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1999
11ème Colloque Européen de Géographie Théorique et Quantitative, Durham, Royaume-Uni, 3-7 septembre 1999
131

Long-term dynamics of European towns and cities : towards a spatial model of urban growth

Anne Bretagnolle, Hélène Mathian, Denise Pumain et Céline Rozenblat

Résumés

L´objectif de l´étude est de construire un modèle, dans l´esprit de la théorie de l´auto-organisation, qui décrirait la manière dont les interactions entre les villes peuvent produire des structures macro-géographiques et des dynamiques à l´échelle du système urbain européen. Des simulations ont été réalisées à l´aide d´un modèle statistique de croissance urbaine dans un système de villes (le modèle de Gibrat). Les résultats montrent cependant des écarts systématiques par rapport aux observations. Des analyses empiriques plus approfondies de la dynamique urbaine dans la longue durée et pour un très large ensemble de villes (Europe 1600-2000) apportent de nouvelles hypothèses qui pourront être réintroduites dans des versions ultérieures du modèle.

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Introduction

1The European Spatial Development Programme adopted by the EC member countries at Postdam in May (ESDP, 1999) recommends among other spatial planning objectives a "polycentric urban development" and initiatives for "rural-urban partnership". Such objectives would tend to counteract spontaneous trends, depending upon the context of globalisation of the economy and which are leading to concentration of population and activities in the largest urban regions whereas some remote rural regions fail to be integrated into the modernised territory. New policies are defined for controlling the spatial evolution of the European settlement system. This could start a new stage in a history where until now there was little regulation and, when it did exist, was operating within the boundaries of national settlement systems, with most of the time very limited effects on the spatial and hierarchical structures (Pumain, 1997a).

2A better understanding of the processes of change in settlement systems could provide insights for the definition of further policies. We think that both a long term perspective on the history of their development and simulations of theoretical models of change are necessary for building an evolutionary theory of settlement systems. This is needed for separating, in the history of the system, the general trends which form the non modifiable part of its dynamics, the specific changes which have altered its structure in a systematic way, and the non reproducible local events. Such a knowledge could help when trying to predict the future possible states of the European settlement system.

3As an empirical basis we use historical data bases which have been collected for European urban agglomerations (Bairoch et al. 1988, Moriconi-Ebrard, 1994). Unfortunately, information is available only for settlements over 5 000 (period 1600-1850) or 10 000 (period 1950-1990) inhabitants. We recall first which theoretical principles can be used as a framework for studying the historical change of a settlement system. We start the simulations with a simple model and after the deviations from historical observations possible improvements of the model are suggested.

Self-organization and urban systems dynamics

4The most remarkable feature of an evolutionary settlement system is the hierarchical and spatial structure which emerges as a consequence of a process of expansion. Every settlement system in the world is organised as a strongly but continuously differentiated hierarchy of sizes and levels of complexity, which tends to reinforce, as the system is expanding. Such systems keep for long their general ranking and structural peculiarities at the macro-geographical scale of the system, despite very fluctuating local responses to the general developing trends. The concept of settlement system has been designed for summarising the specific organisation and evolution of such sets of spatial entities.

5Numerous hypotheses have been formulated for explaining the universality of that structure by a general constraint which would govern the dynamics of the system (i.e. equilibrium between forces of concentration and dispersion, maximisation of social interaction, or agglomeration economies). According to the actual state of knowledge, no evidence has ever been demonstrated of the effectiveness of such constraints. There is no institution of regulation or control, no optimisation principle which can explain the observed dynamics of settlement systems. The most convincing interpretations consider that the macro-geographic structure of these systems is produced by the interactions between the units which compose it at a meso-geographical scale.

6Empirical and comparative studies of changes in population and activities involving large samples of settlements over long periods of time have shown that the changes tend to diffuse in the whole system, in a more and more rapid way as history goes. The general expansion of settlement systems, which adapt to changes without modifying their structure, is explained by the rapid circulation of information between towns and cities, which facilitates the diffusion of innovations. The behaviours of imitation and creative anticipation, which are imposed on urban actors by the competition between towns and cities where they have invested, result in a general growth of the urban system. This growth is distributed between towns and cities, according to their instantaneous capacity of adaptation to change, in a very fluctuating way through time and space. Such a random distribution of growth however, as demonstrated by Gibrat (1931), generates a very persistent hierarchical structure of towns and city sizes. It is therefore the interactions between towns which are producing the conditions of urban growth, and this process itself determines the general structure of the settlement system.

