Skip to main content

The Quantitative Analysis of Mobility: Ecological Techniques and Archaeological Extensions

  • Chapter
  • First Online:
New Perspectives on Old Stones

Abstract

This paper provides an overview of techniques for the quantitative analysis of mobility derived from mathematical ecology. Focusing on the Lévy distribution as a model for movement data, a number of methods for ­identifying power laws are assessed. These methods are applied to a dataset gathered by Yellen (Archaeological Approaches to the Present: Models for Reconstructing the Past, 1977) during research among the Dobe !Kung and allow the complete ­mathematical description of the movement pattern of that group. Results suggest that the group moves between resource patches which are power-law distributed in size but that their camp relocation distances follow a lognormal distribution. These results are interpreted by reference to the “complete radius leapfrog pattern” described by Binford (J Anthropol Archaeol 1:5–31, 1982). In order to extend the study of mobility as practiced by ecologists to the data encountered in the archaeological record, a novel simulation methodology is developed that relates step-length distributions to the distributions of intersite distances in landscape-level archaeological samples. This methodology is discussed with regard to its archaeological implications and certain social and cognitive correlates of specific mobility strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Adams, R.E.W. and Jones, R.C., 1997. Spatial patterns and regional growth among Classic Maya cities. American Antiquity 46: 301–322.

    Article  Google Scholar 

  • Alonso, D., Bartumeus, F. and Catalan, J., 2002. Mutual interference between predators can give rise to Turing spatial patterns. Ecology 83: 28–34.

    Article  Google Scholar 

  • Atkinson, R.P.D., Rhodes, C.J., Macdonald, D.W. and Anderson, R.M., 2002. Scale-free dynamics in the movement patterns of jackals. Oikos 98: 134–140.

    Article  Google Scholar 

  • Austin, D., Bowen, W.D. and McMillan, J.I., 2004. Intraspecific variation in movement patterns: modeling individual behavior in a large marine predator. Oikos 105: 15–30.

    Article  Google Scholar 

  • Bailey, H. and Thompson, P., 2006. Quantitative analysis of bottlenose dolphin movement patterns and their relationship with foraging. Journal of Animal Ecology 75: 456–465.

    Article  Google Scholar 

  • Bartumeus, F., 2007. Levy processes in animal movement: An evolutionary hypothesis. Fractals – Complex Geometry Patterns and Scaling in Nature and Society 15: 151–162.

    Article  Google Scholar 

  • Bartumeus, F., Catalan, J., Fulco, U.L., Lyra, M.L. and Viswanathan, G.M., 2002. Optimizing the encounter rate in biological interactions: Levy versus Brownian strategies. Physical Review Letters 88: 097901.

    Article  Google Scholar 

  • Bartumeus, F., Peters, F., Pueyo S., Marrase, C. and Catalan, J., 2003. Helical Lévy walks: adjusting searching statistics to resource availability in microzooplankton. Proceedings of the National Academy of Sciences of the United States of America 100: 12771–12775.

    Article  Google Scholar 

  • Benedix, J.H., 1993. Area-restricted search by the plains pocket gopher (Geomys-Bursarius) in tallgrass prairie habitat. Behavioral Ecology 4: 318–324.

    Article  Google Scholar 

  • Benhamou, S., 2007. How many animals really do the Lévy walk? Ecology 88: 1962–1969.

    Article  Google Scholar 

  • Benichou, O., Loverdo, C., Moreau, M. and Voituriez, R., 2007. A minimal model of intermittent search in dimension two. Journal of Physics – Condensed Matter 19: 065141.

    Article  Google Scholar 

  • Berg, H.C., 1983. Random Walks in Biology. Princeton University Press, Princeton.

    Google Scholar 

  • Bergman, C.M., Schaefer, J.A. and Luttich, S.N., 2000. Caribou movement as a correlated random walk. Oecologia 123: 364–374.

    Article  Google Scholar 

  • Binford, L.R., 1978a. Dimensional analysis of behavior and site structure: learning from an Eskimo hunting stand. American Antiquity 43: 330–361.

