Skip to main content
×
×
Home

Cultural Transmission and Stochastic Network Growth

  • R. Alexander Bentley (a1) and Stephen J. Shennan (a1)
Abstract

Archaeological theory has traditionally presupposed the existence of “battleship curves” in stylistic evolution, with little understanding about what governs the width (variant frequency) or length (variant lifespan) of these curves. In terms of these variables, we propose that there is a testable difference between independent decisions, unbiased transmission, and biased transmission in cultural evolution. We expect independent decision making to be represented by an exponential distribution of variant prevalence in the population. In contrast, unbiased transmission tends to be characterized by a power law or log-normal distribution of prevalence, while biased transmission should deviate significantly from the unbiased case. The difference between these categories may be fundamental to how cultural traits spread and persist. In order to make analytical predictions for unbiased transmission, we adapt a model of stochastic network growth that, by quantitatively demonstrating the inherent nonlinearity in unbiased transmission, can explain why a few highly popular styles can be expected to emerge in the course of cultural evolution. For the most part, this model predicts the frequencies of pottery decorations remarkably well over a 400-year span of Linearbandkeramik settlement in the Merzbach valley. Because the highest frequencies of actual motifs are somewhat less than predicted by our unbiased transmission model, we identify an anti-conformist, or pro-novelty, bias in the later phases of the Neolithic Merzbach Valley.

Resumen

La teoría arqueológica ha presupuesto tradicionalmente la existencia de las “battleship curves” en la evolución estilística, con poca comprensión sobre qué dicta la anchura (variable frecuencia) o la longitud (variable lapso de vida) de estas curvas. Con estas variables, proponemos que hay una diferencia comprobable entre decisiones independientes, transmisión no sesgada y transmisión sesgada en la evolución cultural. Encontramos que la toma de decisión independiente es representada por una distribución exponential del predominio variable en la población. En contraste, la transmisión no sesgada tiende para ser caracterizada por una distribución power-law o una distribución log-normal del predominio, mientras que el caso de transmisión sesgada se diferencia del caso de transmisión no-sesgada. La diferencia entre estas categorí as puede ser fundamental para la evolución cultural. Para hacer las predicciones de la transmisión no-sesgada, adaptamos un modelo de la red de crecimiento en el que, demostrando cuantitativamente la no-linealidad inherente en la transmisión no-sesgada, pueda explicar como se puede esperar que algunos estilos altamente populares emerjan en el curso de la evolución cultural. Este modelo predice notablemente bien las frecuencias de las decoraciones de la cerámica durante 400 años de la era Neolitica en el valle de Merzbach. Porque nuestro modelo predice más estilos de la cerámica con alta frecuencia de los que hay realmente, identificamos un sesgo anticonformista, o favorable a la novedad en las fases mas tardías del valle Neolitico de Merzbach.

