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Multilevel comparison of large urban systems Denise Pumain∗, Elfie Swerts, Clémentine Cottineau, Céline Vacchiani-Marcuzzo, Antonio Ignazzi, Anne Bretagnolle, François Delisle, Robin Cura, Liliane Lizzi and Solène Baffi Géographie-Cités, CNRS-Paris 1-Paris 7 (UMR 8504), 13 rue du four, FR-75006 Paris, France Forthefirsttimethesystemsofcitiesinsevencountriesorregionsamongthelargestintheworld (China,India,Brazil,Europe,theFormerSovietUnion(FSU),theUnitedStatesandSouthAfrica) aremadecomparablethroughthebuildingofspatio-temporalstandardisedstatisticaldatabases. We firstexplaintheconceptofagenericevolutionaryurbanunit(“city”)anditsnecessaryadaptations to the information provided by each national statistical system. Second, the hierarchical structure 5 and the urban growth process are compared at macro-scale for the seven countries with reference 1 to Zipf’s and Gibrat’s model: in agreement with an evolutionary theory of urban systems, large 0 similarities shape the hierarchical structure and growth processes in BRICS countries as well as in 2 Europe and United States, despite their positions at different stages in the urban transition that n explain some structural peculiarities. Third, the individual trajectories of some 10,000 cities are a mappedatmicro-scalefollowingaclusteranalysisoftheirevolutionoverthelastfiftyyears. Afew J commonprinciplesextractedfromtheevolutionarytheoryofurbansystemscanexplainthediversity 6 ofthesetrajectories,includingaspecificpatternintheirgeographicalrepartitionintheChinesecase. 2 We conclude that the observations at macro-level when summarized as stylised facts can help in designingsimulationmodelsofurbansystemswhereastheurbantrajectoriesidentifiedatmicro-level ] are consistent enough for constituting the basis of plausible future population projections. h p - c isons,wedefineacityasaplaceinwhichthedailyactiv- o ities of most residents are concentrated. Its delineation s constitutes a spatial ”envelope” that evolves through . Urbantheoriesandmodelsaretoorarelytestedonsets s time,generallyinexpansion. Foreachtimeperiod,wese- c ofdatathatareproperlydefinedandstandardized. Many lectanurbandelineationthatissuitedtothelocalregime i contradictoryresultsandsomecontroversialpapersinur- s ofsocio-spatialinteraction: thus,beforethe19thcentury, y ban studies can be explained by a lack of attention paid administrative units (communes, municipios, or places) h to the quality and quantity of empirical data. We think are sufficient to define ”cities without suburbs” (see [1], p ofcrucialimportancetoestablishsolidandreplicablere- [ sultsfromsounddatathataremadecomparablebyusing p.291) that represent a dense body of population having acommontheoreticalbackgroundfordefininganddelin- requested and/or having been granted legal recognition 1 by the political power. The form taken on by this recog- v eatingcities,whatevertheheterogeneityofthepublished nition and the conditions depend on the political and 8 statistical information. We take here the opportunity of 0 several coordinated PhD works[32] for comparing urban institutional setting (for instance, request to be incorpo- 4 systemsinsevenamongthelargestcountriesintheworld: rated into the United States, or demographic threshold 6 inEurope,orpoliticaldecisionasobservedmorerecently China, India, Brazil, Europe, the Former Soviet Union 0 in the USSR or China). With the industrial revolution, (FSU),theUnitedStatesandSouthAfrica. Thissample . 1 includes all the so-called BRICS countries that were for the city became a dense human group extending out- 0 side administrative boundaries, and it then requires a awhilethemostrapidlygrowingcountriesandillustrate 5 morphological definition (i.e. urban agglomeration) so urbansystemsinalmostallcontinentsatdifferentstages 1 as to reflect this continuity of built-up area. More re- of the urbanization process. : v cently,interactionslinkedtotheuseofcartransportand i long-distance commuting by people living in peri-urban X settings but still working in the city centres led on to a r Standardized databases for comparing urban functional description of the city (i.e. functional urban a systems according to an evolutionary concept of area) [6]. cities The present development of urban databases for the sevenstudyzonesisbasedoncommonprinciples,whileat Harmonised databases derived from an evolving con- thesametimeallowingforadaptationtolocalconstraints cept of the city are a prerequisite for comparative urban and political and administrative contexts[33]. Wherever studies. In our perspective of spatio-temporal compar- possible, we have used population numbers derived from