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Settling the World

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Léna Sanders

Chapter 7: Transition 4: Modelling the emergence of cities

Denise Pumain, Clara Schmitt et Sébastien Rey-Coyrehourcq

Texte intégral

Introduction: one or two ‘urban’ transitions?

  • 1  Prigogine Ilya, Stengers Isabelle, La nouvelle alliance, Paris, Éditions Gallimard, 1979.
  • 2  Pumain Denise, Saint-Julien Thérèse, Sanders Lena, Villes et auto-organisation, Paris, Éditions Ec (...)
  • 3  Sanders Lena, Système de villes et synergétique, Paris, Éditions Anthropos, 1992.

1The majority of the world’s population now lives in cities, and the expansion of this form of habitat seems both universal and irreversible. The statistical services of the United Nations predict that, before the end of the twenty-first century, more than three-quarters of human beings will be urban-dwellers. Now, cities appeared in the history of humanity only about 6,000 years ago. With their emergence, which from the beginning situated cities within interconnected groups of systems of cities, and which occurred independently in several regions of the world about 3,000 years after the ‘Neolithic revolution’ had sedentarised and densified the populations, we have a highly interesting example of transition. We might consider it as a major bifurcation in the history of settlement systems, since we are dealing with an apparently irreversible transition involving separation between a regime prior to urbanisation, namely before 6,000-6,500 years BP, when cities emerged, and a regime that still persists, for the urban organisations that emerged at that point have as yet no foreseeable end. We prefer, however, to speak of emergence rather than bifurcation in the sense applied by the modellers of auto-organisation,1 23since forms of alternative organisation to the current model of urban systems are difficult to imagine; in any case, they cannot be observed. This particular status of ‘open transition’, which establishes another durable regime after an emergence, is not a unique case in the history of societies. The invention of language would be another example, since there is no example of a society’s abandoning this practice, even if other forms of interpersonal communication (writing, the book, the telephone, internet…) have since arrived to supplement it.

  • 4  Pumain Denise, Paquot Thierry, Kleinschmager Richard, Dictionnaire La ville et l’urbain, Paris, Éd (...)

2Moreover, it so happens that since it was proposed by the demographer Wilbur Zelinski in 1971, the expression ‘‘urban transition’ (transition urbaine)4 has designated a process other than that which led to the creation of cities and systems of cities. It refers to a phase of acceleration and generalisation of the growth of cities that began towards the end of the eighteenth century in the countries presently developed and has been repeated, especially since 1950, in developing countries. Identified originally as “migratory transition”, it has led human settlement to pass from a more or less sable regime, with a proportion of urban population in the world’s total limited to an upper level of about 10%, to more than 50% today, undoubtedly to attain some 75 or 80% at the end of the century. This ‘urban transition’, in the strict sense, whose bases are studied in chapter 12 of this volume, will have taken all of three centuries to become diffused through the entire world. (In fact, its duration varied between two centuries and fifty years or so, according to its degree of precocity in different regions.) In particular, it has been associated with considerable social, technical and economic transformations, well summed up in the expression ‘industrial revolution’. It has also had major political consequences for the world order.

  • 5  Garmy Pierre, Villes, réseaux, et systèmes de villes, Paris, Éditions Errance, 2012.

3We will concentrate in this chapter exclusively on the question of the emergence of cities. This occurred in several regions of the world independently and at significantly different dates (from 6,000 to 3,000 BP), and the average duration of the ‘transition’ associated with this moment is very difficult to determine. Its beginning is sufficiently well documented in each region, but at what date can one consider that the cities have definitively ‘emerged’ in a given region? What criterion should be applied to decide this? Should one consider the proportion reached by the urban population within the total population, or a size threshold fixed arbitrarily for one or more large cities, or rather the number or density of cities, or their resilience in the face of natural catastrophes or various invasions or hostile actions? The sources, still relatively incomplete, that bear on these processes scarcely make possible reasonable choices. Whatever the case, the very nature of this ‘open’ transition over a considerably extended historical span obliges one to make choices regarding the period to be considered which have important consequences for the modelling. Our representation of the period of emergence of cities also integrates the fact that the cities do not appear in an isolated manner but are organised from the start into ‘systems of cities’, as is stressed by the archaeologist Pierre Garmy,5 although journalists sometimes seem unwilling to understand this. For example, the New York Times still used the title, ‘the city that was at the origin of all the cities’, in an article of 10 May 2010, taken up by the Courrier International, on the subject of the richness in artefacts in the tell discovered on the site of Zeidan in northern Syria. The underlying idea of an ‘invention’ of the city, supposed to have appeared suddenly in one place alone and subsequent diffused throughout the whole world, is fallacious.

A multi-situated transition

  • 6  Schmitt Clara, ‘Modélisation de la dynamique des systèmes de peuplement : de simpopLocal à simpopN (...)
  • 7  Rey-Coyrehourcq Sébastien, ‘Une plateforme intégrée pour la construction et l’évaluation de modèle (...)
  • 8 The ERC programme GeoDiverCity developed a number of models of urban dynamics. See URL online: http (...)

4Let us begin by explaining our decision to model this transition by means of a model of simulation. In the absence of a historical theory well enough established to account for the emergence of cities, we have wished to realise a model permitting us to test plausible generic theoretical propositions in order to furnish a viable interpretation of this transition, even if it remains partial and conditioned by the hypotheses we have introduced. The simulation model SimpopLocal,6 7which we developed within the framework of the ERC GeoDiverCity,8 was the object of a number of presentations during meetings of the ANR TransMonDyn, at which its authors benefitted from interactions with historians and archaeologists. This model constitutes an innovation, by virtue of its employment of original methods of validation (set out below). For the first time it is possible to verify the character, at once necessary and sufficient, of the explanatory propositions which are included in the rules of a model. SimpopLocal is designed to reconstruct the emergence of a system of cities whose properties are common to systems observed historically. In a second phase, that generic model thus constructed and validated could be confronted with particular case studies observed by the historians and archaeologists and perhaps acquire a second level of validation through confrontation with empirical data.

