Ý Notes

Outline

Slide 1

Kinship in GraphsÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ 1. Data and Representation:

Defining the phenomena of endogamy: By categories/attributes: suffers from problems of specification error By network relinking: structural endogamy consists of blocks of relinkings: blocks of blood marriage as same-family relinking blocks of k-family relinkings, with depth g generations network cohesion is the more general concept

to study cohesive blocks in social networks generally, sociological uses of this approach are discussed in White, Douglas R. and Frank Harary. 2001. "The Cohesiveness of Blocks in Social Networks: Connectivity and Conditional Density." To appear in Sociological Methodology 2001. White, Douglas R. and Mark E. J. Newman. 2001. ìFast approximation algorithms for finding node-independent paths.î Submitted to Sociological Methodology 2002. Moody, James, and Douglas R. White. 2001. ìStructural Cohesion and Embeddedness:A hierarchical conception of social groups.î Santa Fe Institute Working Paper 00-08-049, submitted to the American Journal of Sociology. example (from plenary session): Powell, Walter W., Douglas R. White, Kenneth W. Koput and Jason Owen-Smith. 2001. ìEvolution of a Science-Based Industry: Dynamic Analyses and Network Visualization of Biotechnology.îÝ Informal working paper: Santa Fe Institute.

Kinship Software: PAJEK PAJEK is a program for large network analysis (Batagelj and Mrvar 1999).Ý In Decemberí97 PAJEK 0.23 implemented the p-graph format of White and Jorion (1992) as the default for genealogical datasets (*.GED files), the drawing of dotted (p Dots) versus solid lines (p Solid) for the different sexes, and a fast version of bicomponents (for the study of structural endogamy). There is also a genealogical representation using triangles or circles as nodes for individuals, and a representation that combines the two systems of representation. Network/Partition/Depth/Genealogy command - implemented to compute genealogical depth. This enabled 2D or 3D drawings of kinship networks.Ý Illustrations will be given. Manuals for p-graph kinship analysis and discussions of software programs and multimedia representations are found at 1) http://eclectic.ss.uci.edu/~drwhite (has links to articles) 2) http://eclectic.ss.uci.edu/~drwhite/pgraph 3) http://vlado.fmf.uni-lj.si/pub/networks/pajek ÝÝÝ (each of these sites has a link to the other)

Pajek 98-2000: Dynamical Analysis of Longitudinal Network Data Pajek keeps evolving.Ý In September-Octoberí98, Pajek 0.33-36 added Vectors (*.vec) whose values can be real numbers, including: Editing vectors, making vectors from a partition, and vector transformations (multiplying by a constant, absolute, sqrt, normalizations), reordering and binary operations on vectors (sum, difference, product, division, min, max) and additional operations according to neighbors. Retrieving and putting coordinates of network to vector and vice versa. In Novemberí99, Pajek 0.50 added automatic demographic vectors for birth, marriage, and death dates, when GEDCOM files are read. April-May 2000, Pajek 0.54-55 implemented: Network/Generate in Time to produce time-series graphs. Draw-Vector and Draw-Partition-Vector with Options/Previous/Next that uses vector values to modify size of nodes in time-series graphs. File/TimeEventsNetwork/Read and /Save for reading and saving a time network in time events format to control every feature of the graphs.

Kinship Software: PGRAPH PGRAPH - graphs and simulations, sidedness, segmentary dual organization, etc. Par-Calc - frequencies for marriages of blood relatives Par-Link - frequencies for two-family relinkings Par-Comp (incorporates Fisher tests) - for outcomes based on types (blood or relinking) Par-Bloc - for global analysis of relinkings Par-Side (binomial test) - computes likelihood of sidedness Par-Coef - computes inbreeding coefficients and relatedness Ego2Cpl UTILITY - converts *.txt files to p-graph/pgraph formats. See http://eclectic.ss.uci.edu/~drwhite/pgraph for guides as to web-site availability with documentation (and multimedia representations)

