Socio-economic urban scaling properties: Influence of regional geographic heterogeneities in Brazil.

The recent efforts dedicated to understanding important features and consequences of city growth have profited from the scaling approach to urban indicators. This kind of analysis can be conveniently used to investigate the impact of geo-economic transformations, like fast urbanization and industrial development, which occurred in continental size countries (e.g., India, China, and Brazil) during the past half-century. Profiting from high quality data, this work explores how scaling relationships among urban indicators are influenced by strong regional heterogeneities in Brazil. It is based on economic, infrastructure and violence related data sets for the time interval 2002-2016. Results indicate that regional specificities related to infrastructure, economic development, and geography have a larger influence on the absolute value of the urban indexes. Regional scaling similarities and differences among Brazilian regions were also uncovered. Interesting enough, the results indicate that the richest and poorest Brazilian regions share similar scaling behavior, despite all huge different local influences. By contrast, the results for the two richest regions, with similar average values of urban indexes and the same kind of local influences have rather different scaling properties. Thus, scaling analysis suggests that distinct political solutions might be necessary to improve life's quality, even for two regions with similar average values of urban indicators.

Introduction

Most of the world population already lives in urban areas, and proportion will most probably increase in the next decades (https://data.worldbank.org/indicator/sp.urb.totl.in.zs). Cities scale over a huge range of population size, from just a few thousand to tens of millions of inhabitants, creating many facets as infrastructural, economic, social and spatial complex systems. Living in cities has proportioned great advantages for economy, creativity and, because of the given facilities to access assistance services and programs, also improve population health. On the other hand, urbanization also brings potential risk to health with problems associated with high population density, such as criminality, landscape changes and complex social interactions of many individuals.

In the last decade, seminal works by West, Bettencourt and other authors have presented and motivated several empirical and theoretical description of urban scaling [1-9]. This perspective does not immediately provide a causal explanation among urban indicators and population size, but rather identifies general and systematic relationship properties among them. Causality assessments require the understanding of how individuals interact with each other, which is still unclear and object of investigation. The scaling approach, which applies to broad range of urban indicators [1-19], has suggested that the population size of the cities is a main determinant of the intensity of socio-economic activity in urban areas.

The allometric scaling relations indicate that rates of human social behavior, urban infrastructure properties, patterns of consumption, diseases, innovation, have worldwide prevalence [1-20]. Thus, regardless their specific historical and cultural backgrounds, on the average, the cities are non-linear scaled versions of each other. In fact, such non-linearities are reality in many agglomeration phenomena, once they are results of the complex interactions in social dynamics and cities organization [3, 4, 19, 21–25].

Despite the recent advances in urban scaling analyzes of socioeconomic activities and health conditions, additional efforts are still necessary to include other social dimensions, like the effects of evident regional disparities in the country. Such regionalities are mainly present in continental size countries as China, India, USA, Russia and Brazil [26, 27]. However, conclusive studies uncovering regional dependence of scaling analyzes for most of these countries are still missing. Based on these considerations, this paper discusses scaling analyzes carried out for different socioeconomic and health dimensions of the Brazilian geographical regions, a country internationally known by its huge inequality levels of income, social and health conditions, as well as regional disparities.

The geography of inequality of regional income and population for the five macro regions of Brazil is illustrated in the Fig 1. As can be seen in the Fig 1(a), the Southeast region historically concentrates more than 50% of the national Gross Domestic Product (GDP). A very slow declining behavior of this share has been observed in the last decades, when Midwest and North regions consistently captured parcels of the GDP. In the same way, Fig 1(b) shows the time evolution of population distribution. The poorest Northwest region concentrates almost 1/3 of population. The long time persistence of such regional inequality pattern actually brings serious socioeconomic consequences for the country’s development, as it affects income, health, violence, innovation, productivity and other key performance indicators. The evolution of the regional urbanization process in Brazil is shown in Fig 2. As can be verified in the Fig 2(a), the process is convergent among the regions. In the highest and lowest urbanized regions, respectively the Southeast and Northeast, more than 90% and 70% of population already lived in the urban areas in 2010. The same process of convergence is verified in the concentration of population in cities with more than 100M inhabitants. The convergence of urbanization process and population living in large cities rise important questions regarding scaling behavior in different Brazilian regions. Nevertheless, it is important to note that the Midwest and North regions have the widest territorial parcels of the country (see Fig 3) and, at the same time, the lowest populational densities. The work addresses a further important aspect, namely the meaningful comparison of the actual values of a given urban index among the ensemble of analyzed cities. Ranks that consider the simple per capita rates can be significantly distorted when the considered index shows nonlinear dependence with respect to the population size. Therefore, in such cases it may be more convenient to use ranks based on the normalized residuals with respect to the expected results.