Defining the city

  • 9  Marcus Joyce, Sabloff Jeremy, The ancient City. New perspectives on Urbanism in Old and New World, (...)

5The standardising approach indispensable to modelling is not, however, universally accepted by historians and archaeologists. Some consider the unique nature of each city as irreducible and thus contest the idea that, beyond the diversity of forms, it would be possible to recover processes common to most urban developments. Joyce Marcus and Jeremy Sabloff9 recall the existence of this debate in the introduction of a volume which proposes, moreover, a survey of knowledge concerning pre-industrial urbanisation.

  • 10  Childe Gordon, ‘The Urban Revolution 1950’, The Town Planning Review, 21(1), 1950, p. 3-17.
  • 11  Wheatley Paul, The pivot of the four quarters, Chicago, Éditions Aldine, 1971.
  • 12  Bairoch P., De Jéricho à Mexico, op. cit.

6Recognising general principles implies, to start with, being able to agree on a definition of what constitutes the city. In the historical sciences (in the broad sense, including archaeologists and historians), the question does not really seem to have been settled, whether one relies on material archaeological traces or on written sources. Discussions on the origin of cities are closely linked to a historical axiology, which leads to hierarchising the factors susceptible of explaining their appearance. This is often associated with a search for the motivation of those responsible for creating the city, and thus generally supposes that the cities were originally conceived for the defence and organisation of a political territory or for the promotion of a religion, an approach that would place them in the category of social institutions responding to a collective intentional function. These theses, defended, for instance, by Gordon Childe10 and Paul Wheatley,11 place politics, but also semiotics and the symbolic, at the heart of the definition of the formation of the urban reality. But others, such as Paul Bairoch,12 defend the idea of the importance of economic factors in the origins of the phenomenon.

  • 13  Bairoch P., De Jéricho à Mexico, op. cit.

7Most historians today seem to agree, at any rate, in recognising that in the majority of the most ancient sites excavated, the palace, the temple and the market are the omnipresent elements. The material traces therefore go as far as including, alongside the decisive interventions of the authorities, political and religious, those accompanying them of the artisans and shopkeepers, no less interested by other motivations. The city is a human conglomeration of greater size than villages, and more organised, issued progressively from the territory which it encompasses and which has permitted it to develop, thanks to a surplus of the resources produced, most often by agriculture.13 The representation one can give of the city at the moment of its emergence, then, is that of an evolving continuity between this settlement, agricultural and rural, and urban settlement. The city develops with a diversity of attributes which testify to the multiple functions it exercises, responding to a diversity of intentions stemming from initiators of action who, while coordinated, are not necessarily hierarchised beneath a single power of conception and action.

  • 14  Mumford Lewis, La Cité à travers l’Histoire, Marseille, Éditions Agone, 1961.
  • 15  Garmy P., Villes, réseaux, …, op. cit.

8Nevertheless, certain archaeologists continue to propose a definition of the city which merges with the list of elements or functions which should be present in order to justify that one is speaking of a city. The exercise, attempted by G. Childe and Lewis Mumford,14 among numerous others, undoubtedly remains useful in guiding the investigations of archaeologists or historians, but from our perspective on urban evolution over the long term, it cannot be disconnected from each period observed in the history of cities, precisely because the cities opened the possibility of greater social division of work and the invention of new functions. More than the presence of this or that attribute at a given moment, therefore, it is rather the progression of the range of functions on a site which would attest to the vitality or decline of the local urban project.15

Independent, therefore ‘necessary’, emergences

  • 16  Diamond Jared, Guns, Germs, and Steel: The Fates of Human Societies, Éditions Norton & Company, 19 (...)

9The Neolithic revolution took place in regions offering conditions apparently favourable to the development of agriculture using rudimentary technical means. It always involves social organisations in groups somewhat larger than those of hunter-gatherers, as well as the production of artefacts for the storage of harvests (see the discussion of this subject in chapter 6). Mesopotemia, the valleys of the Nile and the Indus, southern China and central America are the principal places where this phenomenon appeared, spread out between roughly 10,000 and 3,500 years BP. The biologist and geographer Jared Diamond16 has recorded the resource potentials of these regions in animal species that can be domesticated and vegetation that can be cultivated, hence able to favour these multiple emergences in the Neolithic in subtropical latitudes.

  • 17  Bocquet-Appel Jean-Pierre, ‘La transition démographique agricole au Néolithique’, dans J.-P. Demou (...)
  • 18  Demoule Jean-Paul, Une histoire globale à l’âge du Bronze; online at http://blogs.histoireglobale. (...)

10The main change brought about by this revolution was the multiplication by a factor of about 100 of the population densities in the regions concerned,17 that demographic growth and the considerable increase in the potential for personal interaction that it supposes being already part of the explanation of the appearance of cities. In his blog on global history, Jean-Paul Demoule18 gives the following summary of this emergence, which took place after the agricultural revolution of the Neolithic:

  • 19 Agricultural societies in their turn generated a new global historical phenomenon resulting in lar (...)

‘Les sociétés agricoles à leur tour ont généré un nouveau phénomène historique global issu en grande partie de l’essor démographique provoqué par le nouveau mode de production : l’émergence de sociétés hiérarchisées de plus en plus complexes, lesquelles débouchent à plus ou moins brève échéance sur des formations étatiques et urbaines à partir du IVe millénaire avant notre ère, d’abord aux mêmes endroits que les foyers néolithiques initiaux.’19

  • 20  Bairoch P., De Jéricho à Mexico, op. cit., p. 131.

