Power-law city-size distributions are a statistical regularity researched in many countries and urban systems. In this history of science treatise we reconsider Felix Auerbach’s paper published in 1913. We reviewed his analysis and found (i) that a constant absolute concentration, as introduced by him, is equivalent to a power-law distribution with exponent ≈1, (ii) that Auerbach describes this equivalence, and (iii) that Auerbach also pioneered the empirical analysis of city-size distributions across countries, regions, and time periods. We further investigate his legacy as reflected in citations and find that important follow-up work, e.g. by Lotka (Elements of physical biology. Williams & Wilkins Company, Baltimore, 1925) and Zipf (Human behavior and the principle of least effort: an introduction to human ecology, Martino Publishing, Manfield Centre, CT (2012), 1949), does give proper reference to his discovery - but others do not. For example, only approximately 20% of city-related works citing Zipf (1949) also cite Auerbach (Petermanns Geogr Mitteilungen 59(74):74–76, 1913). To our best knowledge, Lotka (1925) was the first to describe the power-law rank-size rule as it is analyzed today. Saibante (Metron Rivista Internazionale di Statistica 7(2):53–99, 1928), building on Auerbach and Lotka, investigated the power-law rank-size rule across countries, regions, and time periods. Zipf's achievement was to embed these findings in his monumental 1949 book. We suggest that the use of “Auerbach–Lotka–Zipf law” (or "ALZ-law") is more appropriate than "Zipf's law for cities", which also avoids confusion with Zipf’s law for word frequency. We end the treatise with biographical notes on Auerbach.
Agriculture is a major sector responsible for greenhouse gas emissions. Local food production can contribute to reducing transport-related emissions. Since most of the worldwide population lives in cities, locally producing food implies practicing agriculture in urban and peri-urban areas. Exemplary, we analyze the potential to produce fresh vegetables within Berlin, Germany. We investigate the spatial extent of five different urban spaces for soil-based agriculture or gardening, i.e., non-built residential areas, allotment gardens, rooftops, supermarket parking lots, and cemeteries. We also quantify inputs required for such food production in terms of water, human resources, and investment. Our findings highlight that up to 82% of Berlin’s vegetable demand could be produced within the city, based on a reasonable validation of existing areas. Meeting this potential requires 42 km2 of urban spaces for cultivation, a considerable amount of irrigation water, around 17 thousand gardeners, and over 750 million EUR of initial investments. The final vegetable cost would be around 2 EUR to 10 EUR per kg without any profit margin. We conclude that it is realistic to produce a significant amount of Berlin's vegetable demand within the city, even if it comes with great challenges.
City systems are characterized by the functional organization of cities on a regional or country scale. While there is a relatively good empirical and theoretical understanding of city size distributions, insights about their spatial organization remain on a conceptual level. Here, we analyze empirically the correlations between the sizes of cities (in terms of area) across long distances. Therefore, we (i) define city clusters, (ii) obtain the neighborhood network from Voronoi cells, and (iii) apply a fluctuation analysis along all shortest paths. We find that most European countries exhibit long-range correlations but in several cases these are anti-correlations. In an analogous way, we study a model inspired by Central Places Theory and find that it leads to positive long-range correlations, unless there is strong additional spatial disorder - contrary to intuition. We conclude that the interactions between cities extend over large distances reaching the country scale. Our findings have policy relevance as urban development or decline can affect cities at a considerable distance.
