Woodrow W. Denham

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Inuit Regional Summary

  • Dear Doug,

My new paper, entitled “Alyawarra kinship, infant carrying and alloparenting”, plus four Comments and my Responses to them, are available online now at Mathematical Anthropology and Cultural Theory (MACT), Vol. 8 http://mathematicalanthropology.org/toc.html. As you know, earlier works in this series are available at the same MACT web site in Volumes 4-5-6.

Thank you very much for your continuing support of my work on Alyawarra kinship and related matters. I hope the current papers will be of interest to you.

KEY WORDS: Sociobiology, genetics, psychology, kinship in Australian Aboriginal societies, childhood in hunter-gatherer societies, human and nonhuman alloparenting, cultural evolution, distributed computing, complexity, mutual aid, history of Russian biology.

Regards,

Woody

2015

June 20 2014

I haven’t had time to work on the expanded Alyawarra dataset since I last wrote to you. It’s been a busy summer so far.

My new website is now in its advanced-beta-test stage of development and is available online at http://www.culturalsciences.info/. If you have some time to spare, I would appreciate receiving your comments on its content and operation.

It has five major components: Alyawarra Ethnographic Archive Version 2, Group Compositions in Band Societies Database, Middle Eastern Region, Caribbean Region and Nonhuman Primates.

The Alyawarra Archive includes my most recent paper on “Residential Group Compositions among the Alyawarra”, a large file.

I am most interested in receiving your feedback on the Alyawarra Ethnographic Archive and the Group Compositions in Band Societies Database.

As you may remember, the Alyawarra Ethnographic Archive was available online from the Australian Institute of Aboriginal and Torres Strait Island Societies in Canberra, Australia, for several years, but was removed from their site a couple of years ago for technical and financial reasons. In the new version (Version 2) I have revised the parts of it that were bothersome to the Aboriginal Institute and located it in the USA.

The Aboriginal Institute questioned some text and graphics files in the DATA section on grounds that they violated - or could have violated - Aboriginal secrecy. In some cases, I have edited the files to address their concerns. In other cases (especially some slides and prints), I have omitted the problematic files.

To avoid copyright problems, unpublished documents are stored and linked on the CulturalSciences.Info server, while published documents are linked to the publications in which they appear. Unfortunately that means that some links to published documents provide full text access only when you or your library subscribes to a database such as JSTOR. That should be no problem for you, but is a potential nuisance for some others.

The Group Compositions in Band Societies Database has the same data as my datasets at KinSources https://www.kinsources.net/ , but the organization of the entire database is much more compact here.

If you find things that don’t work, that need to be clarified, or that you feel should be deleted, please let me know so I can continue to “fine tune” the site.

If you consider this message to be a useful announcement of my new web site, I would greatly appreciate your posting it in an appropriate place on your Interscience Wiki.