11The historian Paul Bairoch20 insists on the ineluctable character, in a sense, of the appearance of cities, since they arose in all the regions of the world where agriculture was invented, at varying temporal intervals and in an independent manner, thus with no involvement of spatial diffusion:

  • 21 In practically all the cases where agriculture is involved, several millenaries later the urban re (...)

‘Dans pratiquement tous les cas où l’on est en présence d’une agriculture, quelques millénaires plus tard apparaît le fait urbain. Rares sont les régions où, 2000 ans après l’existence d’une véritable agriculture, on ne constate pas l’apparition des villes.’21

12Cities emerged only long after the sedentarisation associated with agricultural production, a period from two to three thousand years being necessary, according to Paul Bairoch, before a sufficient accumulation of surplus production could permit devoting time to other activities besides subsistence and begin the process of social division of labour. Another factor, however, seems to us essential in explaining the rare occurrence of the emergence of cities in the very small territories where a form of agriculture could have been invented and practised – for example, in certain tropical archipelagos of the Pacific. In fact, the social functionalities to which cities respond do not find expression unless exchanges over more or less long distances with other cities can become established and participate in the durability of each.

From dispersed villages to a network of cities

  • 22  Paulus Fabien, ‘Coévolution dans les systèmes de villes : croissance et spécialisation des aires u (...)
  • 23  Berry Brian, Cities as Systems within Systems of Cities 1964’, Papers in Regional Science, 13(1), (...)
  • 24  Pred Alan, City systems in advanced societies, London, Éditions Hutchison, 1977.
  • 25  Pumain Denise, ‘Les systèmes de villes’, dans Encyclopédie de géographie, ed. A. Bailly, R. Ferras (...)

13Thus, most historians have put less emphasis on an aspect that seems to us essential in the dynamic of cities. Indeed, cities have never emerged in an isolated manner: they have always developed more or less simultaneously in relation to other cities, forming relations involving multiple exchanges that give rise to processes of co-evolution,22 and these have led geographers to formulate the concept of ‘system of cities’.23 2425Over the long term of the history of human societies, systems of cities may thus appear as an extremely durable invention, an adaptable instrument for managing resources and controlling territories and networks. This function of social adaptor is multiple; it operates on different scales, within both space and time. It does not especially involve a social ‘institution’, an organisation with clearly defined objectives, which would result from a social convention conceived to that end, even if the ‘civilising’ role of the groups of cities has often been perceived by the religious or political powers, whether the latter were founders of networks of cities, colonisers or improvers.

  • 26  Reymond Henri, ‘Une problématique théorique’, in Problématiques de la géographie, ed. H. Isnard, J (...)

14By virtue of such entering into relations with other territories controlled by other cities, a major societal function of the emergence of cities is thus the reduction of uncertainties tied to the context of the local environment,26 whether the chance factors are of climatic origin or relate to the limits of natural resources, or localised catastrophes, natural or conflictual in origin. Predatory toll or commerce, but also the exchanges of information which accompany them, contribute to reinforcing the basis of knowledge and of local products which assure the resilience of the urban entity. This capacity is linked to the division of urban work, to the degree that it requires professions specialised in these activities, hence a social division of work which frees up for certain persons time for activity not tied to immediate production.

  • 27  Reynaud Jean, ‘Villes’, in Encyclopédie nouvelle, ed. C. Gosselin, Paris, t. VIII, 1841, pp. 670-6 (...)
  • 28  Robic Maric-Claire, ‘Cent ans avant Christaller, une théorie des lieux centraux’. L'Espace Géograp (...)
  • 29  Reclus Elisée, L’homme et la terre, Paris, Éditions Librairie Universelle, 1905.
  • 30  Christaller Walter, Die Zentralen Orte in Süddeutschland : eine Ökonomisch-Geographische Untersuch (...)
  • 31  Kohl Johann Georg, Der Verkehr und die Ansiedelungen der Menschen in ihrer Abhängigkeit des Gestal (...)
  • 32  Reclus Elisée, ‘The evolution of Cities’, The Contemporary Review, 67(2), 1895, pp. 246-264.
  • 33  Pirenne Henri, Les villes du Moyen-Age, Paris, Éditions PUF, 1925.
  • 34  Bird James, Centrality and cities, London, Éditions Routledge, 1977.

15In this regard, it is probable that the process of social interaction, generator of innovation and motor of the development of cities, is multi-scalar from its origin, produced within cities as well as between them. For a long time two ideas of the genesis of cities have been opposed: one which would be endogenous to a given territory, producing cities which were initially local markets, where other functions termed “central functions” developed27 282930; while other cities would have emerged as a result of exogenous factors, as interfaces with the networks of circulation or stopping-places on commercial routes, that process implying interactions over longer distances 31323334. If the circulation of information clearly reinforces the probability of the diffusion of innovations, the two interactive processes, locally and at a distance, no doubt played a part in the development of most cities. That is attested by the existence of exchanges over long distances from the epoch of their emergence (the routes of obsidian in the Mediterranean and the Red Sea have existed for 8,000 years, as has the maritime commerce on the northern shores of the Indian Ocean).

  • 35  Fletscher Roland, ‘Settlement Archaeology: World-Wide Comparison’, World Archaeology, 18(1), 1986, (...)
  • 36  Liu Li, ‘Settlement patterns chiefdom variability and the development of early states in North Chi (...)
  • 37  Pumain Denise (ed.), Hierarchy in natural and social sciences, Dordrecht, Springer, 2006
  • 38  Gibrat Robert, Les inégalités économiques, Paris, Éditions Sirey, 1931.