Fig 1

Share of (a) GDP and (b) population of the Brazilian macro regions, 1939-2010.

Source: Brazilian Institute of Geography and Statistics and Brazilian Institute of Applied Economic Research.

Fig 2

(a) Urbanization and (b) urban population in large cities in the Brazilian macro regions, 1939-2010.

Source: Brazilian Institute of Geography and Statistics and Brazilian Institute of Applied Economic Research.

Fig 3

Here we show how the Brazilian cities are spatially distributed over the country.

The capital of each federal state are written and the Brazilian regions are also characterized by different colors. Map generated with the free and open source geographic information system (QGIS) version 3.4 LTR.

In the following sections we present the scaling analysis of an economic, violence and health, infrastructure and education urban variables, considering the five Brazilian political regions: South, North, Southeast, Northeast and Midwest. We have verified that regions with similar economic development, infrastructure, and level of industrialization, such as South and Southeast do not, necessarily, share analogous scaling features. On the other hand, we have identified similar scaling dependence between one of the poorest and richest regions, suggesting that despite difference of the absolute value between the urban indicator of these regions, the biggest cities are equally different of the smallest cities of their respective regions. Such findings are important once it may indicate that general political interventions in continental countries may not be adequate. Finally, we emphasize the importance of comparing cities using scaling analysis in completeness with per capita indexes, once that most of the urban indicators have presented a non-linear dependence with population size. As we show, ranking cities by per capita indexes may not be similar to scaling indexes leading to either sub or over estimation of the urban variable effect.

Methods

The usual per capita indicators assume that a given urban indicator, Y, depends linearly with population size, N, as Y ∝ N, masking the non-linear interactions in the social dynamics of the cities. However, several relationships between system size and pertinent indicators in urban systems, both related to social [28] and infrastructure [29] aspects, have shown a non-linear behavior described, on average, by a power-law relation, where Y0 is a normalization constant and β is the scaling exponent, which reflects intrinsic properties of Y. Similar results have been obtained in the realm of complex adaptive biological systems [30]. Given a per capita variable written by y = Y/N, one may conclude from Eq 1 that the variation of y satisfies, so that the fraction variation of the population size reads Consequently, β = 1 leads to Δy = 0, which means that Y is linearly dependent on N. In this case, comparing cities by their per capita rates constitutes an adequate approach. On the other hand, assuming β > 1 leads to Δy > 0, indicating that the variable Y increases faster than the population size. Finally, for β < 1, one has Δy < 0, which means that the variable Y increases slower than the population size, corresponding to an economy of scale. Thus, the allometric analysis hints that superlinear and sublinear beahavior are not random events, but suffer the influence of other features related to agglomeration size. Curiously, many such indexes have been classified similarly for different sets of studied cities worldwide [9, 13].

A qualitative assessment of the β values for urban indicators depends on their intrinsic nature. This means that, both β > 1 and β < 1 may indicate either a positive or negative (desired or undesired) aspect, depending on which urban indicator is being analyzed. For example, while a good scenario is indicated by superlinear behavior of urban indicators like wages, income, gross domestic product, we can not say the same for pollution rates, crimes and disease incidence. On the other hand, cases of sublinear behavior of urban indicators related to infrastructure and material (length of electrical cables, gas station) represent an optimized scenario. In general, Eq 1 is transformed logarithmically as Working with the logarithm (on base 10) of the original data, we have used the Ordinary Least Squares regression (OLS) to estimate the log-linear relation (Eq 4), where the slope provides an estimation for β.

The average behavior of the urban factors is expressed by Eq 1. However, to measure the statistical fluctuation over such average behavior and, consequently, to access the local characteristic of every individual city (index i), we have estimated the urban indicator residuals (UIR) ζ [31], where Y is the value of the urban factor for a specific city. Then, cities will be compared by their ζ values, which provide a quantitative estimation of development or under-development with respect to the average behavior.

