Realistic preindustrial dispersal kernels applied to the Neolithic

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Realistic pre-industrial dispersal
kernelsapplied to the Neolithic
FEPRE European Project 2nd annual workshop St
Petersburg 5-10 April 2008

• Neus IsernUniversitat de Girona
• Catalonia, Spain

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Contents

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

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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
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Front speed
Fisher and HRD equations
Diffusion coefficient D
Evolution equation
Dispersion kernel
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Evolution equation
Reaction
Dispersion

• Logistic growth

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Evolution equation
Sequential
Reaction
Dispersion
Non sequential
Reaction
Dispersion
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Discrete dispersion kernel
Dispersion data
Dispersion data from three pre-industrial farmer
populations (J. Stauder)

• Dispersion kernel f (Dx,Dy)

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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

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Several-distance kernel
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Continuous dispersion 2D-kernel
Gauss
Laplace
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Gauss / Laplace kernel