Alyawarra

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THE DISCOVERY OF OPEN/CLOSED MARRIAGE CHOICE AS DEMOGRAPHIC FILTER IN AN AUSTRALIAN SOCIETY

Douglas R. White, Woodrow W. Denham (c) May 15, 2012 (see P-graph generation levels)
Fig.1. Kamara man 1 and Pityara wife 4 with Burla children 7/8 and Kamara grandchildren 13/14; Pityara siblings 3&4 have opposite matri and generational moieties with 3's Burla children 9-10 in the next generation; 4's children are of opposite patri and matri moieties and thus fully "cross" marriageable relatives with 3's children.

Alyawarra marriages are simultaneously forbidden between intersecting patrimoieties and matrimoieties (defining four sections and prohibiting marriage between even and odd generations). One exogamous patrimoiety has a pair of sections named Kamara and Burla, the other patrimoiety has the pair of sections named Pityara and Ngwariya. Similarly, one exogamous matrimoiety has the pair of sections named Ngwariya and Kamara, the other matrimoiety has the pair of sections named Pityara and Burla. Finally, one endogamous generation moiety has a pair of sections named Kamara and Pityara, the other has sections name Burla and Nigariya. The section rules of marriage are shown in the diagram. Patrlines are within the vertical boxes; Matrilines are within the horizonta (slanted) boxes. Alternating (i.e., non-adjacent) columns are same-patrimoiety, alternating diagonals are same-matrimony, and alternating rows are same-generation moiety. Their intersections define four sections, which are implicit in the use of kinship terms that classify which marriages are permitted or prohibited. This sounds simple because Bs marry Ns and an N girl's father P marries a K girl whose brother also marries a P man whose children are Bs and sister's children are Ns, eligible to marry as cross-cousins (1st, 2nd, 3rd, 4th).

The network diagram below puts new genealogical data on 1461 individuals into a framework where males locate their marriages one or three boxes below their parents's generation (alternating generation marriages have a parent three generations above them, not just one). Daughters marry into a section an odd number of generations down and to the left or right. Further nstructions for reading the graph are below the graph.
Fig.2.

Previous: [[File:P-aly1470cpls768bico157LeftRightSkew21No idsGrid.png]]

  • Here are instructions for reading this particular graph, which is a special case of a directed asymmetric (p-)graph where a vertex represents at most a couple (singleton or opposite-sex pair or parental couple) that has no connections more than an up arrow to son's parental vertex and daughter's parental vertex. Generations are slanted because of age biases in marriage with a dominant pattern shown for girls marrying men of their own genealogical generation who are older, while older women may marry or remarry men who are two generations above.
  1. There are six columns separated by dotted lines that are "classificatory patrilines" within which lineages are represented by vertical thin black solid lines pointing upward within the lineage to parental nodes.
  2. The six "classificatory patrilines" amalgamate lineages for which there are more outgoing than incoming red arrows in those that have no endogamy and are not yet classified: this defines the first set (first, lineage, second that has no endogamy, etc., then closing the first set), a second set, and in this case terminates with a sixth.
  3. Horizontal but age-slanted generations are separated by black dotted lines. The black dots represent not just one but all the marriages of a man, who will have the same parents as his full brothers and sisters. Half-brothers or sisters will have common grandparents. One man may have marriages in different alternating generations: 0 (same) 2, or 4 generations apart.
  4. Daughters are shown by arrows pointing upward to parents across 1, 3, or 5 vertical generation separators, and cannot marry within their matrimoieties and patrimoieties, their own or grandparents' or great-great grandparents' generation.
  5. To check correctness all arrows should point upwards to 1, 3, 5, or 7 generations, men's within their classificatory patrilines (with a pair of "sections" in alternating generations) and women's arrows will always point diagonally to their parents.
  6. Pajek insists there are 142 vertices in the bicomponent (and 26 in the partitioning) but by actual count there are between 152 and 159, while 157 is evident from the file construction. The Pajek algorithm incorrectly attributes 142 vertices to the giant bicomponent and treats four that belong there to a separate bicomponent, which would bring the number to 146.