thefinestpossibleadministrativelevel(thebasicunitsin the databases) and we performed aggregations of these ∗Correspondenceandrequestsformaterialsshouldbeaddressedto elementaryentitiesinordertofollowtheevolutionofthe DP(Email: [email protected]). urban object in the seven selected countries over long 2 time spans (see Figure 1). Forms of urban hierarchy and growth processes Table I sums up the final content of these databases There is a vast corpus of literature about the forms and the method used to adapt our generic definition to taken on by urban hierarchies, and in particular the de- the information available in each country. Few of these scriptions that refer to Zipf’s rank-size rule. Recent syn- countriesprovidedatabasedonafunctionaldefinitionof theses [20, 26] have not reached a consensus on the uni- the urban object, and the information is available only versal nature of this rule, nor on the factors that might for certain dates (USA, Brazil). The database for Eu- explainitswideapplicability,orthemainreasonsforthe rope, which covers a longer historical time span, groups variations that are observed. entities according to a morphological definition. Certain A first obstacle to the construction of scientific knowl- countries only give information at administrative level, edgeonthisissueistheextremeheterogeneityofthesam- fortunately in fairly wide units that are able to evolve ples of cities that have been used to perform the tests, (Russia: [9]). Different aggregation methods have been andsometimesthedoubtfulqualityofthedefinitionsand implemented to harmonise these databases: morpholog- delineations used to measure city size. We do not claim ical aggregation on the basis of aerial photographs or heretoprovideafinalsolutiontothisproblem,butwedo satellite images (Europe, India, FSU); for South Africa, bringmorecredibleresultsbyusingdatabasesthatareas since the morphological definition lacks relevance in the comparable as possible, applying this to a large number case of the Apartheid city, entities that were function- of cities over fairly long time spans and for a variety of ally linked to the city, such as the black townships, were large countries of the world. integrated [29] ; the database for the USA uses an evolv- Another question is that of the definition of the city ing definition of the city, considering legal entities alone systems observed. Most often, Zipf’s law is tested on a until the change to urban agglomerations in 1870 and set of cities in a single country. We are aware that this finally metropolitan areas (which are functional areas) use of the nation-state framework (or a quasi continen- from 1940 [5]; For China, the principle of urban agglom- tal framework in the case of Europe, US, China, India eration was applied, adjusting delineations of built-up andtheformerSovietUnion)isprobablynolongercom- areas collected on satellite images on the administrative pletely suited to the delineation of city systems, since grid of the qu, shi and xian [27]. the globalisation of exchanges brings cities to new interactions, the intensity and range of which vary according to city size. Nevertheless, urban hierarchical patterns, precisely because of the growth processes resulting from their interaction patterns, tend to be sustained over pe- The urban entities included in table 1 are those with riodsofseveraldecadesorevenseveralcenturies, andwe more than 10,000 inhabitants at the date indicated. At think that the hierarchies observed here have been en- the start of the 21st century, the numbers can vary from gaged in strong interactions for sufficiently long time for a few hundred to several thousands according to the the patterns to continue to show up, even if the state country, but they remain fairly closely linked to the to- borders enclosing them are no longer as impermeable as tal urban population of the country, as shown in Figure they were earlier. 2, where a simple linear regression adequately fits three quartersofthevariationsofthesetwovalues. Eachfigure isforeseeableiftheotherisknown,whichmeansthatthe Macro-level analysis of urban hierarchies explained degree of concentration of the urban population varies by territorial history little in the present-day world (a very approximate measure of the present degree of concentration in these large Our main results widely confirm the results reported countries can be obtained by calculating an average size byMoriconi-Ebrard[18]whousedtheGeopolisdatabase per city, about 100,000 inhabitants, which has of course tocomparestatesacrosstheworld. Theyalsogoagainst no real geographical meaning) and this reflects a certain theideaofahistoricalconvergencetowardsaregularZipf