3. Marriage Rules and Strategies: Controlled Demographic Simulation via a Network Approach in a science of social structure and dynamics that includes marriage and kinship, how to define and evaluate marriage strategies against random baselines? separate ërandomizingí strategy from ëpreferentialí strategy? detect atomistic strategies (partial, selective) as well as global or ìelementaryî marriage-rules or strategies? detect changes in marriage rules or strategies? D. White. 1997. Structural Endogamy and the graphe de parentÈ.Ý MathÈmatique, informatique et sciences humaines 137:107-125. Paris: Ecole des Hautes Etudes en Sciences Sociales ÝÝÝÝÝ D. White. 1999. ìControlled Simulation of Marriage Systems.î Journal of Artificial Societies and Social Simulation 3(2). http://www.soc.surrey.ac.uk/2/3/5/JASSS.html ÝÝÝÝÝ See: http://eclectic.ss.uci.edu/~drwhite

the technique is simple: In each generation of marriages in an actual p-graph ñ number the set K of marriages 1 to k Reassign each person married into the generation to a random marriage in K, allowing additional rules to prevent incest as defined culturally But donít change the parents: that keeps each sibling set intact ÝÝÝÝ (all this is done automatically by the Pgraph software) This gives a simulated dataset that has the same numbers of people and of marriages, the same distribution of sibling sets, hence the same sex ratio in each generation, etc.

Iíll show applications of the simulation method to study structural endogamy as it pertains to: Social class, Elite structural endogamy, Wealth consolidation, Community/ethnic integration, Testing alliance, descent, and proscriptive theories and models

4. Case Study Examples: Kinship Social Class and Structural Endogamy in the Austrian village of Feistritz:Ý Strategic Relinking (w/ Lilyan Brudner) Status Endogamy in a Javanese village (Dukuh hamlet and Muslim) Elites: Marriages frequencies governed by demographic constraints, not by different consanguineal marriage preferences (w/ Thomas Schweizer) Dual Organization in Sri Lanka: Preferred Marriages and Sidedness in Pul Eliya Village (w/ Michael Houseman) Tzintzuntzan (w/ Eric Widmer and Robert van Kemper) Clan Organization among Nomadic Herders (w/ Ulla Johansen 2001)

Example 1: Carinthian Farmers Graphic technique: showed households as a macro-unit of analysis, containing successive nuclear or stem families as nodes in the graph. Key concepts: marital relinking, p-graph (where nodes are marriages and lines are filiation), structural endogamy, bicomponent of the p-graph defines endogamous boundary (in those case, of social class). Predicted social class and heirship among farmers from the cohesive set of marriages in the farming valley (non heirs did not enter in the kinship bicomponent) 1997 ìClass, Property and Structural Endogamy: Visualizing Networked Histories,î Theory and Society 25:161-208. Lilyan Brudner and Douglas White. http://eclectic.ss.uci.edu/~drwhite/T&S/T&Spage1.htm

"SOCIAL CLASS in Feistritz:" SOCIAL CLASS in Feistritz:Ý Comparison of Relinking Frequencies for Actual and Simulated Data (*=actual frequencies greater than chance as determined by simulation)

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Example 2: Rural Javanese Elites Graphic technique: nuclear families as the unit of p-graph analysis, additional arrows for property flows (used in the publication) showed extended family rules for partitioning of mercantile resources and property of groups constituted by relinking. Key concepts: blood marriage as a form of marital relinking, p-graph, structural endogamy, bicomponent of the p-graph, the social biography of things (property flows). ShowedÝ (1) apparent differences in marriage patterns of elites and commoners were due to a common cultural practice of status endogamy, which for elites implied a set of potential mates whose smaller size implied marriage among blood relatives within a few generations, (2) given a common rule of division of inheritance, closer marital relinkings among elites facilitated the reconsolid-ation of wealth within extended families, and (3) extended families so constituted operated with a definite set of rules for the division of productive resources so as to distribute access to mercantile as well as landed resources. Douglas White and Thomas Schweizer, 1998 ìKinship, Property and Stratification in Rural Java: A Network Analysisî pp. 36-58 in Schweizer and White, eds. Kinship, Networks, and Exchange. Cambridge Univ. Press.

