Zipf’s law and city size distribution: A survey of the literature and future research agenda

Arshad, Sidra; Hu, Shougeng; Ashraf, Badar Nadeem

doi:10.1016/j.physa.2017.10.005

Cited by 119 publications

(85 citation statements)

References 121 publications

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“…The fractality has also been studied regarding the inner structures of cities [33][34][35] and their growth patterns [36][37][38][39]. On the other hand, the power-law distribution of urban populations was presented in the classic paper by Zipf [9] as well as in a number of recent studies [40][41][42][43][44]. The power-law exponent of the population distribution of cities is found to have the value ranging from 1.7 to 3 [9,40,42,45].…”

Section: Modeling Heterogeneous Population Landscapesmentioning

confidence: 99%

Gravity model explained by the radiation model on a population landscape

Hong

Jung

2019

PLoS ONE

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Understanding the mechanisms behind human mobility patterns is crucial to improve our ability to optimize and predict traffic flows. Two representative mobility models, i.e., radiation and gravity models, have been extensively compared to each other against various empirical data sets, while their fundamental relation is far from being fully understood. In order to study such a relation, we first model the heterogeneous population landscape by generating a fractal geometry of sites and then by assigning to each site a population independently drawn from a power-law distribution. Then the radiation model on this population landscape, which we call the radiation-on-landscape (RoL) model, is compared to the gravity model to derive the distance exponent in the gravity model in terms of the properties of the population landscape, which is confirmed by the numerical simulations. Consequently, we provide a possible explanation for the origin of the distance exponent in terms of the properties of the heterogeneous population landscape, enabling us to better understand mobility patterns constrained by the travel distance.

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Section: Modeling Heterogeneous Population Landscapesmentioning

confidence: 99%

Gravity model explained by the radiation model on a population landscape

Hong

Jung

2019

PLoS ONE

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“…This is not unexpected. Numerous studies have shown divergences from Zipf's Law for city rank size distributions [30,32,63]. While other rank size power law estimators have been proposed, the use of Lorenz Curves and urban settlement Gini coefficients provides a clear method to compare inequality within and between urban hierarchies.…”

Section: Discussionmentioning

confidence: 99%

“…Nonetheless, substantial variation exists across countries ( (table 3). Additionally, the noticeable deviations in rank-size α values from 1 suggest that the rank-size distribution of African urban settlements does not follow Zipf's law (table 3), though this is not unexpected [30,32,55]. Visually this is quite apparent for countries like Nigeria and Ethiopia, where the log ranked size plotted against the log population is nonlinear (see supplement, available online at stacks.iop.org/ERL/ 14/085009/mmedia).…”

Section: Change In Urban Population Distribution 2000-2015 By Countrymentioning

confidence: 99%

“…Countries with Gini coefficients closer to zero have a larger share of the total urban population distributed among smaller and medium-sized cities. Third, we assess the rank size distribution across all African countries following Zipf's Law for city size distribution [30]. For urban hierarchies in agreement with Zipf's Law, the second largest city has half the population of the largest, and the third largest city has a third of the population of the largest and so forth.…”

Section: Estimating Change In the Distribution Of Urban Population 20mentioning

confidence: 99%

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Variability in urban population distributions across Africa

Tuholske

Caylor

Avery

2019

Environ. Res. Lett.

