Heterogeneity and scale of sustainable development in cities

Neighborhood Priorities in Developing Cities.

Slums constitute a substantial fraction of all neighborhoods in cities of South and Southeast Asia and in sub-Saharan Africa (9) and illustrate the direst challenges of urban sustainable development. Worldwide one in seven people is presently estimated to live in slums, but this number rises to one in two or more in parts of South Asia and Africa (2, 9). International development agencies have stressed the critical need for better understanding the nature of human and economic development in these poor neighborhoods, and of acquiring detailed empirical information on their primary needs and priorities (2, 9). However, extensive direct information on residents’ priorities is still rare. Recent efforts provide us with some new insights on the most important development needs expressed by slum residents (15, 28). Table 1 and Fig. 1C show residents’ priorities in 677 neighborhoods in 10 nations and 59 cities mostly in low-income nations in sub-Saharan Africa (Materials and Methods and SI Appendix, Fig. S12). Most of these data pertain to large and fast-growing urban areas, such as Lagos, Nairobi, Dar-es-Salam, Kampala, Blantyre, Freetown, Johannesburg, Cape Town, or Windhoek.

Although there is broad agreement on the most important priorities, there are also a number of differences across nations (and cities). Overall, water and drainage is the most frequent problem, mentioned 36.9% of the time, followed by issues of housing (21.3%), sanitation and sewage (13.9%), land tenure (13.7%), and electricity (6.2%). These priorities emphasize the dual role of basic services and improved housing in promoting the resilience of communities against both chronic stresses and extreme events, such as flooding and diseases associated with local environmental degradation (15, 29). Other issues, related to health access, transportation, waste collection, jobs, and education, also come up frequently but are stated as less critical. Apart from land tenure, all other issues deal with daily living challenges and are intimately connected to access to improved basic services and local environmental conditions. These findings resonate with recent definitions of sustainable development (9, 29) to which we now turn using extensive neighborhood data from two large middle-income nations: Brazil and South Africa.

City Size and Agglomeration Effects.

Agglomeration effects are at the root of the advantages of larger cities at creating greater resources per capita, which historically have led to innovation and development along a broad range of human and environmental issues (2, 30, 31). Cities are characterized by two general phenomena: agglomeration effects and high socioeconomic and spatial heterogeneity (32⇓⇓–35). Both have long been understood as having a strong scale (population size) dependence (36). The strength of these scaling effects and the nature of urban heterogeneity have, however, remained poorly studied in rapidly developing cities, in large part due to the absence of systematic data for appropriate units of analysis.

Scaling effects are expressed in terms of the mean expected values for urban quantities, such as the size of the overall economy (gross domestic product, GDP), personal income, amounts of infrastructure, rates of innovation, and so on, as functions of city population size (31, 34, 35). Nonlinear scaling of all these quantities is predicted for functional cities, defined as spatially embedded networks of socioeconomic interaction (35, 37), known as MAs. MAs are integrated labor markets circumscribing areas of work and residence for most of their inhabitants. For other definitions of cities, whether political or resulting from density thresholds, agglomeration effects may vanish or seem inconsistent, possibly because not all heterogeneity is included (38, 39).

To illustrate these effects, Fig. 2A shows total income for MAs in South Africa and Brazil, versus their population size (see also Table 2). In Brazil, MAs typically include many (political) municipalities, whereas in South Africa they are made up of a single large municipality, with the exception of Greater Johannesburg (SI Appendix, Figs. S1–S5 and Table 2).

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Fig. 2.

Agglomeration effects and heterogeneity of sustainable development in cities of Brazil and South Africa. (A) Scaling of personal income with population for Brazil (squares) and South Africa's MAs (triangles). The yellow line shows the theoretical slope of 1 + 1/6 (35), the red shows the best fit, and the gray line shows the 1:1 line for reference. The best fit demonstrates that larger cities have on average higher resources per capita, at least in nominal terms, which can be invested in sustainable development. (B) The relationship between the SD, σi, and mean, X¯i, of the Sustainable Development Index, X_i, for Brazil's 38 MAs (purple) and 207 South African municipal regions (orange), where the size of the circle is proportional to population. The two black lines bind the area in which (X¯i,σi) pairs can exist, with the upper curved line showing maximal inequality (Kuznets curve, b = 1) and the horizontal line corresponding to total equality (b = 0). The dashed line shows the estimated best fit for the mean heterogeneity index b. (C) The decomposition of X_i into subcomponents: X_i^electricity (orange), X_i^water (blue), X_i^sanitation (green), and X_i^homes (purple) for Brazil's metropolitan regions, which allows us to see the role of larger cities at providing improved services. (D) The positive association between Moran’s I (distance threshold = 5km) and σi for South African municipalities, showing that higher spatial clustering is associated with higher inequality of access to services. (Inset) The variation of Moran’s I with the distance threshold s for South Africa’s major metropolitan regions.

