave are likely to be those with 17 lower cohesion.
Here is another kind of network with Joking
Relations (Cohesive) as the Cooperative Glue
In the sample of 34 foragers the six groups with Br/Si Avoidance with the regressor “Fishing” as the
predictor, p=.01. The Tenino are foraging traders at the gulf of the Columbia River. The other 5
foragers are also central in trading
networks.
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Like kinship Joking behaviors that create cooperation between Brothersin-law in the Pul Eliya or !Kung cases, Tenino brothers-in-law
(WiBr/SiHu) form chains of trading partners with special privileges;
e.g., borrowing property and returning something of lesser value.
Chains of brothers-in-law operated the trading routes. WiBr's
daughters is also a “Joking” relative and can pass intimate
information; you can joke with his sons. These foragers were the
major trading society at the mouth of the Columbia River. WiBrDa, Da of
a trade partner WiBr, is “intimate but not sexually” with the FaSiHu trade
partner. Between siblings-in-law of opposite sex—BrWi & SiHu,
“Intimacy” occurs, even sexual intercourse. (Murdock 1965). Formal kintype expectations for Joking relatives generally promote cooperation.
Brother and Sister reinforce this with an avoidance relation: they cannot
even sit together or talk. WiBrWi is “like” a prohibited sister and also
entails that Br/Si avoid each other. By avoiding WiBrWi there is no
possibility of jealousy between WiBr and SiHu, the trade partners. The
Br/Si → WiBrWi entailment (WBW more widespread than Br/Si) goes
against a universal “extensionist” priority of the nuclear family
(Murdock, Shapiro, etc.)
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Forager Cooperation 4: Binford 2001
Binford (p.469): “Below the packing [settlement] threshold, hunter-gatherers are
organized so that all participating individuals have maximal access to the [essential]
vital resources that are accessible in their subsistence ranges. Participation in an
economically integrated group means that all individuals endeavor to minimize the
risk and maximize the return from cooperative labor that is directed toward obtaining
the vital resources needed to sustain the group as a whole.” This statement about
nonpacked hunter-gatherers does not imply that equal rights are assured by the
society. “Rather, in their social world, trust and respect are built upon the lifelong
associations and interactions of individual members.” Joking cooperativity fits here.
“Persons who are not considered trustworthy or 'respectable' by the community may
be denied not only equal access to resources but even their very right to exist,
which is hardly compatible with the idea of an egalitarian society in which all
individuals have rights to the corporately shared largesse." We learn from a social
network viewpoint not only that “sharing is very common among hunter-gatherer
groups that have not approached the packing threshold, as is the practice—when
necessary—of using tools and supplies that belong to other persons,” but also that
these are societies with “kin conventions extending food procurement rights to
distant kinsmen,” rights that “tend to disappear” as mobility declines above the
packing threshold. These networks persist intergenerationally, and relatively
continuous cooperation was likely to have been part of the evolution of
cooperation among nonpacked foragers.
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A full dataset for 160 cases showing Avoidances (and some of
the Joking data, both coded by Murdock) are at:
http://intersci.ss.uci.edu/wiki/index.php/Kin_Avoidances
http://intersci.ss.uci.edu/wiki/index.php/Kin_Avoidances#Data_a
nd_Concept_Lattice
Data on hunting, fishing, gathering, density etc. is found in
Binford (2001:117-129) Constructing Frames of Reference: An
Analytical Method for Archaeological Theory Building Using
Hunter-Gatherer and Environmental Datasets (N=339)
Merger of *.Rdata files is accomplished in the Irvine Social
Science Gateway, linked to online training and courses.
Note: As part of the Pleistocene comparability argument, Binford's “terrestrial”
environmental model estimates carrying capacity for a non-cultural animal shaped
like us, eating what we eat, helps to compare forager constraints archaeologically
with the ethnographic present.
