• Oliver Nakoinz
  • Daniel Knitter
Part of the Quantitative Archaeology and Archaeological Modelling book series (QAAM)


Interactions between individuals, places and the natural environment are the driving forces of history. Interaction models map the likeliness or intensity of interaction to certain parameters. The most important class of parameters influencing interaction is the distance between the interacting entities. Distances may be calculated in geographical, economic, cultural or any other space. The relationship between interaction and distance is first addressed with distance graphs and fall-off curves. The combination of different types of distance and different types of distance graphs leads to a wide range of methods, each illuminating a specific facet of interaction. The empirical interaction models are compared with theoretical ones realised by distance decay functions. In addition to distance, gravity models involve the size of the interacting entities.


Interaction Spatial interaction Interaction measures Communication Distance decay Distance diagram Gravity model 


  1. 1.
    Blumer, H. (1969). Symbolic interactionism; perspective and method. Eaglewood Cliffs: Prentice-Hall.Google Scholar
  2. 2.
    Burmeister, S. (2000). Archaeology and migration: Approaches to an archaeological proof of migration. Current Anthropology, 41, 539–567.CrossRefGoogle Scholar
  3. 3.
    Christaller, W. (1933). Die Zentralen Orte in Süddeutschland. Jena: Fischer.Google Scholar
  4. 4.
    Cliff, A. D., & Ord, J. K. (1973). Spatial autocorrelation. London: Pion.Google Scholar
  5. 5.
    Daudé, E. (2004). Apports de la simulation multi-agents à l’étude des processus de diffusion, Cybergeo. Revue européenne de géographie, 255.; doi:  10.4000/cybergeo.3835
  6. 6.
    Diachenko, A. (2013). Settlement growth as a fractal. Jungsteinsite. Journal of Neolithic Archaeology, 15, 88–105.Google Scholar
  7. 7.
    Diachenko, A., & Menotti, F. (2012). The gravity model: Monitoring the formation and development of the Tripolye culture giant-settlements in Ukraine. Journal of Archaeological Science, 39, 2810–2817.CrossRefGoogle Scholar
  8. 8.
    Dunn, J. (1993). Social interaction, relationships, and the development of causal discourse and conflict management. European Journal of Psychology of Education, 111, 391–401.CrossRefGoogle Scholar
  9. 9.
    Earle, T. K., & Ericson, J. E. (Eds.) (1977). Exchange systems in prehistory. New York: Academic Press.Google Scholar
  10. 10.
    Fetter, F. A. (1924). The economic law of market areas. Quarterly Journal of Economics, 38, 520–529.CrossRefGoogle Scholar
  11. 11.
    Fotheringham, A. S., & O’Kelly, M. E. (1989). Spatial interaction models: Formulations and applications. Dordrecht: Kluver.Google Scholar
  12. 12.
    Garrod, S., & Pickering, M. J. (2009). Joint action, interactive alignment, and dialog. Topics Cognitive Science, 1, 292–304.CrossRefGoogle Scholar
  13. 13.
    Getis, A. (1991). Spatial interaction and spatial autocorrelation: A cross-product approach. Environment and Planning A, 23, 1269–1277.CrossRefGoogle Scholar
  14. 14.
    Getis, A., & Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24, 189–206.CrossRefGoogle Scholar
  15. 15.
    Haggett, P., & Chorley, R. J. (1969). Network analysis in geography. London: Arnold.Google Scholar
  16. 16.
    Hägerstrand, T. (1967). Innovation diffusion as a spatial process. Chicago: University of Chicago Press.Google Scholar
  17. 17.
    Hårdh, B., Larsson, L., Olausson, D., & Petré, R. (1988). Trade and exchange in prehistory. Studies in honour of Berta Stjernquist: Vol. 16. Acta Archaeologica Lundensia. Lund: Lunds Universitets Historiska Museum.Google Scholar
  18. 18.
    Harris, B. (1964). A note on the probability of interaction at a distance. Journal of Regional Science, 5/2, 31–35.Google Scholar
  19. 19.
    Isard, W. (1998). Gravity and spatial interaction models. In: W. Isard, I. J. Azis, M. P. Drennan, R. E. Miller, S. Saltzman & E. Thorbecke (Eds.), Methods of interregional and regional analysis (pp. 243–279). Aldershot/Brookfield/Singapore/Sydney: Ashgate.Google Scholar
  20. 20.
    Kimes, T., Haselgrove, C., & Hodder, I. (1982). A method for identification of the location of regional cultural boundaries. Journal of Anthropological Archaeology, 1, 113–131.CrossRefGoogle Scholar
