Urban scaling, the observation that certain urban metrics exhibit power-law scaling relationships with city size, has been widely studied for various geographical regions and city types. Europe, with its rich history and many long-standing cities, offers an interesting opportunity to explore whether urban scaling applies to its oldest cities, which face unique challenges due to historic preservation concerns and the impacts of time and adaptation. Several studies have investigated this question with diverse findings. Some key factors to consider include:

City Characteristics: Europe's oldest cities are often characterized by dense and compact urban cores, narrow streets, and buildings designed in older architectural styles. These architectural characteristics might influence the nature of urban scaling relationships.

Urban Metrics: Studies on European cities commonly examine diverse urban metrics, such as population, urban GDP, nighttime light intensity, building height, or street length. The selection of metrics, along with the methods used for measurement and data analysis, can affect the outcomes.

Geographical Scope: Different studies focus on different geographical regions, varying in size and urban dynamics. The inclusion or exclusion of certain cities with contrasting characteristics can impact results.

Scale Range: The range of city sizes considered in an analysis can influence the observed scaling relationships. Some studies analyze a broad range of cities, while others focus on a subset.

For instance, a study by Bettencourt et al. (2007), focusing on a large city sample across countries (including European cities), observed power-law scaling relationships for some urban metrics such as urban GDP and infrastructure length.

Another study by Louf and Barthelemy (2014), analyzed European metropolitan areas and cities. They reported sub-linear and multifractal patterns in indicators like road length and number of intersections instead of simple power-law scaling.

Additionally, Martilli et al. (2009) suggested that the allometric scaling laws characterizing modern urban environments can break down in medieval historical cities when considering energy-related factors like the amount of surface covered by traditional residential buildings.

These studies and others indicate that while evidence supports scaling effects in Europe's oldest cities, there might be deviations from standard power-law behaviors, influenced by city characteristics, specific urban metrics, geographical selection, and other factors. The complexity of interactions between historical features, adaptations over time, and modern dynamics makes the urban scaling analysis of Europe's oldest cities a dynamic and intricate problem.