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Kinship and ComplexityAdvances in Kinship Analysis

Douglas R. White

October 24, 2008

Kinship Computing & Complexity: Cohesion, Class, and Community

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0. OutlineI Consequences and causes of Structural Endogamy

(marriage cycles forming bicomponents)

II Constituent elements of Structural Endogamy

(census and overlaps of marriage cycles)

III Mappings onto Networks and further findings

IV Unsolved problems

V Conclusions: Tying it all together

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1. Define a graph

that represents how marriages form cycles

(P-graphs and P-systems)

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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

•A marriage node includes the husband and wife as an

embedded graph

•i.e., a P-system

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2. This representation captures

independent nuclear families,

networks of marriage between them

how families form descent groups

marriages within and between them

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3. Now link this representation

to actual marriage network data

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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, Tipp), 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)

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4. What are the properties

of how marriages form cycles?

they form bicomponents =maximal sets of nodes, in which each pair is connected in two or

more independent ways

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This is a bicomponent with no cut-point and with two+ independent paths between every node pair.

By Menger’s theorem, these are equivalent.

It has 8 independent cycles m-n+1 m=24 edges (parent-child) n=17 nodes (couples)

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This is a bicomponent with no cut-point and with two+ independent paths between every node.

It’s also ORDERED, by a time dimension, through generations.

It has 8 independent cycles m-n+1 m edges n nodes

FZDDFZDFZ MZD

MBD MMZDDZDDD

Generation 5

And 8 corresponding named cycles

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Ancestral generation 1

Generation 2

Generation 3

Generation 4

FZDDFZDFZ MZD

MBD MMZDDZDDD

Generation 5

The 8 constituent marriage cycles of the bicomponent

(PART II)

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Mapping data onto networks• Migration• Residence• Wealth owned• Heirship--- PART III• Kin Behaviors• Kin Terms &

Products in relation to marriage

• By structural endogamy

• By generation time-series, patrilineages, matrilineages

• By viri-sides, uxori-sides

Analyses of such data can be crossed:

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e.g., Data about kin behavior (III)

• Kin behaviors mapped by kin type/kin term– Avoidance– Sexual Prohibition– Respect– Informality– Joking– Privileged sexual relation

• Associated expectations– (additional features for a given society)

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5. Bicomponents (I), asmaximal sets of marriages, each pair

connected in two independent ways,…

... identify the boundaries of structural endogamy (& so - define a new term).

This talk will focus on the consequences and causes of these units – part of the implicate order of structural endogamy.

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The idea of consequences is that structurally endogamous units define the local

boundaries of one or more implicate order groups that gain cohesion or are the cause

of cohesion, such as: religious groups, social class, ethnicities, stayers versus

migrants, endo-clans, factions, regions of exchange, etc. The consequences may run

from or to structural endogamy as implicated in the actions or activities of

those inside or outside the group.

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E.g., 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

Jacob and Esau are included in the main unit of structural endogamy

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6. This Middle-Eastern Example

shows for marriages with relatives by common descent (here, same patrilineage) and membership in a founding religious group (Judiasm).

So …

by way of contrast:

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7. Apply marriage bicomponents to a European town

(here, no blood marriages)

How do marriage cycles and structural endogamy have

consequences in this case?

Relinkings are marriages that reconnect 1 or more families

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with heirship

THE NEXT SLIDES WILL TREAT THESE

Feistritz, Austria – structural endogamy by affinal relinking

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

8. There are consequences but not that heirs marry heirs – its THOSE IN THE BICOMPONENT WHO DO RELINK BECOME THE HEIRS

Attribute endogamy = e.g., heirs marry heirsPearson’s R = .15

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Feistritz Austria – structural endogamy

9. This is social class constituted by marital relinking

The

Time

Dimens ion

1970

1520

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Feistritz Austria – structural endogamy by affinal relinking

10. BUT IS IT JUST RANDOM CHOICES THAT CREATE THE MARRIAGE BICOMPONENT IN THIS TOWN? OR IS THIS BEHAVIOR TARGETED AND INTENTIONAL?

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Feistritz Austria – structural endogamy

(i.e., bicomponent) with heirship 11. Pearson’s R = .54

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12. Here is a test of randomness as “non-intentional behavior” for

each generation

For each generation,permute the marriages

randomly

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For example, take these three generations and permute the red lines so existing marriage and child positions are occupied

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30

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Random in all higher generations 3+

13. Comparing Feistritz actual to simulated rnd relinking frequencies:- Relinking frequency >>

random back 1 and 2 generations, those where there is most knowledge & availability

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14. We look next at Arabized Turkish Nomads, similar in structure to the

Canaanites, and show how a similar implicate order of structural

endogamy applies to how lineages are linked into clans, and

consequences for those who stay and those who leave the clan.

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Turkish nomads

Names of members

allmembers

Black=patri-Descent linesBlue=female lines

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Turkish nomads

SCALING

All known members but many have emigrated

dotted= female lines

Black=patri-descent lines

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Turkish nomads: Relinking only (Structural Endogamy)

Stayers in the community ~ cohesive core

Relinking +yes no

160 14 Stay

18 71 Leave

Pearson’s R =.73

Dotted=female lines

Black=patri-Descent lines

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15. Cycles within Structural Endogamy (II)A 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

FFZSD FFBSD FZD MBD FBD

# of couples

# of kin types

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Cycles within Structural Endogamy (II) log-logA 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

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16. We look next at the Omaha, where chiefly elites are stratified

and do not relink with other social strata. Their structural endogamy is

fragmented early on into factions and decays in later generations.

