Kinship and Complexity
Advances in Kinship Analysis
Kinship Computing &
Complexity: Cohesion,
Class, and Community
Douglas R. White
October 24, 2008
1
0. Outline
I 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
2
1. Define a graph
that represents how
marriages form cycles
(P-graphs and P-systems)
3
Data and Representation:
P-graphs link parents (flexible & culturally defined) to offspring
They are constructed by showing:
•Each couple (as) a node
• Each individual a line
•Each gender a different
type of line
•A marriage node includes the
husband and wife as an
embedded graph
•i.e., a P-system
4
2. This representation captures
independent nuclear families,
networks of marriage between them
how families form descent groups
marriages within and between them
5
3. Now link this representation
to actual marriage network data
6
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)
7
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
8
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)
9
This is a bicomponent
with no cut-point and with
two+ independent paths
between every node.
And 8 corresponding
named cycles
WB
MBD
FZ
MZD
ZDDD
It has 8
independent
cycles m-n+1
m edges
n nodes
MMZDD
FZD
FZDD
Generation 5
It’s also ORDERED,
by a time dimension,
10
through generations.
Ancestral generation 1
Generation 2
Generation 3
WB
The 8 constituent marriage
cycles of the bicomponent
MBD
ZDDD
(PART II)
MMZDD
Generation 4
FZ
MZD
FZD
FZDD
Generation 5
11
Mapping data
onto networks
• Migration
• Residence
• Wealth owned
• Heirship
--- PART III
• Kin Behaviors
• Kin Terms &
Products in
relation to
marriage
Analyses of such
data can be crossed:
• By structural endogamy
• By generation time-series,
patrilineages, matrilineages
• By viri-sides, uxori-sides
12
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)
13
5. Bicomponents (I), as
maximal 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.
14
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.
15
E.g., Measuring boundaries of structural endogamy
Jacob and Esau
are included in the
main unit of
structural
endogamy
Lot married to
his daughters
Abram
Sarai
Abram
Hagar
Ishmael
Male Descent
Female Descent
Same person
(polygamy)
Structurally endogamous Canaanite Marriages
16
in the narrative of the Patriarchs (White/Jorion)
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:
17
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
18
Feistritz, Austria – structural endogamy by affinal relinking
THE NEXT SLIDES WILL TREAT THESE
with heirship
19
Feistritz, Austria – structural endogamy by affinal relinking
(no blood marriages)
Pearson’s
Attribute endogamy = e.g., heirs marry heirs R = .15
8. There are consequences but not that heirs
marry heirs – its THOSE IN THE BICOMPONENT
20
WHO DO RELINK BECOME THE HEIRS
Feistritz Austria – structural endogamy
1520 T
h
e
9. This is social class constituted by marital relinking
T
i
m
e
D
i
m
e
n
s
i
o
n
21
1970
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?
22
Feistritz Austria – structural endogamy
(i.e., bicomponent) with heirship
11. Pearson’s R = .54
23
12. Here is a test of randomness
as “non-intentional behavior” for
each generation
For each generation,
permute the marriages
randomly
24
For example, take these three generations and permute the
red lines so existing marriage and child positions are occupied
25
26
27
28
29
30
13. Comparing Feistritz actual to simulated rnd
relinking frequencies:- Relinking frequency >>
random back 1 and 2 generations, those where
there is most knowledge & availability
Random in all higher generations 3+
31
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.
32
Turkish nomads
Names of members
all
members
Black=patriDescent lines
Blue=female lines
33
Turkish nomads
SCALING
All known
members but
many have
emigrated
dotted=
female lines
Black=patridescent lines
34
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=patriDescent lines
35
15. Cycles within Structural Endogamy (II)
A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:
The Role of Marital Cohesion
Results: Rather than treat types of marriage one by one: FBD, MBD etc., we
treat them as an ensemble and plot their frequency distribution
A power-law decay of marriage frequencies with kinship distance
180
160
140
M
Frequency
M =206/x
0 + 156/x^2
2
120
##ofofTypes
kin types
100
(power law preferential curve)
80
60
## of
couples
of Couples
40
FFZSD FFBSD:10-11
FZD:14 MBD
MBD:16
FFZSD
FFBSD FZD
FBD:31
FBD
20
0
0
Raw
5 frequency 10
15
20
25
36
Cycles within Structural Endogamy (II) log-log
A 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
37
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.
38
Omaha Genealogies – Chiefs and Siblings –
no relinking of chiefly lines:- disconnected
ELK CLAN
39
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
40
Omaha – all generations – structural endogamy
41
Omaha – 8 generations – disintegration
42
Omaha – loss of structural endogamy
1
2
Nonrelinked
singles
Bicomponent
Omaha
relinking
marriages
4
Genera 1
tion
2
Levels 3
29
41.40%
41
58.60%
70
50
32.90%
102
67.10%
152
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
1 early
3
Total
8Relinking
late
marriages decrease in later generations
5
6
7
8
43
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.
44
Systemic age differences of wives and husbands complicates generational simulation: Alyawarra of Australia
G2
G3
G1
G4
G2
G5
G3
G6
G4
G7
G5
G8
G6
G7
Key: Vertical black lines male descent, red dots, females:
the generations are sloped (pink and blue) in a P-graph. 45
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.
46
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.
47
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.
48
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).
49
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
50
social consequences that need to be properly understood.
afterword
Local structure -- ranging from marriagetype 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.
51
52
Ancestral generation 1
Generation 2
Generation 3
WB
The 8 constituent marriage
cycles of the bicomponent
MBD
ZDDD
(PART II)
MMZDD
Generation 4
FZ
MZD
FZD
FZDD
Generation 5
It’s also ORDERED,
by a time dimension,
53
through generations.
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.
54
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?
55