    Article  Google Scholar 

  • Binford, L.R., 1978b. Nunamiut Ethnoarchaeology. Academic Press, London.

    Google Scholar 

  • Binford, L.R., 1980. Willow smoke and dogs’ tails: hunter-gatherer settlement systems and archaeological site formation. American Antiquity 45: 1–17.

    Article  Google Scholar 

  • Binford, L.R., 1982. The archaeology of place. Journal of Anthropological Archaeology 1: 5–31.

    Article  Google Scholar 

  • Binford, L.R., 2001. Constructing Frames of Reference: An Analytical Method for Archaeological Theory Building Using Hunter-Gatherer and Environmental Data Sets. University of California Press, Berkeley.

    Google Scholar 

  • Blackwell, P.G., 1997. Random diffusion models for animal movement. Ecological Modeling 100: 87–102.

    Article  Google Scholar 

  • Bovet, P. and Benhamou, S., 1988. Spatial analysis of animals’ movements using a correlated random walk model. Journal of Theoretical Biology 131: 419–433.

    Article  Google Scholar 

  • Boyer, D., Ramos-Fernandez, G., Miramontes, O., Mateos, J.L., Cocho, G., Larralde, H., Ramos, H. and Rojas, F., 2006. Scale-free foraging by primates emerges from their interaction with a complex environment. Proceedings of the Royal Society B 273: 1743–1750.

    Article  Google Scholar 

  • Boyle, K.V., 1996. From Laugerie Basse to Jolivet: the organization of Final Magdalenian settlement in the Vezere Valley. World Archaeology 27: 477–491.

    Article  Google Scholar 

  • Brantingham, P.J., 2003. A neutral model of stone raw material procurement. American Antiquity 68: 487–509.

    Article  Google Scholar 

  • Brantingham, P.J., 2006. Measuring forager mobility. Current Anthropology 47: 435–459.

    Article  Google Scholar 

  • Brown, C.T., 2001. The fractal dimensions of lithic reduction. Journal of Archaeological Science 28: 619–631.

    Article  Google Scholar 

  • Brown, C.T., Liebovitch, L.S. and Glendon, R., 2007. Levy flights in Dobe Ju/’hoansi foraging patterns. Human Ecology 35: 129–138.

    Article  Google Scholar 

  • Brown, C.T. and Witschey, W.R.T., 2003. The fractal geometry of ancient Maya settlement. Journal of Archaeological Science 30: 1619–1632.

    Article  Google Scholar 

  • Brown, C.T., Witschey, W.R.T. and Liebovitch, L.S., 2005. The broken past: Fractals in archaeology. Journal of Archaeological Method and Theory 12: 37–78.

    Article  Google Scholar 

  • Burger, O., Hamilton, M.J. and Walker, R., 2005. The prey as patch model: optimal handling of resources with diminishing returns. Journal of Archaeological Science 32: 1147–1158.

    Article  Google Scholar 

  • Chorley, R.J. and Haggett, P., 1967. Models in Geography. Methuen, London.

    Google Scholar 

  • Clarke, D.L., 1968. Analytical Archaeology. Methuen, London.

    Google Scholar 

  • Clarke, D.L., 1972. Models and paradigms in contemporary archaeology. In Models in Archaeology, edited by D.L. Clarke, pp. 1–80. Methuen, London.

    Google Scholar 

  • Clarke, D.L., editor., 1977a. Spatial Archaeology. Academic Press, London.

    Google Scholar 

  • Clarke, D.L., 1977b. Spatial information in archaeology. In Spatial Archaeology, edited by D.L. Clarke, pp. 1–32. Academic Press, London.

    Google Scholar 

  • Clarke, D.L., 1979. Analytical Archaeologist: Collected Papers of David L. Clarke. Academic Press, London.

    Google Scholar 

  • Cole, B.J., 1995. Fractal time in animal behavior – the movement activity of drosophila. Animal Behaviour 50: 1317–1324.

    Article  Google Scholar 

  • Coscoy, S., Huguet, E. and Amblard, F., 2007. Statistical analysis of sets of random walks: how to resolve their generating mechanism. Bulletin of Mathematical Biology 69: 2467–2492.