Many thanks for your continuing interest in my work

Regards, Woody

Datasets at Kinsources

Fields > CODER Woodrow W. Denham

Dataset Name	Author	Region
!Kung 1952 AF01	Loma Marshall	Southern Africa
Ainu 1880 AS01	Hitoshi Watanabe	East Asia
Alyawarra 1971 AU01	Woodrow W. Denham	Australia and New Zealand
Alyawarra enlarged (1462 records)) AU10 Alyawarra 1818-1979 new: 2015 the data file is accompanied by 53-page ReadMeFirst user manual.
Angmagsalik 1884 NU01	J. Hansen (G. Holms, W. Thalbitzer]	North America
Apache 1932 ND01	Grenville Goodwin	North America
Apache 1935 ND02	Grenville Goodwin	North America
Apache 1936 ND03	Grenville Goodwin	North America
Belcher Island 1958 NU04	Milton MR Freeman	North America
Chenchu 1940 AS02	Christoph von Furer-Heimendorf	South Asia
Copper 1922 NU10	Knud Rasmussen, David Damas	North America
Dogrib 1911/25/59 ND04	June Helm, Nancy O. Lurie	North America
Gundangborn 1948 AU02	Frederick D. McCarthy, Margaret McArthur	Australia and New Zealand
Hare 1956 ND05	June Helm	North America
Igluligmiut 1921 NU05	David Damas, Therkel Mathiassen	North America
Igluligmiut 1949 NU06	David Damas, Fr. J. M. Trebaol	North America
Igluligmiut 1960-61 NU08	David Damas	North America
Igluligmiut 1961 NU07	David Damas	North America
Konkama 1931/44/51 EU02	Robert N. Pehrson	Northern Europe
Konkama 1951 EU01	Robert N. Pehrson	Northern Europe
Kutchin 1947 ND06	Richard Slobodin	North America
Labrador Inuit 1776 NU02	J. L. Beck, Garth J. Taylor	North America
Lainiovouma 1952 EU03	Ian Withaker	Northern Europe
Mbuti Forest 1957 AF02	Colin M. Turnbull	Central Africa
Mbuti Village 1957 AF03	Colin M. Turnbull	Central Africa
Miwuyt 1967 AU03	Warren Shapiro	Australia and New Zealand
Netsilik 1922 NU09	Knud Rasmussen, David Damas	North America
Ngatatjara 1966 AU04	Richard A. Gould	Australia and New Zealand
Nunamiut 1885 NU11	Ernest S. Burch Jr., Robert F. Spencer	North America
Nunamiut 1960 NU13	N. J. Gubser	North America
Nunamiut-Tareumiut 1900 NU12	Ernest S. Burch	North America
Ojibwa 1949 ND08	J. G. Taylor	North America
Paiute 1880 ND09	Julian H. Steward	North America
Semang 1924/50 AS03	Paul Schebesta	Southeast Asia
Shoshone 1860 ND10	Julian H. Steward	North America
Shoshone 1880 ND11	Julian H. Steward	North America
Slavey 1911 ND12	June Helm	North America
Takamiut 1927/64 NU03	Nelson H. H. Graburn	North America
Vedda 1905 AS04	Charles G. et Brenda Seligmann	South Asia
Wanindiljaugwa 1941 AU05	F.G.G. Rose	Australia and New Zealand
Wanindiljaugwa 1948 AU06	F. D. McCarthy and M. McArthur	Australia and New Zealand

New GCBS AIM paper May 2011

DRW view

Given Figures 3-7, with one correction, this is what I see: some long six-cycles as in your helix some short four cycles, mostly all directed cycles not pairwise reciprocal at the level of genealogy. That would match or 2005 diagram. And when drawn say, for the alternating generation subgroups of each country, this would look a bit more like the Valda Blundell graphs that you describe. The cycles of course are more often MBD and MMBDD, real or classificatory rather than Blundell's FaMoBrSoDa, real or classificatory.

Country marriage patterns (movement of women)
              70
              |
              v
14 --> 15 <-> 38
        ^     ^
        |     |
        v     v
       31 <-> 44
        ^     ^
        |     |
        v     v
       58 <-- 43

The references to my 2010a, 2010b papers are online at 2010a Comment "On the Structure of Dravidian Relationship Systems" by Barbosa de Almeida. Douglas R. White. Mathematical Anthropology and Cultural Theory 3(6) art 4: 1-9. 2010b Egocentric and Sociocentric Structure in Classificatory Kinship Systems: Four Theorems. Douglas R. White. Mathematical Anthropology and Cultural Theory 3(6) art 6: 1-19.

This will all make great sense in your kmz

Best, Doug

GCBS Sources for Kinsources network files

Alyawarra ethnographic archive

http://www1.aiatsis.gov.au/exhibitions/alyaweb/

Introduction to Alyawarra Interactive Map (AIM) Visualization project

Current version: 10/2010

This is an experiment in using Google Earth as a platform for interactively displaying and analyzing a broad range of geographical and social data from WW Denham’s Alyawarra Ethnographic Archive (see below), a dataset that pertains to the Alyawarra speaking people of Central Australia. The AIM package in its present state of development contains three files:

AlyaCoord11.kmz powers the interactive visualization. Install Google Earth 5.2.1 or higher, right click to download kmz, and left click the kmz file to launch AIM.