Discussion and results

The Brazilian data at city level is quite consistent, and most urban indexes cover all Brazilian cities. In order to show how scaling analysis has the potential to uncover regional discrepancies, we have studied 4 socioeconomic variables: the Gross Domestic Product (GDP), the number of homicides, the length (in kilometer) of the water distribution system (WDS), and the number of high knowledge employees in the service sector (SHT). These variables are able to capture essential aspects related to economic, violence, infrastructure and technology standards of the cities. Of course, other choices are also possible. The analyzed data was collected from the department of computing of the Brazilian health care system DATASUS [32] and from the Brazilian Institute of Geography and Statistics (IBGE) [33] from 2002 to 2016 for near 5000 Brazilian cities. From DATASUS, where a set of health information of all Brazilian city is stored, we have extracted the total of homicides of every Brazilian city aggregated by year. The IBGE is a official Brazilian agency responsible for collecting and estimating social-economic information. Based on data from DATASUS and IBGE many public policies are planned at all government levels. We have analized 6 different sets of cities: the first one comprises all Brazilian cities, while the other are subsets of cities in the 5 Brazilian geographical regions (North, Northeast, Midwest, Southeast and South). The distribution of cities among the different regions in Brazil is the following: approximately 32% in the Northeast, 30% in the Southeast, 20% in the South and 8% in the North and Midwest regions. As shown in Fig 3, most of the cities are on the coast and while, as compared with other regions, the Midwest and North have lower city density and concentrate less population. The percentage of population by region is show in Fig 1b. The population in the cities range from ∼103 to 1.2 × 107 (São Paulo). This work is divided into two sequences of investigation: in first place, we evaluated the scaling dependency of the urban indicators with respect to the population size. After that, we proceeded with a local characterization of cities by the relative parameter ζ, which quantifies the deviation of the city indicators from the average scaling expected behavior.

From the Ordinary Least Squares regression regression, we have initially estimated the baseline average behavior of the urban indicators. For the purpose of obtaining more information on the influence of the scatterd data on the linear regression, we also provide results from by Nadaraya-Watson Kernel (NWK) regression. Fig 4 shows the log-log plots of the urban indicators with respect to the population size. The almost general good consonance between NWK regression and the linear regression supports the assumption that the dependency of GDP, homicides, water distribution system and the number of high knowledge employees in the service sector with respect to population size may be expressed by Eq 4, indicating a power-law scaling dependency. The main discrepancy revealed by NWK refers to the large scale regime in the midwest region.

Fig 4

Examples of typical urban indicator × population size plots in double logarithm scale in base 10.

(a) 2010 Brazilian Gross Domestic Product, GDP, of the ensemble Northeast, (b) 2007 homicides of the ensemble Brazil, (c) 2016 water distribution system, in Kilometers, of the ensemble Brazil and (d) 2006 numbers of high knowledge employees of the Southeast ensemble. The red and blue lines correspond to the NWK regression and linear regressions, respectively. The NWK results show that despite the fluctuations the urban indicators may be described by Eq 1. In the red boxes are indicated the values β, corresponding to the slope of the blue line described by Eq 4. For the β values of all ensembles for the whole time range see Fig 5.

Fig 5

Longitudinal evaluation of β for all ensembles from 2002 to 2016: (a) GDP, (b) homicides, (c) water distribution system, and (d) high knowledge employees.

For a better visualization of the plots, we have hidden the error bars which are approximately 0.01 for the βGDP, 0.1 for βHom, [0.07, 0.15] for βWDS, and [0.05, 0.1] for βSHT.

Based on the evidences of the power-law scaling dependency, we have studied the longitudinal behavior of β’s values, related to every Brazilian region and all Brazilian cities (see Fig 5). For a solid interpretation, it is important mentioning the Brazilian economic heterogeneity between and within the Brazilian regions, as we have shown in the supporting information. In addition, we have also calculated the degree of Spatial stratified heterogeneity (SSH) [34] for the four socioeconomic variables, which is expressed by the parameter . Considering Brazil as our sample, L = 5 is the number of strata in correspondence with the number of Brazilian regions. The number of units (cities) is represented by N, and σ2 is the variance of the socioeconomic variable of all Brazilian cities. N and are the number of cities and the variance of the socioeconomic variable of cities for a specific Brazilian region. As the definition of q is based on the ratio between the variance within strata and the variance of the entire study area, the interpretation of the limiting values of q ∈ [0, 1] is the following: (a) as the values of q become closer to 1, the heterogeneities within strata are more similar than those between strata; (b) as the values of q become closer to 0, the heterogeneities between strata are more similar than those within strata. Therefore, the results in Table 1, where q-values are closer to 0 than 1, can be interpreted as heterogeneities within regions are higher than between them. The larger values of q for WDS and SHT can express the fact that discrepancies in education, and infrastructure between the Brazilian regions are relatively larger than those in wealth and violence. It is well known that the South and Southeast regions are the most rich and developed Brazilian regions. Their GDP average value present an immense gap compared with those of other Brazilian regions. Also, the South and Southeast regions present larger consumer market, better connectivity among cities, general infrastructure, population density as well as they have almost 50% of the total number of Brazilian cities.

Table 1

q-values obtained from the 2016 data indicating that all Brazilian regions present high similar heterogeneity within them.

Socioeconomic variable	Geodetector q
GDP	0.00238
Homicide	0.00304
WDS	0.11289
SHT	0.03603

Large concentration of wealth, infrastructure, high level education employees and violence within the regions, which are mainly observed in the metropolitan area of every Brazilian state, are responsible for the values of q close to zero.