7Such a process is very similar to the dynamics of self-organising systems where "order by fluctuation" is occurring (Prigogine and Stengers, 1973, Allen, 1997). Most of the local changes in the intensity and speed of urban growth, apparently random, contribute to maintain the general macro geographic structure of the system. It is only at given times, that some of these internal fluctuations (as produced by a major innovation being invented in a few towns and not being immediately adaptable elsewhere) or a possible external perturbation (like a changes in political borders or a redefinition of foreign markets) may amplify the differences in the trajectories of the elements and alter in a significant way the relative position of some towns and cities in the system, changing the structure of the latter. Such bifurcation rarely occur but are responsible for the variety of hierarchical, functional and spatial patterns of urban systems which may be observed for instance among the European countries (Cattan et al., 1994). Because of that, settlement systems dynamics can be simulated by simple models of growth in a first approximation only, for periods of the history where strong path dependency effects maintain the system on a rather stable trajectory. Major historical changes have to be integrated as specific parameters when a more complex evolution has to be simulated (Pumain, 1997b).

8Among those, the modification of the properties of the geographical space where interurban interactions are developing is essential to consider. For centuries, interactions between towns have had only a local range, they were characterised by exchanges and rivalries between neighbouring towns. It is only because those effects, which limit at a local scale the growth of each town, are propagated from one town to the next, that a general structure which is perceptible and persistent can emerge at the macro-scale of the settlement system, as it can be observed in the case of the European urban system in Middle Age and modern time periods (Bretagnolle et al. 1998). Of course long distance travelling did exist since very ancient times and played a role in the diffusion of information (Braudel, 1979), but was not important enough for explaining the self-organization of urban systems. The general coherence of the historical development of the system was mainly produced by the local interactions. It is only with the Industrial Revolution that a considerable change in the range of spatial interactions has occurred, and that interurban competition has involved more and more distant cities. A major transformation happened in the structure of the settlement system as a consequence, involving a process of selection of cities after their accessibility and size, and producing a dramatic concentration of urban population and hierarchisation of the system.

9We shall see how a simple statistical model, which is a reasonable tool for simulating the effects of urban growth for periods where the dynamics trajectory of the urban system is stable, is unable to explain the changes which are observed when the properties of the interaction space are rapidly changing, and this spatial parameter has then to be included in the simulation model.

A simple model of urban growth

10In 1931 the statistician Gibrat suggested that the distribution of the population size in a set of settlements could be approximated by a lognormal distribution and that this particular form could be explained by a simple stochastic process of growth, that he called "law of the proportional effect" : if settlements of any initial size are growing during short times intervals according to small increases (compared to their size) which are proportional to their size and distributed at random respective to their size and to the previous pattern of growth distribution, then the final resulting distribution of settlement sizes is lognormal.

11Gibrat’s model, however stochastic, somehow postulates, in an implicit way, a form of interdependency between towns and cities : the order of magnitude of their growth rates is the same and modelled as a normal distribution defined by a mean and a standard deviation. The model can therefore only be applied to subset of settlements which share a common probability of growing (through natural increase and/or migrations). It is known from empirical studies that average growth rates can differ widely according to the time and subset of towns under consideration : for instance 1% of 2% per year during the urban transition of industrialised countries (Robson, 1972, see also Table 2), but 4 to 5% for towns of developing countries, and for shorter periods growth rates may rise as high as 10% per year in average (with a lognormal form of statistical distribution, Madden, 1955) for new settlement colonies.

12The intention is to reproduce the growth process which has occurred in developed countries during the last 300 years period, including the urban transition process.

13The simulation process includes the following steps :

  • start with an initial distribution of 200 settlement size and location. The statistical distribution of sizes can be uniform (mean initial size of 1500 inhabitants), or of a lognormal type (mean size around 1700 inhabitants), with a variable degree of concentration (maximum size between 16000 and 25000 inhabitants) ;

  • choose in the range of observed values for such parameters a mean value for settlement growth rates (between 1 and 4% per year) and their statistical dispersion (between 2% and 10% per year). A normal distribution of growth rates is generated for each time interval (ten years, the total period of simulation is 300 years long) ;

  • apply randomly one of the growth rates to the population of each settlement and compute the resulting population after each time interval (the growth rates are applied in a random way respective to settlement size and previous growth) ;

  • compute global indicators of the structure of the settlement system as slope of the rank-size distribution, mean and standard deviation of the distribution of logarithms of size at six date, primacy index, correlation between initial and final (after 300 years) population size distribution .