As in many other urban systems, total personal income, Y_j, for each urban area, j, is well described statistically by a scale-free function of the formYj=Y0Njβeξj,[1]where the prefactor, Y₀, is independent of city population size, N_j, and where β is a scaling exponent (or elasticity: β = dlnY/dlnN). The quantities ξ_j are (scale-independent) deviations from the mean (scaling) expectation and are characterized by a zero mean and a small variance. Fig. 2A and Table 2 show the scaling results for the two nations as well as their combined behavior (after centering the regression and pooling the data; see ref. 37). The scaling exponent β = 1.11 estimated for Brazil is very similar to that of the United States and to the GDP of Brazilian MAs (35). The relatively large number of MAs in Brazil and their size range allows us to establish with high confidence that this result is broadly consistent with theory (35), which derives quantitative expectations for scaling exponents from calculating rates of socioeconomic interactions for a population in a spatial steady state, determined by the balance of benefits and transportation costs in the tradition of urban economic geography (37). The smaller number of South African MAs show stronger scaling effects with a larger β = 1.35 but also with a wider confidence interval. The combined dataset, Fig. 2A, shows scaling that is statistically indistinguishable from the simplest prediction of urban scaling theory, β = 7/6 (35), shown as a yellow line in Fig. 2A.

A consequence of this scaling behavior is that larger cities have greater average incomes per capita and thus may exhibit greater capacity to dedicate more resources to services and infrastructure (34⇓–36, 40). Such allocations may happen directly via local taxes or indirectly via higher receipts and reinvestments managed at the national level (30). To investigate this issue empirically, we define a sustainable development index, X_i, characterizing a population in a given spatial unit of analysis i, asXi=∏j=1nXijn.[2]This index spans a number of dimensions n of sustainable development. Because much of the underlying data for assessing sustainable development goals (SDGs) remain to be collected, we illustrate here its properties in terms of access to basic services and housing (SDG goals 6, 7, 11; or 4 of the STI’s components):Xi=[XiwaterXielectricityXisanitationXihomes]1/4,[3]where Xiwater is the fraction of the population in unit i with access to an improved water source. Similarly the superscripts electricity, sanitation, and homes refer to access to electrical power, improved sanitation, and permanent housing. Descriptions and emerging international standards for their use as indicators are given in Materials and Methods and SI Appendix.

This index is bounded between X_i = 0, when one or more services are totally absent, and X_i = 1, when there is universal access within area i. The multiplicative character of the index follows the construction of the HDI and emphasizes that all components are essential for achieving a set level of development (41) and are not substitutable. This form is also consistent with the HDI (20, 21) and UN-Habitat's definition of a “slum household” as a household that lacks access to any one of these services in the composite STI (9). For purposes of illustration, we show in SI Appendix, Figs. S13–S16 and section 1.5 the comparison between the multiplicative and additive forms of X and refer the reader to the relevant discussions leading to changes in the definition of the HDI to a multiplicative form, which motivate Eq. 2 (20, 21).

Fig. 2B shows the average value of X_i for urban areas of different population sizes in Brazil and South Africa. In general, the level of services increases with city size (SI Appendix, Figs. S17 and S18), a trend that is especially clear in South Africa. In some parts of Brazil, service provision has expanded more systematically to smaller cities and rural areas (SI Appendix, Fig. S8). These results answer our first question: The relative performance of larger cities in terms of access to services and thus some of the dimensions of sustainable development is consistent with advantages derived from urban agglomeration effects and points to a wide range of reasons why urbanization continues to grow in low- and middle-income nations beyond strictly economic motives. As SI Appendix, Figs. S17 and S18 show, living in larger cities means that, on average, residents obtain access to many dimensions of sustainable development sooner. However, these averages hide large heterogeneities, to which we now turn.

Heterogeneity of Development Across Scales.

Measures of heterogeneity within MAs are especially important because at this scale residents share the same labor and real-estate markets and thus face many of the same opportunities and costs (35, 42).