    Article  Google Scholar 

  • Crist, T.O., Guertin, D.S., Wiens, J.A. and Milne, B.T., 1992. Animal movement in heterogeneous landscapes – an experiment with Eleodes beetles in shortgrass prairie. Functional Ecology 6: 536–544.

    Article  Google Scholar 

  • da Luz, M.G.E., Buldyrev, S.V., Havlin, S., Raposo, E.P., Stanley, H.E. and Viswanathan, G.M., 2001. Improvements in the statistical approach to random Lévy flight searches. Physica A – Statistical Mechanics and Its Applications 295: 89–92.

    Article  Google Scholar 

  • Dai, X.H., Shannon, G., Slotow, R., Page, B. and Duffy, K.J., 2007. Short-duration daytime movements of a cow herd of African elephants. Journal of Mammalogy 88: 151–157.

    Article  Google Scholar 

  • de Knegt, H.J., Hengeveld, G.M., van Langevelde, F., de Boer, W.F. and Kirkman, K.P., 2007. Patch density determines movement patterns and foraging efficiency of large herbivores. Behavioral Ecology 18: 1065–1072.

    Article  Google Scholar 

  • Edwards, A.M., Phillips, R.A., Watkins, N.W., Freeman, M.P., Murphy, E.J., Afanasyev, V., Buldyrev, S.V., da Luz, M.G.E., Raposo, E.P., Stanley, H.E. and Viswanathan G.M., 2007. Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature 449: 1044–1048.

    Article  Google Scholar 

  • Einstein, A., 1905. Uber die von der molekularkinetischen theorie der warme geforderte bewegung von in ruhenden flussigkeiten suspendierten teilchen. Annals of Physics 17: 549–560.

    Google Scholar 

  • Einstein, A., 1906. Zur theorie der Brownschen bewegung. Annals of Physics 19: 371–381.

    Google Scholar 

  • Faugeras, B. and Maury, O., 2007. Modeling fish population movements: From an individual-based representation to an advection-diffusion equation. Journal of Theoretical Biology 247: 837–848.

    Article  Google Scholar 

  • Fritz, H., Said, S. and Weimerskirch, H., 2003. Scale-dependent hierarchical adjustments of movement patterns in a long-range foraging seabird. Proceedings of the Royal Society of London Series B 270: 1143–1148.

    Article  Google Scholar 

  • Gamble, C., 1983. Culture and society in the Upper Paleolithic of Europe. In Hunter-Gatherer Economy in Prehistory, edited by G.N. Bailey, pp. 201–211. Cambridge University Press, Cambridge.

    Google Scholar 

  • Gamble, C., 1996. Making tracks: hominid networks and the evolution of the social landscape. In The Archaeology of Human Ancestry: Power, Sex and Tradition, edited by J. Steele and S.J. Shennan, pp. 253–277. Routledge, London.

    Google Scholar 

  • Gamble, C., 1998. Paleolithic society and the release from proximity: a network approach to intimate relations. World Archaeology 29: 429–449.

    Article  Google Scholar 

  • Gamble, C., 1999. The Paleolithic Societies of Europe. Cambridge University Press, Cambridge.

    Google Scholar 

  • Gautestad, A.O. and Mysterud, I., 1993. Physical and biological mechanisms in animal movement processes. Journal of Applied Ecology 30: 523–535.

    Article  Google Scholar 

  • Gautestad, A.O. and Mysterud, I., 1995. The home range ghost. Oikos 74: 195–204.

    Article  Google Scholar 

  • Gautestad, A.O. and Mysterud, I., 2005. Intrinsic scaling complexity in animal dispersion and abundance. American Naturalist 165: 44–55.

    Article  Google Scholar 

  • Gautestad, A.O. and Mysterud, I., 2006. Complex animal distribution and abundance from memory-dependent kinetics. Ecological Complexity 3: 44–55.

    Article  Google Scholar 

  • Gautestad, A.O., Mysterud, I. and Pelton, M.R., 1998. Complex movement and scale-free habitat use: testing the multiscaled home-range model on black bear telemetry data. Ursus 10: 219–234.