14Simulations were made by applying to the same initial size distribution different combinations of values for mean and standard deviation of the growth rates. Each set of values was applied for twenty different simulations with the same initial distribution. In total more than six hundred simulations have been made.

Results of simulations versus observations

15We present the results of the various simulations in linking the characteristics of the final distribution of settlement sizes to the parameters of the growth process, in order to check the ability of the model to replicate the evolution of observed settlement systems.

Effect of the type of the initial distribution

16Despite Gibrat’s affirmation, which corresponds to the mathematical properties of his model, pretending that the statistical form of the final distribution is lognormal, even if at the beginning of the process all settlements were of the same size, it is not possible to get a realistic town size distribution, starting with an initial uniform size distribution, after a 300 years simulation of urban growth. Whatever the values chosen for the mean and standard deviation of growth rates, among the realistic figures we have chosen, the sizes are not contrasted enough and their inequality index never reaches plausible values. This result tends to confirm an evolutionary view of urban systems, which proceed in a continuous way from already well differentiated sets of settlement (empirical evidence of a lognormal distribution of sizes for archaeological settlements has been brought by Fletcher, 1986). Therefore, all further results presented below rely on simulation experiences starting with a lognormal distribution.

Effect of the variation of the mean growth rates and standard deviation

17The variations of the mean growth rates have, as could be expected, an influence on the mean and total population size, but they remain without any effect on the inequalities of city sizes (slope of the adjusted Pareto distribution) nor on the primacy index. One may infer that the high primacy level which is observed more frequently in developing countries is not directly related to the highest speed of their urban transition.

18The variations in standard deviation can influence the maximum size, the degree of inequality of city sizes, and the primacy index, in the expected way : the larger it is, the higher the values are. It also affects the level of the correlation coefficient between the initial and final sizes of settlements : for values around 2% per year of the standard deviation of the growth rates, the correlation between the logarithms of initial and final size is above .9, whereas it drops to .7 for a value of 5% per year, .5 or .6 for 8% and .4 or .5 for values of 10%. The degree of persistency of the urban hierarchy is then strongly linked to the degree of heterogeneity in the growth rate. This effect is only slightly reinforced if the mean level of growth is high (Table 1). In any case, the degree of perturbation of the urban hierarchy in the simulations is, in average, less than what we get in the observed evolution of the urban system : for the same values of mean and dispersion of urban growth rates, the correlation between initial and final town size distributions is above .9 in the simulation and below .8 in the observations.

More regular initial situation

More contrasted initial situation

Standard Deviation

Mean growth rate = 0.01

Mean growth rate = 0.02

Mean growth rate = 0.01

Mean growth rate = 0.02

0.01

0.98

0.94

0.02

0.94

0.94

0.94

0.94

0.05

0.94

0.70

0.77

0.70

0.08

0.60

0.60

0.55

Table 1 : Mean correlation coefficient between initial and final size distribution of settlements in 20 simulations

19Indeed, between 1600 and 1990, the observed value of the correlation coefficient is only 0.69 between initial and final size of the 523 towns which had more than 5000 inhabitants in 1600 (which from another point of view can be interpreted as a remarkable persistency of the urban hierarchy over a three centuries period!). The observed correlation coefficient would be 0.81 for the 1172 towns and cities observed from 1800 to 1990.

20The initial distribution also has an effect : if it includes a larger town, it is more likely that the final distribution at the end of the simulation also has a larger main city.

Inequalities in city sizes

21The main departure of the model from reality is its incapacity to produce values of inequality in city sizes, which would be high enough to meet the observations. Initial distributions were given Pareto slope values which oscillate between .6 and .7, which are those observed by historians for city size distributions of the XVIIth or XVIIIth centuries. Contemporary values of this index are close to 1 in most European countries today (Table 2 and Figure 1).

Year

Number of cities (*)

Total population of the cities (in thousands)

Slope of the fitted Pareto distribution

R square of the fitted Pareto distribution

1600

606

9314

0.75

0.99

1700

603

10481

0.80

0.99

1800

1583

22149

0.69

0.99

1850

1706

36037

0.78

0.99

1950

3632

198061

0.91

0.99

1960

4090

233506

0.93

0.99

1970

4575

273948

0.94

0.99

1980

4970

300099

0.94

0.99

Table 2 : Evolution of concentration of European towns and cities

* : cities which have had, at some time between 1600 and 1850, 5000 or more inhabitants, and between 1950 and 1980, 10000 or more inhabitants.