coherenceinurbanisationprocessesoverall,whateverthe model with a slope of -1 as suggested in a recent article country considered. The United States appear as an ex- by Berry and Okulicz-Kozaryn [4]. ception, with far less urban units than expected from their total urban population. That huge concentration Indeed,slopevaluesforrank-sizeadjustedonthesedis- of the urban system can be explained by the historical tributions vary, clearly differentiating countries and con- process of settlement in the “New world” as well as by tinents according to how long-standing their settlement the very large size of the elementary spatial units aggre- is. The value of the rank-size slope is an index of size gated in SMA’s (the counties). Even if we had included inequalities of cities. The variations of this index of ur- in the database the urban agglomerations instead of the ban size amplitude in a given territory can be fairly well SMA’s,theexceptionwouldremain,sincethereare1380 explained by differences in the speed of transport sys- “urbanized areas and urban clusters” over 10 000 inhab- tems enabling exchanges among cities, at the time when itants for a total of 237 million urban population (US the urban networks become established: the lowest val- Census Bureau, 2014)[34]. ues (absolute value, i.e. without sign) are observed in 3 S R N Brazil és C China cit e- Europe* hi p Former Soviet Union gra o India é G South Africa MR U United States y - Cit er v Di o e G 1300 1800 1850 1900 1950 2000 © * European continent, Turkey and the former Soviet Union excepted FIG. 1: Historical range of the urban data bases. Database N (initial date) N (final date) D Method 0 F Brazil (a) 531 (1872) 2615 (2010) 11 Administrative (municipios + metropolitan areas) Former Soviet Union Morphological (municipalities at three administrative 91 (1840) 1929 (2010) 11 (DARIUS) (b) levels) India (IndiaCities) 503 (1901) 5841 (2011) 12 Combined morphological, and functional (c) Combined administrative (xian, qu, xianjishi (district China (ChinaCities) 605 (1964) 9294 (2000) 4 level) and zhen, xiang (subdistrict level)) morphological (d) and functional South Africa Combined morphological and functional (white cities + 14 (1911) 220 (2001) 10 (DYSTURB) (e) black townships) Europe (PARIS- Bairoch-Geopolis) 3619 (1950) 4413 (2010) 14 Morphological (municipalities then agglomerations) (f) Combined administrative then morphological and United States 5 (1790) 909 (2010) 23 functional (places, cities, retropolated micropolitan and (Harmonie-cités) (g) metropolitan areas) TABLE I: Harmonised urban databases for international comparisons (urban units > 10,000 inhab.). N : 0 number of cities at (initial date) ; N : Number of cities at (final date) ; D : number of dates considered in the database. F Sources : (a) IBGE, Instituto Brasileiro de Geografia e Estatistica. Statistical tables for the Brazilian Empire and the Federal RepublicofBrazil;(b)StatisticaltablesfortheRussianEmpire,RussianEmpirecensuses,USSRcensuses(archives),National censuses;(c)CensusofIndia;(d)ChinaDataCenterandChineseNationalCensusBureau;(e)StatisticsSouthAfrica,South AfricaninstituteofRacerelations,Urbanfoundation,CensusStatisticsSA,DYSTURB(see[15]);(f)[1,19];(g)USAcensus data: Census of Population and Housing. countries that have been populated for a long time (In- the politico-administrative organisation of the territories dia, China, Europe) and the highest values for countries concerned (see Figure 3). In countries that have been that were settled more recently, higher transportation run under socialist regimes aiming at restraining urban speed enabling a wider spacing between settlements as growth, there is a levelling-off of the curves (in the FSU well as larger urban concentrations emerging on sparser aroundonemillioninhabitants,inChinaaround100000 spatial distributions of rural population (South Africa, inhabitants, corresponding to city sizes for which tar- the United States). The fairly high values for the Soviet geted investments have been made [8, 18]. Conversely Union could be explained by its relatively late industri- thecountrieswiththemostmarkedmacrocephaly(South alisation compared to Europe, and a more recent urban Africa, India, Brazil) are those that have allowed their developmentofitsEasternareasintheAsiaticpart,while metropolises the greatest latitude. Brazil escapes the general pattern with a moderate de- Compared to the United States and Europe, the gree of urban concentration (see Table II). BRICScountriesstandoutfortheparticularshapeofthe The qualitative variations in shape of the size dis- upper part of their urban hierarchies: Russia is the only tribution are explained above all by the diversity of BRICScountrytopresentacaseofurbanprimacy,where 4 Country N a P /P M P (×106) 1 2 tot Brazil 2615 0.88 2 2 161 FSU 1929 1.10 3 0 173.5 India 5121 0.95 1.1 3 427 China 9294 0.80 1.3 0 481 South Africa 220 1.15 2 4 25 Europe 4413 0.96 1.2 2 291 United States 909 1.23 1.5 0 287 TABLEII:Comparing urban hierarchies: city size distributions around 2010. Weconsidertheurbanagglomerations larger than 10000 inhabitants. Rank size slope a is estimated from equation log(P) = K −alog(R) with P the population of the city and R its rank, using OLS method. P /P : primacy index; M: number of macrocephalic cities; P : total urban 1 2 tot population. 