    Google Scholar 

  • Gibson, E., 2007. The archaeology of movement in a Mediterranean landscape. Journal of Mediterranean Archaeology 20: 61–87.

    Google Scholar 

  • Grove, M.J., 2008a. The Evolution of Hominin Group Size and Land Use: An Archaeological Perspective. Unpublished PhD Thesis, University of London, London.

    Google Scholar 

  • Grove, M.J., 2008b. Estimating hunter-gatherer group size via spatio-allometric analysis. PaleoAnthropology 2008: e10.

    Google Scholar 

  • Grove, M.J., 2009. Hunter-gatherer movement patterns: causes and constraints. Journal of Anthropological Archaeology 28: 222–233.

    Article  Google Scholar 

  • Grove, M.J., 2010. The archaeology of group size. Proceedings of the British Academy 158: 395–416.

    Google Scholar 

  • Grove, M.J. and Coward, F., 2008. From individual neurons to social brains. Cambridge Archaeological Journal 18: 373–386.

    Article  Google Scholar 

  • Grunbaum, D., 1998. Schooling as a strategy for taxis in a noisy environment. Evolutionary Ecology 12: 503–522.

    Article  Google Scholar 

  • Hagerstrand, T., 1967. Innovation Diffusion as a Spatial Process. University of Chicago Press, Chicago.

    Google Scholar 

  • Haggett, P., 1965. Locational Analysis in Human Geography. Edward Arnold Ltd., London.

    Google Scholar 

  • Haggett, P., Cliff, A.D. and Frey, A., 1977. Locational Analysis in Human Geography. Arnold, London.

    Google Scholar 

  • Hamilton, M.J., Milne, B.T., Walker, R.S., Burger, O. and Brown, J.H., 2007. The complex structure of hunter-gatherer social networks. Proceedings of the Royal Society B 274: 2195–2202.

    Article  Google Scholar 

  • Hammond, N., 1979. David Clarke: a biographical sketch. In Analytical Archaeologist: Collected Papers of David L Clarke, pp. 1–10. Academic Press, London.

    Google Scholar 

  • Hancock, P.A. and Milner-Gulland, E.J., 2006. Optimal movement strategies for social foragers in unpredictable environments. Ecology 87: 2094–2102.

    Article  Google Scholar 

  • Harnos, A., Horváth, G., Lawrence, A.B. and Vattay G., 2000. Scaling and intermittency in animal behavior. Physica A – Statistical Mechanics and its Applications 286: 312–320.

    Article  Google Scholar 

  • Hays, G.C., Hobson, V.J., Metcalfe, J.D., Righton, D. and Sims, D.W., 2006. Flexible foraging movements of leatherback turtles across the North Atlantic Ocean. Ecology 87: 2647–2656.

    Article  Google Scholar 

  • Higgs, E.S. and Vita-Finzi, C., 1972. Prehistoric economies: a territorial approach. In Papers in Economic Prehistory, edited by E.S. Higgs, pp. 27–36. Cambridge University Press, Cambridge.

    Google Scholar 

  • Hodder, I., 1979. Simulating the growth of hierarchies. In Transformations: Mathematical Approaches to Culture Change, edited by C. Renfrew and K.L. Cooke, pp. 117–144. Academic Press, New York.

    Google Scholar 

  • Hodder, I. and Orton, C., 1976. Spatial Analysis in Archaeology. Cambridge University Press, Cambridge.

    Google Scholar 

  • Houston, A.I. and McNamara, J.M., 1999. Models of Adaptive Behaviour: An Approach Based on State. Cambridge University Press, Cambridge.

    Google Scholar 

  • Howell, N., 1976. The population of the Dobe Area !Kung. In Kalahari Hunter-Gatherers: Studies of the !Kung San and Their Neighbours, edited by R.B. Lee and I. DeVore, pp. 137–151. Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Howell, N., 1979. Demography of the Dobe !Kung. Academic Press, New York.

