Theory of Reaction-Diffusion and Emergence of the Geographical Forms

Abstract

Geography studies the organisation of territories in their physical dimensions as well as in their social dimensions. This is thus a knowledge about emergence of forms such as the scattering of fallows and then forests over abandoned agricultural soils, the growth of a city or of a transport network, or the spreading of a pioneer front in Brazil or Siberia. In order to account for the emergence of spreading or stationary forms, a lot of scientists from other disciplines often refer to a theory simultaneously suggested by Fisher, Kolmogorov, Petrovskii and Piskunov, and usually designated by the acronym FKPP. Numerous papers and books dedicated to this theory and to the models derived from, such as Turing activator-inhibitor model or their generalisation by Meinhardt. As the creation of a chemical, its production and growth in time, is usually obtained by reaction, this theory is generally called ``theory of reaction-diffusion{''}. We have highlighted the interest of this theory since 1985, at the European Colloquium on Theoretical and Quantitative Geography. But it was not a source of inspiration for the geographers. We suggest then to insist on the components that should be added to make this theory effective in geography. Beyond the long distance interactions designated as convection, advection, turbulence in nature sciences or transport in the societal sphere, it is advisable to think about the initial conditions that strongly influence the emergence of the geographical forms and more about the introduction of human actors adaptability