This next graph has no terminology grid lines:

Previous version File:P-aly1470cpls768bico157LeftRightSkew6ids.png

1480 Alyawarra and their marriages showing only the 157 relinked couples and their linking relatives

P-graph for Denham's field study dataset with 377 individuals. 204 marriages in large lineages. Roughly 82 in the bicomponent.

See 377-person Alyawarra graphic below.

DRW: May 2012 The Alyawarra 1470 person file, which combines Denham's field study dataset with 377 individuals, has a number of different bicomponents, which may mean that there are different endogamous ("structurally cohesive") units within the dataset. There are three remaining issues. One is the use of 9999s which have not yet been erased, and the other is how to replace these with 0s (zeros) as an identifier for the missing partner. The unit examined here is a bicomponent containing 157 couples. There are no other bicomponents.

  • 377 person datafile model. 204 marriages in large lineages. Many fewer in the bicomponent.
  • The evidence from this 142 couple bicomponent of the 1480 person file, a network of relinked couples, is that females -- the red lines directed between 9 classificatory patrilines (grouped together) -- flow mostly left to right in the graph. The leftmost patrilines has two reciprocal FBD exchanges among similar classificatory lines linked through the dark green patriline. Those marriages seem to come from a different marriage system concept and shift in their last of 4 generations from actual FBD to actual rather than classificatory MBD marriage. Some females marry in the opposite direction, closing in 1 or 3 lines but not 5 to the right. Marriages to lines 1, 3, 5, 7 classificatory lines distant are in opposite patrmoieties; those that are 2, 4, 6 or 8 distant are in the same patrimoiety. There are no directional helices of six classificatory lines as attested by Denham et al. 1979. If marriages were between husbands and wives of the same age, the adjacent generations here would represent opposite generation moieties. Wives, however, average 2/3rds the age of their husbands. When the graph is adjusted for shorter generations for daughters than for sons, the graph retains its structure, but generations are seen to be slanted by the age-bias. THERE ARE 128 daughters and 102 sons WHICH OCCURS BECAUSE OF 26 SECOND OR THIRD WIVES, resulting in 157 vertices in the graph. BECAUSE FEMALES TEND TO MARRY EARLIER THE AVERAGE AGE BIAS COULD BE SHOWN BY MOVING THE MALE LINES DOWN BY 1/3rd i of the male generation interval for males (42 years for males as opposed to 28 for females) IN EACH CLASSIFICATORY LINEAGE, moving from left to right. This shortens the average age of marriage for daughters marrying to the immediate left by 1/3 of a generation of 14 years. It raises the average of HUSBANDS for daughter's marriages to the immediate right by 14 years (i.e., age 56). The ANCESTORS in the leftmost patrilines should be on average three generations older than those on the right (and the same for their descendants at the bottom of the line. (Is it true that: When daughters marriage into the third classificatory lineage to the right, they will be marrying a younger man, usually in widow marriage?)
The ratios of right/left versus left/right diagonal flow of women in this diagram is 1:1 between generations 2-3 and 1:6 between generations 1-2, 3/4, 4/5, and 5/6. Ignoring 2-3 the ratio is 1/6 (9/53). Historically, then it seems that this ratio changes from an asymmetric marriage system to symmetric (only in one generation), flowing down through the age-skewed generation from the earliest ancestors (upper right) and in a particular pair of alternating generations, starting in the 18860s- 1900. Thereafter the marriage structure becomes 6:1 asymmetric.
P-graph for Denham's field study dataset with 377 individuals. 204 marriages in large lineages. Roughly 82 in the bicomponent.
Comments welcome here from Denham.
230 marriages in the bicomponent compared to 82 in the 377 person field data graph above, i.e., almost three times as many, but including more remote ancestors.

interlineage matrix

http://en.wikipedia.org/wiki/Permutation_matrix#Permutation_of_rows_and_columns

This is the way to do the Alyawarra sorting model on the interlineage matrix

Create your NxN matrix P

P * (1,2,3,4)T = (4,1,3,2)T

Let A and B be two 3x3 matrices such that


A
=
\begin{bmatrix}
 0 &   1 &   2 \\
 1 &   0 & 1.5 \\
 2 & 1.5 &   0
\end{bmatrix} \text{, and}

B
=
\begin{bmatrix}
 0   & 1 & 1.5 \\
 1   & 0 &   2 \\
 1.5 & 2 &   0
\end{bmatrix}.