    Google Scholar 

  • Isaac, G.L., 1981. Stone Age visiting cards: approaches to the study of early land use patterns. In Pattern of the Past: Studies in Honour of David Clarke, edited by I. Hodder, G.L. Isaac and N. Hammond, pp. 131–155. Cambridge University Press, Cambridge.

    Google Scholar 

  • Johnson, A.R., Milne, B.T. and Wiens J.A., 1992. Diffusion in fractal landscapes – simulations and experimental studies of Tenebrionid beetle movements. Ecology 73: 1968–1983.

    Article  Google Scholar 

  • Johnson, D.S., London, J.M., Lea, M.A. and Durban, J.W., 2008. Continuous-time correlated random walk model for animal telemetry data. Ecology 89: 1208–1215.

    Article  Google Scholar 

  • Johnson, G.A., 1980. Rank-size convexity and system integration: a view from archaeology. Economic Geography 56: 234–247.

    Article  Google Scholar 

  • Johnson, G.A., 1980. Rank-size convexity and system integration: a view from archaeology. Economic Geography 56: 234–247.

    Google Scholar 

  • Kareiva, P.M. and Shigesada, N., 1983. Analyzing insect movement as a correlated random walk. Oecologia 56: 234–238.

    Article  Google Scholar 

  • Kelly, R.L., 1983. Hunter-gatherer mobility strategies. Journal of Anthropological Research 39: 277–306.

    Google Scholar 

  • Kelly, R.L., 1992. Mobility/sedentism – concepts, archaeological measures, and effects. Annual Review of Anthropology 21: 43–66.

    Article  Google Scholar 

  • Kelly, R.L., 1995. The Foraging Spectrum: Diversity in Hunter-Gatherer Lifeways. Smithsonian Institution Press, Washington.

    Google Scholar 

  • Lee, R.B., 1976. !Kung spatial organization. In Kalahari Hunter-Gatherers: Studies of the !Kung San and Their Neighbours, edited by R.B. Lee and I. DeVore, pp. 73–97. Harvard University Press Cambridge, MA.

    Google Scholar 

  • Levandowsky, M., Klafter, J. and White B.S., 1988a. Feeding and swimming behavior in grazing microzooplankton. Journal of Protozoology 35: 243–246.

    Google Scholar 

  • Levandowsky, M., Klafter, J. and White B.S., 1988b. Swimming behavior and chemosensory responses in the protistan microzooplankton as a function of the hydrodynamic regime. Bulletin of Marine Science 43: 758–763.

    Google Scholar 

  • Levandowsky, M., White, B.S. and Schuster, F.L., 1997. Random movements of soil amebas. Acta Protozoologica 36: 237–248.

    Google Scholar 

  • Lévy, P., 1937. Theorie de l’Addition des Variables Aleatoires. Gauthier-Villars, Paris.

    Google Scholar 

  • Liebovitch, L.S., Scheurle, D., Rusek, M. and Zochowski, M., 2001. Fractal methods to analyze ion channel kinetics. Methods 24: 359–375.

    Article  Google Scholar 

  • Liebovitch, L.S., Todorov, A.T., Zochowski, M., Scheurle, D., Colgin, L., Wood, M.A., Ellenbogen, K.A., Herre, J.M. and Bernstein, R.C., 1999. Nonlinear properties of cardiac rhythm abnormalities. Physical Review E 59: 3312–3319.

    Article  Google Scholar 

  • Mandelbrot, B.B., 1983. The Fractal Geometry of Nature. W.H. Freeman and Company, New York

    Google Scholar 

  • Marell, A., Ball, J.P. and Hofgaard. A., 2002. Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Lévy flights. Canadian Journal of ZoologyRevue Canadienne De Zoologie 80: 854–865.

    Article  Google Scholar 

  • McAndrews, T.L., Albarracin-Jordan, J. and Bermann, M., 1997. Regional settlement patterns in the Tiwanaku Valley of Bolivia. Journal of Field Archaeology 24: 67–83.