AIM_Methods.pdf describes the installation, setup, structure, operation and content of the interactive visualization, plus supporting files that contain demographic, genealogical, census, kinship and residential group composition data.

AIM_Findings.pdf demonstrates some of the uses of the visualization through preliminary analyses of language group exogamy, intermarriage among Countries, and residential group compositions. This file makes use of comparative data from the Ngarinjin people of northwestern Australia. At right appears a crucial map of the Ngarinjin by Blundell and Layton (1978), fully referenced in the .pdf file, with ongoing enhancements and network analysis by DR White.


"Klaus Hamberger" Mon, November 22, 2010 12:12 pm Re : Computing affinal relinkings in Alyawarra data

To:   "Woodrow Denham" <wwdenham@gmail.com> 
Cc:   "Doug White" <drwhite@uci.edu> 

Dear Woody,

Here is a complete consanguineal and affinal census of the Alyawarra corpus (one without and one with distinction of full and half siblings). There is also a nominative list contained so you can easily check them.

To run a census just open Puck's "Count" screen, put "7 7" in the right field (that means, a maximal distance of 7 from the apical ancestor for consanguineal chains in both consanguineal and affinal circuits - as the maximal depth of the network is 6, this means completeness), choose the sibling type (1 or 3), and press "count".

Kind regards Klaus

Newer (11/17/2010)

Subject:   	Detailed mapping of generation moieties
From:   	"Woodrow Denham" <wwdenham@gmail.com>

I have spent the last week working on the attached Table and Figure based on the AU01 dataset.

The Table is an expanded version of (and replacement for) the one I sent you last week, and serves as the basis for constructing the attached Figure. Finding the circuits was not so hard, but laying out the Figure required a LOT of trial and error.

The Figure depicts ALL KNOWN and LIVING consanguineal + affinal circuits organized horizontally in generation moieties. It omits almost everyone who is NOT a member of one of the circuits (most of the dead; all unmarried people; almost all married people whose spouses are not related to them consanguineally). The Figure does NOT incorporate a diagonal age bias, but the oldest living members of the sibling-in-law chains are at the left and the youngest members are at the right (just waiting to be tipped at the proper angle).

Assume that Ego is a member of the generation moiety in the middle panel. Then the top and bottom panels together constitute the opposite generation moiety, the top panel containing Ego's parents and the bottom panel containing Ego's children.

The top panel contains only a few living ancestors of the mature adults in the middle panel, but it would be easy enough to use it to depict all of the parents, living and dead, of the people in the middle panel.

The middle panel contains most of the consanguineal and affinal circuits and most of the extended sibling-in-law chains.

The bottom panel contains the married children of Ego's generation who are members of consanguineal circuits.

The composition and structure of the top, middle and bottom panels make perfectly good sense, but I'm surprised by the absolute precision that appears here. I shouldn't be - the Alyawarra do it right, whatever "it" might be. Presumably by now the Burla+Ngwariya generation moiety has matured to the peak of its fullness and complexity, and the Kamara+Pityara moiety has assumed a kind of "supporting role" ... a kind of endlessly shifting equilibrium.

Now that I see what's happening here, I'll ask Klaus for help in finding other affinal circuits.

Doug's questions

Beautiful. Now, am I understanding right, if I label generations 3-12 in the middle panel, there are generations 1-2 in the panel above and 9-16! generations in the lower panel. How did you get so many generations? Does this include the new historical data? How is it that the bottom panel have generations 13-16 that are not shared by the middle panel?

Also looks to me like there are very strong repetition patterns, those we saw in the network diagram, of two kinds:

1) in patriines, repetitions (inheritance) of 9 MBD marriages, 3 MMBDD, 1 FZD, 0 ZHZ

2) in sibling-in-law chains: 4 MBD, 1 MMBDD, 2 HZH, 1 FZDDD

Transitions: 3) ditto, 3 FZD/MBD and MBD/FZD transitions

4) 2 MMBDD/MBD

I would speculate that Valda's data would have these too, an she just picked out the MMBDD sibling-in-law chains whereas if thats true you have more MBD chains that she does.

