Human dispersals: Mathematical models and the archaeological record

Human Biology

Volumn 81, Issue 2-3, 2009, Pages 121-140

  Steele, James ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Advection; Allee effect; Anomalous and stratified diffusion; Biological invasions; Density dependent dispersal; Fisher KPP reaction diffusion system; Human population dispersal; Lotka Volterra system; Paleolithic; Spatial and temporal heterogeneity; Time delay

Indexed keywords

EID: 73649148754     PISSN: 00187143     EISSN: 15346617     Source Type: Journal    
DOI: 10.3378/027.081.0302     Document Type: Article

References (78)

1. Ackland, G. J., M. Signitzer, K. Stratford et al. 2007. Cultural hitchhiking on the wave of advance of beneficial technologies. Proc. Natl Acad. Sci. USA 104:8714-8719.
2. Allee, W. C. 1938. The Social Life of Animals. New York: Norton.
3. Alroy, J. 2001. A multispecies overkill simulation of the end-Pleistocene megafaunal mass extinction. Science 292:1893-1896.
4. Ammerman, A. J., and L. L. Cavalli-Sforza. 1984. The Neolithic Transition and the Genetics of Populations in Europe. Princeton, NJ: Princeton University Press.
5. Aoki, K. 1987. Gene-culture waves of advance. J. Math. Biol. 25:453-464.
6. Aoki, K., M. Shida, and N. Shigesada. 1996. Traveling wave solutions for the spread of farmers into a region occupied by hunter gatherers. Theor. Popul. Biol. 50:1-17.
7. Binford, L. R. 2001. Constructing Frames of Reference: An Analytical Method for Archaeological Theory Building Using Ethnographic and Environmental Data Sets. Berkeley: University of California Press.
8. Brockmann, D., and L. Hufnagel. 2007. Front propagation in reaction-superdiffusion dynamics: Taming Levy flights with fluctuations. Phys. Rev. Lett. 98(17):8301.1-8301.4.
9. Brown, C. T., L. S. Liebovitch, and R. Glendon. 2007. Lévy flights in Dobe Ju/'hoansi foraging patterns. Hum. Ecol. 35:129-138.
10. Campos, D., J. Fort, and V. Mendez. 2006. Transport on fractal river network: Application to migration fronts. Theor. Popul. Biol. 69:88-93.
11. Clark, J. S., M. Lewis, and L. Horvath. 2001. Invasion by extremes: Population spread with variation in dispersal and reproduction. Am. Natur. 157:537-554.
12. Cohen, M. H. 1992. Nonlinearity, disorder, the spread of Neolithic farming, and the origin of the Indo-European languages. In Nonlinearity with Disorder, F. Abdullaev, A. R. Bishop, and S. Pnevmatikos, eds. Springer Proceedings in Physics 67. Berlin: Springer, 161-170.
13. Cuddington, K., and A. Hastings. 2004. Invasive engineers. Ecol. Model. 178:335-347.
14. Currat, M., and L. Excoffier. 2005. The effect of the Neolithic expansion on European molecular diversity. Proc. Biol. Sci. 272:679-688.
15. Davison, K., P. M. Dolukhanov, G. R. Sarson et al. 2006. The role of waterways in the spread of the Neolithic. J. Archaeol. Sci. 33:641-652.
16. Dobson, A. P., and A. M. Lyles. 1989. The population dynamics and conservation of primate populations. Conserv. Biol. 3:362-380.
17. Einstein, A. 1905. Über die von der molekularkinetischen Theorie der Warme geforderte Bewegung von in ruhenden Flussigkeiten suspendierten Teilchen. Ann. Phys. (Leipzig) 17:549-560.
18. Fedotov, S., D. Moss, and D. Campos. 2008. Stochastic model for population migration and the growth of human settlements during the Neolithic transition. Phys. Rev. E 78(2):026107.1-026107.7.
19. Fisher, R. A. 1937. The wave of advance of advantageous genes. Ann. Eugen. 7:355-369.
20. Fort, J. 2004. Population expansion in the western Pacific (Austronesia): A wave of advance model. Antiquity 77:520-530.
21. Fort, J., and V. Méndez. 1999. Time-delayed theory of the Neolithic transition in Europe. Phys. Rev. Lett. 82:867-870.
22. Fort, J., and V. Méndez. 2002. Wave fronts in time-delayed reaction-diffusion systems: Theory and comparison to experiment. Rep. Progr. Phys. 65:895-954.
23. Fort, J., J. Pérez-Losada, J. J. Suñol et al. 2008. Integrodifference equations for interacting species and the Neolithic transition. New J. Phys. 10(4):1-18.