Figure 1. Rank-size distributions of th European towns and cities (1600-1980)

22In order to get such a level of concentration of urban population, one has to use parameters values (standard deviation of growth rates) which are out of range compared to observations. Usually, the standard deviation values are less than the mean value, they may be slightly above sometimes but very rarely reach twice the mean, over ten years as well as for longer time intervals (Table 3). On the contrary, in most of the simulations, standard deviation values which are needed to reach a realistic level of contrast in the hierarchy of city sizes are at least twice the mean or more in order (Table 4).

Mean growth rate

Standard deviation

1700-1750

0.0033

0.0059

1750-1800

0.0035

0.0059

1800-1850

0.0073

0.0073

1850-1950

0.0105

0.0073

1950-1990

0.0101

0.0113

1950-1960

0.0138

0.190

1960-1970

0.151

0.186

1970-1980

0.107

0.170

1980-1990

0.048

0.104

1800-1990

0.0093

0.0049

Table 3 : Observed parameters values for the European system of cities

More regular initial situation

More contrasted initial situation

Standard Deviation

Mean growth rate = 0.01

Mean growth rate = 0.02

Mean growth rate = 0.01

Mean growth rate = 0.02

0.005

0.66

0.01

0.67

0.68

0.98

0.02

0.69

0.71

0.70

0.97

0.05

0.69

0.85

0.96

0.96

0.08

1.10

1.09

0.1

1.25

1.30

Table 4 : Mean slope of the adjusted Pareto distribution

23Therefore, there must be in reality some selection process affecting the urban growth process, which was actually detected from careful statistical analysis, and which gives a slight but systematic advantage in growth level to the largest cities when compared to the smaller towns. Such a process departs from Gibrat’s hypothesis and has to be added to the model.

24The same remark can be applied to the incapacity of the model to make emerge realistic level for the primacy index, which should be around 3 for urban systems in developed countries (Table 5 for national systems of cities, and Figure 2 for the European system of cities) but only reaches values below 2 in most of the simulations.

1600

1700

1750

1800

1850

1950

1990

France

4.3

5.2

5

5

6

8.3

7.4

Great-Britain

10

16

12

11

6

3.6

3.3

Belgium

1

1.2

1

1.1

1.2

1.7

1.8

Germany

1.1

1.3

1.3

1.3

2.9

1.1

1.3

Italy

1.8

2.2

2.1

2.8

2

1.2

1.3

Netherlands

1.2

3

4.7

4

2.5

1.1

1.2

Spain

1.7

1.9

2.3

1.7

1.3

1.1

1.2

Table 5 : Primacy index computed for several European countries

Table 5 : Primacy index computed for several European countries

Figure 2. Primary index of the European cities (1600-1990)

25It is only when very unrealistic values are given to the standard deviation parameter (10% per year) that in some simulations the index can take values well above three. Another process has then to be imagined if this particular feature of the urban systems has to be simulated.

Integrating two more processes : town selection and space-time compression

A general trend toward an increased hierarchical concentration

26The evolution of the concentration of urban population in Europe, when measured with such an index as the slope of the adjusted Pareto distribution, appears to be much more intense than it would be expected from a pure stochastic process of growth following all Gibrat´s hypothesis. It happens that for Europe, for all dates considered between 1600 and today, the quality of adjustment of the rank-size (or Paretian) model is good enough for using the values of the slope as a concentration index. The result shows a general trend towards a higher concentration in the European urban system (Table 2 and Figure 1). The trend is not a continuous one but has two stages of deconcentration, first between 1700 and 1800 (the explanation is that the smallest towns have grown much faster than the large cities during that period, de Vries (1984) also had noticed that) and after 1970 (that time, the growth of the largest cities is transferred towards their periphery, according to a suburbanisation process).

27This hierarchisation process has also been observed in national urban systems and in other parts of the world during the urban transition (Moriconi, 1993, Bretagnolle, 1999). Obviously it could be related mainly to the transformations which have happened since the revolution in industry and transportation means in the XIXth century, and which have affected the relative dimensions of the geographical space, according to a process of time-space contraction (Janelle, 1969, Forer, 1974 and 1978, Parkes and Thrift, 1980).