A huge difference exists between the Southeast and Northeast regions if they are compared by their absolute GDP values, as they are, respectively, the richest and poorest regions. Despite that, we have found that the GDP of Southeast and Northeast regions share a similar intensity scaling relation, characterized by a strong superlinear dependence. In Table 1, the small values of q for the socioeconomic variables indicates that heterogeneity within the regions are more relevant than those between them. On the other hand, the largest value of q associated with WDS indicates a comparatively smaller infrastructure discrepancy between the richest regions with the poorest ones. This can be explained, among other reasons as political and historical, by the fact that the poorer regions have globally had less investments in infrastructure. In contrast to that, the South and Midwest regions have much weaker superlinear dependency. These results make evident that, despite the fact that small and medium cities of the Southeast are more developed than their counterparts in the Northeast, the comparison of these subsets with those formed by larger cities, in their respective regions, indicates that, on the average, the small cities suffer a similar kind of local inequality with respect to wealth distribution. A comparison among the South, North, and Midwest regions shows a small scaling dependency, irrespective of the global GDP disparity among them.

In an ideal scenario, higher GDP values would indicate how intense the economic activity of a city is, since GDP is an indicator of consumption, a good proxy of welfare. The comparison among small, medium and large cities within either the Midwest or South regions shows that they have quite similar proportional growth of offer of public services. On the other hand, analyzing Southeast or Northeast regions, the difference between small, medium and large cities would be more evident, once the GDP grows much faster than the population sizes. The GDP is just one of several socioeconomic quantities that have shown superlinear behavior. Results for the complete set of Brazilian cities show that the GDP presents a low scaling dependency indicating that, despite disparities in inter-regional wealth distribution and intra-regional scaling properties, small and medium cities have strong contribution to the Brazilian GDP. This is a clear indication that, for large countries with strong regional differences, the scaling analysis based only on national data is not able to reveal huge non linear discrepancies existing at a regional scale. It is also noteworthy that these indicators have been quite stable for the whole period of analysis.

One may also conjecture whether such scenario would be more perceptible in urban indicators of violence, where the individual safety feeling is related not only to the number of cases, but also depends on the population size. Results for β along the considered 15 years indicate that almost all regions present stronger dependency as compared with β, with exception for the South and Southeast regions. The strong scaling dependency expresses the fact that violence in large cities is more noticeable than small cities. The fact that the Southeast region has shown a decreasing scaling dependency in more recent years should not be interpreted by reduction of homicides cases. Actually, the number of homicides in Brazil has grown in most cities. The interpretation based on city sizes indicates that, in the South, North, and Northeast regions, the number of homicides has increased rather proportionally in all city scales, whereas in the Midwest larger cities have become more violent. The same happens with the small and medium cities in the Southeast region.

The water distribution system, an infrastructure variable, presented sublinear scaling dependency. It is possible to identify in Fig 5(c) the strongest sublinear dependency for North region. It should be noted that this Brazilian region is by far the least optimized one in terms of urban structure. It has the lowest population density in the country, and comprises almost all Amazon ecosystem area in Brazil. These features explain the low coverage of water distribution systems in large North cities, actually the lowest among the Brazilian regions. Overall, the other Brazilian regions have shown being sublinear as most of infrastructure variable analyzed worldwide, with an almost linear behavior in the Northeast region. In the opposite way, the number of high knowledge employees in the service sector is clearly superlinear for all Brazilian regions, following the superlinear characteristic of high knowlegde/technologies variables. Fig 5(d) shows that the Northeast region has the largest proportional increase in the number of high knowledge employees in the service sector when one considers small, medium, and large cities, represented by the highest values of β among all regions.

The analyzes based on the residual distribution makes it possible a relative comparison between the cities. The negative (positive) residual values mean that the cities are below (above) the average behavior for the same size range. Whether being above or below the average behavior means a good or bad scenario depends on the nature of the urban index. For the indexes studied in this paper, being above the average behavior is a good sign only for the GDP. However, this is not actually observed when we consider the ensemble of Brazilian cities, as we see in Fig 6(a), which shows that most Brazilian cities have GDP below the expected scaling value. When we consider the regional ensembles, most of the cities are near the average scaling behavior, as shown in Fig 7. We have investigated the UIR distribution over time for all sets. The shape of the UIR distribution can be well described by the Gaussian function. As a matter of fact, a bi-modal UIR distribution appears only for the GDP involving the complete Brazil set, as shown in Fig 6. Such distribution shows that most Brazilian cities stay below the average expected values predicted by the scaling analysis represented by Eq 4. Fig 6 shows the UIR distributions for GDP, homicides, water distribution system and the number of high knowledge employees in the service sector in the complete Brazil set in 2016, while in Fig 7 we draw similar results for all regions and urban indexes. The UIR distribution graphs considering all indexes for every region over the years are not shown here because their shape are essentially the same.