  21. 21.
    Knappett, C., Evans, T., & Rivers, R. (2008). Modelling maritime interaction in the Aegean bronze age. Antiquity, 82, 1009–1024.CrossRefGoogle Scholar
  22. 22.
    Mallinowski, B. (1922). Argonauts of the Western Pacific. An account of native enterprise and adventure in the archipelagoes of Melanesian New Guinea. London: Routledge and Kegan Paul Ltd.Google Scholar
  23. 23.
    Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37, 17–23.CrossRefGoogle Scholar
  24. 24.
    Nakoinz, O. (2013). Models of interaction and economical archaeology. Metalla, 20/2, 107–115.Google Scholar
  25. 25.
    Nakoinz, O. (2013). Archäologische Kulturgeographie der ältereisenzeitlichen Zentralorte Südwestdeutschlands: Vol. 224. Universitätsforschung zur Prähistorischen Archäologie. Bonn: Habelt.Google Scholar
  26. 26.
    Nakoinz, O. (2014). Räumliche Interaktionsmodelle in der Archäologie. Prähistorische Zeitschr, 88, 225–256.Google Scholar
  27. 27.
    Parsons, T. (1937). Structure of social action. New York: McGraw Hill.Google Scholar
  28. 28.
    Polanyi, K. (1944). The great transformation. New York: Farrar and Rinehart.Google Scholar
  29. 29.
    Ravenstein, E. G. (1885). The laws of migration. Journal of the Royal Statistical Society, 48, 167–235.Google Scholar
  30. 30.
    Ravenstein, E. G. (1889). The laws of migration. Journal of the Royal Statistical Society, 52, 241–305.CrossRefGoogle Scholar
  31. 31.
    Renfrew, C. (1977). Alternative models for exchange and spatial distribution. In T. E. Earle & J. E. Ericson (Eds.), Exchange systems in prehistory (pp. 71–90). New York: Academic Press.Google Scholar
  32. 32.
    Renfrew, C. & Level, E. V. (1979). Exploring dominance: predicting polities from centers. In C. Renfrew & K. L. Cooke (Hrsg.), Transformations. Mathematical approaches to cultural change (pp. 145–167). New York: Academic Press.Google Scholar
  33. 33.
    Rouse, I. (1986). Migrations in prehistory: Inferring population movement from cultural remains. New Haven: Yale University Press.Google Scholar
  34. 34.
    Salač, V. (2002). Kommunikationswege, Handel und das Ende der Oppidazivilisation. In: C. Dobiat, S. Sievers & T. Stöllner (Eds.), Dürrnberg und Manching. Wirtschaftsarchäologie im ostkeltischen Raum: Vol. 7. Kolloquien Vor- und Frühgesch (pp. 349–354) [Tagung Hallein 1998]. Bonn: Habelt.Google Scholar
  35. 35.
    Sindbœk, S. M. (2007). Networks and nodal points: The emergence of towns in early viking age Scandinavia. Antiquity, 81, 119–132.CrossRefGoogle Scholar
  36. 36.
    Stewart, J. Q. (1948). Demographic gravitation: Evidence and applications. Sociometry, 11(1/2), 31–58.CrossRefGoogle Scholar
  37. 37.
    Stouffer, S. A. (1940). Intervening opportunities: A theory relating to mobility and distance. American Sociological Review, 5, 845–867.CrossRefGoogle Scholar
  38. 38.
    Taylor, P. J. (1971). Distance transformation and distance decay function. Geographical Analysis, 3, 221–238.CrossRefGoogle Scholar
  39. 39.
    Taylor, P. J. (1983). Distance decay in spatial interactions. Catmog, 2, 3–35.Google Scholar
  40. 40.
    Tiefelsdorf, M. (2000). Modelling spatial processes: The identification and analysis of spatial relationships in regression residuals by means of Moran’s I. Berlin: Springer.CrossRefGoogle Scholar
  41. 41.
    Tobler, W. (1970). A computer movie simulating urban growth in the Detroit region. Economic Geography, 46, 234–240.CrossRefGoogle Scholar
  42. 42.
    Tobler, W. (2004). On the first law of geography: A reply. Annals of the Association of American Geographers, 94, 304–310.CrossRefGoogle Scholar
  43. 43.
    Wilson, A. G. (1978). Spatial interaction and settlement structure: Towards an explicit central place theory. In S. Karlqvist, L. Lundqvist, F. Snickars & J. W. Weibull (Eds.), Spatial interaction theory and planning models (pp. 137–156). Amsterdam: North-Holland.Google Scholar
  44. 44.
    Zipf, G. (1946). The PP/D hypothesis: On the intercity movement of persons. American Sociological Review, 11, 677–686.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Oliver Nakoinz
    • 1
  • Daniel Knitter
    • 2
  1. 1.University of KielKielGermany
  2. 2.Excellence Cluster TopoiFreie UniversitätBerlinGermany

Personalised recommendations