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

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

3. 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. 4 Neolithisation time 2400 yr Data from Gkiasta et al., Antiquity (2003) 2000 yr Time necessary for the population of farmers to reach saturation density

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

6. 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. 7 No trend. Is the effect too small? France >47ºN France <47ºN Greece Italy Germany Belgium Yugoslavia

8. 8 No trend. Is the effect too small?

9. 9 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 Plan of this talk

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

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

12. 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. 13 How to estimate the interaction parameter Γ ? Effect of the interaction (no dispersal and R 0N =1) 0 Γ 1/P N max 1/P N

14. 14 R 0N = 2.2 (Birdsell 1957) T = 32 yr (Stauder 1971) Currant & Excoffier (2005): p e = 0.38 (Stauder 1971) P max P = 0.064 people/km 2 r = 50 km (Stauder 1971) P max N =20 P max P =1.28 people/km 2 Speed of the neolithic front This maximum difference of speeds is only 1% !! This effect seems negligible. Reason: P max P << P maxN New J Phys (2008)

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

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

17. 17 Is there a trend?

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

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

20. 20 But the Mediterranean spread is faster

21. 21

22. 22 MEDITERRANEAN

23. 23 Trend with latitude

24. 24 Trend also in some smaller regions (but only at latitude>47º)

25. 25 How to find the speed direction? What should the surface of C14 arrival dates look like? W S N fast slow Near East Russia Britain Portugal E t arrival 5000 cal yr BP 13000 cal yr BP

26. 26 How to find the speed direction? The gradient is orthogonal to the level lines* *N. Piskunov, Differential and Integral Calculus (Moscow, 1966), Sec. 8.15 y x t arrival surface level line level plane

27. 27 The speed is also orthogonal to the level lines of arrival time (isochrones): How to find the speed direction? Speed vector 8500 CAL yr BP 8000 CAL yr BP So the speed vector is parallel to the gradient

28. 28 Germany

29. 29 1.Archaeological data No observed trend of speed versus neolithisation time 2. Mathematical models The effect is too small because P max P << P maxN 3. Archaeological data Local trends of speed versus latitude >47ºN. Cause? Conclusions

30. 30 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? To model local trends, the cause has to be known