"key:" key: A = frequency of actual marriages with a given type of relative ÝÝÝÝ B = frequency of simulated random marriages with a given type of relative ÝÝÝ TA = total of actual relatives of this type ÝÝÝ TS = total of simulated relatives of this type ÝJavanese elitesÝÝÝÝÝÝÝÝÝÝÝ Dukuh HamletÝÝÝÝÝÝÝÝÝÝÝÝÝÝ 3-Way Test ÝÝÝ A S TA TS p=ÝÝ typeÝÝÝÝ A S TA TS p=ÝÝ type Ý1: 1 0Ý 4Ý 3 .625 FBDÝÝÝÝÝ 0 1Ý 9 12 .591 FBDÝÝÝÝÝÝÝÝÝÝ p=1.0 Ý2: 1 2Ý 2Ý 3 .714 MBDÝÝÝÝÝ 1 0 11 16 .429 MBDÝÝÝÝÝÝÝÝÝÝ p=1.0 Ý3: 2 1Ý 3Ý 2 .714 FZDDÝÝÝÝ 0 0 11Ý 0ÝÝÝÝÝ FZDDÝÝÝÝÝÝÝÝÝ p=1.0 Ý4: 0 1Ý 6Ý 7 .571 ZDÝÝÝÝÝÝ 0 0 18 24ÝÝÝÝÝ ZDÝÝÝÝÝÝÝÝÝÝÝ p=1.0 ÝÝÝ 0 0 11 11ÝÝÝÝÝ ZÝÝÝÝÝÝÝ 0 0 36 43ÝÝÝÝÝ Z ÝÝÝ 0 0Ý 4Ý 4ÝÝÝÝÝ BDÝÝÝÝÝÝ 0 0 22 27ÝÝÝÝÝ BD ÝÝÝ 0 0Ý 2Ý 2ÝÝÝÝÝ ZSD ÝÝÝ 0 0Ý 3Ý 3ÝÝÝÝÝ BDDÝÝÝÝÝ 0 0Ý 8Ý 8ÝÝÝÝÝ BDD ÝÝÝ 0 0Ý 3Ý 3ÝÝÝÝÝ ZDD ÝÝÝ 0 0Ý 4Ý 4ÝÝÝÝÝ FZÝÝÝÝÝÝ 0 0 21 27ÝÝÝÝÝ FZ ÝÝÝ 0 0Ý 1Ý 1ÝÝÝÝÝ FZSD ÝÝÝ 0 0Ý 3Ý 3ÝÝÝÝÝ FZDÝÝÝÝÝ 0 0 13 14ÝÝÝÝÝ FZD ÝÝÝ 0 0Ý 3Ý 3ÝÝÝÝÝ FBDDÝÝÝÝ 0 0Ý 3Ý 2ÝÝÝÝÝ FBDD ÝÝÝ 0 0Ý 5Ý 4ÝÝÝÝÝ MZÝÝÝÝÝÝ 0 0 18 23ÝÝÝÝÝ MZ ÝÝÝ 0 0Ý 2Ý 2ÝÝÝÝÝ MZSD ÝÝÝ 0 0Ý 4Ý 4ÝÝÝÝÝ MZDÝÝÝÝÝ 0 0 13 14ÝÝÝÝÝ MZD ÝÝÝ 0 0Ý 1Ý 2ÝÝÝÝÝ MBDDÝÝÝÝ 0 0Ý 6Ý 5ÝÝÝÝÝ MBDD ÝÝÝ 0 0Ý 2Ý 3ÝÝÝÝÝ MZDD

Example 3: Kandyan Irrigation Farmers in Sri Lanka Graphic technique: nuclear families as the unit of p-graph analysis, analysis of blood marriages, sibling sets and of inheritance or bequests revealed an underlying logic of marital sidedness. Key concepts: bipartite graph and sidedness (empirical bipartition of a matrimonial network, reiterated from one generation to another following a sexual criterion). ìThis remarkable work, among other merits, has that of reconstituting the near-totality of the data of Leachís study of Pul Eliya, reexamined by means of the PGRAPH program.Ý It reveals that Leach had not seen, and could not for lack of requisite tools of analysis, that marriages were organized in response to a logic that the authors call dividedness and in another form sidedness:Ý invisible to the untrained eye, the matrimonial network is bipartite, the marriages of the parents and those of the children divide themselves into two distinct ensembles (which have nothing to do with moieties)î (review by Georg Augustins, LíHomme 2000) Michael Houseman and Douglas White. 1998 ìNetwork Mediation of Exchange Structures: Ambilateral Sidedness and Property Flows in Pul Eliya, Sri Lankaî pp. 59-89 in Schweizer and White, eds. Kinship, Networks, and Exchange. Cambridge Univ. Press.