    Article  Google Scholar 

  • Morales, J.M., Haydon, D.T., Frair, J., Holsiner, K.E. and Fryxell, J.M., 2004. Extracting more out of relocation data: Building movement models as mixtures of random walks. Ecology 85: 2436–2445.

    Article  Google Scholar 

  • Newman, M.E.J., 2005. Power laws, Pareto distributions and Zipf’s law. Contemporary Physics 46: 323–351.

    Article  Google Scholar 

  • Ogata, Y. and Katsura, K., 1991. Maximum likelihood estimates of the fractal dimension for random spatial patterns. Biometrika 78: 463–474.

    Article  Google Scholar 

  • Okubo, A., 1980. Diffusion and Ecological Problems: Mathematical Models. Springer-Verlag, Berlin.

    Google Scholar 

  • Patlak, C.S., 1953a. Random walk with persistence and external bias. Bulletin of Mathematical Biophysics 15: 311–338.

    Article  Google Scholar 

  • Patlak, C.S., 1953b. A mathematical contribution to the study of orientation of organisms. Bulletin of Mathematical Biophysics 15: 431–476.

    Article  Google Scholar 

  • Pearson, C.E., 1980. Rank-size distributions and the analysis of prehistoric settlement systems. Journal of Anthropological Research 36: 453–462.

    Google Scholar 

  • Pearson, K., 1905. The problem of the random walk. Nature 72: 294.

    Article  Google Scholar 

  • Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P., 2007. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge.

    Google Scholar 

  • Ramos-Fernandez, G. and Ayala-Orozco, B., 2003. Population size and habitat use in spider monkeys at Punta Laguna, Mexico. In Primates in Fragments: Ecology and Conservation, edited by L.K. Marsh, pp. 191–210. Kluwer Academic Publishers, New York.

    Google Scholar 

  • Ramos-Fernandez, G., Boyer D. and Gomez, V.P., 2006. A complex social structure with fission–fusion properties can emerge from a simple foraging model. Behavioral Ecology and Sociobiology 60: 536–549.

    Article  Google Scholar 

  • Ramos-Fernandez, G., Mateos, J.L., Miramontes, O., Cocho, G., Larralde, H. and Ayala-Orozco, B., 2004. Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi). Behavioral Ecology and Sociobiology 55: 223–230.

    Article  Google Scholar 

  • Raposo, E.P., Buldyrev, S.V., da Luz, M.G.E., Santos, M.C., Stanley, H.E. and Viswanathan, G.M., 2003. Dynamical robustness of Lévy search strategies. Physical Review Letters 91: 240601.

    Article  Google Scholar 

  • Rayleigh, L., 1905. The problem of the random walk. Nature 72: 318.

    Article  Google Scholar 

  • Reid, A.T., 1953. On stochastic processes in biology. Biometrics 9: 275–289.

    Article  Google Scholar 

  • Reynolds, A.M., 2007. Avoidance of conspecific odour trails results in scale-free movement patterns and the execution of an optimal searching strategy. Europhys Lett 79: 30006

    Article  Google Scholar 

  • Reynolds, A.M., 2008. Optimal random Levy-loop searching: new insights into the searching behaviors of central-place foragers. Europhys Lett 82: 20001

    Article  Google Scholar 

  • Reynolds, A.M. and Frye, M.A., 2007. Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PloS One 2: e354.

    Article  Google Scholar 

  • Reynolds, A.M., Reynolds, D.R., Smith, A.D., Svensson, G.P. and Lofstedt, C., 2007a. Appetitive flight patterns of male Agrotis segetum moths over landscape scales. Journal of Theoretical Biology 245: 141–149.

    Article  Google Scholar 

  • Reynolds, A.M., Smith, A.D., Menzel, R., Greggers, U., Reynolds, D.R. and Riley. J.R., 2007b. Displaced honey bees perform optimal scale-free search flights. Ecology 88: 1955–1961.

    Article  Google Scholar 

  • Reynolds, A.M., Smith, A.D., Reynolds, D.R., Carreck, N.L. and Osborne, J.L., 2007c. Honeybees perform optimal scale-free searching flights when attempting to locate a food source. Journal of Experimental Biology 210: 3763–3770.

