The diffusion model of T. H.gestrand. An application to livestock farming in the Catalan Pyrenees

Abstract

Modern agriculture should be analyzed according to the degree of acceptance of the technical innovations that allow it to increase its efficiency. The process of change in agrarian activities is the most frequently encountered element in economic specialization in rural areas. Innovation almost inevitably involves considerable capital investment, the acceptance of new crops or varieties, and the learning of new methods and techniques. In summary, increased efficiency results from the enhanced productivity of both production factors—capital and labor—and this principle is equally valid for both intensive and extensive agricultural practices. This article offers a mathematical viewpoint of the evolutionary process in livestock farming in a mountainous area, already outlined in a "Classification of Agrarian Change in Mountainous Areas" published in the previous issue of this publication. That article focused on the local typologies of such evolution, whereas the present article analyzes the spatial evolution process of the commercial agricultural enterprises that can be considered innovators. To do so, T. Hagerstrand's diffusion model was applied, making it possible to predict the spatial distribution and varying importance of commercial agricultural enterprises up until the year 2015. For the purpose of this study, traditional administrative boundaries were replaced by a Lambert rectilinear 2.5 x 2.5 km grid (625 hectares). Relevant information was noted in each square of the grid (a) for the variable—the volume of milk produced by commercial enterprises in 1980; and (b) for the four most significant explanatory variables—potential for mechanized irrigation in pastures and forage-producing land; relative accessibility to processing plants; an indicator of the suitability of the physical environment; and the residual element of the regression analysis is accounted for by the distance between recently established and long-standing commercial enterprises. This leads to the formulation of the hypothesis that contact with innovators impacts the dependent variable beyond the explanation offered by the significant independent variables. The results obtained for the period 1950-2015 have been tested, with positive results, for the period 1950-1980. The validity of the model used in this research study is therefore established.