16From their origin, settlement systems have been characterised by a highly unequal distribution in the size of the settlements composing them 3536. These sizes were spread out according to a lognormal distribution, and over time cities maintained that property of hierarchical inequality, reinforcing it over the course of history.37 This hierarchical differentiation is explained by the multiple exchanges that took place between the cities, and which induced interdependencies between them, a co-evolution of ‘proportional effect’ formulated in 1931 by the statistician Robert Gibrat.38

A highly stylised generic model

17We have thus developed a model of the emergence of cities that reproduces a progressive transition linked to the emergence of cities in settlement systems based on spatial interactions. This transition is defined as the passage from a group of localised villages of small size (counting their populations by a few dozens) and little differentiated, to a hierarchised system of cities (the largest able to attain the level of several thousand inhabitants), the driving force of this evolution being the innovation engendered by social interaction and its diffusion between cities).

18In doing this, we have therefore chosen to reduce the difficultly of a properly historical modelling of the appearance of cities, which would suppose representations relative to the socio-geopolitical and technical organisation of the spaces inhabited, particular to each epoch and also, undoubtedly, to each of the territories considered. Instead, we construct a model inspired by a geographic dynamic of cities and the relations they possess with each other. We reconstruct by this simulation the passage between two regimes applying to the existence of settlement systems – from those constituted exclusively of villages more or less homogenous in their dimensions and composition, formed of aggregates of small size, and whose survival depends essentially on ‘ecological’ relations with an environment close at hand, towards more hierarchised settlement systems including more socially complex cities than those of villages, and whose survival depends to a growing extent on distant relations with other cities and more remote resource sites.

19The model which we have conceived to represent the stylised facts associated with this emergence is thus generic, in that the properties which are simulated are still current for representing the evolution of settlement systems, based on an abstract conception of cities and systems of cities. Our modelling is certainly directed, in its realisation and its own parameters, towards the period of the emergence of cities, but it may also suit, because of the fundamental rules that have been selected for the model, an understanding of urban transition according to a definition which would apply as far as the contemporary period.

Multi-agent modelling

  • 39  Site Simpop : http://simpop.parisgeo.cnrs.fr
  • 40  Cottineau Clémentine, ‘L’évolution des villes dans l’espace post-soviétique: observation et modéli (...)

20Since 1996, we have developed a series of SIMPOP39 models whose objective is to simulate the evolution of systems of cities over the medium and long term. These models translate the principles of an evolutive theory of cities, which integrates the stylised facts observed from medium and long-term evolutions of numerous systems of cities world-wide. These are the multi-agent models that have the particularity of situating themselves on an intermediate geographic scale, for they represent interactions, not between individuals, but between cities, thus between localised and heterogenous collectives. The SIMPOP models reconstruct the asymmetries of the flow of exchanges between cities to engender differential increases and specialisations, which reproduce the hierarchical and functional characteristics of the territorial organisation of systems of cities.40 Until now, the models that we constructed represented this evolution as a relatively autonomous evolution, in which relations with the environment played only a minor role. In the SimpopLocal model, conceived to simulate the emergence of cities, the presence of a constraint on population increase exercised by the availability of resources in the neighbourhood of each settlement marks the specificity of this historical period, in which the dependence of habitats in respect of local conditions was still very great.

21With reference to modelling, SimpopLocal also adds a double originality compared with previous Simpop models. First, SimpopLocal represents a simplified version of the urban dynamic, which does not any longer qualitatively distinguish the successive urban functions during the evolution of urban systems but transposes them in an abstract process of innovation. Moreover, the process of the appearance of these innovations is built as an endogenous component into the dynamic of the model, while in other Simpop models it was still managed as something exogenous. In this way, SimpopLocal involves lighter modelling than the other Simpop models, for the number of mechanisms and rules of simulation is considerably reduced. In turn, this simplification is an advantage which permits better exploration of the simulations with the aim of improving the evaluation of multi-agent modelling.

22Simplification was all the more necessary in any case because, despite what Kohler and Crabtree were able to do (cf. chapter 6), we do not have available, in any of the regions where cities emerged, data sufficient, in quantity and precision, to envisage a rigorous calibration of the model according to empirical observations. We have taken from the literature not merely stylised facts to establish the rules of functioning of the model, but also related information to estimate a priori the orders of magnitude characteristic of urban evolutions at this period.

Principal rules of the model

23The SimpopLocal model simulates growth centres in settlements consisting mainly of sedentarised farmers. This growth is limited by local constraints, which are progressively pushed back by successive innovations. This scenario takes place in regions whose population density is already markedly augmented with respect to the density characteristic of hunter-gatherers, thanks to the effect of the sedentarisation of agricultural practices and the accumulation of resources by means of storage. The landscape simulated is composed of 100 places of settlement. Each place of settlement corresponds to a localised human group, identified by its permanent habitat and exploiting, for its survival, the resources of its immediate environment. The settlements are modelled by fixed agents.

24Each is described according to three variables: location within a simulated space (x, y), size of the population (P) and quantity of resources available in its local environment (R). The quantity of available resources is quantified by the number of inhabitants and may be understood as the carrying capacity allowed by the local environment. This environment is not considered explicitly, for the resources allowing population increase cannot be reduced to the agricultural production under the city’s control but include the ensemble of its capacities for production and trade. The quantity of available resources of each settlement depends on an initial value but especially on the abilities applied by the local population for their exploitation, which evolve over time. This exploitation is realised locally, and the division or trade of resources between different centres are not explicitly represented in this model. The skills in exploiting resources are expressed in the model by the number of innovations which each settlement was able to acquire, whether through local invention or by exchange with other settlements.