28The possible consequences of the acceleration of movements have given rise in the middle of XIXth century to contradictory hypotheses, which may recall the debates of today about the predictable effects of the new communication technologies. For a few observers of the development of the railway system, the improvements in accessibility would diffuse everywhere and then allow for a new spread out of population and activities (Pecqueur, 1839 quoted by Bretagnolle, 1999). Most of the analysts however have underlined the trends towards a higher concentration which is produced by the increase in the speed of transportation means. On one hand, the largest centres, which receive in a first stage the new infrastructure, spread their attraction over a broader field and capture the customers of the smallest. Small and medium-sized towns which are in an intermediary position between larger cities are especially threaten of decline. The reason for this trend is the shrinking of distance consequent on faster communications. On the other hand, the small- and medium-sized cities which had a relay function are short-circuited and their clientele is taken by the larger cities which thus extend their range of influence. The gain in communication speed allows for a reduction in the number of nodes which are necessary for serving a given surface. As in the same time the general wealth has been increasing, as well as urban population (from natural growth and rural exodus), the need for more urban centres and urban functions also has increased, and the small and medium size towns have not disappeared (whereas many villages died with the diminution of agricultural employment), but on the contrary most of small and medium size towns have not disappeared (whereas many villages died with the diminution of agricultural employment), but on the contrary most of them have developed themselves. However, the relative shrinking of space has been much more intense than the space filling processes, so the relative growth of small and medium-size towns has been in average less than the growth of the large cities.

29As measures of concentration give a transversal view of the urban system, a complementary information is needed through the longitudinal study of the evolution of the relative position of each city in the whole system. Dynamic trajectories of towns and cities can be provided by a clustering method for classifying towns and cities after the evolution of their population between 1600 and 1990.

Urban trajectories 1600-1990

30Due to the historical sources, the population figures before 1600 are not accurate nor complete enough for being considered in a mathematical treatment. The method also imposes the constraint that each town or city has to be described by a population figure at each date. So we arrive at a subset of about 450 towns and cities with complete series of population, for dates 1600, 1700, 1800, 1850, 1950, 60, 70, 80 and 90. The cluster analysis has been made with a chi-square distance, which allows for the comparison of towns and cities of different sizes and provides classes of towns which have the same profiles in terms of evolution of their growth rates.

31The groupings of these profiles give solid confirmations of the hypothesis which have been put forward in the theory. We get two groups, the first one subdivided in five subtypes and the second one in four subtypes (Figure 3 and 4). The largest group is made of more than 300 towns which underwent a relative decline. They are partly concentrated in regions like Sicilia, south of Spain, also along the Po river and in Flandria, but most of them are scattered all over Europe and many of them were already among the smallest urban centres in 1800. This result illustrates the theory of the tendency in the long term history towards a systematic relative decline of the weakest part of the urban hierarchies.

Figure 3. Dynamic tajectories of European cities (1600-2000)

Figure 3. Dynamic tajectories of European cities (1600-2000)

Figure 4. Dynamic tajectories of European cities (1600-2000)

32The second group illustrates another selection process, which systematically reinforces the upper part of urban hierarchies. Those cities have a larger size in average than the other groups, they have had a rather continuous growth, especially since the middle of nineteenth century. Some of them have slowed down their development in the recent period, they appear on the map as the large cities of the old industrial regions of Belgium, Germany, The Netherlands and United Kingdom. Another subgroup has had a more intense growth in the recent period, after 1950. It comprises mainly the capitals and metropolises of Mediterranean and Eastern countries.

33The selection process which determines the type of trajectory according to the initial size of the towns seems to be a more decisive constraint in the evolution of the urban system after the time of the industrial revolution, as it appears from the larger divergence of the curves of figure 3 between 1800 and today. More detail on this selection process linked to the main period of the urban transition can be attained by enlarging the scope of the analysis : a second typology of population trajectories between 1800 and 1990 has been made for the 1172 towns and cities larger than 5000 inhabitants in 1800 and for which we have complete series of population.

Urban trajectories 1800-1990

34This second typology clearly opposes two groups : towns and cities which have lost of their relative importance in the system, and cities which have increased it (figure 5 and 6). Among the first group, a category of 236 towns which had once reached populations close to 5000 inhabitants no longer appear in the most recent data base since they never reached the threshold of 10 000 inhabitants. The other classes of relatively declining towns and cities were all of a smallest size (10 to 14 000 inhabitants) at the beginning of the process in 1800 than those which succeeded in maintaining and increasing their relative weight (which had in average 21 000 to 29 000 in 1800, see table 6). The only exceptions are in the first group a class of large cities (even when London is excluded, their average size is 29 000 inhabitants), most of them located in Britain, which boomed during the first half of the nineteenth century and slowed down after, but their large size probably explain that in total they reach a global growth rate almost equivalent to the average on the whole period ; and in the second group a class of rather small towns in 1800 (14000 inhabitants) which happened to undergo a mushrooming growth in the second half of the twentieth century. Comparison of the graphs of figure 3 (typology on the period 1600-1990) and of figure 5 (1800-1990) shows very well that the appearance of a clear effect of the initial size on further growth trajectory of cities coincides with the time of the revolution in transportation means and space-time convergence.