10000 NRS 100000 NRS 8000 CFEBourharrimzonipaleer Soviet Union graphie-cités C 10000 CBhrainzail Géographie-cités C er of cities 6000 IUSnonduiitatehd A Sftraictaes DiverCity - UMR Géo n (thousands) 1000 FormerU SSnooivtuieetdhtE USuAItrnnfaoridtiopceineaas © GeoDiverCity - UMR b eo o m 4000 © G ati u ul N p o P 100 2000 0 10 0 100 200 300 400 500 1 10 100 1000 10000 100000 Total urban population (millions) Rank FIG. 2: Total urban population and number of cities FIG. 3: City size distributions in seven countries per country. around 2010. Moscow is three times the size of St Petersburg (see Ta- also ranks first for the number of cities of over a million bleII)whilealltheothersexceptChinaarecharacterised inhabitants, 66 in all. In contrast, India, ranking sec- by macrocephaly comprising two to four cities that are ond for the weight of its total urban population (around clearly discontinuous with the rest of the distribution. 400 million) ranks only 4th for the number of cities with Thus in India, the three cities of Delhi, Mumbai and more than a million inhabitants – with 44 of these, it is Kolkata, with around 16 million inhabitants each, stand outranked by the USA which has 51 for an urban popu- out from the other cities in India, as do Durban, Cape- lation of only 287 million, which is therefore much more town and Johannesburg agglomeration in South Africa, concentrated spatially. In contrast again, Europe where whileinBrazilthediscontinuityislessmarked, withSao the urban population is more or less the same than in Paulo (20 million inhabitants) and Rio de Janeiro (12 the USA (291 million) has only 39 cities of over a mil- million)somewayaheadofBeloHorizontewithjustover lioninhabitants,andthedegreeofconcentrationisfairly 5 million. similar to that of the former Soviet Union (173.5 million The largest cities are remarkable by their size, which city-dwellers and 28 cities of over a million), or Brazil obviously depends on the mass of the urban population (161 and 23 respectively). While Europe remains the in the country (see Figure 2), but this top part of the continentofsmalltomediumcitiesandtowns,andwhile urban hierarchy is not sufficient to characterise the de- India stillhas many small cities, the urbanprocesses un- gree of concentration of an urban population, and it is derway in India suggest that many of these cities are set relevant to look at the other parts of the distribution. to expand in the coming decades [28], and in China, al- Thus China, which ranks first for its mass, with a to- though population concentration is still moderate, the tal urban population of around 500 million inhabitants, massive size of the country and the closeness of certain 5 cities one to the other suggests that several large conur- monfeaturesdespitemajordifferencesintheirhistoryas bations or megalopolises are likely to develop with 30 wellasterritorialandpoliticalorganization. Thatiswhy to 40 million inhabitants each, around the Pearl River Zipf’s law and Gibrat’s model albeit purely statistical Delta,intheregionsroundShanghai,orbetweenBeijing models remain rather good standard references enabling and Tianjin. international comparisons for a synthetic description of empirical urban hierarchies and urban growth processes, even though they do not directly provide an explanation Urban hierarchies and urban growth at micro-level: for the underlying generative geographical processes (we testing Gibrat’s model suggestfurthertheoreticalcomplementaryinvestigations inthisdirection, forinstancebydevelopingthefamilyof Simpop models, [10, 22]. This conclusion is consolidated The universal shape of urban hierarchies that can be by the consistency of deviations from the models that summarized by Zipf’s rank-size rule as above or by a can be rather easily related to different families of the lognormal statistical distribution is explained as a first historicaldevelopmentofurbansettlementsandpolitico- approximation by a stochastic repartition of the growth