1. Realistic pre-industrial dispersal kernels applied to the Neolithic
FEPRE European Project
2nd annual workshop
St Petersburg
April 2008
Neus Isern Universitat de Girona
Catalonia, Spain

2. Contents Aplication to the Neolithic transition:
Introduction to reaction-dispersion fronts. Evolution equation
Aplication to the Neolithic transition:
Discrete 2D dispersion kernels
Continuous 2D dispersion kernels

3. Reaction-dispersion fronts
Reaction-dispersion fronts: aplications
Physics: superconductors, solidification...
Biological systems: viral infections, biological invasions, tumor growth, Neolithic transition...
Neolithic expansion in Europe
Reaction or
reproduction
Dispersion

4. Front speed Fisher and HRD equations Evolution equation
Diffusion coefficient: D
Evolution equation
Dispersion kernel:

5. Evolution equation
Reaction
Dispersion
Logistic growth

6. Evolution equation Sequential Non sequential Reaction Dispersion

7. Discrete dispersion kernel
Dispersion data
< 4.8km
4.8 – 24.1km
24.1 – 48.3km
>48.3km
<d2> (km2) A
0.54
0.17
0.04
0.25
1115.7 B
0.40
0.26
1325.6 C
0.19
0.07
0.22
0.52
2153.0
< 4.8km
4.8 – 24.1km
24.1 – 48.3km
>48.3km
<d2> (km2) A
0.54
0.17
0.04
0.25
1115.7 B
0.40
0.26
1325.6 C
0.19
0.07
0.22
0.52
2153.0
Dispersion data from three pre-industrial farmer populations (J. Stauder)
Dispersion kernel f (Dx,Dy)

8. Single-distance kernel
Data
Realistic initial growth rate: a  [0.029 , 0.035] yr-1
Estimated Neolithic transition speed: c  [0.6 , 1.3] km/yr

9. Several-distance kernel

10. Continuous dispersion 2D-kernel
Gauss
Laplace

11. Gauss / Laplace kernel

12. Thank you for the attention!!