Figure 5. Dynamic tajectories of European cities (1800-2000)

Figure 5. Dynamic tajectories of European cities (1800-2000)

Figure 6. Dynamic tajectories of European cities (1800-2000)

Average population in 1800

1800-1850

1850-1950

1950-1990

1800-1990

Very strong decline

10 000

0.24

0.18

0.61

0.28

Strong decline

10 000

0.88

0.51

0.32

0.57

Moderate then strong decline

14 000

0.75

1.01

0.39

0.81

Strong then moderate decline

14 000

0.44

0.67

1.80

0.84

Relative decline after 1850

56 000

1.89

1.31

-0.29

1.12

Nineteenth century growth

29 000

1.69

1.90

-0.01

1.44

Highest nineteenth century growth

21 000

1.23

2.41

0.61

1.72

Twentieth century growth

21 000

0.73

1.50

1.18

1.23

Highest twentieth century growth

14 000

0.84

1.53

2.57

1.56

Continuous growth

29 000

0.88

2.28

1.69

1.79

Average

20 000

0.92

1.45

0.87

1.19

Table 6 : Types of urban growth trajectories 1800-1990

(mean growth rate (percentage per year) for each class of cities in the cluster analysis)

N.-B. : The numbers written in bold are above average

35The effect of initial size in reducing the chances of growth of smallest towns is obvious, even if not deterministic. It also appears very well in table 7 which shows how towns slide into different size classes (as they are defined after a geometric progression, the number of jumps are comparable in terms of growth rates all over the table) : towns with largest initial size in majority have jumped three steps whereas the smallest only have jumped two.

Table 7 : Transition matrix of cities between sizes classes between 1800 and 1990 (population in thousands)

N.-B. : The numbers written in bold represent the maximum of the line and the diagonal of the table is underlined in grey colour.

36Comparing typologies on the two periods also attracts attention on another important fact. The map on figure 6 shows a rather systematic spatial pattern. The declining towns are scattered all over Europe, they illustrate the trend of simplification from below of urban hierarchies. But the other classes of trajectories are organised roughly in a centre-periphery pattern, starting from a core located in England and diffusing wavelike to north-western and middle continental Europe and then to southern and eastern Europe. The graphs on figure 6 (continued) show that the waves of relatively more rapid growth correspond to the first, then the second half of the nineteenth century, then to the recent period. One recognises the cycles of urbanisation which have crossed Europe since 200 years in accompanying the first and second industrial revolution and the end of the urban transition. On the contrary, on the map of the first typology (1600-1990), these waves were not apparent since this cycle was superimposed on the one of modern times, which smoothed the evolution of the towns and cities of British Isles and North-Western Europe. If a growth model is to be designed for helping in predicting the future dynamics of cities in a European competition, such "path dependency" effects also have to be considered in the model.

37In order to check the impact of the shrinking of space on the increasing hierachisation of urban systems, a few experiments have already been made (Bretagnolle, 1999). A growth model including spatial interaction between towns and cities, like the one used by Wong and Fotheringham (1990) for studying the fractal behaviour of urban systems or by Fik and Mulligan (1990) for analysing hierarchical interaction could be a starting point.

Conclusion and discussion

38Results of simulations show that a simple urban growth process like the Gibrat’s stochastic model is not sophisticated enough and has to integrate a spatial dimension in order to reproduce reasonably the hierarchical pattern of the evolution of the urban systems. Modern economic theory (see for instance the recent discussion about cities competitiveness and Krugman’s ideas between Begg and Boddy in Urban Studies, 1999) postulates that increasing returns to scale are the explanation for cumulative urban growth. The theory points out essentially to agglomeration economies (which makes the process of urban growth non-linear) and unequal information (which allows for differences according to location decision). If to a certain extent space is therefore introduced in the theory, as well as time (via the non linear process of accumulation), the theory obviously miss history, not in the idiographic sense, but as a set of nomothetic processes which introduce a path dependency and cyclical features in the relative dynamics of competing cities. Many authors have studied this (for instance P. Allen, D. Dendrinos in modelling, P. Bairoch, F. Braudel, J. de Vries, N. Cattan et al. about the case of European cities) but they are never referred to in the discussion... We think that hypotheses deserve to be tested, which would link the comparative advantage of the large cities to the level of complexity of their economy. This gives them a temporary advance in the hierarchical process of diffusion of the innovations and a spatial advantage in the interurban competition by enlarging the range of their activities. In other words, we would substitute, or at least add, a geographical explanation to the economic one. We also would like, instead of deriving entirely the explanation from micro-economic processes, to assess a relative autonomy of the dynamics of the urban systems at the macro geographic level. A simulation model is experimented in order to test these hypotheses (Bura et al. 1996).