"Type" ÝTypeÝ Actual SimulÝ TotalÝ Total Fisher|-----Blood Marriage------|ÝÝÝÝÝÝ (2)Patri-Sided? of Mar. Freq. Freq.Ý Actual Simul ExactÝ typeÝÝ P-graph notationÝÝÝÝÝÝÝÝÝÝ ActualÝÝÝÝ Simul ÝÝ 12:ÝÝ 5ÝÝ 0Ý 40Ý 38 p=.042 MBD(1)GF=FGÝÝÝÝ yes ÝÝÝ 2:ÝÝÝ 3ÝÝÝ 1ÝÝ 39ÝÝ 40ÝÝ .317 FZDÝÝÝÝÝ GG=FFÝÝÝÝ yes ÝÝÝ 1:ÝÝÝ 0ÝÝÝ 1ÝÝ 56ÝÝ 57ÝÝ .508 FZÝÝÝÝÝÝ GG=FÝÝÝÝÝ no ÝÝÝ 3:ÝÝÝ 0ÝÝÝ 1ÝÝÝ 6ÝÝÝ 6ÝÝ .538 FFFZDSDÝ GGGG=FGFF no ÝÝÝ 4:ÝÝÝ 1ÝÝÝ 0ÝÝÝ 3ÝÝÝ 1ÝÝ .800 FFMZDSSD GGGF=FGGFF yes ÝÝÝ 5:ÝÝÝ 0ÝÝÝ 1ÝÝÝ 5ÝÝÝ 3ÝÝ .444 FFMBDSDD GGGF=FFGFG no ÝÝÝ 6:ÝÝÝ 1ÝÝÝ 0ÝÝ 18ÝÝ 15ÝÝ .558 FMBSDÝÝÝ GGF=FGGÝÝ yes ÝÝÝ 7:ÝÝÝ 0ÝÝÝ 1ÝÝ 17ÝÝ 12ÝÝ .433 FMBDDÝÝÝ GGF=FFGÝÝ no ÝÝÝ 8:ÝÝÝ 2ÝÝÝ 1ÝÝ 18ÝÝ 12ÝÝ .661 FMZDDÝÝÝ GGF=FFFÝÝ yes ÝÝÝ 9:ÝÝÝ 0ÝÝÝ 1ÝÝÝ 9ÝÝÝ 5ÝÝ .399 FMMBSSDÝ GGFF=FGGG no ÝÝ 10:ÝÝÝ 0ÝÝÝ 1ÝÝÝ 4ÝÝÝ 5ÝÝ .600 FMMFZSSD GGFFG=FGGF yes ÝÝ 11:ÝÝÝ 0ÝÝÝ 1ÝÝÝ 6ÝÝÝ 3ÝÝ .400 FMMFZDSD GGFFG=FGFF yes ÝÝ 13:ÝÝÝ 0ÝÝÝ 1ÝÝ 25ÝÝ 27ÝÝ .528 MBSDÝÝÝÝ GF=FGGÝÝÝ yes ÝÝ 14:ÝÝÝ 1ÝÝÝ 0ÝÝ 14ÝÝ 10ÝÝ .600 MFZDDÝÝÝ GFG=FFFÝÝ yes ÝÝ 15:ÝÝÝ 1ÝÝÝ 0ÝÝÝ 7ÝÝÝ 3ÝÝ .727 MFFZDSSD GFGG=FGGFF yes ÝÝ 16:ÝÝÝ 1ÝÝÝ 0ÝÝÝ 8ÝÝÝ 4ÝÝ .692 MFFZDSDÝ GFGG=FGFF yes ÝÝ 17:ÝÝÝ 1ÝÝÝ 0ÝÝÝ 8ÝÝÝ 2ÝÝ .818 MFMBDSSD GFGF=FGGFG yes ÝÝ 18:ÝÝÝ 1ÝÝÝ 0ÝÝÝ 9ÝÝÝ 3ÝÝ .769 MFMBDDÝÝ GFGF=FFGÝ yes ÝÝ 19:ÝÝÝ 1ÝÝÝ 0ÝÝÝ 3ÝÝÝ 0Ý 1.000 MFMBDDDD GFGF=FFFFG yes ÝÝ 20:ÝÝÝ 1ÝÝÝ 0ÝÝÝ 8ÝÝÝ 2ÝÝ .818 MFMFZSSD GFGFG=FGGF yes ÝÝ 21:ÝÝÝ 1ÝÝÝ 0ÝÝÝ 3ÝÝÝ 0Ý 1.000 MFMFZDDD GFGFG=FFFF yes ÝÝ 22:ÝÝÝ 1ÝÝÝ 0ÝÝ 13ÝÝÝ 8ÝÝ .636 MMZSSDÝÝ GFF=FGGFÝ yes ÝÝ 23:ÝÝÝ 1ÝÝÝ 0ÝÝ 15ÝÝ 13ÝÝ .551 MMBDDÝÝÝ GFF=FFGÝÝ yes ÝÝ 24:ÝÝÝ 0ÝÝÝ 1ÝÝ 11ÝÝÝ 5ÝÝ .352 MMZSDDÝÝ GFF=FFGFÝ no ÝÝ 25:ÝÝÝ 0ÝÝÝ 1ÝÝ 11ÝÝÝ 5ÝÝ .352 MMBDDDÝÝ GFF=FFFGÝ no ÝÝ 26:ÝÝÝ 1ÝÝÝ 0ÝÝ 11ÝÝÝ 4ÝÝ .749 MMZDDDÝÝ GFF=FFFFÝ yes