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Table 1: population density & a packing threshold at 9 people/kmsq
Differentially related to Joking relations and Avoidances (p=.008)
Joking high at low density & decreases
at higher densities; p=.005.
Avoidances are uniform with density.
Triangular limited relation of Joking/Avoidance
varies with density.
Density: Packing threshold at 9.1 people/kmsq at which
there is no longer unoccupied space into which mobile
hunter-gatherers could move (Binford 2001). 22
Table 1: population density & a packing threshold at 9 people/kmsq
Differentially related to Joking relations and Avoidances (p=.008)
Avoidances more frequent than
Joking at higher density &
lower hunting. 3-way p=.008.
Density: Packing threshold at 9.1 people/kmsq at which
there is no longer unoccupied space into which mobile
hunter-gatherers could move (Binford 2001).
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The packing density threshold (9.1 persons/sqkm) is a
significant separator of Joking-Cooperation versus
Avoidance-as Conflict reduction. It is a density value at
which there is no longer unoccupied space into which a
new members of minimal mobile hunter-gatherer group can
be sustained (Binford 2001).
All but two of our 34 forager groups have Joking or
Avoidance or both. THIS IS PROBABLY AN INDICATOR THAT
THESE PATTERNED AND OBLIGATORY KIN RELATIONSHIPS HAVE
BEEN PRESENT IN PROTOTYPICAL FORAGER SOCIETIES. THERE IS
NO REASON WHY THESE REGULATOR KIN BEHAVIORS SHOULD NOT
HAVE BEEN COMMON IN THE LATE PALEOLITHIC, EVEN BEFORE THE
ADVENT OF HUMAN LANGUAGES. They co-occur even below the
packing threshold, but Joking, which creates cooperation,
is more common, and declines above the threshold, as
populations grow large. Avoidance, which avoids conflict,
is also common, but tends to replace Joking as
populations grow and kin relations grow thinner, with
more potential for conflicts between non-kin. Presumably,
these are prototypical integrative behavioral mechanisms
for early cooperativity.
Because certain Avoidances eliminate many of the Joking
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relations, but not vice versa, Avoidances have precise
Kin Avoidances
1995 DRW worldwide comparative result: kin avoidance entailments across kin types, drawn by
Wille. Again: The Br/Si → WiBrWi entailment (WBW more widespread than Br/Si) goes against a
universal “extentionist” priority of the nuclear family. These avoidance rules do hold for foragers
above the packing threshold.
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Simulations: What kinds of (kinship) networks do foragers have?
© Helbing, Dirk. 2012. Social Self-Organization]. Springer Berlin. Chapter 14. Systemic Risks in Society and Economics] 285-299
Fig. 14.10 Establishment of cooperation in a world with local interactions
and local mobility (left) in comparison with the breakdown of
cooperation in a world with global interactions and global mobility
(right) (blue square= cooperators, red = defectors/cheaters/free-riders)
(after [p140]). The loss of solidarity results from a lack of neighborhood
interactions, not from larger mobility. (see Boorman and Levitt 1980 Chs.
2-5. The Genetics of Altruism. NY: Academic Press)
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Simulations: ©Helbing 2012 Social SelfOrganization. Springer Berlin.
# (6) [http://www.springerlink.com/content/8u273nk752q31wj5/fulltext.html
Cooperation in Social Dilemmas] 139-151. Summary: adaptive group pressure,
which makes the payoffs to cooperation dependent on the endogeneous dynamics
in the population. This could explain the extent of cooperation among foragers.
# (7) [http://www.springerlink.com/content/u81821078n335152/fulltext.html Coevolution of Social Behavior and Spatial Organization] 153-167. Summary: the
sudden outbreak of predominant cooperation in a noisy world dominated by
selfishness and defection, when individuals imitate superior strategies and show
success-driven migration. In our model, individuals are unrelated, and do not
inherit behavioral traits. They defect or cooperate selfishly when the opportunity
arises, and they do not know how often they will interact or have interacted with
someone else. Moreover, our individuals have no reputation mechanism to form
friendship networks…. the outbreak of prevailing cooperation, when directed
motion is integrated in a game-theoretical model, is remarkable, particularly when
random strategy mutations and random relocations challenge the formation and
survival of cooperative clusters. Our results suggest that mobility is significant for
the evolution of social order, and essential for its stabilization and maintenance.