Measures of heterogeneity may be spatially explicit or they may consider only variation within a population. The Gini coefficient (Fig. 1B and SI Appendix, Figs. S9–S11) is a well-known nonspatial measure of heterogeneity. A simpler measure of variation is the SD, σ, and its relation to the mean of any socioeconomic variable. Moran’s I, by contrast, is the most widely used measure of spatial heterogeneity (43): It accounts for the level of correlation between characteristics at two spatial locations separated by a distance. The Gini coefficient (or the SD) and Moran’s I are not necessarily correlated because this depends on the spatial structure of mixing between different people. Any resource within a population may be spatially distributed in a manner that is maximally clustered, meaning that Moran’s I approaches I = 1, or perfectly anticorrelated (like a checkerboard), so that Moran’s I approaches I = −1, or a random (well-mixed) pattern, when Moran’s I approaches I = 0 (see SI Appendix, Figs. S19 and S20 for illustrations).

These quantities, taken together, characterize the heterogeneity of sustainable development indices in cities. From its definition, we see that the variance of X must be a function of the mean, and vanish when everyone in unit i has services, X = 1, or when they are nonexistent, X = 0. It typically is maximal when the mean X¯= 1/2, because then there are more configurations possible, for example by having households with different levels of access within and across neighborhoods i. Thus, we can parameterize the SD of X_i, σ_i, asσi=biX¯i(1−X¯i),[4]where the square root corresponds to the SD of a random Bernoulli process. This relation means that b = 1 gives the maximal variance at each value of the average X¯(Fig. 2 B and C). Note also that it follows from the properties of the SD that b ≥ 0. Thus, we can characterize two-dimensional trajectories in the space of (X¯i,σi) as levels of development change in each unit, i, and the values of (X¯i,σi) → (1,0). Given X¯i, these trajectories are characterized by a single number: the value of b_i as a function of place and time. There are two special trajectories—of maximal and minimal heterogeneity—characterized by b_i = 1 and b_i = 0, respectively, indicated in Fig. 2 B and C by solid black lines. Because of these properties we refer to b_i as a (normalized) heterogeneity index.

Although our present data are cross-sectional, we can compare different urban areas by estimating levels of heterogeneity in terms of b. Fig. 2B shows the plot of X¯ versus σ for Brazilian MAs and South African municipalities (see also SI Appendix, Figs. S21 and S22). Across different urban areas, we observe a Kusnetz-curve type behavior (24), where intermediate levels of access are associated with the greatest variance. We estimated the values of b (SI Appendix, Figs. S21–S23) to determine the expected value of b = 0.58 for Brazil and b = 0.57 for South Africa, which are statistically indistinguishable from each other (Table 2). The frequency of residuals (SI Appendix, Figs. S24 and S25) shows that the variation of b across different cities is small and slightly left-skewed so that trajectories with considerably lower inequality are possible. It is also important to realize that levels of heterogeneity are scale-dependent, as shown in Fig. 1B. Adopting smaller units of analysis, such as neighborhoods, obtains lower values of b. These results answer our second question: They suggest that there are generic trajectories of local development (Fig. 2 B and C). Empirically, the variation between neighborhoods is closer to the case where access is distributed in an all-or-nothing manner (b→1) rather than when access, though limited, is provided equally to everyone (b→0). These results provide a set of specific expectations for local urban development as longitudinal data become available.

To explicitly take into account the effects of space, we now use Moran’s I to measure the similarity of conditions between nearby neighborhoods (SI Appendix, Figs. S19 and S20 and Materials and Methods). We varied the distance between neighborhoods to measure the corresponding strength of spatial correlation for various quantities (Fig. 2D, Inset, SI Appendix, Fig. S26, and Table 2). In all cases, we find clear evidence of strong spatial clustering in access to services with a magnitude that is strongest at a “walkable” distance below a few kilometers (Fig. 2D, Inset). This spatial correlation is even higher for socioeconomic quantities, such as income and racial composition (SI Appendix, Fig. S26). These results suggest that assortative dynamics, which generate strong spatial economic and racial inequalities in US cities (25, 33), are likely also at play in urban areas of Brazil and South Africa. Higher levels of spatial clustering, measured by the magnitude of I, are also statistically associated with higher levels of heterogeneity in access to services, measured via the magnitude of b (Fig. 2D). These findings answer our final question: Heterogeneity between people is expressed spatially as differences between places within a city defined at about a kilometer scale, rather than differences within spatially well-mixed populations. In other words, heterogeneity is expressed in these cities systematically as spatially concentrated (dis)advantage (14, 25, 33).