Fig 6

Histograms of the residuals, ζ, from the 2016 data: (a) GDP, (b) homicides, (c) water distribution system, and (d) the number of high knowledge employees in the service sector data of the ensemble Brazil.

The black lines are Gaussian curves where A and B are constants, is the residual mean and ω the standard deviation). They have been used to describe the statistic of ζ for all but the GDP data, which is approximated by a bimodal Gaussian distribution. The corresponding histograms for all other years are very similar.

Fig 7

Histograms of the residuals, ζ, from the 2016 data: GDP, homicides, water distribution system and the number of high knowledge employees in the service sector for the Brazilian political regions.

The restricted sample of 4 out the 20 obtained curves is representative, once for all studied urban indicators and regions we have identified the same Gaussian shape. The black lines are Gaussian curves where A and B are constants, is the residual mean and ω the standard deviation), that describe the statistic of ζ. The histograms for all other years are very similar.

Considering the Gaussian approximations to the UIR distributions, we have quantified how their asymmetry changed over time based on their skewness. Positive skewness values indicate right side asymmetry (ζ < 0), i.e., larger number of cities below the average expected behavior. On the other hand, negative skewness (left side asymmetry) indicates that more cities are above the average expected behavior, ζ > 0. As shown in Fig 8, skewness are positive for GDP over the years for all regions, being the largest values obtained for Northeast region. This indicates, therefore, that most cities are below the average scaling behavior. We also detected an increasing trend of the Southeast region skewness, while the Midwest region has shown a opposite behavior. In the last decade, more small and medium cities in the Midwest region had a systematically increase in their GDP, becoming larger than the expected average value, while the Southeast has shown an opposite tendency. Again, the South and North regions presented similar behavior, showing a small right asymmetry.

Fig 8

Longitudinal analysis of the skewness of the residual distributions.

We have not done such analysis for the GDP of ensemble Brazil once its ζ distributions follow a bimodel Gaussian distribution.

The homicide data lead to UIR distributions with a slight left asymmetry for all ensembles, indicating that most cities are above the average expected scaling behavior. As the homicide is a collateral consequence of agglomeration, such characteristic is undesired, since being above the average means that in such cities the homicides cases even are higher than the average scaling prediction. For water distribution system, the skewness of the residuals of the Brazilian regions fluctuates around zero over time, which may be a good sign as it represents a natural random fluctuation. Some exceptions occur in the Midwest region for the last years. Regarding the the number of high knowledge employees in the service sector (SHT) residuals (see Fig 8), we can identify different behaviors: whereas the Midwest and Southeast regions became more left asymmetric, the South region kept the intensity of its left asymmetry. The North region oscillates between right asymmetry and symmetric distributions, while the Northeast has preserved its right asymmetry over time.

Comparisons among city indicators, identifying critical states and cases of extreme conditions, e.g., large number of homicides, are usually used by policy makers in order to adopt well succeeded strategies to improve citizen living conditions and to plan future actions. Usually, such comparisons are made by per capita rates and number of case per 100M, both of which neglect the scaling dependency between the indicator and population size. This may lead to the adoption of wrong policies to undermine this effect.

Finally, to provide a deeper insight into the properties resulting from scaling analysis, we have produced and compared two ranks of all Brazilian cities based on the 2016 data for GDP, homicide, water distribution system and the number of high knowledge employees in the service sector. One of the ranks corresponds to the usual one, based on the number of cases per 100M inhabitants (or per capita for the GDP data), while the second rank was generated considering the highest residual values resulting from the scaling analysis. While the residual of each city is quantified by their distance to the average scaling behavior, which takes into account all Brazilian cities, the rate of cases per 100M just considers the linear dependency of the urban index and population size, independently of the characteristic of the ensemble. Fig 9 illustrates the results for both ranks. The yellow and blue dots indicate, respectively, the cities belonging the usual and the scaling analysis rank. The red dots represent the cities belonging to both ranks. It reveals a clear difference between the results produced by distinct criteria, for homicide and water distribution system data, which have shown, respectively, strong superlinear and sublinear scaling dependency. As expected, due to weak scaling dependency for GDP, both ranks comprise almost the same set of cities. Despite this fact, it is important to observe that, as a secondary effect, the position of the cities in the rank have changed for most of the cities. Moreover, the average population size in the rank generated by cases per 100M is considerably larger than that obtained from the scaling rank.

Fig 9

Maps showing the location of the top fifty ranked Brazilian cities according to the following criteria: (a) Brazilian GDP, (b) most violent Brazilian cities according to the number of homicides, (c) length of the water distribution system, and (d) the number of high knowledge employees in the service sector, in 2016.

The yellow dots indicate the cities according to the cases per 100.000 rank, while the blue dots represent the cities of the scaling rank generated by the residuals of the cities. The red dots represent the cities that appeared in both ranks. Maps generated with the free and open source geographic information system (QGIS) version 3.4 LTR.