25Modelling dynamics of growth for each settlement supposes that its demographic size is conditioned by the resources available and thus by the skills employed by the population for exploiting them. The acquisition of innovations makes it possible to develop the skills for exploiting the resources and thus to increase the quantity of resources available locally. Innovation is understood here in a broad and abstract manner, as every socially accepted invention. It may represent a technical invention, a discovery, a form of social organisation, a new practice… Each new acquisition of an innovation by a settlement permits it to cross a new threshold of the carrying capacity of its place of implantation, and therefore to gain a margin of demographic growth.

26The simulated innovations are not differentiated qualitatively. The effect of their acquisition on each settlement will depend on the state of that settlement. Each innovation acquired by a settlement is modelled as an agent. It may appear spontaneously within this settlement, according to the probability of interaction between the local inhabitants, or be acquired through spatial diffusion, as a function of an interaction potential of the gravitational kind between settlements. Indeed, although commercial exchange is not explicit in the model, the settlement units interact in a network, and this permits the inhabitants to exchange knowledge regarding innovations which improve their skills for exploiting resources (figure 1).

  • 41  Schmitt C., ‘Modélisation de la dynamique…’, op. cit., p. 169.

Figure 1: Graph41 of settlements showing the initial situation of the SimpopLocal model.

Figure 1: Graph41 of settlements showing the initial situation of the SimpopLocal model.

27The dynamics of settlement growth is simulated according to the hypothesis that their size is a function of the quantity of the resources locally available. This growth function is inspired by Verhulst’s model (1838) in its discrete form, also called logistic growth model up. In the course of the simulation, the size of the settlement tends progressively towards the maximum population, defined by the limiting factor (available resources), following a curve in S known as a logistic curve and characteristic of evolutions with a tendency toward exponential increase but constrained by a limiting value – though here, of course, with a possible change of the maximum in the course of time; the result, therefore, is a sort of succession of logistic curves.

Measuring and calibrating the parameters of the model

  • 42  Hansen Mogens Herman, ‘Analyzing Cities’, in The Ancient City, ed. J. Marcus, J. Sabloff, 2008.

28SimpopLocal depends on a limited number of parameters, less than ten in all, which must be estimated to calibrate the model (tab 1). Rather than trying to come close to a particular situation observed in archaeology, we have drawn on the literature to estimate the approximate possible value of these parameters. It is, for instance, relatively easy to attribute a value to ‘Rmax’, the maximum size attained by the cities, which is generally a few thousand inhabitants.42 The cities with populations above 10,000 stand out as remarkable instances, indeed exceptional, during the entire period between the Neolithic and the Middle Ages. Attempting to establish a generic model, we have not included the cases of the rare capital cities of great empires supposed to have attained a million inhabitants, such as Rome. Other very large cities for which the archaeologists have measured surfaces of unusually great extent are, for instance, Xian, in Henan, during the Longshan period (70 ha) or indeed Teotihuacan in Mexico (20 km2), that is, thirty times greater than any other walled city among the cities observed at the same epoch.

  • 43  Schmitt C., ‘Modélisation de la dynamique…’, op. cit., p. 167.

Table 1: The parameters of the SimpopLocal43 model.

Parameter

Description

Rmax

The maximum reception capacity for each settlement (expressed in number of inhabitants)

rgrowth

The constant of growth of the model of Verhulst (expressed as an annual rate of growth)

InnovationImpact

The general impact of innovations on the quantity of resources available

Pcreation

The probability of the appearance of an innovation during the interaction between two individuals in the same settlement

Pdiffusion

The probability of the transmission of the innovation during interaction between two individuals from different settlements

DistanceDecay

The effect of distance on the diffusion of innovations

InnovationLife

The longevity of the innovation during which it can be diffused

MaxInnovation

The total number of innovation agents able to be generated before the end of the simulation

Pcatastrophe

The probability of occurrence of a catastrophe in a settlement at every stage of simulation

Popcatastrophe

The value of reinitialisation of the population of a settlement afflicted by a catastrophe

Rcatastrophe

The value of reinitialisation of resources available in a settlement afflicted by a catastrophe

  • 44  Bairoch P., De Jéricho à Mexico, op. cit.
  • 45  Renfrew Colin, Poston Tim, ‘Discontinuities in the endogenous change of settlement pattern’, in Tr (...)

29The average annual growth of sedentary and agricultural settlements in the Neolithic periods is on the order of 0.02%, according to a number of authors.44 45a figure which permits us to calculate a value for the parameter ‘rgrowth’ in the logistic function. Certain parameters have been fixed arbitrarily, such as that of the durable life of an innovation, ‘InnovationLife’ – but the first simulations and a later calibration have shown that this value was of little discriminant significance and could be removed from the model) – and that of the total number of innovations, ‘MaxInnovation’, fixed at 10,000 for technical and theoretical reasons (respectively, the time length of the simulation and calibration of the notion of innovation). Five parameters therefore remain to be estimated – Rmax, InnovationImpact, Pcreation, Pdiffusion et DistanceDecay – for which the limits of the continuous domain of their possible variation have been specified.

  • 46 Reuillon Romain, Leclaire Mathieu, Rey-Coyrehourcq Sébastien, ‘Openmole, a workflow engine speciall (...)
  • 47  Website of the OpenMOLE platform: http://www.openmole.org/
  • 48  Schmitt C., ‘Modélisation de la dynamique…’, op. cit.
  • 49  Rey-Coyrehourcq S., ‘Une plateforme intégrée pour…’, op. cit.
  • 50  Schmitt Clara, Rey-Coyrehourcq Sébastien, Reuillon Romain, Pumain Denise, ‘Half a billion simulati (...)