administrativeorganisationoftheterritoriestheybelong rates of individual cities in an urban system [21, 24]. to. Gibrat’s law [14] predicts the statistical form of urban hierarchies and their persistence over time. This model assumesthatcitiesgrowinamannerthatisproportional Macro and micro-dynamics: urban transitions and to their size. It is a growth model of the exponential cities trajectories type, but with growth rates (or relative population variations)thatvaryinthecourseoftime. Accordingtothis As we have seen before, understanding city size dis- model, despite considerable fluctuations in growth rates tribution and moreover urban growth processes cannot fromonecitytoanotherovershorttimespans,long-term be done without referring to the history of each ur- growth averages out at the same level for all cities in a ban system and at least, even in a parsimonious ab- given system. stract approach, to its stage in the seemingly univer- WetestedthehypothesesofGibrat’slawfortheinter- sal urban transition. This process named by W. Zelin- vals between these two dates for which city population sky [31] using an analogy with the demographic tran- data is known in our bases. The hypothesis for generat- sition describes the universal change from a dispersed ingalognormaldistributionstipulatesthatthevariations andhomogeneousspatialrepartitionofpopulationinru- in growth rate at each time interval do not depend on ral habitat towards much more concentrated diversified city size, and are distributed randomly from one period and hierarchized forms in urban settlements. The pro- to another. Overall, the process observed in the BRICS cess which generally accompanies economic development complies with the model, which thus, at least in first ap- started roughly at the beginning of 19th century in first proximation, remains a relevant reference for analysing industrialized countries and around 1950 in the less de- the process of growth distribution in the city systems. veloped ones. Everywhere, the correlation between city size and growth is low or absent. In South Africa, in India and China, whether at national level or for the main regions, Macro-level trajectories of urban systems thehypothesesoftheGibratmodelareverified,andfrom the start of the 20th century [28, 29]. There is a discrep- Different stages in urban transition clearly appear al- ancy with the model, particularly in periods of vigorous readyfromthecondensedinformationinTableIIIwhere growth, for the USA throughout the 19th century and countries that experimented earlier urban transitions in Europe after 1950, where there is a positive tempo- (Europe, Former Soviet Union, USA, Brazil) have much ral autocorrelation of the growth rates. In Russia the lower average urban growth rates during the last forty process also appears in the course of the second phase yearsthancountriesthatarestillintheexponentialstage of industrialisation in the 1930s and in the two decades of the growing curve of their urbanization rate. during which there was a trend towards metropolisation China appears clearly as the country in which recent of the largest cities and a cumulative decline of certain urban development is the most rapid, with an average specialisedcities[9]. Wehavedemonstratedinaprevious urban population growth rate of over 5% per year over paper [13] how such deviations from a purely stochastic 40years. TheIndianurbangrowthrateishalfofthis,but growthmodelcouldbeexplainedbyintegratinginanur- nevertheless vigorous during the period, with an average ban growth model the interaction processes that convey rate of 2% per year, while South Africa, with 3.2%, still innovationwavesintheurbanhierarchies. Aconsequence reflects the fast urban growth rates across the African is that inequalities in city sizes are growing faster in real continent. In the USA and in Brazil growth is still over urban systems than according to a pure Gibrat’s rule. 1%, while in Europe and Russia it is just 1% or much To conclude, the urban hierarchies and growth pro- lower. cesses in a variety of large urban systems all over the world,includingtheBRICScountries,sharegenericcom- These trends are partly determined by the stage 6 Country Average growth rate (%/year) Period Brazil 1.11 1960-2010 China 5.20 1964-2000 India 2.10 1961-2001 Former Soviet Union 0.78 1959-2010 South Africa 3.15 1960-2001 Europe 1.01 1960-2010 USA 1.52 1960-2010 TABLE III: Average annual growth rates of population for cities of over 10.000 inhabitants during second half of the 20th century. reachedbythedifferentcountriesintheurbantransition, 100 S buttheyarealsoinfluencedbytheirparticularhistoryof NR C urbanisation: inChinapoliticalaction,inparticularthat