You have surprisingly many first-cross cousins relative to second cross-cousins.

Woody

You said: "why dont the father/son etc links alternate (1 or 3) in their section affiliation."

F-S links DO alternate in accordance with their section affiliations.

In the top panel 324 is 3Burla while in the middle panel his S 40 is 1Kamara.

In the middle panel 13 is 2Pityara while in the bottom panel his S 37 is 4Ngwariya.

In the middle panel 311 is 1Kamara while in the bottom panel his S 39 + 48 are 3Burla.

WWD

My first truncated attempt to explain my mapping of the data was unclear. Let me try again.

There are only THREE "generations" in the Figure: Ego is in the middle panel, Ego's parents are in the top panel, Ego's children in the bottom panel. Each of those "generations" actually is a "generation moiety" that contains multiple parallel and entangled sibling-in-law chains.

In theory a sibling-in-law chain may be a simple "straight line" (Ego,W,WB,WBW,WBWB,...), but in practice virtually all of them in this Figure are more complex than that, and some of them are a *great deal *more complex. The complexity is due in large part to the fact that a single sibling-in-law chain often contains multiple links that contain multiple brothers and/or multiple sisters who can marry people in multiple descent lines. In the Findings paper, Fig. 16 is a schematic view of the convergence of multiple sibling-in-law chains through multiple siblings at multiple linking points.

The convention that I have adopted for denoting multiple same-sex siblings within a sibling set, or marriages between 1 man and 2 or more women, is a short vertical line. It is a "sibling extension" if it connects 2 or more brothers or 2 or more sisters to each other in a column; it is a "polygynous marriage extention" if it connects a husband with his second or third wives. In the top panel of the attached Figure, both are illustrated. The short vertical line between brothers 112 and 15 is a "sibling extension", as are the short vertical lines that connect sisters 171 and 178, and sisters 157 and 162. The slightly longer vertical line that extends below 15 to accommodate a marriage connection to his second wife (178) below his first wife (171) is a "polygynous marriage extention"; the same usage appears below 324 to accommodate a marriage connection to his second wife 162.

First consider the top panel in the attached Figure which shows one not-very-complex sibling-in-law chain.

At the left end of the chain in the top panel, 112 and 15 are brothers. 12 is married to 164, while 15 is married to both 171 and 178 who are sisters. The "-" between the men and their wives indicates that their ancestries do not contain proximate consanguineal or affinal links. The sibling-in-law link in this chain is formed by the sibling relationship between 164 and her brother 324. 324 is married to both 157 and 162 who are sisters. The label indicates that these sisters are 324's MMBDD. The "x" to the right of 157 indicates that 157 has no sisters, so the chain terminates there. This is a very short chain, but it contains one pair of brothers (112 + 15) and two pairs of sisters (171 + 178 who are not related to their husband, and 157 + 162 who are their husband's MMBDD).

Next notice the vertical descent line that extends downward from 324 and his wives, across the red line into the central panel, and connects to the sibling set whose uppermost members are 198 (female) to the left and 40 (male) to the right; 198 and 40 are children of 324 so are members of the "next generation" in traditional terms.