Conclusions

Vast territorial countries are usually characterized by regions with different economic, social, infrastructure and cultural characteristics. Once the socioeconomic indicators reflect these non-homogeneities, it is natural to wonder whether they also influence the results of urban scaling analyzes. As a general rule, agglomeration effects have a strong influence also at the regional level. After performing a regional scaling analysis based on economic, violence and health indicators, we were able to verify that the Brazilian regions present some similar features in the scaling dependency of regional economic and health urban indicators. It is important to register the high quality of the Brazilian data from DATASUS and IBGE, specially when compared to other middle income countries, as India [27]. Furthermore, amazing findings of our analyzes reveal peculiarities among scaling properties across the different regions. Indeed, the comparison between results for the richest and poorest Brazilian regions show stronger scaling similarities than those resulting from the comparison between the results for the richest and second-richest regions. Also, comparable values of scaling exponent for regions with huge differences, as is the case of the South and North regions, appear rather unexpectedly. Indeed, despite comparable exponents, the South has a much larger population, is economically more developed and industrialized, and has a better infrastructure than the North region. Being a country with huge inequalities at many different levels, Brazil provides an ideal case study for the observation of regional scaling properties, which allow for such surprising results. Our results suggest that the same kind of regional approach presented here, besides being directly applicable to countries with similar features, might also be well adapted for smaller and more homogeneous cases. It worth to point out that the definition of a city is still a discussion topic and depending on the focus of the investigation different interpretations may arise [35, 36]. Also, the reasons why most of the urban indicators have followed the power law dependency is still a research question [37].

We have emphasized that the use of per capita urban indicators overlooks the presence of the non-linear scaling relations for the four analyzed cases, a fact that may also happen to other urban features affected by non-linear interactions produced by the agglomeration phenomena. Indeed, the rank produced based on the residuals with respect to the scaling analyzes has sensible differences to that based on per capita indicators. We understand that a regional based scaling analysis may help scholars and policymakers get a more comprehensive view of urbanization related problems, being able to interfere locally in a more specific way rather than by uniform public actions designed for the whole country. Our analysis intend to initiate a discussion about the influence of the regional Brazilian heterogeneities over the scaling dependency of the urban variables. This may be evidenced by the differences in the scaling dependency of the GDP of the richest Brazilian regions, Southeast and South. Also, the Northeast and North regions despite of being the poorest Brazilian regions, appearing with considerable differences on the scaling dependency of the high knowledge employees. Therefore, as also verified by Bettencourt from his study about India [27], such regional analysis may show which regions of continental countries should have priority to social-economic policies implementations in order to develop, in a efficient way, all country. Frequently the Brazilian govern do not consider the hererogeneities. An example is the new cash transfer programme due to the SARS-CoV2 (COVID-19) pandemic. The main criteria to be eligible to receive the money was being unemployed. Once one is eligible, the govern just stipulated a fix value that a person may receive. The problem of such general programme is that people who live in capitals and in developed regions as South and Southeast are less assisted than those living in other regions mainly due to the cost of life. Despite we have limited our analysis to 4 urban variables, we have selected them in such a way that they cover distinct and representative urban characteristics as economics, violence and health, infrastructure and education. Thus, they are able to provide a general view confirming the existence of important differences and similarities among the urban scaling properties of socio-economic indicators from distinct regions in a same country.

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17 Apr 2020

PONE-D-20-02779

Socio-economic urban scaling properties: influence of regional geographic heterogeneities in Brazil

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NASA Earth Observatory (public domain): http://earthobservatory.nasa.gov/

Landsat: http://landsat.visibleearth.nasa.gov/

USGS EROS (Earth Resources Observatory and Science (EROS) Center) (public domain): http://eros.usgs.gov/#

Natural Earth (public domain): http://www.naturalearthdata.com/

3. We note that in your methods section you provide the reference citation for the dataset used in the study. We would like to recommend that you also include a link to the data in the methods section such that readers can more easily access it.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Thank you for the opportunity to review this interesting paper. While I found it to be reasonably well-written and interesting, I cannot recommend publication at this time. After reading the manuscript carefully, I think the scientific contribution and novel knowledge of the research need to be specified. What problems should be solved, such as theory, method or policy of urban development in Brazil? Compared with the relevant research, where is the innovation and contribution of this study? I think some clarifications and major alterations will increment the general quality of the paper.

1.Authors need to better address the goals of the paper in the end of the Introduction section. They are poorly or insufficiently addressed.

2.Data sources require explanation and critical discussion.

3.Figure 3 and Figure 9 could be improved by drawing.

4.Line 62: the title "Discussion" is not appropriate.

