Kinship and ComplexityAdvances in Kinship Analysis

Douglas R. White

October 24, 2008

Kinship Computing & Complexity: Cohesion, Class, and Community

1. Define a graph

that represents how marriages form cycles

Data and Representation:P-graphs link parents (flexible & culturally defined) to offspring

They are constructed by showing:

• Each individual a line

•Each gender a different type of line

•Each couple (as) a node

2. Link this representation

to actual marriage network data

Data and Representation:Building Kinship Networks

P-graphs link pairs of parents (flexible & culturally defined) to their decedents

P-graphs can be constructed from standard genealogical data files (.GED), using PAJEK and a number of other programs.

See:http://eclectic.ss.uci.edu/~drwhite for guides as to web-site availability with documentation (& multimedia representations)

3. What are the properties

of how marriages form cycles?

they form bicomponents =maximal sets on nodes connected in two or more independent ways

4. Bicomponents, asmaximal sets of marriages connected

in two independent ways,

measure boundaries of structural endogamy (so-define this new term)

Measure boundaries of structural endogamy

Male Descent

Female Descent

Same person (polygamy)

Lot married to his daughters

Structurally endogamous Canaanite Marriages in the narrative of the Patriarchs (White/Jorion)

Abram Sarai

Abram Hagar

Ishmael

5. That Mid-Eastern Example

was for marriages with relatives by common descent (same lineage, here, for obvious

reasons). So

By way of contrast:

6. Apply marriage bicomponents to a European town

(here, no blood marriages)

Ask: does how marriages form cycles still have consequences?

with heirship

NO LEGIBILITY HERE BUT WE’LL SEE THESE IN THE NEXT SLIDES

Feistritz Austria – structural endogamy by affinal relinking

Feistritz Austria – structural endogamy by affinal relinking (no blood marriages)

7 There are consequences but not that heirs marry heirs – we will see it is that THOSE WHO RELINK IN THE BIG BICOMPONENT ARE THE HEIRS

Attribute endogamy = e.g., heirs marry heirs

Feistritz Austria – structural endogamy

8. This is social class constituted by marital relinking

The

Time

Dimens ion

1970

1520

Feistritz Austria – structural endogamy by affinal relinking

9. BUT IS THIS JUST RANDOMNESS CREATING THE BICOMPONENT IN THIS TOWN? IS THIS BEHAVIOR INTENTIONAL?

Feistritz Austria – structural endogamy

10 Pearson’s R = .54 bicomponent with heirship

11. Lets test the randomness hypothesis as “non-intentional behavior” for each generation

For each generation,permute the marriages randomly

For example, take these three generations and permute the red lines so each existing place is occupies

Nonrandom relinking only 1-2 generations back

Random in all higher generations 3+

13 The first case we looked at in the Middle East (lineage of Abraham and

Sarah, repeated in next slide) has historical similarities with contemporary ME societies. We will look at Arabized

Turkish Nomads next, and show similar consequences of structural endogamy apply to how lineages are linked into class, and to consequences for those

who stay and those who leave the clan.

Measuring boundaries of structural endogamy

Male Descent

Female Descent

Same person (polygamy)

Lot married to his daughters

Structurally endogamous Canaanite Marriages in the narrative of the Patriarchs (White/Jorion)

Abram Sarai

Abram Hagar

Ishmael

Turkish nomads

All known members but many have emigrated

dotted= female lines

Black=patri-descent lines

Turkish nomads

Relinking only

(Structural

Endogamy)

Stayers in the community = the cohesive core

Relinking +yes no

160 14 Stay

18 71 Leave

Dotted=female lines

Black=patri-Descent lines

Turkish nomads

Names of members

allmembers

Black=patri-Descent lines

Blue=female lines

Structural EndogamyA Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:

The Role of Marital Cohesion

A power-law decay of marriage frequencies with kinship distance

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25

Frequency

0 + 156/x 2̂

FFZSD FFBSD:10-11 FZD:14 MBD:16 FBD:31

MM =206/x2

Raw frequency

(power law preferential curve)

# of Couples

# of Types

Results: Rather than treat types of marriage one by one: FBD, MBD etc., we treat them as an ensemble and plot their frequency distribution

Applications of Structural EndogamyA Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:

The Role of Marital Cohesion

types of marriage are ranked here to show that

numbers of blood marriages follow a power-law (indexical of self-organizing preferential attachments) while affinal relinking frequencies follow an exponential distribution

