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Realistic pre-industrial dispersal kernels applied to the Neolithic

Realistic pre-industrial dispersal kernels applied to the Neolithic. Neus Isern Universitat de Girona Catalonia, Spain. FEPRE European Project 2nd annual workshop St Petersburg April 2008. Contents. Introduction to reaction-dispersion fronts. Evolution equation

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Realistic pre-industrial dispersal kernels applied to the Neolithic

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

  2. Contents • 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 Diffusion coefficient: D Evolution equation Dispersion kernel:

  5. Evolution equation Reaction Dispersion • Logistic growth

  6. Evolution equation Sequential Reaction Dispersion Non sequential Reaction Dispersion

  7. Discrete dispersion kernel Dispersion data Dispersion data from three pre-industrial farmer populations (J. Stauder) • Dispersion kernelf (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!!

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