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Data and mathematical approaches to the neolithic transition

FEPRE European project 3 rd annual workshop Girona, 16-18 March 2009. Data and mathematical approaches to the neolithic transition. Joaquim Fort Universitat de Girona Catalonia, Spain. Plan of this talk. 1. Archaeological data: Speed versus neolithisation time

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Data and mathematical approaches to the neolithic transition

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  1. FEPRE European project 3rd annual workshop Girona, 16-18 March 2009 Data and mathematical approaches to the neolithic transition Joaquim Fort Universitat de Girona Catalonia, Spain

  2. Plan of this talk 1. Archaeological data: Speed versus neolithisation time 2. Mathematical models: Interpretation of the data 3. Archaeological data: Speed versus latitude

  3. Motivation If some hunter-gatherers become farmers: · The front speed should be faster, and · The neolithisation time* should be shorter *Time necessary for the population of farmers to reach saturation density · Theory: New J Phys (2008) · Comparison to archaeological data: this talk

  4. 2400 yr 2000 yr Neolithisation time Data from Gkiasta et al., Antiquity (2003) Time necessary for the population of farmers to reach saturation density

  5. How to estimate local speeds?One way is from isochrones Data by M. Vander Linden (919 sites) Interpolation with GIS software

  6. Bocquet-Appel et al., J. Arch. Sci. (2009), Fig. 8 Another way is to fit a surface of C-14 dates and estimate the gradient

  7. Italy Greece Yugoslavia France >47ºN France <47ºN Germany No trend. Is the effect too small? Belgium

  8. No trend. Is the effect too small?

  9. Plan of this talk 1. Archaeological data: Speed versus neolithisation time→ no trend 2. Mathematical models: Do they predict that this effect is too small? 3. Archaeological data: Speed versus latitude

  10. “Predator-prey” models 1. Ammerman and Cavalli-Sforza→ (1984) 2. Lotka-Volterra: births-deaths

  11. 3. Cohabitation models Example: if all individuals disperse: pN time t gentime t + 1 gen time t + 1 gen x x-r x x+r x-r x x+r before migration cohabitation non-cohabitation (e.g., Lotka-Volterra)

  12. Cohabitation models • F et al, Phys Rev E (2007) • F et al, New J Phys (2008) • Isern et al, J Stat Mechs (2008) Dispersal probability distribution

  13. 0 Γ 1/PNmax 1/PN How to estimate the interaction parameter Γ ?Effect of the interaction (no dispersal and R0N=1)

  14. Speed of the neolithic front R0N = 2.2 (Birdsell 1957) T = 32 yr (Stauder 1971) Currant & Excoffier (2005): pe = 0.38 (Stauder 1971) Pmax P = 0.064 people/km2 r = 50 km (Stauder 1971) Pmax N =20 Pmax P=1.28people/km2 New J Phys (2008) This maximum difference of speeds is only 1% !! This effect seems negligible. Reason: Pmax P << PmaxN

  15. Plan of this talk 1. Archaeological data: Speed versus neolithisation time 2. Mathematical models: The effect is too small 3. Archaeological data: Speed versus latitude

  16. The same data versus latitude Italy Greece Yugoslavia France>47º France<47º Germany Belgium

  17. Is there a trend?

  18. But many nodes are on the sea...

  19. Bocquet-Appel et al., J. Arch. Sci. (2009), Fig. 8 Is there a trend using all grid nodes?

  20. But the Mediterranean spread is faster

  21. MEDITERRANEAN

  22. Trend with latitude

  23. Trend also in some smaller regions (but only at latitude>47º)

  24. How to find the speed direction? t arrival What should the surface of C14 arrival dates look like? 5000 cal yr BP slow 13000 cal yr BP fast N E W Russia Britain S Portugal Near East

  25. How to find the speed direction? The gradient is orthogonal to the level lines* t arrival surface level plane y level line x *N. Piskunov, Differential and Integral Calculus (Moscow, 1966), Sec. 8.15

  26. How to find the speed direction? The speed is also orthogonal to the level lines of arrival time (isochrones): 8000 CAL yr BP Speed vector 8500 CAL yr BP So the speed vector is parallel to the gradient

  27. Germany

  28. Conclusions 1. Archaeological data No observed trend of speed versus neolithisation time 2. Mathematical models The effect is too small because Pmax P << PmaxN 3. Archaeological data Local trends of speed versus latitude >47ºN. Cause?

  29. To model local trends, the cause has to be known Possible causes 1. Reproduction and/or mobility decreases with increasing latitude NO DATA AVAILABLE 2. More density of hunter-gatherers to the North + resistance to farmers? DATA AVAILABLE? 3. Time needed for crop to adapt to colder climates to the North? DATA AVAILABLE?

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