Applying Zipf's law to land-use classes in a tourism-specialized metropolitan context

The present study examines metropolitan growth dynamics employing Zipf's law to investigate, likely for the first time in literature, the spatial organization of landscape across the urban-rural hierarchy based on a vast and diversified ensemble of land-use classes. Using high-resolution data from Copernicus Urban Atlas initiative, the approach evaluates the actual rank-size distribution of 20 distinct land-use categories within metropolitan Athens, Greece. As a novel contribution to regional science, three model specifications were tested on the individual land parcel: (i) a baseline model verifying the rank-size relationship for each land-use class, (ii) an extended model incorporating a fractal index to capture landscape complexity, and (iii) a model adding the distance from downtown Athens to verify the mono-centric assumption à la Von Thünen. Empirical findings reveal significant variations in Zipf's applicability across different land-use classes, highlighting the influence of spatial convolution and metropolitan gradient on the rank-size distribution. The spatially explicit Multi-scale Geographically Weighted Regression (MGWR) method outperforms the Ordinary Least Squares (OLS) approach, confirming the appropriateness of accounting for both spatial distribution and local heterogeneity of land parcels when testing the rank-size relationship. Results indicate that, while certain land-use classes exhibit patterns closely aligned with Zipf's law, others demonstrate deviations that reflect varying levels of spatial regularity, underlying economic and/or natural constraints. The study underscores the importance of land-use specificity in spatial planning and suggests policy interventions aimed at sustainable land management when planning the long-term evolution of metropolitan hierarchies. These insights contribute to refining regional development strategies, promoting balanced growth, and preserving land resources in metropolitan areas.