30Since two of the parameters involved distributions of probability, the model is stochastic. Consequently, the two techniques (trial and error and complete plan) usually employed to calibrate a model are not adapted to calibrating the SimpopLocal model, nor, in general, to multi-agent models with multiple parameters. We have had recourse to innovative methods of automatic exploration of the space of behaviour of models developed on the simulation platform OpenMole46 47and utilising genetic algorithms and a calculating grid to explore the space of the parameters in the most detailed and exhaustive fashion possible.48 4950In the absence of empirical data, the calibration here is instead a theoretical adaptation, realised to match objectives which the settlement must satisfy in order for the simulated solution to be recognised as valid. The objective function identified on the basis of stylised facts describing the systems of cities of the period includes three quantifiable elements which must be obtained at the end of the simulation:

  • a lognormal distribution of the size of settlement

  • the size of the largest settlement cluster on the order of 10,000 inhabitants

  • a total duration of the simulation of 4,000 time-steps, that is, equivalent to 4,000 years. This duration, considered necessary for the emergence of an ‘urban’ and hierarchised settlement, is thus represented by 4,000 time-steps in the simulation.

  • 51  Rey-Coyrehourcq S., ‘Une plateforme intégrée pour… , op. cit., pp. 331-375

31Satisfaction of these objectives, which entail contradictory dynamic tendencies, the necessity of effecting a hundred reproductions of simulations using the same range of values as parameters to take account of stochasticity, and the broad statistical range attributed a priori to the five unknown parameters have induced us to employ an evolutionary algorithm51 to resolve this problem of multi-objective optimisation. We have had recourse to high performance computing for fully exploring the space of the parameters.

Results of the simulations and implications of the observations

  • 52  I.e. twenty years of calculation using a single processor, reduced to three of four days thanks to (...)
  • 53  Rey-Coyrehourcq S., ‘Une plateforme intégrée pour… ‘, op. cit., pp. 355-358
  • 54  Schmitt C., ‘Modélisation de la dynamique…’, op. cit.
  • 55  Reuillon Romain, Schmitt Clara, De Aldama Ricardo, Mouret Jean-Baptiste, ‘A new method to evaluate (...)

32In all, 500 million executions of the model were effected52 to put in place the implementation of the parameters. In facing format, Table 2 shows for each parameter, in a first column, the hypothetical range of variation initially supposed, which was deliberately conceived very broadly, with, in a second column, the range of possible variation it could be reduced to, on the basis of simulations aimed at putting the model in place. This result does not take the form of a unique value but of a range of values possible for each parameter, in that a ‘Pareto front’53 54establishes compromises between values capable of assuring multiple optimisation of the objective function. A third column shows that a gain in precision was realised for each parameter by employing a still more effective algorithm, which calculates the sensitivity of the model to variations in one parameter at a time, all being equal in respect of the variations of the others.55 Further, it should be recalled that the values presented in Table 2 do not constitute independent measures; they are integrated, and it is therefore the totality of their configuration that will have to be adapted when applications of the model envisaging a calibration based on empirical data, historical or archaeological, are undertaken.

  • 56 Schmitt C., ‘Modélisation de la dynamique…’, op. cit., p. 203.

Table 2: Possible domains of variation of the parameters obtained after 500 million simulations using SimpopLocal and precision by the algorithm ‘Calibration Profile’ (CP)56

Parameter

Possible search range

Statistical range in the first three fronts

Range of calibration validation

Rmax

[1 ; 40000]

[9969 ;10409]

[10000;10500]
Ideal value = 10277

InnovationImpact

[0 ; 2]

[9.0 10-3 ; 2.2 10-1]

[6.0 10-3 ; 1.2 10-2]

Pcreation

[0 ; 1]

[2.9 10-7 ; 3.5 10-6]

[0.4 10-6 ; 2.2 10-6]

Pdiffusion

[0 ; 1]

[1.2 10-8 ; 9.9 10-6]

[0.2 10-6 ; 2.1 10-6]

DistanceDecay

[0 ; 4]

[0.55 ; 4.0]

[0.15 ; 1.3]

  • 57  Reuillon R., ‘A new method…’, op. cit.

33The other originality of this experiment is that the method of exploring the behaviour of the model is also a validation, making it possible to establish in what measure the hypotheses chosen to implement the mechanisms of the model are at once necessary and sufficient to obtain the desired result – within the framework, obviously, of the description chosen for the model. This second result follows from the perfection of a method known as the ‘profiles method’, which calculates for each parameter the effect of its variation on the quality of the adjustment of the model to the objective function, all things being equal with respect of variations in other parameters.57 It has led to rejecting the parameter ‘InnovationLife’, which did not sufficiently constrain the evolution of the model. Even while providing another vision of the possible behaviour of the model, it has allowed specification of the statistical range of most of the parameters necessary and sufficient to obtain the desired result (last column of Table 2).

34These results, obtained by analysis of the calibration profiles, permit a precious response to the hypotheses from the urban theory that frames the development of the model. The evolutive urban theory, which has guided the construction of the SimpopLocal model and, more generally, all the models of the Simpop family, insist on the notion of system, that is, the relation and interaction between elementary entities (cities, villages or settlements) constitutive of the system. This is the first time, however, in the context of Simpop modelling, that the results of model exploration prove that these mechanisms of interaction between entities of the system are ‘indispensable’ to the production of an evolution close to that of real systems Without these mechanisms of interaction, verified within SimpopLocal by the parameters ‘Pdiffusion’ andDistanceDecay’thus without diffusion of innovations between cities according to a logic of the gravitational kind – it is not possible to generate dynamics of growth that would be representative of dynamics actually observed in real systems. These results also show the importance of the role of space in the organisation of settlement: without the effect of the parameter ‘DistanceDecay’, which reduces interactions with distance, the simulated evolutions of the system are not representative of the evolutions of real systems.