24. Fort, J., and T. Pujol. 2007. Time-delayed fronts from biased random walks. New J. Phys. 9:1-14.
25. Fort, J., T. Pujol, and L. L. Cavalli-Sforza. 2004. Paleolithic population waves of advance. Cambridge Archaeol. J. 14:53-61.
26. Gkiasta, M., T. Russell, S. Shennan et al. 2003. Neolithic transition in Europe: The radiocarbon record revisited. Antiquity 77:45-61.
27. Hamilton, M. J., and B. Buchanan. 2007. Spatial gradients in Clovis-age radiocarbon dates across North America suggest rapid colonization from the north. Proc. Natl Acad. Sci. USA 104:15,625-15,630.
28. Hastings, A. 2005. Unstructured models in ecology: Past, present, and future. In Ecological Paradigms Lost, K. Cuddington and B. Besiner, eds. Orlando: Academic Press, 9-29.
29. Hastings, A., K. Cuddington, K. Davies et al. 2005. The spatial spread of invasions: New developments in theory and evidence. Ecol. Lett. 8:91-101.
30. Hazelwood, L., and J. Steele. 2004. Spatial dynamics of human dispersals: Constraints on modeling and archaeological detection. J. Archaeol. Sci. 31:669-679.
31. Hazelwood, L., J. Steele, and T. Sluckin. 2008. High-velocity human range expansion: Numerical models. Unpublished.
32. Henrich, J. 2001. Cultural transmission and the diffusion of innovations: Adoption dynamics indicate that biased cultural transmission is the predominant force in behavioral change. Am. Anthropol. 103:992-1013.
33. Hewlett, B. S., J. M. H. van de Koppel, and L. L. Cavalli-Sforza. 1986. Exploration and mating range of Aka pygmies of the Central African Republic. In African Pygmies, L. L. Cavalli-Sforza, ed. Orlando, FL: Academic Press, 65-79.
34. Housley, R. A., C. S. Gamble, M. Street et al. 1997. Radiocarbon evidence for the late glacial human recolonization of northern Europe. Proc. Prehist. Soc. 63:25-54.
35. Kandler, A. 2009. Demography and language competition. Hum. Biol. 81(2-3):181-210 (this issue).
36. Kandler, A., and J. Steele. 2008. Ecological models of language competition. Biol. Theory 3:164-173.
37. Kandler, A., and J. Steele. 2009. Social learning, economic inequality, and innovation diffusion. In Innovation in Cultural Systems: Contributions from Evolutionary Anthropology, M. O'Brien and S. Shennan, eds. Cambridge, MA: MIT Press (in press).
38. Kelly, R. L. 1995. The Foraging Spectrum. Washington, DC: Smithsonian Institution Press.
39. Kinezaki, N., K. Kawasaki, and N. Shigesada. 2006. Spatial dynamics of invasion in sinusoidally varying environments. Popul. Ecol. 48:263-270.
40. Kinezaki, N., K. Kawasaki, F. Takasu et al. 2003. Modeling biological invasions into periodically fragmented environments. Theor. Popul. Biol. 64:291-302.
41. King, J. R., and P. M. McCabe. 2003. On the Fisher-KPP equation with fast nonlinear diffusion. Proc. R. Soc. Lond. A 459:2529-2546.
42. Kolmogorov, A. N., I. G. Petrovskii, and N. S. Piskunov. 1937. A study of the diffusion equation with increase in the quantity of matter and its application to a biological problem. Bull. Moscow Univ. Math. Ser. A 1:1-25.
43. Kot, M., M. A. Lewis, and P. van den Driessche. 1996. Dispersal data and the spread of invading organisms. Ecology 77:2027-2042.
44. Lewis, M., and P. Kareiva. 1993. Allee dynamics and the spread of invading organisms. Theor. Popul. Biol. 43:141-158.
45. Lilley, I. 2008. Flights of fancy: Fractal geometry, the Lapita dispersal, and punctuated colonization in the Pacific. In Islands of Inquiry: Colonization, Seafaring, and the Archaeology of Maritime Landscapes, G. Clark, F. Leach, and S. O'Connor, eds. Canberra: Australian National University Press, 75-86.
46. Lutscher, F. 2008. Density-dependent dispersal in integrodifference equations. J. Math. Biol. 54:499-524.
47. Mellars, P. 2006. A new radiocarbon revolution and the dispersal of modern humans in Europe. Nature 439:931-935.
48. Murray, J. D. 1993. Mathematical Biology, 2nd ed. Berlin: Springer.
49. Neubert, M. G., M. Kot, and M. Lewis. 2000. Invasion speeds in fl uctuating environments. Proc. R. Soc. Lond. B 267:1603-1610.
50. Neuhauser, C. 2001. Mathematical challenges in spatial ecology. Notices Am. Math. Soc. 48:1304-1314.
