1. Multiple sources of the European Neolithic Kate Davison School of Mathematics and Statistics Pavel Dolukhanov School of Historical Studies François Feugier School of Mathematics and Statistics Graeme Sarson School of Mathematics and Statistics Anvar Shukurov School of Mathematics and Statistics

2. Model of the spread of the Neolithic + 14C dates:  Western Europe: spread from the Near East  Pan-European model: spread from two centres Outline

3. The spread of farming to Europe: evidence from radiocarbon dating Ammerman & Cavalli-Sforza. Man 6, 674, 1971 Gkiasta et al. Antiquity, 77, 45, 2003 Wave of advance,  Ū  =1 km/yr; regional variations U =5-10 km/yr

4. Standard population dynamics models ( ,  ) = position n( , ,t) = population density  ( , , t) = birth rate n 0 ( , , t) = carrying capacity ( , , t) = diffusivity The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation:

5. Regional variations in the propagation speed  Ū = 1 km/yron average in Europe  U LBK = 4-6 km/yr for the LBK (the Danube-Rhine system)  U coast = 10-20 km/yrin Mediterranean coastal regions Major water ways anisotropic spread advection

6. Rivers and coastlines: global consequences of local effects Anisotropic diffusion  faster spread (advection) within 10 km of major rivers and coastlines V = 5 km/yr for rivers (e.g. A & C-S, 1973) V = 20 km/yrin coastal regions (Zilhão, 2003)

7. Numerical methods Discrete grid on sphere, Δ( ,  ) = 1 o /12, Δ x = 2-9 km Explicit Euler time stepping Zero flux at the boundaries Adaptive time step

8. n 0,,  : functions of position Slower advance beyond 54ºN latitude: Altitude, m n0n0  exp(-d/40 km) : decrease offshore n0=0 in sea

9. V=5 km/yr (rivers) 20 km/yr (coasts) Background n 0 =3.5 people/km 2 Background ν=13 km 2 /yr  = 0.02 yr -1 (population doubles in 30 yr) Spread of a farming population

10. Spread from Jericho

11. Pan-European model East: Limited evidence of farming Well-developed pottery making West: Pre-farming ceramic cultures (La Hoguette & Roucadour)

12. Distance from Jericho, km Calibrated Age BC Spread from the Near East

13. Distance from Jericho, km Calibrated Age BC cannot explain the Eastern Neolithic

14. Single source in Jericho: isochrones (n = const)

15. Single-source model vs 14 C data GOOD FIT yr # MeanStDev Δ t West 291-104 531 Δ t East 183 2661034 Δ t = Time Lag (C14 - Model) Model Arrives Early Model Arrives Late

16. Two sources of the European Neolithic 14 C dates in Eastern Europe do not all belong to the source in the Near East Additional source in Eastern Europe at 71 o N, 56 o E Hunter-gatherers:  = 0.007 yr -1 ; = 90 km 2 /yr ( = 75 km,  = 15 yr); U = 0.8 km/yr; n 0 = 7 people per 100 km 2

17. Two sources Model Arrives Early Model Arrives Late Δ t = Time Lag (C14 - Model) GOOD FIT yr # MeanStDev Δ t West 29174 439 Δ t East 183 -1 614

18. Eastern Source Jericho Source Overlap

19. Eastern Source Jericho Source Overlap

20. Eastern Source Jericho Source Overlap

21. Eastern Source Jericho Source Overlap

22. Eastern Source Jericho Source Overlap

23. Eastern Source Jericho Source Overlap

24. Eastern Source Jericho Source Overlap

25. Eastern Source Jericho Source Overlap

26. Eastern Source Jericho Source Overlap

27. Eastern Source Jericho Source Overlap

28. Eastern Source Jericho Source Overlap

29. Eastern Source Jericho Source Overlap

30. Better fit with two sources,  t = T C14 - T model [yr] Single source (Jericho) Region#MeanSt. Dev. W & E47439786 W291-104531 E1832601034 Two sources (Jericho + Eastern Europe) Region#MeanSt. Dev. W & E47445514 W29174439 E183614

31. Is the improvement significant? 95% confidence intervals for the standard deviation of  t do not overlap:  Single source, 740 <  1 < 840 years  Two sources, 480 <  2 < 550 years F-test:  1 =  2 rejected at 95% level

32. Histograms of  t 1 source 2 sources All sitesWestern sitesEastern sites All sites Western sitesEastern sites

33. Conclusions 1 Mathematical modelling is feasible and productive Anisotropic diffusion near major waterways affects the global pattern of the spread of farming Evidence for a second source of the Neolithic in the East Sites in the East are 50% of Eastern origin and 50% of Near-Eastern origin Sea-faring capabilities: 40 km offshore Mobility of hunter-gatherers: U = 0.8 km/yr  = 90 km 2 /yr ( = 75 km,  = 15 yr)

34. Conclusions 2 but detailed models need to be developed, dominant environmental factors need to be identified and quantified, and methods need to be developed to compare the results with archaeological and radiometric data, post-colonisation development: clustering, proto-urban centres, economic activity

35. Statistical screening of 14 C dates  Multiple 14 C dates: need to isolate the most probable age  Intrinsic statistical scatter in individual dates: need to obtain an accurate age estimate  Multiple evolution phases at a given site: need to isolate and date individual phases

36. Multiple 14 C dates for well-explored sites (RADON Database, http://www.jungsteinzeit.de/radon/radon.htm ) ID DatenKULTURFUNDORTGEMEINDELABNRBPSTD 182LBKStrzelce GrN-5087626060 183LBKStúrovo Bln-5575565120 184LBKStúrovo Bln-5586170100 185LBKStúrovo Bln-5596260100 186LBKTomaszow GrN-7050589540 187LBKUlm-EggingenUlmHv-12982596090 188LBKUlm-EggingenUlmHv-135945740195 189LBKUlm-EggingenUlmHv-13595585580 190LBKUlm-EggingenUlmHv-135966245120 191LBKUlm-EggingenUlmHv-135975840145 192LBKUlm-EggingenUlmHv-13598581080 193LBKUlm-EggingenUlmHv-13599596060 194LBKUlm-EggingenUlmHv-13600620560 195LBKUlm-EggingenUlmHv-13601599560 196LBKUlm-EggingenUlmHv-147215590160

37. Example: Brunn am Gebirge, Austria  Most probable age: T 0 = 5252  99 BC  σ = 100 years adopted as the minimum error for LBK sites  Fine temporal structure implied by archaeological evidence is not visible in 14 C dates due to insufficient accuracy Compact cluster of 20 dates, interpreted as a single date contaminated by noise

38. Example: Zedmar, Kaliningrad, Russia T 0 = 3870  38 BC, σ = 192 years (26 dates) T 0 = 2770  76 BC, σ = 179 years (12 dates) (minimum error 127 years suggested by similar sites) 48 dates in two clusters, interpreted as two dates (using the  2 test)