zbMATH — the first resource for mathematics

Inference for population dynamics in the Neolithic period. (English) Zbl 1257.62117
Summary: We consider parameter estimation for the spread of the Neolithic incipient farming across Europe using radiocarbon dates. We model the arrival time of farming at radiocarbon-dated, early Neolithic sites by a numerical solution to an advancing wavefront. We allow for (technical) uncertainty in the radiocarbon data, lack-of-fit of the deterministic model and use a Gaussian process to smooth spatial deviations from the model. Inference for the parameters in the wavefront model is complicated by the computational cost required to produce a single numerical solution. We therefore employ Gaussian process emulators for the arrival time of the advancing wavefront at each radiocarbon-dated site. We validate our model using predictive simulations.

62P12 Applications of statistics to environmental and related topics
62M99 Inference from stochastic processes
65C40 Numerical analysis or methods applied to Markov chains
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI Euclid
[1] Ackland, G. J., Signitzer, M., Stratford, K. and Cohen, M. H. (2007). Cultural hitchhiking on the wave of advance of beneficial technologies. Proc. Natl. Acad. Sci. USA 104 8714-8719.
[2] Aitken, M. (1990). Science-Based Dating in Archaeology . Longman, Harlow.
[3] Ammerman, A. J. and Cavalli-Sforza, L. L. (1971). Measuring the rate of spread of early farming in Europe. Man 6 674-688.
[4] Ammerman, A. J. and Cavalli-Sforza, L. L. (1973). A population model for the diffusion of early farming in Europe. In The Explanation of Culture Change (C. Renfrew, ed.) 343-357. Duckworth, London.
[5] Aoki, K., Shida, M. and Shigesada, N. (1996). Travelling wave solutions for the spread of farmers into a region occupied by hunter-gatherers. Theor. Popul. Biol. 50 1-17. · Zbl 0856.92026 · doi:10.1006/tpbi.1996.0020
[6] Baggaley, A. W., Barenghi, C. F., Shukurov, A. and Subramanian, K. (2009). Reconnecting flux-rope dynamo. Phys. Rev. E 80 055301. · Zbl 1217.85004
[7] Baggaley, A. W., Boys, R. J., Golightly, A. and Shukurov, A. (2013). Supplement to “Inference for population dynamics in the Neolithic period.” . · Zbl 1257.62117 · dx.doi.org
[8] Bastos, L. S. and O’Hagan, A. (2009). Diagnostics for Gaussian process emulators. Technometrics 51 425-438. · doi:10.1198/TECH.2009.08019
[9] Bayarri, M. J., Berger, J. O., Paulo, R., Sacks, J., Cafeo, J. A., Cavendish, J., Lin, C.-H. and Tu, J. (2007). A framework for validation of computer models. Technometrics 49 138-154. · doi:10.1198/004017007000000092
[10] Birdsell, J. B. (1957). Some population problems involving Pleistocene man. Cold Spring Harbor Symposium on Quantitative Biology 22 47-69.
[11] Blackwell, P. G. and Buck, C. E. (2008). Estimating radiocarbon calibration curves. Bayesian Anal. 3 225-248. · Zbl 1330.86018 · doi:10.1214/08-BA309
[12] Bocquet-Appel, J.-P., Naji, S., Linden, M. V. and Kozlowski, J. K. (2009). Detection of diffusion and contact zones of early farming in Europe from the space-time distribution of 14C dates. J. Archeo. Sci. 36 807-820.
[13] Buck, C. E., Kenworthy, J. B., Litton, C. D. and Smith, A. F. M. (1991). Combining archaeological and radiocarbon information: A Bayesian approach to calibration. Antiquity 65 808-821.
[14] Burger, J. and Thomas, M. G. (2011). The palaeopopulationgenetics of humans, cattle and diarying in neolithic Europe. In Human Bioarchaeology of the Transition to Agriculture (R. Pinhasi and J. T. Stock, eds.) 1029-1058. Wiley, Chichester.
[15] Davison, K., Dolukhanov, P., Sarson, G. R. and Shukurov, A. (2006). The role of waterways in the spread of the Neolithic. J. Archeo. Sci. 33 641-652.
[16] Davison, K., Dolukhanov, P. M., Sarson, G. R., Shukurov, A. and Zaitseva, G. I. (2009). Multiple sources of the European Neolithic: Mathematical modelling constrained by radiocarbon dates. Quaternary International 203 10-18.
[17] Dolukhanov, P. and Shukurov, A. (2004). Modelling the Neolithic dispersal in Northern Eurasia. Documenta Praehistorica 31 35-47.
[18] Dolukhanov, P., Shukurov, A., Gronenborn, D., Sokoloff, D., Timofeev, V. and Zaitseva, G. (2005). The chronology of Neolithic dispersal in Central and Eastern Europe. J. Archeo. Sci. 32 1441-1458.
[19] Fisher, R. A. (1937). The wave of advance of advantageous genes. Ann. Eugenics 7 353-369. · JFM 63.1111.04
[20] Fort, J. and Pujol, P. T. (2008). Progress in front propagation research. Rep. Progr. Phys. 71 086001 (41 pp.).