5.Further analysis on the influence of regional geographic heterogeneities is important.

Reviewer #2: Using economic, infrastructure and violence related data sets for the time interval 2002-2016 in Brazil, the study analyzed socio-economic urban scaling properties in the country. Results indicate that regional specificities related to some selected factors have a larger influence on the absolute value of the urban indexes. Regional scaling similarities and differences among regions were also uncovered. The study was good writing, and these findings are helpful for understanding the socio-economic urban scaling properties. However, there are some issues the authors must response before this manuscript to be published.

1, the study pointed that there exists regional heterogeneities in Brazil, the reviewer suggest authors test the statistical significant of the spatial stratified heterogeneities using statistic methods.

2, comparison of findings between the study and the other related papers should be discussed in the manuscript.

3, limitations and the further studies of the study should be discussed in the manuscript.

4, some findings have been discussed, however some of them need more scientific interpretations.

5, the reviewer suggest authors check structure of the manuscript. For example, in line 62, “discussion” is appeared before “methods” section.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files to be viewed.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at figures@plos.org. Please note that Supporting Information files do not need this step.

23 Jun 2020

Reviewer #1: Thank you for the opportunity to review this interesting paper. While I found it to be reasonably well-written and interesting, I cannot recommend publication at this time. After reading the manuscript carefully, I think the scientific contribution and novel knowledge of the research need to be specified. What problems should be solved, such as theory, method or policy of urban development in Brazil? Compared with the relevant research, where is the innovation and contribution of this study? I think some clarifications and major alterations will increment the general quality of the paper.

Author’s response: The authors thank the reviewer for reading our manuscript and for the important comments in the report. Overall, we believe that after the changes that we introduced in the new version, we have a significant improvement on our manuscript.

1.Authors need to better address the goals of the paper in the end of the Introduction section. They are poorly or insufficiently addressed.

1. As opportunely suggested by the reviewer we have included a new paragraph in the end of the introduction where we clearly address the goals of our work. Please, see text from line 62 to line 76.

2.Data sources require explanation and critical discussion.

2. We have included an additional explanation on the data in the first paragraph of the section “Results and Discussion”. Please, see text from line 124 to line 130.

3.Figure 3 and Figure 9 could be improved by drawing.

3. We have amplified Figure 9 and improved Figure 3. We hope that after the changes the figures have improved their quality.

4.Line 62: the title "Discussion" is not appropriate.

4. We thank the referee for calling our attention to this issue. We have removed “Discussion”, in line 62.

5.Further analysis on the influence of regional geographic heterogeneities is important.

5. We do agree that further analysis in order to understand completely how socio-economic heterogeneities present in continental size countries. This work intends to contribute to such discussion in Brazil, and certainly may be extended to include a larger number of urban variables. For the moment, we understand our work already uncovers a number of interesting findings. Indeed, the quantities selected for our analysis are representative of several sectors of socio-economic indicators, providing a first but wide view of their scaling properties. We intend to proceed further with our investigation, so that new insights coming from our results may be presented in a new future.

===================================================================================

Reviewer #2: Using economic, infrastructure and violence related data sets for the time interval 2002-2016 in Brazil, the study analyzed socio-economic urban scaling properties in the country. Results indicate that regional specificities related to some selected factors have a larger influence on the absolute value of the urban indexes. Regional scaling similarities and differences among regions were also uncovered. The study was good writing, and these findings are helpful for understanding the socio-economic urban scaling properties. However, there are some issues the authors must response before this manuscript to be published.

Author’s response: The authors thank the reviewer for reading our manuscript and for the important comments in the report. Overall, we believe that after the changes that we introduced in the new version, we have a significant improvement on our manuscript.

1, the study pointed that there exists regional heterogeneities in Brazil, the reviewer suggest authors test the statistical significant of the spatial stratified heterogeneities using statistic methods.

1. We have added a supporting information material which presents the Brazilian spatial heterogeneities and also the regional ones.

2, comparison of findings between the study and the other related papers should be discussed in the manuscript.

2. In the section “Conclusion” we have mentioned that our conclusions are in the same direction of the Bettencourt paper, ref. 27, which presents regional scaling analysis for India.

3, limitations and the further studies of the study should be discussed in the manuscript.

3. We have include a new paragraph in the section “conclusion”.

4, some findings have been discussed, however some of them need more scientific interpretations.

4. We believe that we have improve the discussion of our findings by including a new paragraphs in the “Introduction” and in the “Conclusion” sections.

5, the reviewer suggest authors check structure of the manuscript. For example, in line 62, “discussion” is appeared before “methods” section.

5. We thank the referee for calling our attention to this issue. We have removed “Discussion”, in line 62.

Submitted filename: Response to the ReviewersPlosoOneR.docx

Click here for additional data file.