Slide 21

"Correlating Balanced vs." Correlating Balanced vs. Unbalanced cycles in Actual versus Simulated marriage networks for Pul Eliya, showing a perfectly Sided (Dravidian) Marriage Rule A. Viri-sidedness Actual Expected Balanced Cycles (Even length) 25 ÝÝ 17.5 Unbalanced Cycles (Odd Length) 10 ÝÝ 17.5 p=.008 (all exceptions involve relinkings between nonconsanguineal relatives) B. Amblilateral-sidednessÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝÝ (womenës sidedness adjusted by inheritance rules) - not shown in figure but shown in final publication (Houseman and White 1997) Actual Expected Balanced Cycles (Even length) 35 ÝÝ 17.5 Unbalanced Cycles (Odd Length) 0 ÝÝ 17.5 p=.00000000003

Summary: Random Baseline Models for the Study of Social Rules 1999 ìControlled Simulation of Marriage Systems.îÝ Journal of Artificial Societies and Social Simulation 2(3). Douglas R. White. http://www.soc.surrey.ac.uk/2/3/5/JASSS.html software and statistical methodology for comparing systems of marriage-rules to random baseline models with controls for demographic variability. For the Austrian study, random baseline models established the preference for relinking with relatives within 3 generations. For the Javanese study, the lack of difference between commoner and elite marriages is supported, in spite of differences in frequency of different marriage types. For the Pul Eliya study, random baseline models established the patri-sided marriage rule for blood marriages, and the absence of a genealogical rule for determining the marriageability of distant affines. Tzintzuntzan, a 4th example, is in process. If time allows, Iíll give a more extended 5th example, or just show on Pajek slide and stop

Example 4: Tzintzuntzan

Example 5: Social Dynamics of a Nomadic Clan - 6Ý questions put by Ulla Johansen We numbered each person and gave one line for each marriage with number of ego, egoís mother, father and spouse. Using Pgraph and Pajek, this gave a graph for the nomadic clan, ready for analysis:

p-graph of the conical nomad clan