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A scale invariant model for the expansion of agricultural land and government spending on the agricultural sector
Institution:1. Centro de Investigación y Docencia Económicas, A.C. Carretera México-Toluca Núm 3655 col. Lomas de Santa Fe, Ciudad de Mexico, CP 01210, Mexico;2. Centro Transdisciplinario Universitario para la Sustentabilidad (CENTRUS)-Universidad Iberoamericana, Mexico;3. The Food and Agriculture Organization of the United Nations, Proyecto de Evaluación y Análisis de Políticas, Insurgentes Sur 813, piso 12. col. Nápoles, Ciudad deMexico, CP 03810, Mexico;1. Formulas: Mathematics Laboratory, Department of Architecture, University of Roma3, Italy;2. Department of Architecture, University of Roma3, Italy;1. Department of Social Services, The Ministry of Social Welfare, Dhaka, 1207, Bangladesh;2. Environmental Science Discipline, Khulna University, Khulna, 9208, Bangladesh;3. Environmental Policy and Planning (EPP) Group, Department of Urban Studies and Planning (DUSP) Massachusetts Institute of Technology (MIT), 77 Massachusetts Ave, Cambridge, MA, 02139, USA;1. College of Public Administration, Nanjing Agricultural University, Nanjing 210095, PR China;2. Department of Social Sciences, Wageningen University, 6700EW, Wageningen, The Netherlands;1. Institute of Ecological Civilization, Jiangxi University of Finance and Economics, Nanchang, 330013, China;2. School of Economics, Beijing Technology and Business University, Beijing, 100048, China;3. Institute of Agricultural Economics and Development, Jiangsu Academy of Agricultural Science, Nanjing, 210014, China;4. Institute of Agricultural Economics and Information, Anhui Academy of Agricultural Science, Hefei, 230001, China;5. Institute of Food Economics, Nanjing University of Finance and Economics, Nanjing, 210023, China
Abstract:The expansion dynamics of the agricultural surface is a complex process, since it requires decisions among different actors under a multitude of socioeconomic and natural conditions, expectations, and risks. This paper shows that despite this complexity, and at odds with the intuition, the density of agricultural lands and the government spending to foster agriculture around a human settlement displays a simple power-law relationship regarding the distance to such a settlement. The theoretical proof of this relationship is based on theoretical and empirical findings made by several authors on the expansion of population centers, river networks, species and ecosystem’s distribution. The empirical proof is made by fitting a simple power-law model having as response variables: density of agricultural land; government spending coverage, and government spending per unit of agricultural surface, while the distance to the centroid settlement is used as independent variable. Results show that the scaling exponents of the power-law relationship estimated from those models, with data from rural settlements in Mexico, are similar statistically to the expected values from theoretical models for the three expansion processes tested. Three applications of the scale-invariant attribute characterizing the expansion process of agricultural lands are presented:
  • i)monitoring agricultural activities at the territories;
  • ii)a proxy to estimate the expected growth of the agricultural surface; and
  • iii)a typology to characterize government assistance at local level.
Keywords:Agricultural land expansion  Power-law models  Self-organized critically  Fractal dimension
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