Let P be the 3x3 matrix permuting A into B such that


P
=
\begin{bmatrix}
 0 & 1 & 0 \\
 1 & 0 & 0 \\
 0 & 0 & 1
\end{bmatrix}.

Use permutations to put biggest successive (chained) wife-sending lineages together

  1. make a matrix of patrilines with number of directed marriages in cells of the matrix
  2. then to put the next intermediate lineages (from hi wife-senders on left) to high (wife receivers)
  3. the successive classificatory groups must have NO internal marriages

Embedding the 377 Alyawarra helix in the 1460 network

Take p-aly1470.net and use python to extract

  1. only the nodes with individual ID numbers between 1-337
  2. save the series numbers for each, both IDs and series numbers, in both the *Vertices columns and the *Arcs column

Take the p-aly377.net

  1. find corresponding IDs in the both the *Vertices columns and the *Arcs column
  2. make two columns for series numbers
  3. column 1 numbers from 1470 in both the *Vertices columns and the *Arcs column
  4. column 2 numbers from 377 in both the *Vertices columns and the *Arcs column

If the coordinates of 377.net define the helical model

  1. substitute the 337 coordinates for their series (1-337) into
  2. the corresponding coordinates for the 1460 series

Problem is then to find the quasi-helical net file

To find the 337 model with helical coordinates, as in our publications


Improving the "377" database

Msg 3 May 7 later 2012

My advice then would be to make a post a new 377+14=391 person database to Kinsources. That would keep the integrity of your original field data but add to the key "almost helical" model we have been looking at: those deceased parents are obviously EARLY so that would be an important amendment. This is the dataset then that MIT-type guys should have in matching BOTH kinterm AND network structure models AGAINST ACTUAL kinterm AND network data.


Msg 2 May 7 2012 early

Hi Doug,

n377 dataset within n1460 dataset: Record # 1-377 ARE the original people from the AU01 n377 dataset ... YES.

Differences: There about 14-15 (didn't count 'em carefully) NEW spouses that I added to the first 377 records in the AU10 n1460 dataset. These new spouses have ID# >1000.

Another potential problem is that, while building the n1460 dataset, I identified 14 previously unidentified DECEASED PARENTS of people in the n377 dataset. Those people are not "new" people, but rather are recodings of "unknown 999" from the original n377 dataset. These recoded deceased parents appear in the n1460 dataset in Record# 378-391, and I recoded the corresponding 999s as needed in the first 377 records.

Separability: Use Record # 1-377, and disregard all SPOUSE-ID# > 415.

AU10 n377 dataset already in KinSources: When I posted all of my GCBS datasets to KinSources two years ago, the FIRST ONE that went up was my AU01 n377 dataset. It is there now and has been there for 2 years.

I'll get back to you with some questions of my own later this afternoon. My firewood supplier is delivering 2 cords of new wood as I type. Gotta cover it before the next rain soaks it.

wwd


Msg 1 A few days earlier

On Mon, May 7, 2012 at 10:02 AM, Doug White <drwhite@uci.edu> wrote:

   Qn: the numbers 1-377 in the 1470 xls are the original 377: WWD: yes. Then there are also some parents of these with higher numbers: obviously.
   Qn: But are there any new spouse numbers >377 that are (marriages) with entries in the 1-377 series?  WDD: there are parents of the 377 in the new 1480-person database.
   I ask because if so, the 1-377 subseries would not form a separable group (if it also contained higher numbers). Not a big problem, but I wanted to know.
   I still think you should leave a copy of the 337 dataset on Kinsources. Or at least explain that it can be recovered from the first 377 rows of the *.xls.