és apffloescitoinngomf uigrrbaatnioisnast,iofonr[a7l,o1n7g],tifmarepmuotrebrmakaerskoednltyhteheaxn- %) phie-cit isnlowIneddiamwighrearteioint fwroams raruthraelrasroecaiasl[3a,nd23f]a.mSiolyutthieAs ftrhicaat try/on ( Géogra hsiansceretmhaeineenddaotfaAnpaavretrhaegied,leovneltahmeoonngeAhfarnicdanbeccoauunsterieosf counulati 10 y - UMR internal migrations from the former Bantustans, and on of op erCit tm”hnieegwroa”tnhcteosru[1nb1ter,cie2as9u]is.neBtoerframiztissloaafntwtdraatvchetesivoUefnSseeAststbletemoinweganrtadmhsaodfnoagreftioghrne- ation ban p © GeoDiv ulur mer urbanisation rate systematically higher than in ”old pd world”countriesinEuropeandAsia[25]. Theslowingin Porl 1 o urbangrowthrateshasbeenmoremarkedinRussiasince w the1990s,asaresultofdecreasesinthetotalpopulation, especiallyintheNorthernpartsoftheterritoryresulting Brazil China Europe from the dismantling of the Soviet Union [12, 16]. It has even been negative on average over the last two censuses Former Soviet Union India (since 1989). South Africa United States 0.1 As a result, the weights of urban population of these 1950 1980 2000 countriesinthetotalurbanpopulationoftheworldhave beenrelativelyincreasingasshowninFigure4thatcom- Date pares their evolution over almost half a century. These contrasted evolutions explain the very rapid turnover in rankings among the mega-cities (above 10 FIG.4: Comparing the evolution of countries share of millions inhabitants), which are always the subject of world urban population (%). controversy because the delineations chosen to measure these large urban areas have a considerable impact on their rank[35]. We can consider here the subset of (14),andRio(12). TheEuropeancitiesdonotexceed10 these seven large countries included in the harmonised million, and they are joined in this megapolis group by database to demonstrate the upheavals caused by un- Guanzhou, Shenzen, and probably a few other Chinese equal demographic growth over the last four decades. In cities if the migrant populations with more or less illegal the1960s,thethreelargestcitiesbysizewerelocatedout- status are taken into account. sidetheBRICS,withpopulationsof10.6millionforNew York, 8.9 for Greater London, and 7.2 for Paris. These were followed on by Moscow (7.2), Shanghai (6.4), Delhi Differentiating urban trajectories at micro-level (5.9),LosAngeles(6),Kolkata(5.3),Mumbai(4.9),Bei- jing (4), Sao Paulo (with 3.8 having just overtaken Rio Too often however in urban studies the focus is only at 3.3) and Guanzhou (2). By the end of 20th century, directed on these few “global cities” or “world cities” this ranking had been completely overturned, with Sao whosesizeandexpansion islinkedwith thedevelopment Paulo joining or overtaking New York with some 20 mil- of long distance exchange networks but not necessarily lion inhabitants, and 4 cities in the BRICS taking top reflectotherpossibletypesofurbandynamics. Wethink places among the others: Delhi (17 million), Shanghai necessary to develop knowledge about perhaps less pres- (16), Kolkata (16), Mumbai (15), Moscow (14), Beijing tigiousnamesinurbanhierarchiesthatneverthelesspro- 7 videwaysoflivingforamajorityofpopulationsandalso tions–certainStatecapitalsinIndia, provincialcapitals participate in a decisive manner to the maintenance and in China regional capitals in Russia, and medium-sized renewal of urban systems. cities in South Africa. To differentiate city trajectories in each country we developed a method that compares population evolution profilesbywayofacorrespondencefactoranalysisanda In Brazil (Figure 5) almost all the large metropolitan hierarchicalascendingclassificationusingtheχ2 distance areas, which are the capitals of the federal States, have (seeAppendice1). Theimplicitreferencemodelisthere- stronglyascendingtrajectories. Therecentdynamicthus forethatofproportionaldistributedgrowthproposedby hastheeffectofaccentuatingthehierarchicalinequalities Gibrat [14], and the trajectories show the most system- in the country. India too exhibits this process of rein- atic discrepancies in relation to mean growth trend. The forcement at the top of the urban hierarchy, with three types of profile derived from the classification are shown quarters of the largest cities exhibiting ascending or sta- on the left-hand graph (see Figures 5, 6, 7, 8, and 9) by bletrajectories. Incontrast, intheothercountries, what the trajectory of the mean population for each type, and canbeseenisaformof”catchingup”bythesmallercities to the right for a trajectory showing the relative evolu- and peripheral areas. The markedly ascending trajecto- tion of the mean weight of this type of city in the urban