The sibling set headed by 198 and 40 is much more complex than what we saw in the top panel. 198 is connected by a vertical line to her four sisters (182, 204, 179, 180) below her, but those five married women have only one married brother (40). If we focus exclusively on the simplest straight-line horizontal sibling-in-law chain that contains 198 and 40 but none of 198's sisters, we see a sequence from the far left that contains: 3 (Ego) and his MBD 174 (W), 27 (WB) and his MBD 188 (WBW), 30 (WBWB) and his MBD 198 (WBWBW), 40 (WBWBWB) and his MMBDD 195 (WBWBWBW). We can slightly complexify that chain by adding 40's second wife 211 who is not a sister of his first wife but is nevertheless his MMBDD. We can increase the complexity again if we examine male 27 near the middle of the sequence and note that he has a brother 11, and that these brothers (27 and 11) are married to a single set of three sisters (27's W are 188 and 359, while 11's W is 170). Now for a huge increase in complexity, we can examine the marriages of 198's sisters. Her Z 182 is MBD of her H 113; the link to 113 ends there. Her Z 204 is MBDDD to her H 9; notice that 9 has a W 152, a Z 154 and a ZH 1, all of whom are half a century older than 204, so I placed 204 in the column below her other Z and placed 9 in the proper location for himself, his W 152, his Z 154 and his ZH 1. Next we have 198's two Z 179 and 180, both of whom are MBD to their husband 19; note that 19 has a Z 165 who is MBD to her husband 311. So ALL of these complex strands are integrated into the sibling-in-law chain whose core is the B-Z pair 198 - 40.

But the complexity of that sibling-in-law chain doesn't end yet. Look again at 19, the male near the very center of the middle panel, whose wives179 and 180 are his MBD. Just below 19 we see his B 18 and his FZD 158 (W). Continuing to the right, we see 6 (WB) and his MBD 78 (WBW). Below 6 we see 6's B 23 whose first W 201 is his MBD, and his other two W 182+204 who are sisters and are his FZDDD. Now return to 18 and look at his W 158 who is NOT a Z of 198 above her, but is a Z of 168 below her. Now look all the way to the left of 168 to 345. To his right we see his ZHZ 153 (W) (and below her his ZHZ 163, his second wife who is Z of his first wife), then 10 (WB) and his ZHZ 160 (WBW), 13 (WBWB) and his ZHZ 168 (WBWBW). Just below 13 and his W 168 we see 26 and his two MBD 173 + 196 (W) in a "free-standing marriage" that is not linked to any other marriage in the Figure. However, with the sole exception of the marriage between 26 +173 + 196, EVERY other marriage in the middle panel is somehow integrated into the enormously complex sibling-in-law chain whose core is the B-Z pair 198 - 40.

If we disentangle all of these threads to make simple, straight-line WBWBWB... sibling-in-law chains, we lose the reality of the situation. In other words, for all practical purposes, this sibling-in-law chain whose core is the B-Z pair 198-40 is a single "generation" and it (plus the free-standing marriage of 26+173+196) constitutes Ego's entire generation moiety.

I included two descent lines from the middle panel to the bottom panel. The one on the left connects 311 + 165 in the middle panel to their daughter 194 and their two sons 39 + 48 and their spouses in the bottom panel. The one on the right connects 13 + 168 in the middle panel to their son 37 and his brothers 38, 42, 45 below him, plus their spouses, in the bottom panel. Also just above 37 and his two wives, notice 24 and his FZD 177 (W), as well as 31 and his FZD 181 (W). All of these adult married children are in the second descending traditional generation as measured downward from the folks in the top panel, but they are in the "grandchild" half of the grandparent-grandchild generation moiety.

The fragmentary and incomplete nature of the sibling-in-law chains in the * top* half of the grandparent-grandchild generation moiety is due to deaths that have broken the chains. The fragmentary and incomplete nature of the sibling-in-law chains in the *bottom* half is due to the fact that the children who will marry each other to form these chains still are too young to marry or are unborn. So the integration of all of the chains into a single highly complex "generational network" in the middle panel reflects the "maturity" of the people and families in that panel, while the lack of integration in the top and bottom panels reflects their gradual emergence at the bottom and their fading away at the top.

So we have three generations in the traditional sense of that term, or two generation moieties in two different stages of development. The middle panel shows a "mature" moiety in which all of the chains and strands are integrated into a single "generation". The bottom and top panels show respectively the emerging pre-mature and fading post-mature phases of the grandchild-grandparent moiety characterized by fragmentary and incomplete chains.

Translating this Figure into anything even vaguely resembling the English language has been devilishly difficult. If it still isn't clear, let me know and I'll try again.