Copyright
References
Hide All
Adamic, A. L., and Huberman, B. A. 2000 The Nature of Markets on the World Wide Web. Quarterly Journal of Electronic Commerce 1:512.
Albert, R., and Barabási, A.-L. 2002 Statistical Mechanics of Complex Networks. Reviews of Modem Physics 74:4797.
Albert, R., Jeong, H., and Barabási, A.-L. 1999 Internet: Diameter of the World-Wide Web. Nature 401:130.
Allen, M. S. 1995 Style and Function in East Polynesian Fish-hooks. Antiquity 70:97116.
Amaral, L. A. N., Buldyrev, S. V., Havlin, S., Salinger, M. A., and Stanley, H. E. 1998 Power Law Scaling for a System of Interacting Units with Complex Internal Structure. Physical Review Letters 80:13851388.
Amaral, L. A. N., Scala, A., Barthelemy, M., and Stanley, H. E. 2000 Classes of Small-world Networks. Proceedings of the National Academy of Sciences USA 97:1114911152.
Ammerman, A. J., and Cavalli-Svorza, L. L. 1984 The Neolithic Transition and the Genetics of Populations in Europe. Princeton University Press, Princeton, New Jersey.
Arbogast, R. M., Beugnier, V., Delattre, N., Giligny, F., Maitre, A., Pétrequin, A. M., and Pétrequin, P. 1997 La répartition des Témoins et le Fonctionnement de la Cellule Domestique. In Les Sites Littoraux Néolithiques de Clairvaux-Les-Lacs et de Chalain (Jura) III. Chalain station 3, 3200-2900 av. J.C., edited by Pétrequin, P., pp. 583639. Éditions de la Maison des Sciences de l’Homme, Paris.
Bak, P. 1996 How Nature Works: The Science of Self-organized Criticality. Springer-Verlag, New York.
Bak, P, Tang, C., and Wiesenfeld, K. 1987 Self-organized Criticality: An Explanation of 1/f Noise. Physical Review Letters 59:381384.
Barabási, A.-L., and Albert, R. 1999 Emergence of Scaling in Random Networks. Science 286:509512.
Barkow, J. H. 1989 Darwin, Sex and Status. University of Toronto Press, Toronto.
Bentley, R. A., and Maschner, H. D. G. 1999 Subtle Nonlinearities in Popular Album Charts. Advances in Complex Systems 2:197209.
Bentley, R. A., and Maschner, H. D. G. 2000 A Growing Network of Ideas. Fractals 8:227238.
Bentley, R. A., and Maschner, H. D. G. 2001 Stylistic Evolution as a Self-organized Critical Phenomenon. Journal of Archaeological Method and Theory 8:3566.
Bentley, R. A., and Maschner, H. D. G. 2003 Complex Systems and Archaeology. University of Utah Press, Salt Lake City.
Bettinger, R. L., and Eerkens, J. 1999 Point Typologies, Cultural Transmission, and the Spread of Bow-and-Arrow Technology in the Prehistoric Great Basin. American Antiquity 64:231242.
Bogucki, P., and Grygiel, R. 1993 The First Farmers of Central Europe: A Survey Article. Journal of Field Archaeology 20:399426.
Boone, J. L., and Smith, E. A. 1998 Is it Evolution Yet? A Critique of Evolutionary Archaeology. Current Anthropology 39:S141173.
Bouchaud, J. P, and Mézard, M. 2000 Wealth Condensation in a Simple Model of Economy. Physica A 282:536545.
Boyd, R., and Richerson, P. J. 1985 Culture and the Evolutionary Process. University of Chicago Press, Chicago.
Braun, D. P. 1991 Why Decorate a Pot? Midwestern Household Pottery, 200 B.C.–A.D. 600. Journal of Anthropological Archaeology 10:360397.
Buchanan, M. 2001 Ubiquity: The Science of History—Or Why the World Is Simpler Than We Think. Crown, New York.
Burda, Z., Johnston, D., Jurkiewicz, J., Kamiski, M., Nowak, M. A., Papp, G., and Zahed, I. 2002 Wealth Condensation in Pareto Macroeconomies. Physical Review E 65:026102.
Cavalli-Sforza, L. L., and Feldman, M. W. (editors) 1981 Cultural Transmission and Evolution. Princeton University Press, Princeton, New Jersey.
Collard, M., and Shennan, S. 2000 Processes of Culture Change in Prehistory: A Case Study from the European Neolithic. In Archaeogenetics: DNA and the Population Prehistory of Europe, edited by Renfrew, C. and Boyle, K., pp. 8997. McDonald Institute for Archaeological Research, Cambridge.
Crow, E. L., and Shimizu, K. (editors) 1988 Lognormal Distributions: Theory and applications. Marcel Dekker, New York.
Crow, J. F., and Kimura, M. 1970 An Introduction to Population Genetics Theory. Harper Row, New York.