riestendtobecharacteristicofafewsmallercities,often systemunderconsideration(semi-logarithmicgraphsen- in the vicinity of the large metropolises, in India (Fig- ablingontheonehandacomparisonofgrowthintensities ure 7) or South Africa (Figure 9). In the former Soviet representedbytheslopes,andontheotherimmediatevi- Union (Figure 6), it is most of the cities located on the sualisationofanydifferencesinevolution(theyarefairly peripheries of Russia to the South (Central Asia, Azer- frequent) associated with positions in the urban hierar- baijan) and West (Ukraine, Belarus), and some Russian chy). cities near deposits of mineral resources, that gain weigh Naturally, the shape of city trajectories in relation to relativetotheothers. InChina(Figure8),twoprocesses that of the system to which they belong can vary with are seen, where the large cities in the East (Shenzen, Xi- the period considered. We chose the period 1960-2010 amen) are gaining weight in the system while medium- for reasons of comparability between countries, and also sized cities in Xinjian province and Inner Mongolia are to restrict the number of major historical turning points developing fast, illustrating the catching-up by periph- which if too numerous would make it more difficult to eral regions. efficiently anticipate possible evolutions in the 21st century. By construction, these classifications show classes of cities where the ”absolute” evolutions are often all in- There is a long-term trend in most city systems creasing (rarely including an inflexion), but grouped ac- whereby it is mostly the small urban entities that show cording to their relative growth, which may be faster or relative decline. Indeed, all other things being equal, the slower than that of the country as a whole. To compare smallercitiesaremorelikelytobedistantfromthemain the degree of heterogeneity of these trajectories across waves of innovation, or else to be highly specialised in countries, we measured the share of variance remaining declining sectors of activity, so that they lose their influ- between classes. The order of the countries remains the ence on local markets as a result of acceleration in the same, whether the partition is into two, three or five speed and capacity of transport systems. The only ex- classes. In the case of five classes, the Former Soviet ception appears in China (see Figure 8) where classes Union shows the greatest diversity in trajectories (76% of cities with an ascending profile are made up mainly of interclass variance) while in Brazil the trajectories ap- smallcities,athirdofwhichinSpecialEconomicZonesin pear less differentiated (63%), the other countries falling whichinnovatingactivitieshavebeensetupandtowhich between these two (70-73%). populations migrate. The classic process of hierarchical Depending on the form of the classification tree, there diffusionofinnovationispartiallydisconnectedherefrom aretwoclearlydistincttypesoftrajectoryinChina,while the previous structure of the city system. However cities three families of trajectory can be observed in the other with a ”winning” trajectory are mainly located in the countries. To obtain more detail, and in relation to lev- immediate vicinity (roughly less than 200 km) of large els of heterogeneity, for mapping purposes (Figures 5,6, metropolitanareas,forinstanceGuangzhouorShanghai. 7, 8, 9) we retained four classes of city for China (Figure Theimportanceofpolicyinurbandynamicscanthusbe 8),India(Figure7),SouthAfrica(Figure9)andthefor- seen in the creation of new cities, at the same time pre- mer Soviet Union (Figure 6), and five for Brazil (Figure serving a degree of spatial and historical coherence with 5). The classes can be grouped according to the orien- theearliertrendsinthecitysystem. Inaterritorywhere tation of their trajectories in relation to the city system urbanisation is long-standing, like China, these new ur- to which they belong, generally in two types, ”winners” ban developments fit themselves into the previous urban and ”losers”, but a stable type also appears in India, spatial pattern, while in ”new” countries like Brazil, the China,theformerSovietUnionandSouthAfrica. These USA and South Africa, and also the Eastern part of the cities that maintain their relative weight in the system Russian Empire, urban creations ran alongside the set- are often long-standing cities with administrative func- tlement of new territories. 