39Coming back to the practical question of predicting the future evolution of towns and cities in an urban system, we think that considering their trajectories on a long term evolution could be useful, since there is on the whole a very large, if not entirely deterministic, temporal and geographical consistency in the relative dynamics of competing cities. However, some precautions should be taken however when interpreting and prolonging the trends. A population trajectory showing a relative growth (compared to evolution of the total urban system) can be interpreted as an indicator of competitive performance and sustainability of economic growth. But this interpretation has to combine an historical knowledge about the significance of cycles in urban growth. The connection between population and economic growth has to be replaced in the historical context of urbanization. If it is legitimate to interpret population growth as a surrogate for economic growth over the last centuries, for interpreting the last decades evolution correctly, one has to consider the time lag in the urban transition between northern–western and southern-eastern Europe. The recent relative population growth in the south and east is partly the reflection of an economic boom following the "shift to the south" and of the recent development of the East but also partly results from the lagged urban transition in these areas, which will not continue in the future. More simulations for testing that should use a model with variable mean growth rates according to time and region differentials.

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Allen P.M. 1997, Cities and regions as self-organizing systems. Amsterdam, Gordon and Breach.

Bairoch P., Batou J., Chèvre P., 1988, La population des villes européennes de 800 à 1850. Genève, Droz, Centre d’histoire économique internationale.

Begg I. 1999, Cities and Competitiveness. Urban Studies, 5-6, 795-805.

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Boddy M. 1999, Geographical Economies and Urban Competitiveness : a critique. Urban Studies, 5-6, 811-842.
DOI : 10.1080/0042098993231

Bretagnolle A. 1999, Les systèmes de villes dans l’espace-temps : effet de l’accroissement des vitesses de déplacement sur la taille et l’espacement des villes. Université Paris I, thèse de doctorat.

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Bretagnolle A., Pumain D. Rozenblat C. 1998, Space-time contraction and the dynamics of urban systems. Cybergeo, 61, 12 p.
DOI : 10.4000/cybergeo.373

Braudel F. (1979), Civilisation matérielle, économie et capitalisme, XVe-XVIIIe siècle, Paris, Armand Colin, 3 vol., Collection Livre de Poche.

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Bura S. Guérin-Pace F. Mathian H. Pumain D. Sanders L. 1996, Multiagent Systems and the Dynamics of a Settlement. System. Geographical Analysis, 28, 2, 161-178.
DOI : 10.1111/j.1538-4632.1996.tb00927.x

Cattan, N., Pumain, D., Rozenblat, C., Saint-Julien, Th. (1994), Le système des villes

européennes, Anthropos, Coll. Villes, 2e édition 1999.

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Cheshire P. Carbonaro G. 1996, Urban economic growth in Europe : testing theory and policy. Urban Studies, 33, 1111-1128.
DOI : 10.1080/00420989650011537

ESDP 1999, European Spatial Development Perspective, Towards balanced and Sustainable Development of the Territory of the EU. Potsdam, European Committee on Spatial Development, 10-11 May.

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Fik T.J. Mulligan G.F. 1990, Spatial Flows and Competing Central Places : Toward a general Theory of Hierarchical Interaction. Environment and Planning A, 22, 527-549.
DOI : 10.1068/a220527

Fletcher R. 1986, Settlement in Archaeology : world-wide comparison. World Archaeology, 18, 1, 59-83.

Forer P. 1974, Space through time : a case study with New Zeland airlines, in Cripps E. (ed.), Space-time concepts in urban and regional models, London, Pion, 22-45.

Forer P. 1978, Time-space and area in the city of the Plains, in T. Carlstein, D. Parkes, N. Thrift (eds.), Timing space and spacing time, vol. 1, London, E. Arnold.

