Sided with a Twist: Alyawarra Networks, Kinterm and Lifecycle Decision Models

Woodrow W. Denham and Douglas R. White

American Anthropological Association 2002 New Orleans
Some of the gaps in the linkages are due to lack of sufficient numbers of people in the required categories, especially in later generations.

The model derived from kin terms has six classificatory patrilines (vertical) intersecting with four classificatory matrilines (diagonal red dotted lines), with classificatory MMBDD marriage preferred in verbal statements. This p-graph is illustrative of what the actual network fitting that model might look like, but knowledge about relative ages was not used to properly fit the generations. With red lines for females and black for males, marriages are highlighted here (204 marriages in large lineages; 80% of marriages fit the model) when they conform to classificatory MMBDD marriage.
We wanted a more accurate fit that would take the ages of individuals into account to compose generations. Hence we switched to a conventional genealogical diagram (for all 377 individuals). Refitting the model to take actual age into account, we obtained more realistic diagrams:
-- by sections -- by language (1971-72)
In these age-specific models there are only three generations of living males and four of females in play at one time and that while parents of the living are remembered, the grandmothers are forgotten. The system does not close on itself since four male or six female generations are required for closure. Hence it is open to adding or dropping classificatory lines (male or female) that are 100% coherently organized through section memberships (the four colors in the by sections graph).

Old Hypothesis: The kinterms applied to each position in the network are those of the normative network relationships (yellow-highlighted marriage lines), not the exceptional marriages.

Old Hypothesis: Where there are gaps in the network, e.g., no MBD marrriages, structurally equivalent relationships, e.g., MMBDD, will define identical terms for that position.
New Hypothesis: There are network motifs in the network for favored types of marriages both within generations and occasionally with +2/-2 generations. Taking as side information on kinship terms, sizes of the patrilines associated with the sacred sites ("countries) they are responsible for, and the demography of age differences between spouses (because young men are sequestered from marriage by initiatory groups), temporal link prediction can be made as to where marriages will occur within the one of prescribed four-section alternatives that are generationally approproprate, and a key network structural prediction is that the marriages will maximize structural cohesion to provide supportive relationships both near and far. There will be larger cohesive blocks that are less dense but contain more people all with higher multiconnectivity, i.e., multiplcity of independent paths between all members, as per the 1927 dual aspects of connectivity theorem of Menger).
Whether this ability to "self-repair" applies to major rifts, like the absence of connections in the fifth cohort of female lines, remains to be seen. actual data on lineages at 6patrilines htm 6patrilines jpg
Age Skewing Alyawarra men marry later than women, and their average age of parenting is 150% longer than women. Hence they cannot on average marry in their own chronological generation, and female generations MUST be shorter that those for males.

In the abstract model, six classificatory patrilines intersect with four classificatory matrilines. In the actual data, 11% are grandchild generation marriages, and 15% with miscellaneous other marriages such as FZD, but 74% of the blood marriages are consistent with the model (either MMBDD or MBD marriages), marriages that are consistent with age and generational differences between spouses.

Sections. Named "sections" are really alternating generation designations within each of the two patrimoieties. There is perfect correspondence here between model and data: see actual data coded at sections htm sections jpg

COLOR CODES HERE ARE FOR SECTIONS

If we reorganize this model to show the two matrimonial sides (unnamed patrimoieties), we see that men cannot easily marry the classificatory FZD, who is old enough to have already married, but can marry MBD or MMBDD, or any woman in an equivalent genealogical generation.

The 2/3 ratio of men's to women's generations require, in a symmetric moeity, three female generational cohorts for every two male cohorts, which is most simply satisfied in a patrimoiety with six male lines for four female lines.

COLOR CODES HERE ARE FOR LINEAGES

Sections by viri-sides. Here the alternating generation designations are reorganized as above, within each of the two patrimoieties.

Each cohort, say #20 from green section, left moiety, has an exchange partner, in this case red #6, right moiety: #6 gives its daughters to green #8, while #20 gives to red #22. #20 has gotten its wives from red #18, while #6 got its daughters from green #4. So each color group can be seen as a social unit for coordinating marriage exchanges.

Sections by uxori-sides. Here the alternating generation designations are reorganized accorging to two implicity matrimoieties, again colored by named sections.

Recurrent cycles colored by Sections.
4-cycles with black lines are patrilines, 6-cycles with dotted red lines are matrilines.

Bibliography

Denham, Woodrow W., Chad K. McDaniel, and John R. Atkins. 1979. Aranda and Alyawarra Kinship: A Quantitative Argument for a Double Helix Model. American Ethnologist 6:1-24.

To see the equivalence of the network analysis findings here with Denham et al (1979:18) figure 6:

  • Fig. 6 has the 6 vertical patridescent lines, so does the p-graph
  • What the p-graph does is to take the hu/wi connections in Fig. 6, such as Ego and Wife, pull them together into a node, and then from that new node add the matrilineal link from ego/Wife up to Wife's Father.
  • If that were done throughout Fig. 6, systematically, the matrilines would run diagonally from upper right to lower left as they do in the p-graph.
  • The difference in representation is only that Fig. 6 has sibling pairs together, the p-graph has hu/wu pairs together.
    Tjon Sie Fat, Franklin E. 1981. More Complex Formulae of Generalized Exchange. Current Anthropology 22(4):377-399.

    Atkins, John R. 1981. CA* Comment on "More Complex Formulae of Generalized Exchange." Current Anthropology 22(4):390-391.

    Atkins, John R. 1982. A Family of Helical Models for Age-Biased Marriage Systems. Ms. Files of the author.

    Atkins, John R., and Woodrow W. Denham. 1981. CA* Comment on "Genealogical Structures and Consanguineous Marriage Systems." Current Anthropology 22(4):407.