    Article  Google Scholar 

  • Ricotta, C., 2000. From theoretical ecology to statistical physics and back: self-similar landscape metrics as a synthesis of ecological diversity and geometrical complexity. Ecological Modeling 125: 245–253.

    Article  Google Scholar 

  • Rodseth, L., Wrangham, R.W., Harrigan, A.M. and Smuts B.B., 1991. The human community as a primate society. Current Anthropology 32: 221–254.

    Article  Google Scholar 

  • Rudnick, J. and Gaspari, G., 2004. Elements of the Random Walk. Cambridge University Press, Cambridge.

    Book  Google Scholar 

  • Santos, M.C., Boyer, D., Miramontes, O., Viswanathan, G.M., Raposo, E.P., Mateos, J.L. and da Luz, M.G.E., 2007. Origin of power-law distributions in deterministic walks: the influence of landscape geometry. Physical Review E 75: 061114.

    Article  Google Scholar 

  • Schaefer, J.A., Bergman, C.M. and Luttich S.N., 2000. Site fidelity of female caribou at multiple spatial scales. Landscape Ecology 15: 731–739.

    Article  Google Scholar 

  • Shlesinger, M.F. and Klafter, J., 1986. Levy walks versus Levy flights. In On Growth and Form, edited by H.E. Stanley and N. Ostrowski, pp. 279–283. Martinus Nijhof Publishers, Amsterdam.

    Google Scholar 

  • Sims, D.W., Righton, D. and Pitchford, J.W., 2007. Minimizing errors in identifying Levy flight behavior of organisms. Journal of Animal Ecology 76: 222–229.

    Article  Google Scholar 

  • Sims, D.W., Southall, E.J., Humphries, N.E., Hays, G.C., Bradshaw, C.J.A., Pitchford, J.W., James, A., Ahmed, M.Z., Brierley, A.S., Hindell, M.A., Morritt, D., Musyl, M.K., Righton, D., Shepard, E.L.C., Wearmouth, V.J., Wilson, R.P., Witt, M.J. and Metcalfe, J.D., 2008. Scaling laws of marine predator search behavior. Nature 451: 1098–1102.

    Article  Google Scholar 

  • Sims, D.W., Witt, M.J., Richardson, A.J., Southall, E.J. and Metcalfe, J.D., 2006. Encounter success of free-ranging marine predator movements across a dynamic prey landscape. Proceedings of the Royal Society B – Biological Sciences 273: 1195–1201.

    Article  Google Scholar 

  • Skellam, J.G., 1951. Random dispersal in theoretical populations. Biometrika 38: 196–218.

    Google Scholar 

  • Skellam, J.G., 1973. The formulation and interpretation of mathematical models of diffusionary processes in population biology. In The Mathematical Theory of the Dynamics of Biological Populations, edited by M.S. Bartlett and R.W. Hiorns, pp. 63–85. Academic Press, London.

    Google Scholar 

  • Stephens, D.W. and Krebs J.R., 1986. Foraging Theory. Princeton University Press, Princeton.

    Google Scholar 

  • Travis, J., 2008. How a shark finds its next meal. ScienceNOW Daily News, http://sciencenow.sciencemag.org/cgi/content/full/2008/227/1.

  • Turchin, P., 1998. Quantitative Analysis of Movement: Measuring and Modeling Population Redistribution in Animals and Plants. Sinauer Associates, Sunderland, MA.

    Google Scholar 

  • Viswanathan, G.M., Afanasyev, V., Buldyrev, S.V., Havlin, S., da Luz, M.G.E., Raposo, E.P. and Stanley, H.E., 2000. Levy flights in random searches. Physica A 282: 1–12.

    Article  Google Scholar 

  • Viswanathan, G.M., Afanasyev, V., Buldyrev, S.V., Havlin, S., da Luz, M.G.E., Raposo, E.P. and Stanley, H.E., 2001. Levy fights search patterns of biological organisms. Physica A 295: 85–88.