[21] Geophysical Data System (2011). Available at . · www.ngdc.noaa.gov
[22] Gkiasta, M., Russell, T., Shennan, S. and Steele, J. (2003). Neolithic transition in Europe: The radiocarbon record revisited. Antiquity 77 45-62.
[23] Gneiting, T., Balabdaoui, F. and Raftery, A. E. (2007). Probabilistic forecasts, calibration and sharpness. J. R. Stat. Soc. Ser. B Stat. Methodol. 69 243-268. · Zbl 1120.62074 · doi:10.1111/j.1467-9868.2007.00587.x
[24] Hazelwood, L. and Steele, J. (2004). Spatial dynamics of human dispersals. Constraints on modelling and archaeological validation. J. Archeo. Sci. 31 669-679.
[25] Henderson, D. A., Boys, R. J., Krishnan, K. J., Lawless, C. and Wilkinson, D. J. (2009). Bayesian emulation and calibration of a stochastic computer model of mitochondrial DNA deletions in substantia nigra neurons. J. Amer. Statist. Assoc. 104 76-87. · Zbl 1388.92007 · doi:10.1198/jasa.2009.0005
[26] Isern, N. and Fort, J. (2010). Anisotropic dispersion, space competition and the slowdown of the Neolithic transition. New J. Phys. 12 123002.
[27] Kennedy, M. C. and O’Hagan, A. (2001). Bayesian calibration of computer models. J. R. Stat. Soc. Ser. B Stat. Methodol. 63 425-464. · Zbl 1007.62021 · doi:10.1111/1467-9868.00294
[28] Kolmogorov, A., Petrovskii, I. and Piskunov, N. (1937). A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem. Byul. Moskovskogo Gos. Univ. 1 1-25.
[29] McKay, M. D., Beckman, R. J. and Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21 239-245. · Zbl 0415.62011 · doi:10.2307/1268522
[30] Motuzaite-Matuzeviciute, G., Hunt, H. V. and Jones, M. K. (2009). Multiple sources for Neolithic European agriculture: Geographical origins of early domesticates in Moldova and Ukraine. In The East European Plain on the Eve of Agriculture (P. M. Dolukhanov, G. R. Sarson and A. Shukurov, eds.). British Archaeological Reports , International Series 1964 53-64. Archaeopress, Oxford.
[31] Pape, D. (2004). World DataBank II. Available at . · www.evl.uic.edu
[32] Patterson, M. A., Sarson, G. R., Sarson, H. C. and Shukurov, A. (2010). Modelling the Neolithic transition in a heterogeneous environment. J. Archeo. Sci. 37 2929-2937.
[33] Pettitt, P. B., Davies, W., Gamble, C. S. and Richards, M. B. (2003). Palaeolithic radiocarbon chronology: Quantifying our confidence beyond two half-lives. J. Archaeo. Sci. 30 1685-1693.
[34] Rasmussen, C. E. and Williams, C. K. I. (2006). Gaussian Processes for Machine Learning . MIT Press, Cambridge, MA. · Zbl 1177.68165
[35] Reimer, P. J., Baillie, M., Bard, E., Bayliss, A., Beck, J., Bertrand, C., Blackwell, P., Buck, C., Burr, G., Cutler, K., Damon, P., Edwards, R., Fairbanks, R., Friedrich, M., Guilderson, T., Hughen, K., Kromer, B., McCormac, F., Manning, S., Bronk Ramsey, C., Reimer, R., Remmele, S., Southon, J., Stuiver, M., Talamo, S., Taylor, F., van der Plicht, J. and Weyhenmeyer, C. (2004). IntCal04 terrestrial radiocarbon age calibration. Radiocarbon 46 1029-1058.
[36] Rowley-Conwy, P. (2011). Westward ho! The spread of agriculture from Central Europe to the Atlantic. Current Anthropology 52 S431-S451.
[37] Santner, T. J., Williams, B. J. and Notz, W. I. (2003). The Design and Analysis of Computer Experiments . Springer, New York. · Zbl 1041.62068
[38] Scott, E. M., Cook, G. T. and Naysmith, P. (2007). Error and uncertainty in radiocarbon measurements. Radiocarbon 49 427-440.
[39] Steele, J. (2010). Radiocarbon dates as data: Quantitative strategies for estimating colonization front speeds and event densities. J. Archeo. Sci. 37 2017-2030.
[40] Steele, J., Adams, J. and Sluckin, T. (1998). Modelling Paleoindian dispersals. World Archaeology 30 286-305.
[41] Whittle, A. (1996). Europe in the Neolithic : The Creation of New Worlds . Cambridge Univ. Press, Cambridge.
[42] Zilhão, J. (2001). Radiocarbon evidence for maritime pioneer colonization at the origins of farming in west Mediterranean Europe. Proc. Natl. Acad. Sci. USA 98 14180-14185.
[43] Zvelebil, M., Domaní-ska, L. and Dennell, R. (1998). Harvesting the Sea , Farming the Forest : The Emergence of Neolithic Societies in the Baltic Region . Sheffield Academic Press, Sheffield.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.