  • 58  Renfrew Colin, ‘Trade as action at a distance : question of integration and communication’, in Anc (...)

35This initial evaluation of the mechanisms will also be useful for future versions and applications of SimpopLocal. If this model is too simplistic to conform completely to real settlements, contemporary or ancient, in the first refined version, the concepts at the origin of the processes simulated can resonate with certain contexts (the proto-historical cities, for instance) or with archaeological theories such as that of ‘Peer polity interaction’.58 Colin Renfrew has pointed out to what extent it was widespread that the first small states came into being, not in isolation, but in ‘cluster’ form, with marked similarities in terms of size, social structure, material culture, etc. He observed, as well, that the political entities comparable in size and organisation (such as the first forms of states) had a tendency to be located in the same regions and to evolve simultaneously. Moreover, the archaeological data indicate that these tendencies to change did not stem from one single source of innovation but emerged contemporaneously in a number of mutually interacting units. This theory suggests, then, that the mechanism underlying these remarkable observations is trade, and it places these processes of interaction at the centre of mechanisms of social change. The SimpopLocal model, which likewise founds its dynamic on social interactions, might serve as a kernel for construction of a model testing this theory through simulation.

Conclusion

36In this chapter we have presented a model for the transition of the appearance of cities. The emergence of cities introduces a major transformation in the way of inhabiting the earth, which evolves from a dispersed and homogenous form, with little hierarchisation, adapted to the exploitation of diffuse local resources, towards a form more concentrated, highly heterogenous and hierarchised, permitting production of wealth on the basis of multi-scale networks of interaction.

37Since little quantified information is available as to the conditions of the emergence of cities and the orders of magnitude associated with the evolution of settlement systems in these epochs, it has not been possible to envisage a calibration based on empirical data. We have chosen to produce a theoretical model – abstract, generic and much simplified. Nevertheless, thanks to the selection of hypotheses allowed by the qualitative and quantitative knowledge of historians and archaeologists, as well as by a geographic theory of the dynamic of cities tested for more recent periods, and also by accepting the constraint of parsimony in the construction of the model, which has permitted elaboration of an original and effective method of validating these hypotheses, we have constructed instruments which should make it possible to advance in the experiments that remain to be conducted in order better to understand the major inflection of the history of settlement systems constituted by the emergence of cities organised in spatial systems.

Notes

1  Prigogine Ilya, Stengers Isabelle, La nouvelle alliance, Paris, Éditions Gallimard, 1979.

2  Pumain Denise, Saint-Julien Thérèse, Sanders Lena, Villes et auto-organisation, Paris, Éditions Economica, 1989.

3  Sanders Lena, Système de villes et synergétique, Paris, Éditions Anthropos, 1992.

4  Pumain Denise, Paquot Thierry, Kleinschmager Richard, Dictionnaire La ville et l’urbain, Paris, Éditions Anthropos, 2006.

5  Garmy Pierre, Villes, réseaux, et systèmes de villes, Paris, Éditions Errance, 2012.

6  Schmitt Clara, ‘Modélisation de la dynamique des systèmes de peuplement : de simpopLocal à simpopNet’, doctoral thesis, Université Paris 1, 2014.

7  Rey-Coyrehourcq Sébastien, ‘Une plateforme intégrée pour la construction et l’évaluation de modèles multi-agents en géographie’ doctoral thesis, Université Paris 1, 2015.

8 The ERC programme GeoDiverCity developed a number of models of urban dynamics. See URL online: http://geodivercity.parisgeo.cnrs.fr/blog/ et http://www.simpop.parisgeo.cnrs.fr/.

9  Marcus Joyce, Sabloff Jeremy, The ancient City. New perspectives on Urbanism in Old and New World, Éditions SAR Press, 2008.

10  Childe Gordon, ‘The Urban Revolution 1950’, The Town Planning Review, 21(1), 1950, p. 3-17.

11  Wheatley Paul, The pivot of the four quarters, Chicago, Éditions Aldine, 1971.

12  Bairoch P., De Jéricho à Mexico, op. cit.

13  Bairoch P., De Jéricho à Mexico, op. cit.

14  Mumford Lewis, La Cité à travers l’Histoire, Marseille, Éditions Agone, 1961.

15  Garmy P., Villes, réseaux, …, op. cit.

16  Diamond Jared, Guns, Germs, and Steel: The Fates of Human Societies, Éditions Norton & Company, 1997.

17  Bocquet-Appel Jean-Pierre, ‘La transition démographique agricole au Néolithique’, dans J.-P. Demoule, La révolution néolithique dans le monde, Paris, Éditions CNRS, 2010, p. 301-317.

18  Demoule Jean-Paul, Une histoire globale à l’âge du Bronze; online at http://blogs.histoireglobale.com/author/jean-paul-demoule.

19 Agricultural societies in their turn generated a new global historical phenomenon resulting in large measure from the demographic impulsion provoked by the new mode of production: the emergence of hierarchised societies, ever more complex, which over the more or less short term issued in state and city formations, beginning in the third millenary before our era, at first in the same places as the initial Neolithic foyers.’

20  Bairoch P., De Jéricho à Mexico, op. cit., p. 131.

21 In practically all the cases where agriculture is involved, several millenaries later the urban reality appeared. Rare are the regions where, 2,000 years after the existence of true agriculture, one does not find the appearance of cities.’