    Article  Google Scholar 

  • Viswanathan, G.M., Afanasyev, V., Buldyrev, S.V., Murphy, E.J., Prince, P.A. and Stanley, H.E., 1996. Levy flight search patterns of wandering albatrosses. Nature 381: 413–415.

    Article  Google Scholar 

  • Viswanathan, G M., Bartumeus, F., Buldyrev, S.V., Catalan, J., Fulco, U.L., Havlin, S., da Luz, M.G.E., Lyra, M.L., Raposo, E.P. and Stanley, H.E., 2002. Levy flight random searches in biological phenomena. Physica A – Statistical Mechanics and Its Applications 314: 208–213.

    Article  Google Scholar 

  • Viswanathan, G.M., Buldyrev, S.V., Havlin, S., da Luz, M.G.E., Raposo, E.P. and Stanley, H.E., 1999. Optimizing the success of random searches. Nature 401: 911–914.

    Article  Google Scholar 

  • Viswanathan, G.M., Raposo, E.P. and da Luz, M.G.E., 2008. Lévy flights and superdiffusion in the context of biological encounters and random searches. Physics of Life Reviews 5: 133–150.

    Article  Google Scholar 

  • Vita-Finzi, C. and Higgs, E.S., 1970. Prehistoric economy in the Mount Carmel area of Palestine: site catchment analysis. Proceedings of the Prehistoric Society 36: 1–37.

    Google Scholar 

  • Ward, D. and Saltz D., 1994. Foraging at different spatial scales – Dorcas gazelles foraging for lilies in the Negev Desert. Ecology 75: 48–58.

    Article  Google Scholar 

  • Whallon, R., 2006. Social networks and information: non-“utilitarian” mobility among hunter-gatherers. Journal of Anthropological Archaeology 25: 259–270.

    Article  Google Scholar 

  • Yellen, J.E., 1976. Settlement patterns of the !Kung. In Kalahari Hunter-Gatherers: Studies of the !Kung San and Their Neighbours, edited by R.B. Lee and I. DeVore, pp. 47–72. Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Yellen, J.E., 1977. Archaeological Approaches to the Present: Models for Reconstructing the Past. Academic Press, New York.

    Google Scholar 

  • Zhang, X.X., Johnson, S.N., Crawford, J.W., Gregory, P.J. and Young, I.M., 2007. A general random walk model for the leptokurtic distribution of organism movement: theory and application. Ecological Modeling 200: 79–88.

    Article  Google Scholar 

  • Zhou, W.X., Sornette, D., Hill, R.A. and Dunbar, R.I.M., 2005. Discrete hierarchical organization of social group sizes. Proceedings of the Royal Society B 272: 439–444.

    Article  Google Scholar 

  • Zipf, G.K., 1949. Human Behaviour and the Principle of Least Effort. Addison-Wesley, Cambridge.

    Google Scholar 

  • Zubrow, E.B.W., 1985. Fractals, cultural behavior, and prehistory. American Archeology 5: 63–77.

    Google Scholar 

Download references

Acknowledgments

This paper was originally presented at the Society for American Archaeology Annual Conference in Vancouver in the spring of 2008. I would like to thank Stephen Lycett and Parth Chauhan for organizing and inviting me to participate in the “Analytical Approaches to Palaeolithic Technologies” session at that conference, and for their editorship of the current ­volume. James Steele provided stimulating discussions of many of the ideas pursued in “Lévy Walks in Hunter-Gatherers” and has helped clarify my thoughts in key areas. Clive Gamble and Fiona Coward both provided comments on earlier drafts of the paper for which I am very grateful. Finally, a comprehensive review by Jeff Brantingham led to substantial modification of the original manuscript, improving it in both structure and coherence. This research was funded by the British Academy Centenary Research Project, “Lucy to Language: the Archaeology of the Social Brain.” I would particularly like to thank Robin Dunbar and Clive Gamble for their continued support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Matt Grove .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Grove, M. (2010). The Quantitative Analysis of Mobility: Ecological Techniques and Archaeological Extensions. In: Lycett, S., Chauhan, P. (eds) New Perspectives on Old Stones. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6861-6_5

Download citation

Publish with us

Policies and ethics