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Omaha Genealogies – Chiefs and Siblings – no relinking of chiefly lines:- disconnected

ELK CLAN

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Omaha – top 4 generations - structural endogamy weak

Five disconnected components in the top four generations: sizes 643, 46, 38, 29, 15

Bicomponents of sizes 141, 4

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Omaha – all generations – structural endogamy

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Omaha – 8 generations – disintegration

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Omaha – loss of structural endogamy

OmahaBicomponent

relinking marriages

Non-relinked singles

Total

Generation Levels 1 early

8 late

1 29 41.40% 41 58.60% 70

2 50 32.90% 102 67.10% 152

3 60 22.60% 205 77.40% 265

4 36 12.70% 248 87.30% 284

5 18 8.70% 188 91.30% 206

6 7 15.60% 38 84.40% 45

7 3 17.60% 14 82.40% 17

8 1 4.80% 20 95.20% 21

Relinking marriages decrease in later generations

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2

3

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7

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17. The age-bias simulation problem (IV – Unsolved)

• The current random-simulation of marriage solution assumes that persons in the same structural generation have a uniform age distributions, a biased assumption.

• But if there are Hu-Wife age differences, then successive WiBr linkages generate younger and younger men in the same structural generation, as seen for the actual Alyawarra case where ages are known, next slide.

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Systemic age differences of wives and husbands compli-cates generational simulation: Alyawarra of Australia

G2

G3

G4

G5

G6

G7

G8

G1

G2

G3

G4

G5

G6

G7

Key: Vertical black lines male descent, red dots, females: the generations are sloped (pink and blue) in a P-graph.

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18. Solutions to the simulation problem• (Problem here is that “same generation” WiBr chains are

not a group of contemporaries but stretched in time)• Simulation for Alyawarra and similar examples can

be done considering male and females to have different average generational time, α and ß, where Δ= ß-α is the average age preference Δ ± ε for a younger spouse. We can get ß/α ratios without knowing actual ages. Varying α, ß, ε, these parameters define marriage-age probability distributions for simulations where wives can come from different generations.

• E.g., given section rules for marriage in Australia, different parameter ranges, generate varying distributions of marriage types and configurations of successive and branching WiBr chains.

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Daughters are moving to husbands in groups that are “adjacent” in a flow of directed (asymmetric, “generalized”) exchange. The flow of personnel, however, like a terracing model, also has constrained alternative flows. All these elements allow more generalizable probabilistic modeling.

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That is• Inside the structurally endogamous group we have• A “random” distribution of simulated types of

marriage, constrained by age-bias parameters and section rules and the

• Compared to the actual distribution of types of marriage

• And that actual distribution might be a function of the age-biases.

• An implicate order relation between the macro parameters of the structural endogamy group and its micro patterns of marriage-type frequencies, e.g. MBD, FZD, MMBDD, etc.

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Advances and Benefits• Network Visualization of Kinship• Variables for testing theory• The coherent probabilistic approach that is

needed can include not only comparisons against the null hypothesis, as shown, but bootstrap inferential methods for testing complex models of kinship structure, given discrete constraints where they occur (strict Australian section rules, or incest prohibitions).

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V Conclusions: Tying it all together – Back to II: Constituent Elements of Structural Endogamy

Ethnographers characterize marriage systems by “rules” of preferential behavior. This may be sufficient for some societies, E.g., which cousin marriages are favored over others.

Networks show a much broader range of marriage behaviors in most cases, e.g., Australia, East Asia, Africa. There are complex distributions of behavioral frequencies – e.g., power laws for blood marriage frequencies (Middle East) or for broad in-law relinking cycles (Europe) – and demographic constraints and factors like relative marriage ages that alter marriage probabilities. A coherent probabilistic approach is both possible and needed. Why is this important?

Because structural endogamy and cohesion has huge social consequences that need to be properly understood.

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afterword

Local structure -- ranging from marriage-type rules and frequencies to the appearance of nuclear families as autonomous -- may be part of an implicate order of wholeness within structural endogamy.

Though not explored, structurally endogamous groups could be part of a larger implicate order.

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It’s also ORDERED, by a time dimension, through generations.

Ancestral generation 1

Generation 2

Generation 3

Generation 4

FZDDFZDFZ MZD

MBD MMZDDZDDD

Generation 5

The 8 constituent marriage cycles of the bicomponent

(PART II)

WB

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Larger view

Local structure, ranging from marriage rules to the appearance of nuclear families as autonomous, may be part of an implicate order of wholeness within structural endogamy, and structurally endogamous groups part of a larger implicate order.

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18. Solutions to the simulation problem

• (Problem here is that “same generation” is not a group of contemporaries but stretched in time)

• With known ages of marriage data, simulation for Alyawarra and similar examples can be done considering marriages “filled” sequentially in time, 1-by-1, from marriageable-age probability distributions.

• Where actual ages are unknown, can they be estimated from successive WiBr chains and guesstimates from ethnographers of average Hu-Wife age differences?