Cullen, B. R. S. 1996 Cultural Virus Theory and the Eusocial Pottery Assemblage. In Darwinian Archaeologies, edited by Maschner, H.D.G., pp. 4359. Plenum, New York.
Dunnell, R. C. 1978 Style and Function: A Fundamental Dichotomy. American Antiquity 43:192202.
Dunnell, R. C. 1982 Science, Social Science and Common Sense: The Agonizing Dilemma of Modern Archaeology. Journal of Anthropological Research 38:125.
Dunnell, R. C. 1989 Aspects of the Application of Evolutionary Theory. In Archaeological Thought in America, edited by Lamberg-Karlovsky, C.C., pp. 3449. Cambridge University Press, Cambridge.
Durham, W. H. 1991 Coevolution: Genes, Culture and Human Diversity. Stanford University Press, Stanford.
Edgerton, R. B., with Goldschmidt, W. 1971 The Individual in Cultural Adaptation: A Study of Four East African Peoples. University of California Press, Berkeley.
Eldredge, N., and Gould, S. J. 1972 Punctuated Equilibria: An Alternative to Phyletic Gradualism. In Models in Paleobiology, edited by Schopf, T. J. M., pp. 82115. Freeman, Cooper, San Francisco.
Flinn, M. 1997 Culture and the Evolution of Social Learning. Evolution and Human Behavior 18:2367.
Frirdich, C. 1994 Kulturgeschichtliche Betrachungen zur Bandkeramik im Merzbachtal. In Die Bandkeramik im Merzbachtal auf der Aldenhovener Platte, edited by Lüning, J. and Stehli, P., pp. 207394. Habelt, Bonn.
Gould, S. J., and Eldredge, N. 1993 Punctuated Equilibrium Comes of Age. Nature 366:223227.
Gronenborn, D. 1997 A Variation on a Basic Theme: The Transition to Farming in Southern Central Europe. Journal of World Prehistory 2:23210.
Guglielmino, C. R., Viganotti, C., Hewlett, B., and Cavalli-Sforza, L. L. 1995 Cultural Variation in Africa: Role of Mechanisms of Transmission and Adaptation. Proceedings of the National Academy of Sciences, USA 92:585589.
Hahn, M. W., and Bentley, R. A. 2003 Drift as a Mechanism for Cultural Change: An Example from Baby Names. Submitted to Proceedings of the Royal Society Biology Letters, in press.
Henrich, J. 2001 Cultural Transmission and the Diffusion of Innovations. American Anthropologist 103:9921013.
Henrich, I., and Boyd, R. 2001 Why People Punish Defectors: Peak Conformist Transmission Can Stabilize Costly Enforcement of Norms in Cooperative Dilemmas. Journal of Theoretical Biology 208:7989.
Henrich, J. R. Boyd, Bowles, S., Gintis, H., and Fehr, E. In Search of Homo Economicus:. Experiments in 15 Small-scale Societies. American Economic Review 91:7378.
Henrich, J., and Gil-White, F. J. 2001 The Evolution of Prestige: Freely Conferred Deference as a Mechanism for Enhancing the Benefits of Cultural Transmission. Evolution and Human Behavior 22:165196.
Huberman, B. A., and Adamic, A. L. 1999 Growth Dynamics of the World Wide Web. Nature 401:131132.
Hull, D. L. 1982 The Naked Meme. In Learning, Development and Culture: Essays in Evolution Epistemology, edited by Plotkin, H. C., pp. 272327. MIT Press, Cambridge, Massachusetts.
Ketchum, W. C. 1987 Potters and Potteries of New York State, 1650-1950. Syracuse University Press, Syracuse, New York.
Kimura, M., and Crow, J. F. 1964 The Number of Alleles that Can Be Maintained in a Finite Population. Genetics 49:725738.
Krapivsky, P. L., Redner, S., and Leyvraz, F. 2000 Connectivity of Growing Random Networks. Physical Review Letters 85:46294632.
Lake, M. 1998 Digging for Memes: The Role of Material Objects in Cultural Evolution. In Cognition and Material Culture: The Archaeology of Symbolic Storage, edited by Scarre, C. and Renfrew, C., pp. 7788. MacDonald Institute for Archaeological Research, Cambridge.
Leonard, R.D. 1998 Reply to Boone and Smith. Current Anthropology 39:S162S163.
Lipo, C., and Madsen, M. E. 2001 Neutrality, ‘Style,’ and Drift: Building Methods for Studying Cultural Transmission in the Archaeological Record, In Style and Function: Conceptual Issues in Evolutionary Archaeology, edited by Hurt, T. D. and Rakita, G. F. M., pp. 91118. Bergin and Garvey, Westport, Connecticut.