WWD

Subject: Re: Detailed mapping of generation moieties From: "Woodrow Denham" <wwdenham@gmail.com> Date: Thu, November 18, 2010 12:53 pm To: Douglas.White@uci.edu Options: View Full Header | View Printable Version | Download this as a file | View Message Details | View as HTML

At the end of my message last night, I said:

"Presumably by now the Burla+Ngwariya generation moiety has matured to the peak of its fullness and complexity, and the Kamara+Pityara moiety has assumed a kind of "supporting role" ... a kind of endlessly shifting equilibrium."

If that is true, it seems to follow that by working with the Alyawarra in 1971, I just happened to arrive there at a time when the Kamara+Pityara generation moiety was more dominant and the Burla+Ngwariya moiety was less so. In making the transition from K+P ascendant to B+N ascendant, the society as a whole should have passed through a phase in which the two generation moieties were more or less "equally ascendant"; i.e., the structure and composition of both moieties would be more fully developed than what we see in B-N of 1971, but less fully developed than what we see in K+P of 1971. This suggests that the way the Alyawarra look ethnographically depends upon when we look at them; i.e., we will see different configurations at different times because of CYCLICAL changes in the society as it oscillates repeatedly from K+P ascendant to B+N ascendant and back again. These of course are quite different from cumulative directional evolutionary changes.

WWD


Subject: Re: Detailed mapping of generation moieties From: "Woodrow Denham" <wwdenham@gmail.com> Date: Thu, November 18, 2010 1:02 pm To: drwhite@uci.edu Options: View Full Header | View Printable Version | Download this as a file | View Message Details | View as HTML

You said:

"You have surprisingly many first-cross cousins relative to second cross-cousins."

Some people may be both 1st X-C and 2nd X-C. I looked only for the shortest circuits without searching for longer ones. I probably could find several simultaneous 1st and 2nd X-C sets if I hunted really hard, but you said I should search for shortest circuits so I didn't pursue the longer ones. Should I go back to the data and hunt for longer ones?

WWD

New (10/2010)

Obsolete (7/2010)

Valda Blundell map

Blundell and Layton (1978:237), showing FaMoBrDoDa circulating exchange.connecting diverse ecozones
FaMoBrDaSo marriages among Western Kimberley clans

Comment from Denham need attention.

Her article talks at some length about preferred marriage with FMBSD, and about the asymmetrical transfer of women without really specifying the ideal ZH in the sibling-in-law chain: ZH-Z-Ego-W.Yet the caption to your enhanced version of her map (Fig 5).

In Fig. 2 thru 4, and Table 1, she includes no age data that would support or refute anything having to do with the age bias that shows up so clearly in the Alyawarra data and seems to be implied in her asymmetrical flow of women. Do you have a copy of her data? Does it contain YoB for more than a couple of stray cases?

Archives and Archived

Group Compositions in Band Societies Database This folder contains 351 genealogical, demographic and census data files, in both numerical and graphic formats, from 41 hunter-gatherer societies for whom systematic and reasonably thorough records were made by reputable observers during the two centuries between 1776 and 1976. I extracted these datasets (except for the Alyawarra set) from historical and ethnographic sources that pertain to Africa, Asia, Australia, Europe and North America.

Recent pubs

Woodrow W. Denham and Douglas R. White. 2005. Multiple Measures of Alyawarra Kinship. Field Methods 17: 70-101. http://eclectic.ss.uci.edu/~drwhite/pw/MultiMeas03a.pdf http://fmx.sagepub.com/content/vol17/issue1

Douglas R. White and Woodrow W. Denham. 2008. The Indigenous Australian Marriage Paradox: Small-World Dynamics on a Continental Scale, Structure and Dynamics 3(2).5. http://intersci.ss.uci.edu/wiki/pub/Paradox07b.pdf REVISED 4/14/2008

Douglas R. White, Vladimir Batagelj, and Andrej Mrvar (1999) developed the Pajek algorithms for kinship analysis.Renderings in SVG (scalable vector graphics) provided visualizations such as this genealogy for W. W. Denham's study of the Alyawarra. Genealogies and networks from anthropological field data

See:

Charles Kemp on the Alyawarra blockmodeling - Thanks again for making your data available and helping me figure out the best way to use it. I know at least two subsequent papers that analyze your data:

  http://www.cs.washington.edu/homes/pedrod/papers/mlc07.pdf
  http://www.cs.berkeley.edu/~jordan/papers/miller-griffiths-jordan-nips10.pdf
    
  Clearly I'm not the only person in the machine learning community who
  appreciates your data set!
  