8 Conclusion evolutions are disseminated in all parts of each territory with few remarkable spatial concentrations. Whendealingwithcomplexsystems,itisimportantto relatetheconfigurationsofurbanhierarchiesobservedon macro-geographical scale of States to the trajectories of Appendice 1. TrajPop software (author:Robin Cura) the urban entities they comprise on micro-geographical level. This paper thus demonstrates the usefulness of constructingaharmoniseddatabaseenablingthedescrip- TheseanalysesareperformedusingtheTrajPopscript, tion of the evolution of urban entities and their spatial developed in the ERC GeoDiverCity project. This tool, extension over time. based on the free statistical environment R, performs a We provide for the first time a comparable overview CorrespondenceAnalysisonatemporalpopulationtable. of the systems of cities in the five BRICS countries. Us- The coordinates of cities on the orthogonal components ing Zipf’s distribution of city sizes and Gibrat’s urban then make it possible, after re-entering the weights of growth models as benchmarks for the comparison, we the cities, to generate a matrix for population discrep- have demonstrated that the dynamic urban processes in ancies among cities (measured using a khi2 distance); BRICS during the last fifty years were rather similar to this matrix is applied a Hierarchical Cluster Analy- to those observed for instance in Europe or the United sis (using the Ward method, which tends to minimise States. There is nothing resembling a specific urban dy- intra-classvarianceandtomaximiseinter-classvariance). namicinBRICSwhetherweconsidertheshapeofurban From the tree generated by this clustering, the number hierarchies,citysizedistribution,ordistributionofurban of clusters is chosen so that it sufficiently distinguishes growth among individual cities. the trajectories while at the same time enables them to Of course differences do exist, but they relate to the be mapped. It is then possible to analyse trajectory specific developmental pathway of these countries, in- classes using the TrajPop graphic and numerical print- cluding the relative delay in the urban transition com- outs,forinstancebystudyingtheevolutionoftherelative pared to more developed countries, which explains their weights of the classes in the system in the course of time very high mean urban growth rates – the case of Rus- (http://trajpop.parisgeo.cnrs.fr). sia being excepted. History matters too for differentiating the evolution of urbanisation rates, which registered higher values earlier in Russia and Brazil compared to Acknowledgements South Africa, China and India. Whenshiftingfromthemacro-scaleofcountriestothe micro-scale of individual cities, the most striking fact The authors acknowledge funding from the European is the diversity of urban trajectories that exhibit con- Research Council through project GeoDiverCity (ad- trasted patterns of booming growth or relative decline vanced grant programme, number 269826, PI Denise everywhere. Moreover,thesequalitativelydivergentlocal Pumain). [1] Bairoch, P., 1985, De Jéricho a` Mexico, Villes et 8 July 2011), http://halshs.archives-ouvertes.fr/halshs- économie dans l’histoire. Arcades, Paris, Gallimard. 00624473/fr/ [2] Bairoch,P.Batou,J.andChèvre,P.1988,Lapopulation [7] Chan,K.W.andXuX.1985,“UrbanPopulationGrowth des villes européennes de 800 a` 1850. 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Paris, Eco- Cosmo Ignazzi, 2015, Solène Baffi, 2015 nomica, 231 p. [33] We would like to acknowledge the assistance of Hélène [22] PumainD.2012,“Multi-agentsSystemModellingforUr- Mathian in the conception of the data models. ban Systems : the Series of SIMPOP models”, in Hep- [34] Island Areas, Alaska and Porto Rico excluded penstall A. J., Crooks A.T., See L.M., Batty M. (eds), [35] See for instance the classifications given on websites Agent-based Models of Geographical Systems. Springer, http://citypopulation.de, http://population.data.net, Population Studies, pp. 721-738. or those provided by the United Nations [23] Ramachandran, R. 2011. Urbanization and urban sys- (http://esa.un.org/unup). tems in India, Oxford University Press.3ed 10 TRAJECTORIES OF 1800 CITIES FROM 1960 TO 2010 IN BRAZIL Population in 2010 (millions) 20 1 0 500 Km Sources IBGE, Censos Demogràficos 1872-2010 Made with Philcarto http://philcarto.free.fr © Cosmo Antonio Ignazzi, Géographie-cités - GeoDiverCity, 2013 CLUSTERING TREE AND FACTORIAL MAP F1 (x) : 79% Continuous trend F2 (y) : 12% Classes A : Fast growing cities (138) E Slow growth Fast growth B : Growing cities (297) D B A C C : Slow growing cities (758) D : Declining cities (451) E : Fast declining cities (156) ABSOLUTE EVOLUTION RELATIVE EVOLUTION s) 1000 an 0.5 d b an ur 0.4 us al %) on (tho 100 on / toton (in 0.3 ati atiati 0.2 ul ulul p pp po popo 0.1 n n Mea 10 Mea 0 1960 1970 1980 1990 2000 2010 1960 1970 1980 1990 2000 2010 FIG. 5: Urban trajectories in Brazil.