51. Newman, W. I. 1980. Some exact solutions to a nonlinear diffusion problem in population genetics and combustion. J. Theor. Biol. 85:325-334.
52. Okubo, A., P. K. Maini, M. H. Williamson et al. 1989. On the spatial spread of the gray squirrel in Britain. Proc. R. Soc. Lond. B 238:113-125.
53. Ortega-Cejas, V., J. Fort, and V. Mendez. 2004. The role of the delay time in the modeling of biological range expansions. Ecology 85:258-264.
54. Petrovskii, S. V. and B.-L. Li. 2003. An exactly solvable model of population dynamics with densitydependent migrations and the Allee effect. Math. Biosci. 186:79-91.
55. Pinhasi, R., J. Fort, and A. J. Ammerman. 2005. Tracing the origin and spread of agriculture in Europe. PLoS Biol. 3:e410.
56. Ray, N., and L. Excoffier. 2009. Inferring past demography using spatially explicit population genetic models. Hum. Biol. 81(2-3):141-157 (this issue).
57. Renfrew, C. 2001. From molecular genetics to archaeogenetics. Proc. Natl. Acad. Sci. USA 98:4830-4832.
58. Rockman, M., and J. Steele, eds. 2003. Colonization of Unfamiliar Landscapes: The Archaeology of Adaptation. London: Routledge.
59. Shennan, S. J., and K. Edinborough. 2007. Prehistoric population history: From the late glacial to the late Neolithic in central and northern Europe. J. Archaeol. Sci. 34:1339-1345.
60. Shigesada, N., K. Kawasaki, and Y. Takeda. 1995. Modeling stratifi ed diffusion in biological invasions. Am. Nat. 146:229-251.
61. Shigesada, N., K. Kawasaki, and E. Teramoto. 1986. Traveling periodic waves in heterogeneous environments. Theor. Popul. Biol. 30:143-160.
62. Shigesada, N., K. Kawasaki, and E. Teramoto. 1987. The speeds of traveling frontal waves in heterogeneous environments. In Mathematical Topics in Population Biology, Morphogenesis, and Neurosciences, E. Teramoto and M. Yamaguti, eds. Lecture Notes in Biomathematics 71. New York: Springer, 87-97.
63. Skellam, J. G. 1951. Random dispersal in theoretical populations. Biometrika 38:196-218.
64. Steele, J. 2009. Prehistoric population dynamics from radiocarbon data: A new approach to estimating front speeds and occupation densities. Unpublished.
65. Steele, J., J. Adams, and T. Sluckin. 1998. Modeling Paleo-Indian dispersals. World Archaeol. 30:286-305.
66. Steele, J., and A. Kandler. 2010. Two-population competition system with sex-specifi c switching term. Phil. Trans. R. Soc. Lond. B. (in press).
67. Steele, J., and G. Politis. 2009. AMS 14C dating of early human occupation of southern South America. J. Archaeol. Sci. 36:419-429.
68. Steele, J., T. Sluckin, D. Denholm et al. 1996. Simulating hunter-gatherer colonization of the Americas. In Interfacing the Past, H. Kamermans and K. Fennema, eds. Analecta Praehistorica Leidensia 28. Leiden, Netherlands: Institute of Prehistory, University of Leiden, 223-227.
69. Surovell, T. 2000. Early Paleo-Indian women, children, mobility, and fertility. Am. Antiquity 65:493-508.
70. Taylor, C. M., and A. Hastings. 2005. Allee effects in biological invasions. Ecol. Lett. 8:895-908.
71. Turney, C. S. M., R. G. Roberts, and Z. Jacobs. 2006. Progress and pitfalls in radiocarbon dating. Nature 443:E3-E4.
72. Van den Bosch, F., R. Hengeveld, and J. A. J. Metz. 1992. Analyzing the velocity of animal range expansion. J. Biogeogr. 19:135-150.
73. Van den Bosch, F., J. A. J. Metz, and O. Diekmann. 1990. The velocity of spatial population expansion. J. Math. Biol. 28:529-565.
74. Verhulst, P. F. 1838. Notice sur la loi que la population pursuit dans son accroissement. Corresp. Math. Phys. 10:113-121.
75. Waters, M. R., and T. W. Stafford Jr. 2007. Redefi ning the age of Clovis: Implications for the peopling of the Americas. Science 315:1122-1126.
76. Wells, H., E. Strauss, M. Rutter et al. 1998. Mate location, population growth, and species extinction. Biol. Conserv. 86:317-324.
77. Young, D., and R. Bettinger. 1992. The Numic spread: A computer simulation. Am. Antiq. 57:85-99.
78. Young, D., and R. Bettinger. 1995. Simulating the global human expansion in the late Pleistocene. J. Archaeol. Sci. 22:89-92.