Laws of population growth

Rozenfeld, Hernán D.; Rybski, Diego; Andrade, José S.; Batty, Michael; Stanley, H. Eugene; Makse, Hernán A.

doi:10.1073/pnas.0807435105

Cited by 344 publications

(326 citation statements)

References 22 publications

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“…Different from observed dynamics of clusters identified with CCA from 1981 to 1991, which exhibit all five types of changes (that is, no change, expansion, reduction, division and merge) in cluster shape (Rozenfeld et al, 2008), our model exhibits only three types (that is, no change, expansion and merge) in computer simulations. Since clusters may collide each other and merge together over time, they are generally not independent.…”

Section: (A)mentioning

confidence: 91%

“…It is a long-standing problem that different definitions of spatial units based on administrative boundaries give rise to inconsistent conclusions at different scales (Rozenfeld et al, 2008). In comparison with our definition of natural cities, administrative boundaries of MSAs provided by the US Census Bureau (available online at http://www.census.gov/ geo/maps-data/data/cbf/cbf_msa.html) are constructed manually based on the subjective judgement.…”

Section: (A)mentioning

confidence: 99%

“…A recently introduced algorithm, the City Clustering Algorithm (CCA) (Rozenfeld et al, 2008), defines cities as maximally connected clusters of populated sites identified from gridded data at high resolution (Rozenfeld et al, 2011). In comparison with data collected from conventional "manual" sources such as the traditional population census and household interview, remote sensing data in the form of nighttime light are a more uniform, consistent and independent record for all world land areas (except for high latitudes) (Zhang and Seto, 2011).…”

Section: Introductionmentioning

confidence: 99%

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Allometric scaling, size distribution and pattern formation of natural cities

Li¹,

Wang²,

Zhang³

et al. 2015

Palgrave Commun

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There has been a strong interest in more cogent definitions on economies of scale to reveal general urban growth laws and to develop urban performance metrics. Unstructured data, including satellite images, will provide us with new sources to do so by defining cities as aggregates of human activities. Such a uniform definition on the basis of nighttime light clusters is more consistent and economically meaningful than administrative or official boundaries. In comparison with patterns of city systems found in traditional census data, we examined the allometric scaling, size distribution and fractal geometry of natural cities. It can be concluded from our empirical analysis on regional, country and continental scales that a super-linear scaling between lightness and area with a stable exponent across different low light threshold levels generally holds for natural cities. But Zipf 's Law does not always apply over the whole range of lightness thresholds. Furthermore, we build a model based on the simple geometric matching mechanism to reproduce the self-organized formation process of nighttime light patterns. The statistical properties including allometries, size distributions and fractal geometries generated by our model are in good agreement with empirical evidence. These findings have profound implications for understanding the effects of simple aggregation behaviour in primitive stages of city formation and the urbanization process.

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Section: (A)mentioning

confidence: 91%

Section: (A)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Allometric scaling, size distribution and pattern formation of natural cities

Li¹,

Wang²,

Zhang³

et al. 2015

Palgrave Commun

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“…We can generate these rank size relations using various models: proportionate effect and preferential attachment of course, but also by subdividing a large hinterland into mutually exclusive subdivisions in a modular and regular manner, making various assumptions about population densities. This ties this kind of scaling back to both central place theory in the interurban context and to urban economics in the intraurban (Simon, 1955;Gabaix, 1999, Rozenfeld, Rybski, Andrade, Batty, Stanley, andMakse, 2008). In fact although rank-size scaling is highly stable through time, changes in the population of cities that make up such scaling can be highly volatile, and this remains a major puzzle in reconciling aggregate with disaggregate space-time correlations (Batty, 2010).…”

Section: Size Shape Scale and Space: Three Laws Of Scalingmentioning

confidence: 99%

Building a science of cities

Batty

2012

Cities

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225

140

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Our understanding of cities is being transformed by new approaches from the complexity sciences (Batty, 2005). Here we review progress, sketching the background beginning with the systems approach which treated systems as being organised from the top down to that which now dominates where systems are treated as evolving from the bottom up. The switch in thinking we describe is best pictured in the transition from thinking of 'cities as machines' to 'cities as organisms'. We first review developments in the dynamics of cities where the notion of equilibrium has been replaced by a veritable potpourri of different types such as chaos, catastrophes, and bifurcations. We then look at patterns and processes that give rise to morphologies that illustrate fractal patterns and self-similarity. We follow this with ideas about networks and interactions that sustain cities through their transport and then we show how such processes of movement and mobility can give rise to the diffusion and segregation of different spatial activities. In all these developments, ideas about scaling that relate size, shape and scale in space and time are evident and we thus sketch three scaling laws based on rank-size, allometry and gravitation that are central to our synthesis of how spatial processes give rise to physical morphologies. We conclude with notions about how these ideas are being embedded into models that have potential applications to inform policy.

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“…Socio-economic data exhibit enough empirical evidences in support of universality, which prompt a community of researchers to propose simple, minimalistic models to understand them, similar to those commonly used in statistical physics. Typical examples are elections [26,27], population growth [28] and economy [29], income and wealth distributions [6], languages [30], etc. (see Refs.…”

Section: Introductionmentioning

confidence: 99%

Invariant features of spatial inequality in consumption: The case of India

Chatterjee

Chakrabarti

Ghosh

et al. 2016

Physica A: Statistical Mechanics and its Applications

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We study the distributional features and inequality of consumption expenditure across India, for different states, castes, religion and urban-rural divide. We find that even though the aggregate measures of inequality are fairly diversified across states, the consumption distributions show near identical statistics, once properly normalized. This feature is seen to be robust with respect to variations in sociological and economic factors. We also show that state-wise inequality seems to be positively correlated with growth which is in accord with the traditional idea of Kuznets' curve. We present a brief model to account for the invariance found empirically and show that better but riskier technology draws can create a positive correlation between inequality and growth.

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Laws of population growth

Cited by 344 publications

References 22 publications

Allometric scaling, size distribution and pattern formation of natural cities

Allometric scaling, size distribution and pattern formation of natural cities

Building a science of cities

Invariant features of spatial inequality in consumption: The case of India

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