22  Paulus Fabien, ‘Coévolution dans les systèmes de villes : croissance et spécialisation des aires urbaines françaises de 1950 à 2000’, doctoral thesis, Université Paris 1, 2004.

23  Berry Brian, Cities as Systems within Systems of Cities 1964’, Papers in Regional Science, 13(1), 1964.

24  Pred Alan, City systems in advanced societies, London, Éditions Hutchison, 1977.

25  Pumain Denise, ‘Les systèmes de villes’, dans Encyclopédie de géographie, ed. A. Bailly, R. Ferras, D. Pumain, Paris, Economica, chap. 34, 1992, pp. 645-664.

26  Reymond Henri, ‘Une problématique théorique’, in Problématiques de la géographie, ed. H. Isnard, J.-B. Racine, H. Reymond, Paris, PUF, 1981.

27  Reynaud Jean, ‘Villes’, in Encyclopédie nouvelle, ed. C. Gosselin, Paris, t. VIII, 1841, pp. 670-687.

28  Robic Maric-Claire, ‘Cent ans avant Christaller, une théorie des lieux centraux’. L'Espace Géographique, 1, 1982, pp. 5-12.

29  Reclus Elisée, L’homme et la terre, Paris, Éditions Librairie Universelle, 1905.

30  Christaller Walter, Die Zentralen Orte in Süddeutschland : eine Ökonomisch-Geographische Untersuchung Über die Gesetz Massigkeit der Verbreitung und Entwicklung der Siedlungen mit Städitschen Funktionen, Jena, Éditions Fischer Verlag, 1933.

31  Kohl Johann Georg, Der Verkehr und die Ansiedelungen der Menschen in ihrer Abhängigkeit des Gestaltung der Erdoberfläche, Dresden, Éditions Arnold, 1841.

32  Reclus Elisée, ‘The evolution of Cities’, The Contemporary Review, 67(2), 1895, pp. 246-264.

33  Pirenne Henri, Les villes du Moyen-Age, Paris, Éditions PUF, 1925.

34  Bird James, Centrality and cities, London, Éditions Routledge, 1977.

35  Fletscher Roland, ‘Settlement Archaeology: World-Wide Comparison’, World Archaeology, 18(1), 1986, p. 59-83.

36  Liu Li, ‘Settlement patterns chiefdom variability and the development of early states in North China’, Journal of Anthropological Archaeology, 15(3), 1996, pp. 237-288.

37  Pumain Denise (ed.), Hierarchy in natural and social sciences, Dordrecht, Springer, 2006

38  Gibrat Robert, Les inégalités économiques, Paris, Éditions Sirey, 1931.

39  Site Simpop : http://simpop.parisgeo.cnrs.fr

40  Cottineau Clémentine, ‘L’évolution des villes dans l’espace post-soviétique: observation et modélisations’ doctoral thesis, Université Paris 1, 2014.

41  Schmitt C., ‘Modélisation de la dynamique…’, op. cit., p. 169.

42  Hansen Mogens Herman, ‘Analyzing Cities’, in The Ancient City, ed. J. Marcus, J. Sabloff, 2008.

43  Schmitt C., ‘Modélisation de la dynamique…’, op. cit., p. 167.

44  Bairoch P., De Jéricho à Mexico, op. cit.

45  Renfrew Colin, Poston Tim, ‘Discontinuities in the endogenous change of settlement pattern’, in Transformations : Mathematical approaches to culture change, ed. C. Renfrew, K. L. Cooke, Éditions Academic Press, 1979, p. 437-461.

46 Reuillon Romain, Leclaire Mathieu, Rey-Coyrehourcq Sébastien, ‘Openmole, a workflow engine specially tailored for the distributed exploration of simulation models’, Future Generation Computer Systems, 29, p. 1981-1900, 2013.

47  Website of the OpenMOLE platform: http://www.openmole.org/

48  Schmitt C., ‘Modélisation de la dynamique…’, op. cit.

49  Rey-Coyrehourcq S., ‘Une plateforme intégrée pour…’, op. cit.

50  Schmitt Clara, Rey-Coyrehourcq Sébastien, Reuillon Romain, Pumain Denise, ‘Half a billion simulations, Evolutionary algorithms and distributed computing for calibrating the SimpopLocal geographical model’, Environment and Planning B, 42(2), 2015, pp. 300-315.

51  Rey-Coyrehourcq S., ‘Une plateforme intégrée pour… , op. cit., pp. 331-375

52  I.e. twenty years of calculation using a single processor, reduced to three of four days thanks to the parallelling of the calculation on the network of France Grilles.

53  Rey-Coyrehourcq S., ‘Une plateforme intégrée pour… ‘, op. cit., pp. 355-358

54  Schmitt C., ‘Modélisation de la dynamique…’, op. cit.

55  Reuillon Romain, Schmitt Clara, De Aldama Ricardo, Mouret Jean-Baptiste, ‘A new method to evaluate simulation models: The Calibration Profile algorithm’, Journal of Artificial Societies and Social Simulation, 18 (1), 2015.

56 Schmitt C., ‘Modélisation de la dynamique…’, op. cit., p. 203.

57  Reuillon R., ‘A new method…’, op. cit.

58  Renfrew Colin, ‘Trade as action at a distance : question of integration and communication’, in Ancient civilization and trade, ed. A. Sabloff, C. C. Lamberg-Karlovsky, Albuquerque, Éditions University of New Mexico Press, 1975, pp. 3-59.

Table des illustrations

Titre Figure 1: Graph41 of settlements showing the initial situation of the SimpopLocal model.
URL http://books.openedition.org/pufr/docannexe/image/19837/img-1.jpg
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