Gibrat R. 1931, Les inégalités économiques. Paris, Sirey.

Janelle D. G. 1969, Spatial reorganisation : a model and concept. Annals of the Association of American Geographers, 343-368.

Jensen-Butler C., Shachar A. van Wesep J. (eds) 1997) European Cities in Competition. Aldershot, Avebury.

Kunzmann, K.R., Wegener, M. (1991), The pattern of urbanisation in Western Europe 1960-

1990. Institut für Raumplanung, Universitat Dortmund.

Moriconi-Ebrard F. 1993, L’urbanisation du monde depuis 1950. Paris, Anthropos-Economica.

Moriconi-Ebrard F. 1994, Geopolis. Paris, Anthropos-Economica.

Parkes D. N., Thrift N. J. 1980, Times, spaces and places : a chronogeographic perspective, England, John Wiley & Sons.

Pecqueur C. 1839, Economie sociale : des intérêts du commerce, de l’industrie, de l’agriculture, et de la civilisation en général, sous l’influence des applications de la vapeur. Paris, Dessaert éditeurs.

Prigogine I. Stengers I. 1973, La nouvelle alliance. Paris, Gallimard.

Pumain D. Haag G. 1994, Spatial patterns of urban systems and multifractality, in Evolution of Natural Structures, 3rd International Symposium of the Sonderforschungsbereich 230, Universität Stuttgart, 4-7 oct., Natürliche Konstruktionen, Mitteilungen des SFB 230, Heft 9, 243-252.

Pumain D. Saint-Julien T. 1996 (eds), Urban networks in Europe. Paris, John Libbey-INED, Congresses and Colloquia, 15, 252 p.

Pumain D. 1997a , Settlement Size Dynamics in History, in Holm E. (ed), Modelling Space and Networks. Umea, GERUM, Proceedings from 7th Colloquium of Theoretical and Quantitative Geography, Stockholm, sept. 1991, 3-32.

Pumain D. 1997b, Vers une théorie évolutive des villes. L’Espace Géographique, 2, 119-134.

Pumain D. 1998, An evolutionary model of urban systems. IGU Commission on Urban Development and Urban Life, Bucarest.

de Vries J. 1984, European Urbanization 1500-1800. London, Methuen.

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Wong D.W.S. Fotheringham A.S. 1990, Urban systems as examples of bounded chaos : exploring the relationship between fractal dimension, rank-size, and rural-to-urban migration. Geografiska Annaler, 2-3, 89-99.
DOI : 10.2307/490553

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Table des illustrations

URL http://cybergeo.revues.org/docannexe/image/566/img-1.png
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Titre Table 5 : Primacy index computed for several European countries
URL http://cybergeo.revues.org/docannexe/image/566/img-2.png
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URL http://cybergeo.revues.org/docannexe/image/566/img-3.png
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Titre Figure 3. Dynamic tajectories of European cities (1600-2000)
URL http://cybergeo.revues.org/docannexe/image/566/img-4.png
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URL http://cybergeo.revues.org/docannexe/image/566/img-5.png
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Titre Figure 5. Dynamic tajectories of European cities (1800-2000)
URL http://cybergeo.revues.org/docannexe/image/566/img-6.png
Fichier image/png, 38k
URL http://cybergeo.revues.org/docannexe/image/566/img-7.png
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Référence électronique

Anne Bretagnolle, Hélène Mathian, Denise Pumain et Céline Rozenblat, « Long-term dynamics of European towns and cities : towards a spatial model of urban growth  », Cybergeo : European Journal of Geography [En ligne], Dossiers, document 131, mis en ligne le 29 mars 2000, consulté le 03 décembre 2016. URL : http://cybergeo.revues.org/566 ; DOI : 10.4000/cybergeo.566

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Auteurs

Anne Bretagnolle

UMR Géographie-cités, Université Paris I13 rue du Four 75 006 Paris, Franceanne.bretagnolle@parisgeo.cnrs.fr

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Hélène Mathian

UMR Géographie-cités, Université Paris I13 rue du Four 75 006 Paris, Francemathian@parisgeo.cnrs.fr

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Denise Pumain

UMR Géographie-cités, Université Paris I13 rue du Four 75 006 Paris, Francepumain@parisgeo.cnrs.fr

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Céline Rozenblat

UMR Espace, Université de Montpellier 317 rue Abbé de l’Epée 34 000 Montpellier, Francerozenblat@mgm.fr

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Droits d’auteur

© CNRS-UMR Géographie-cités 8504

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