11 Aug 2020

PONE-D-20-02779R1

Socio-economic urban scaling properties: influence of regional geographic heterogeneities in Brazil

PLOS ONE

Dear Dr. de Castro,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

I have received mixed feedback from the two reviewers. While Reviewer 1 is satisfied with your revision and reply, Reviewer 2 suggests another round of major revision before this manuscript can move forward.

Please submit your revised manuscript by Sep 25 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Mingxing Chen, Ph.D.

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: All comments have been addressed. The present document has been largely improved from its previous version.

Reviewer #2: This version has been improved much. Some issues, however, should be addressed. Regional geographic heterogeneities of the research object is the core content of the article, in the manuscript, the authors test the statistical significant of the spatial stratified heterogeneities using Local Spatial Autocorrelation Moran Index (LISA). The reviewer think that LISA can be used to test the local heterogeneities, however, the regional heterogeneity studied in the manuscript is more suitable to be expressed by spatial hierarchical heterogeneity, which can be calculated by geodetector q statistic (Wang, et al. A Measure of Spatial Stratified Heterogeneity. Ecological Indicators 2016), so that the reviewer suggest authors complement the analysis and added in the main text.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

28 Sep 2020

Response to the Reviewers

We would like to thank the editor and reviewers for their contributions. Please, find below, in red color, our point by point comments to the reviewers.

Reviewer #1: All comments have been addressed. The present document has been largely improved from its previous version.

Author’s response: The authors thank the reviewer for the previous comments. We believe that after the changes, we have an improvement in our manuscript.

Reviewer #2: This version has been improved much. Some issues, however, should be addressed. Regional geographic heterogeneities of the research object is the core content of the article, in the manuscript, the authors test the statistical significant of the spatial stratified heterogeneities using Local Spatial Autocorrelation Moran Index (LISA). The reviewer think that LISA can be used to test the local heterogeneities, however, the regional heterogeneity studied in the manuscript is more suitable to be expressed by spatial hierarchical heterogeneity, which can be calculated by geodetector q statistic (Wang, et al. A Measure of Spatial Stratified Heterogeneity. Ecological Indicators 2016), so that the reviewer suggest authors complement the analysis and added in the main text.

Author’s response: The authors thank the reviewer for this new suggestion and fully agree with it. We have included new results and a discussion of the parameter q, reported in Wang, et al. A Measure of Spatial Stratified Heterogeneity, Ecological Indicators 2016. In fact, the results we have found support our discussion regarding regional geographic heterogeneities. Metropolitan areas in every Brazilian region concentrates wealth, infrastructure, high level education employees and violence, which explain the values of q close to zero (heterogeneity within the regions are more significant than between them). The regions present similar heterogeneity, despite the discrepancy on the absolute value of the socioeconomic variables. On the other hand, the largest value of q associated with WDS indicates a comparatively smaller infrastructure discrepancy between the richest regions with the poorest ones. This can be explained, among other reasons as political and historical, by the fact that the poorer regions, as North and Northeast, have globally had less investments in infrastructure. We have included such discussion (in red) in pages 5 and 6 of the manuscript.

Submitted filename: Response to the Reviewers2.docx

Click here for additional data file.

21 Oct 2020

PONE-D-20-02779R2

Socio-economic urban scaling properties: influence of regional geographic heterogeneities in Brazil

PLOS ONE

Dear Dr. de Castro,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

I am glad to inform you that after the second round of reviews, the paper was accepted with minor revisions.

Please submit your revised manuscript by Dec 05 2020 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols

We look forward to receiving your revised manuscript.

Kind regards,

Mingxing Chen, Ph.D.

Academic Editor

PLOS ONE

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: The present document has been largely improved from its previous version.

In addition, in table1, it’s better to replace the statistical symbol q with Geodetector q.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

28 Oct 2020

Reviewer #2: The present document has been largely improved from its previous version.

In addition, in table1, it’s better to replace the statistical symbol q with Geodetector q.

Author’s response: The authors thank the reviewer for this suggestion. We have replaced the symbol q with Geodetector q in table 1.

Submitted filename: Response to the Reviewers3.docx

Click here for additional data file.

10 Nov 2020

Socio-economic urban scaling properties: influence of regional geographic heterogeneities in Brazil

PONE-D-20-02779R3

Dear Dr. de Castro,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Mingxing Chen, Ph.D.

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

17 Nov 2020

PONE-D-20-02779R3

Socio-economic urban scaling properties: influence of regional geographic heterogeneities in Brazil

Dear Dr. de Castro:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

If we can help with anything else, please email us at plosone@plos.org.

Thank you for submitting your work to PLOS ONE and supporting open access.

Kind regards,

PLOS ONE Editorial Office Staff

on behalf of

Prof. Mingxing Chen

Academic Editor

PLOS ONE