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Africa is projected to add one billion urban residents by 2050. Yet developing sustainable solutions to tackle the host of challenges posed by rapid urban population growth is stymied by a lack municipality-level population data across the continent. To fill this gap, we intersect volunteered urban settlement data from OpenStreetMap with five synthetic gridded population datasets to estimate the how Africa's urban population is distributed among over 4750 individual urban settlements across Africa. We assess how urban settlement distributions changed from 2000 to 2015 within and between countries and across moisture zones. To this end, we construct urban settlement Lorenz curves to calculate change in Gini coefficients and test the degree to which Africa's urban settlements distributions fit power law distributions exhibited by Zipf's law. Our results reveal that 77%-85% of urban settlements in Africa have fewer than 100 000 people and that at least 50% of Africa's urban population live in urban settlements with fewer than 1 million residents. Across almost all African countries, the distribution of urban population shifted towards larger cities between 2000 and 2015. However, in arid regions, our results indicate that small-and medium-sized urban settlements are absorbing a greater share of urban population growth compared to large urban settlements. While our urban population estimates vary across gridded population datasets and differ from United Nations estimates, this is the first paper to measure urban population across Africa using a consistent methodology to identify urban settlement populations. Unlike UN urban population data for Africa, our results can readily be incorporated with geolocated environmental, public health, and economic data to support efforts to monitor United Nations Sustainable Development Goals related to urban sustainability, poverty reduction, and food security across Africa's ever-growing urban settlements.

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“…An urban agglomeration is a typical multi-level urban system composed of large, medium, and small cities. Consequently, in this study, the Lotka rank-size model was introduced into revealing the hierarchical distribution and the scale structure of urban factors aggregating ability [28][29][30], written by:…”

Section: Rank-size Modelmentioning

confidence: 99%

Factors Aggregating Ability and the Regional Differences among China’s Urban Agglomerations

2018

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Continuous aggregation of socioeconomic factors is the key issue of sustainable development in urban agglomerations. To date, more attention has been paid to single urban agglomeration than to multiple agglomerations. In this paper, China's 19 urban agglomerations were selected as the case study and their spatial differences in factors aggregating ability were portrayed comparatively. Firstly, the spatial pattern of urban factors aggregating ability is relatively well distributed in all China's cases, most noticeably in the Yangtze River Delta urban agglomeration, closely followed by the Beijing-Tianjin-Hebei and the Pearl River Delta urban agglomerations. However, more significant differences on factors aggregating ability are noticeably seen between cities than among urban agglomerations. Meanwhile, the rank-size structure distribution of factors aggregating ability in China's 19 cases is in line with the Zipf's law of their urban systems, and divided into three types: Optimized, balanced, and discrete. Furthermore, the urban factors aggregation ability in one urban agglomeration is roughly negatively correlated with its primacy ratio of factors aggregating ability distribution. Lastly, urban agglomerations with higher average values of factors aggregating ability are concentrated on the three major urban agglomerations: The Yangtze River Delta, the Beijing-Tianjin-Hebei and the Pearl River Delta. Otherwise, high-high clusters in the three urban agglomerations are distinctly observed as well.Sustainability 2018, 10, 4179 2 of 20 gradually becoming vital growth poles of new-style urbanization development and the main body of China's participation in global competition, which depends on the support of continuous factor flows. Driven by "rent-seeking behavior" [8], variety of factors such as talents, technology, knowledge, information, and capital obey profit-seeking law, which leads to their continuous concentration on advantageous places [9]. As a result, the more competitive urban agglomerations tend to occupy a higher position in national urban systems and thus gain more developing opportunities. Moreover, their competitiveness and potential are accumulatively enlarged under the cyclical cumulative causal effect or Matthew effect. Therefore, the factors aggregating ability has become a key criterion to measure the sustainable competitiveness of urban agglomerations in national and inter-country competition contexts.Although factors aggregating ability is specially measured and documented by few scholars at present, much more attention is paid to theoretically refer to factors and their aggregation, such as factor endowment theory and factor flow theory. Generally, factors were classified to primary production factors (i.e., general natural resources such as land, water, forests, minerals) and created production factors (including knowledge and technology, innovation, capital and facility, etc.) by Porter [10]. Oskenbayev et al. further pointed out that the role of the first factors such as land, oil and coal i...

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Zipf’s law and city size distribution: A survey of the literature and future research agenda

Cited by 119 publications

References 121 publications

Gravity model explained by the radiation model on a population landscape

Gravity model explained by the radiation model on a population landscape

Variability in urban population distributions across Africa

Factors Aggregating Ability and the Regional Differences among China’s Urban Agglomerations

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