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A model of urban scaling laws based on distance dependent interactions

View Article: PubMed Central - PubMed

ABSTRACT

Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log–log plot, the so-called superlinear scaling. Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling on these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences.

No MeSH data available.


Sublinear behaviour between the number of amenities at equilibrium (normalized by the division by P0≡P(N=1000)) and the population size, presented by the simulation of the model. The parameters of simulations are: γ=1.41666…, Df=2 (homogeneous distribution) and Df=1.7 (DLA algorithm). Points (circles and squares) represent averages over 30 independent samples of numerical simulations, where each simulation is performed keeping N fixed. The error bars are smaller than the size of the points. Continuous lines are theoretical predictions (equation (2.16)) where  (blue line) and βinfra=0.708 (red line). Dashed line represents the linear scaling.
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RSOS160926F6: Sublinear behaviour between the number of amenities at equilibrium (normalized by the division by P0≡P(N=1000)) and the population size, presented by the simulation of the model. The parameters of simulations are: γ=1.41666…, Df=2 (homogeneous distribution) and Df=1.7 (DLA algorithm). Points (circles and squares) represent averages over 30 independent samples of numerical simulations, where each simulation is performed keeping N fixed. The error bars are smaller than the size of the points. Continuous lines are theoretical predictions (equation (2.16)) where (blue line) and βinfra=0.708 (red line). Dashed line represents the linear scaling.

Mentions: Figure 6 shows us that the equilibrium quantity of amenities scales sublinearly with the population size (given γ<Df, i.e. long-range interaction regime). That means we have scale economies, and therefore, greater cities need less amenities per capita. These scale economies (sublinear behaviour), according to the model, are a direct consequence of the long-range interaction regime. The opposite situation, that is the short-range interaction regime, must conduct to a linear behaviour, which does not correspond to the empirical evidence.Figure 6.


A model of urban scaling laws based on distance dependent interactions
Sublinear behaviour between the number of amenities at equilibrium (normalized by the division by P0≡P(N=1000)) and the population size, presented by the simulation of the model. The parameters of simulations are: γ=1.41666…, Df=2 (homogeneous distribution) and Df=1.7 (DLA algorithm). Points (circles and squares) represent averages over 30 independent samples of numerical simulations, where each simulation is performed keeping N fixed. The error bars are smaller than the size of the points. Continuous lines are theoretical predictions (equation (2.16)) where  (blue line) and βinfra=0.708 (red line). Dashed line represents the linear scaling.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5383838&req=5

RSOS160926F6: Sublinear behaviour between the number of amenities at equilibrium (normalized by the division by P0≡P(N=1000)) and the population size, presented by the simulation of the model. The parameters of simulations are: γ=1.41666…, Df=2 (homogeneous distribution) and Df=1.7 (DLA algorithm). Points (circles and squares) represent averages over 30 independent samples of numerical simulations, where each simulation is performed keeping N fixed. The error bars are smaller than the size of the points. Continuous lines are theoretical predictions (equation (2.16)) where (blue line) and βinfra=0.708 (red line). Dashed line represents the linear scaling.
Mentions: Figure 6 shows us that the equilibrium quantity of amenities scales sublinearly with the population size (given γ<Df, i.e. long-range interaction regime). That means we have scale economies, and therefore, greater cities need less amenities per capita. These scale economies (sublinear behaviour), according to the model, are a direct consequence of the long-range interaction regime. The opposite situation, that is the short-range interaction regime, must conduct to a linear behaviour, which does not correspond to the empirical evidence.Figure 6.

View Article: PubMed Central - PubMed

ABSTRACT

Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log&ndash;log plot, the so-called superlinear scaling. Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling on these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences.

No MeSH data available.