Omaha – 8 generations

Omaha – structural endogamy

Omaha – structural endogamy

OmahaBicomponent relinking

marriages

Non-relinked singles

1 1 0 0 Total

Generation Level,

1 late

8 early

1 1 4.8% 20 95.2% 21

2 3 17.6% 14 82.4% 17

3 7 15.6% 38 84.4% 45

4 18 8.7% 188 91.3% 206

5 36 12.7% 248 87.3% 284

6 60 22.6% 205 77.4% 265

7 50 32.9% 102 67.1% 152

8 29 41.4% 41 58.6% 70

Total 204 19.2% 856 80.8% 1060

Increases in relinking marriages with depth of ancestry

8

7

6

5

4

3

2

1

Omaha – stratification / segregation of leadership

How do we make sense of a complex kinship network?

• Start with the real network, compute generations, within each generation

• Permute each spousal choice (males or females) with equal or biased probabilities, keeping everything else the same.

• Do this 1000s of times, keeping track of network characteristic distributions

• See where the actual network occurs in this distribution for each characteristic

How do we make sense of a complex kinship network?

• The descriptive statistical use is to test the null hypothesis to see if the characteristic is different from chance (significance test p<.001) a single equal-sized simulation (rewiring) is all that is needed.

• The inferential statistic is to test whether datas are correctly generated at close to p~1.00 by biased probabilities in bootstraps generated 1000s of times

• The permute-spouse method uses TOTAL CONTROL, keeping everything else the same: unilineal genealogy, nuclear family sizes, generational changes.

How do we make sense of a complex kinship network?

• The inferential statistic is to test whether datas are correctly generated at close to p~1.00 by biased probabilities in bootstraps generated 1000s of times

• The permute-spouse method controls for everything but marriage choices: unilineal genealogy, nuclear family sizes and gender composition, generational changes.

• What is a complex network? – We can begin with power-law spread of the frequencies of

different types of blood marriage / or / affinal relinking

What data do we have about kin

• Kin term products 1) defined independently and 2) mapped onto a kin type map

• Kin type behaviors– Avoidance– Sexuality Prohibited– Respect– Informality– Joking– Privileged sexual relation

in-law extensions

Same generation avoidances

Parents-in-law

X cousins

White and Wille 1995: four dimensions of avoidances in world cultures

Advances and Benefits

• Network Visualization of Kinship

• Variables for testing theory

Network Visualization of Kinship• I want to start with a form of kinship that

Nick Allen thinks has great antiquity, the TETRADIC model, an “elementary structure” equivalent to the Kariera section system. Patrilineages are co-resident in each of the waterhole “countries” of a linguistic group. The 2 sections within a country are of alternating generations, and section exogamy creates links between countries with matching pairs of opposites.

Sale R.

Its really simple• Multiple countries, paired pairs of sections

Each gives wives, takes wives for 2 sections

But is it really simple• With pairs of generation moieties in distinct pairs of sections?

• And different numbers of patrilines in each country?

A simple test: sidedness

A real kinship network-Alyawarra

What about generations?

A simple test: two viri-sides

A simple test: two uxori-sides

A simple test: two uxori-sides(are 2% taking wrong-sided spouses?)

What about generations?

all marriages same generation

Variables so far

• Generation rank

• – same generation marriage?

• Viri-sidedness (implicit patrimoieties?)

• Uxori-sidedness (implicit matrimoieties?)

• – Uxori + Viri sides = Sections =

• – Uxori + same generation marriage =

• – Viri sides + same generation marriage

Patriline classes

Here is the same kinship network

Daughters are moving to husbands in groups that are “adjacent” in a flow of directed (asymmetric, “generalized”) exchange

A study of AGES of men and women shows that alternating generations slope away from the flow of daughters, indicating that WIVES ARE YOUNGER THAN HUSBANDS, and WiBr WiBr WiBr directed same-generation chains flow indefinitely toward the future

Patriline classes

They marry Aranda next door

Variables so far

• Viri-sidedness (implicit patrimoieties?)

• Uxori-sidedness (implicit matrimoieties?)

• Sections = Any 2 of (Viri, same generation marriage, Uxori-sidedness)

• Generation rank

• – same generation marriage?

• – age-biased slope of generation

Findings so far

• Sections outlaw adjacent-generation marriages– So competition for mates is within not between marriages

polygyny, gerontocracy– Marriage strategies and environmental conditions interact

• Sections have the effect with no age biases– Of creating closure in symmetric marriages,

• With age biases sections have the effect– Of creating aperture in asymmetric marriages, long open

chains, greater possibilities for bridging different language groups, can build intersocietal networks for survival