  Charles.

New Bibliography

Fenner, Jack N. 2005. Cross-cultural estimation of the human generation interval for use in genetics-based population divergence studies. American Journal of Physical Anthropology 128(2):415-423. http://www3.interscience.wiley.com/journal/110433666/abstract

Tremblay, Marc and Ve´zina, He´le`ne 2000. New Estimates of Intergenerational Time Intervals for the Calculation of Age and Origins of Mutations. Am. J. Hum. Genet. 66:651–658 http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1288116/

Hammel, E.A. 2005. Demographic dynamics and kinship in anthropological populations. PNAS 102.6:2248-2253 http://www.escholarship.org/uc/item/2g7395s5

Hammel , E.A. 2005. Kinship-based politics and the optimal size of kin groups. PNAS 102.33:11951-11956 http://www.escholarship.org/uc/item/8t82s20x

Patrick McConvell and Rachel Hendery. 2010. Using queries on the AustKin database to find kinship patterns and systems. Society for the Anthropological Sciences/Society for Cross-cultural research conference, 19th February 2010

Citation of Denham and White 2005.

Age Skew generations

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.

Woodrow W. Denham and John Atkins. 1982. More on the Double Helix Model. American Ethnologist. Volume 9, Issue 1, pages 191–192.

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

F. Tjon Sie Fat (1983) Circulating connubium and transitive ranking: a second solution to Leach's problem Bijdragen tot de Taal-, Land- en Volkenkunde 139(1):140-151. Leiden. Tjon Sie Fat (in press) extends the work of Denham, McDaniel, and Atkins .... In this article he uses their work as a model of an age spiral....

Tjon Sie Fat, F. 1983. Age metrics and twisted cylinders: Predictions from a structural model. American Ethnologist 10:583-604. http://www.jstor.org/pss/644271

Some Australian kinship network models

Here are two successive BWBWBWBWBWBW chains, with nodes as couples, solid lines to a male’s parents, dotted to a female’s parents, and three colors to differentiate the three different generations formed by. The slope of the colored generations reflect a constant average of wives compared to their husbands. What is deceptive here is (1) the SAME male lines are accessed in successive BWBW connections when in fact these may differ, and (2) since these “male lines” are purely classificatory, no MBD≠FZD marriages are implied. http://intersci.ss.uci.edu/wiki/pub/kin/Aus3Gen.htm (MBD)

In fig. 2 the marriages are moved over to exclude MBD marriages, and now become MBMBD marriages. Then: (3) there is no need for consanguinal marriages at all. The appearance of a double helix SEEMS to disappear, a figment of imagination. However, these are all WRONG marriages. Three patrlines cannot form a marriage circle, only an even number of patrilines. http://intersci.ss.uci.edu/wiki/pub/kin/Aus3GenMBMBD.htm

Fig. 4 shows MBMBD marriages, and patrilines 2,6,10 and 4,8,12 can be folded over on top of one another, giving the appearance of MBD marriages that exist only in a classificatory sense. Now the double helix model reappears, but only for chains of classificatory MBD marriages. http://intersci.ss.uci.edu/wiki/pub/kin/Aus3GenMBMBMBD.htm

Aux. References

Michael C. Whitlock. 2004 Fixation Probability and Time in Subdivided Populations Genetics, Vol. 164, 767-779.

Noy-Meir, Imanuel. Desert Ecosystems: Higher Trophic Levels Annual Review of Ecology and Systematics 5: 195-214. http://www.jstor.org/stable/2096887