Scale-Free Relationships between Social and Landscape Factors in Urban Systems

Urban planners and ecologists have long debated the relationship between the structure of urban landscapes and social activities. There have, however, been very few discussions as to whether any such relationships might depend on the scales of observation. This work applies a hierarchical zoning technique to data from the city of Quito, Ecuador, to examine how relationships between typical spatial landscape metrics and social indicators depend on zoning scales. Our results showed that the estimates of both landscape heterogeneity features and social indicators significantly depend on the zoning scale. The mean values of the typical landscape metrics and the social indicators all exhibited predictable responses to a changing zoning scale, suggesting a consistent and significant scaling relationship within the multiple zoning scales. Yet relationships between these pairs of variables remain notably invariant to scale. This quantitative demonstration of the scale-free nature of the relationship between landscape characteristics and social indicators furthers our understanding of the relationships between landscape structures and social aspects of urban spaces, including deprivation and public service accessibility. The relationships between social indicators and one typical landscape aggregation metric (represented as the percentage of like adjacencies) were nevertheless significantly dependent on scale, suggesting the importance of zoning scale decisions for analyzing the relationships between the social indicators and the landscape characteristics related with landscape adjacency. Aside from this typical landscape aggregation metric, the general invariance to the zoning scale of relationships between landscape structures and socioeconomic indicators in Quito suggests the importance of applying these scale-free relationships in understanding complex socio-ecological systems in other cities, which are shaped by the conflated influences of both anthropogenic and natural factors. Moreover, this scale-free behavior of landscape-social relationships challenges the traditional modifiable area unit problem, and provides mechanistic insight into the conflicts and compatibilities between human activities and human-induced land use change.