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Succinct summary of a Network Theory for Evolution of Cooperation among
Foragers. D.R. White 2012.
*Definitions are given in the discussion.
(1) The perspective, evidence and simulations presented here lead to a novel
conception of human evolution as emerging from generalized cooperativity
among archaic and later foragers, at variance with an intrinsic selfishness
thought to imply universal competitive gaming, as Dawkins and Nowak suggested.
(2) In general, for friendships, political & corporate alliances, growth of successful
family groups, and, in kin groups--residence, inheritance and lower outmigration--,
groups identified by structural (stru-)cohesion* show consistent side effects
not replicable by other measures. White et al. citations.
(3) Forager evolution benefited from large brains, recognition of extensive biparental kinship networks, and of marriage within the group, i.e., .structural
endogamy (technically, 2-cohesive or bi-connected* networks of kinship). But
forager population density is often so low -- !Kung 6.6pl/sqkm, 21 Inuit average
2.4pl/sqkm (Binford 2001)-- that stru-cohesion may be insignificant, with too few
effective cycles.
(4) Foragers at low densities have small tightly kin-integrated groups (family,
band, composites of bands) with near-universal access to resources and use-rights
mediated through kinship roles. Reputation for generosity is the basis for prestige
and attempts at leadership domination are punished. Children acquire skills
introduced by kin with diverse abilities and knowledge. Binford 2001.
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(5) Stru-cohesion provides a basis for forager cooperation, augmented by pairwise
k-cohesion* between ancestors with many children (White & Oztan), while
stereotyped kinship roles (Murdock) such as Joking relations* can facilitate a
direct basis for cooperation that is either group-extended, as between two
subgroups marrying reciprocally, or as extended along chains, e.g., in trade
partnership circuits. Within-generation cooperation is a common result of
such role structures.
(6) A second type of stereotyped pairwise roles that ameliorate potential kinship
conflicts are those of Avoidance* of parents-in-law (which reduces conflict and
loosens access to within-generation spouses) or Avoidance in WiBrWi and in
Br/Si dyads (when siblings-in-law transitivity is at risk, e.g., in trader-circuits).
(7) The great majority of foragers worldwide utilize these various mechanisms to
facilitate cooperation, and have done so in the past. Below the forager packingdensity threshold (9.1/sqkm)*, Joking is most frequent, and declines with
population density; while Avoidance is less frequent, and increases with
population density. Both eventually decrease as complex societies develop with
higher population densities.
(8) As complex societies develop with high population density, local kinship
networks may densify due to greater numbers of children, and as other nonkin relationships develop with high structural levels of cohesion, often marked by
bullying others, success in defense of the group, and new conflict-avoidance
mechanisms.
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Cohesion and behavior 3rd-4th grades
Links= self reported friendships
classes with egalitarian (low-k)
classes with hierarchical (hi-k)
cohesion have little bullying,
cohesion have bullying,
bullies liked,
aggressors unpopular
<--(no class size effect)--> victims unpopular
All: aggression corr. with popularity but
neg. corr. with social preference.
All: victimization neg. corr. with both pop.&pref but not corr.30
with aggression
UC Davis Faris & Felmlee bullying study: school-wide
Links= self reported
friendships
12th
green
9th
11th
yellow
8th blue
scattered
N ~ 6-700 more
bullying within
grades than
between
10th
orange
10th
dark
orange
Better interpretation in
the next slide where
variance is examined
http://vidi.cs.ucdavis.edu/projects/AggressionNetworks/
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