Lipo, C. P., Madsen, M. E., Dunnell, R. C., and Hunt, T. 1997 Population Structure, Cultural Transmission and Frequency Seriation. Journal of Anthropological Archaeology 16:301333.
Lumsden, C. J., and Wilson, E. O. 1981 Genes, Mind, and Culture: The Coevolutionary Process. Harvard University Press, Cambridge, Massachusetts.
Lüning, J. 1984 Neolithische Hausgrundrisse in Schwanfeld, Ldkr. Schweinfurt, Unterfranken. Arch. Jahr Bayern 3132.
Lüning, J., and Stehli, P. (editors) 1994 Die Bandkeramik im Merzbachtal auf der Aldenhovener Platte. Habelt, Bonn.
Lyman, R. L., and O’Brien, M. J. 1998 The Goals of Evolutionary Archaeology. Current Anthropology 39:615652.
Lyman, R. L., and O’Brien, M. J. 2000 Measuring and Explaining Change in Artifact Variation with Clade-Diversity Diagrams. Journal of Anthropological Archaeology 19:3974.
Lyman, R. L., and O’Brien, M. J. 2001 On Misconceptions of Evolutionary Archaeology : Confusing Macroevolution and Microevolution. Current Anthropology 42:408409
Mainberger, M. 1998 Das Moordorf von Reute. Teraqua CAP, Staufen.
Milgram, S. 1967 The Small World Problem. Psychology Today 2:6067.
Neff, H. 1992 Ceramics and Evolution. Archaeological Method and Theory 4:141193.
Neiman, F. D. 1995 Stylistic Variation in Evolutionary Perspective: Inferences from Decorative Density and Interassemblage Distance in Illinois Woodland and Ceramic Assemblages. American Antiquity 60:736.
Newman, M. E. J. 2001 The Structure of Scientific Collaboration Networks. Proceedings of the National Academy of Sciences USA 98:404409.
O’Brien, M. J. 1996 The Foundations of Evolutionary Archaeology. In Evolutionary Archaeology, edited by O’Brien, M. J., pp. 1723. University of Utah Press, Salt Lake City.
O’Brien, M. J., and Holland, T. 1995 The Nature and Premise of a Selection-based Archaeology. In Evolutionary Archaeology: Methodological Issues, edited by Teltser, P. A., pp. 175200. University of Arizona Press, Tucson.
Paczuski, M., Maslov, S., and Bak, P. 1996 Avalanche Dynamics in Evolution, Growth, and Depinning Models. Physical Review E 53:414443.
Pastor-Satorras, R., and Vespignani, A. 2001 Epidemic Spreading in Scale-free Networks. Physical Review Letters 86:32003203.
Plotkin, H. C. 1994 The Nature of Knowledge: Concerning Adaptations, Instinct and the Evolution of Intelligence. Allen Lane, London.
Pocklington, R., and Best, M. L. 1997 Cultural Evolution and Units of Selection in Replicating Text. Journal of Theoretical Biology 188:7987.
Shennan, S. J., and Wilkinson, J. R. 2001 Ceramic Style Change and Neutral Evolution: A Case Study from Neolithic Europe. American Antiquity 66:577594.
Simon, H. A. 1955 On a Class of Skew Distribution Functions. Biometrica 42:425440.
Stehli, P. 1989 Merzbachtal—Umwelt und Geschichte Einer Bandkeramischen Siedlungskammer. Germania 67:5176.
Stehli, P. 1994 Chronologie der Bandkeramik im Merzbachtal. In Die Bandkeramik im Merzbachtal auf der Aldenhovener Platte, edited by Lüning, J. and Stehli, P., pp. 79192. Habelt, Bonn.
Turcotte, D. L. 1997 Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge.
Turcotte, D. L. 1999 Self-organized Criticality. Reports on Progress in Physics 62:13771429.
United States Census Bureau 1995Documentation and Methodology for Frequently Occurring Names in the U.S.- 1990.” <http://www.census.gov/ftp/pub/genealogy/www/freqnames.html>
Wilkinson, J. R. 1997 Ceramics as Viral Quasi-Species. Unpublished M.A. dissertation, Institute of Archaeology, University College London.
Witten, T. A., and Sander, L. M. 1981 Diffusion Limited Aggregation, a Kinetic Critical Phenomenon. Physical Review Letters 47:14001403.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

American Antiquity
  • ISSN: 0002-7316
  • EISSN: 2325-5064
  • URL: /core/journals/american-antiquity
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 8 *
Loading metrics...

Abstract views

Total abstract views: 260 *
Loading metrics...

* Views captured on Cambridge Core between 20th January 2017 - 20th August 2018. This data will be updated every 24 hours.