Multi-scale analysis of rural and urban areas: a case study of Indian districts

It is well known that the urban systems, in particular cities, display scaling behaviour regarding socio-economic, infrastructural and individual basic services indicators. However, understanding urbanisation and the links between rural and urban areas is fundamental to making the most of the global transformations happening around the world. In this context, it is important to study the scaling laws based on both the urban and rural regions, going beyond cities. This paper explores the extension of the idea of allometric urban scaling law to study the scaling behaviour of Indian districts, with both the urban and rural population. To proceed, we have chosen districts (both rural and urban) of India, a relatively larger local administrative units, which are more or less independently functional within a country. This interdisciplinary work focus on the scaling analysis of various socio-economic indicators (SEIs) corresponding to the size (population) of four distinct urbanisation classes, namely rural, semi-rural, semi-urban and urban districts. The scaling exponents ( $$\beta $$ β ) were estimated for each classes for the years 2001 and 2011 along with their goodness-of-fit measured by the $$R^2$$ R 2 values. Our rigorous statistical analysis indicates that the scaling laws indeed exist even at the district level for most of the SEIs considered, related to education, employment, housing, health, etc.; the $$R^2$$ R 2 values obtained for these SEIs are very high (often greater than 0.8 or 0.9) in both the years. Moreover, linearity of the scaling factors have been statistically tested and it has been found, at 95% level of confidence, that not all the SEIs behave linearly ( $$\beta =1$$ β = 1 ); some of them are characterised by super-linear ( $$\beta >1$$ β > 1 ) behaviour and some behave sub-linearly ( $$\beta