We try here to illustrate the relevance of an evolutionary theory of urban systems for explaining their hierarchical properties. The largest cities became larger because they were successful in adopting many successive innovations. Larger cities capture innovations in a continuous way (through adaptation, imitation, anticipation), and they concentrate a larger part of anything « new » at any time. Their functions demonstrate a higher level of complexity or sophistication of their urban activity and society. The most advanced technologies concentrate in largest cities, the common place activities are ubiquitous, whereas old ones remain in small towns only (or, in economic terms, there are increasing, constant or decreasing returns to urban scale). Such regularities can be expressed in the form of scaling laws that were recognised as revealing specific constraints on the structure and evolution of complex systems in physics and biology. Approaching urban activities by scaling laws provides a linkage between the concepts of urban function, city size, and innovation cycles. Over time, there is a substitution among the activities of the largest cities, where the oldest technologies and professions are replaced by the new ones, while the old ones are relatively concentrating in the smallest towns. Such an evolution is observed within urban systems where cities are fully connected and interdependent. There are processes of cooperation through exchanges of information and learning that enable an incremental diffusion of innovation and a continuous adaptation of urban activities and society in all parts of the system. Meanwhile, there are also processes of competition between cities that enhance their capacity to innovate and to levy the benefits of innovation. A distributed process of urban growth including a slight but continuing advantage for the largest cities is the result of that competitive process, while the successive adaptation of the urban functions follows the economic and social innovation cycles.

We define the urban field as the spatial organisation of urban densities according to decreasing gradients from centre to periphery. This urban field can be estimated from the encroachment of built-up areas. The CORINE Land Cover database enables the measurement of the gradient values for the spatial distribution of built-up areas in European cities. Instead of the exponential or power functions, which usually provide the best fit for the distributions of population densities, we find that two linear functions strongly differentiating a central and a peripheral gradient provide the best fit for built-up surfaces. The comparison between the 1990 and 2000 CORINE images demonstrates a convergence in the trend of urban spread between Northern and Southern European cities. However, it is still difficult from the data to decide which of the models of urban field is winning: will the steeper central gradient become diluted into the less dense periphery, or are the closer fringes of the central parts becoming integrated into the ordered pattern of the urban central agglomerations?

Simpop2 is a generic multi-agent model designed for simulating any system of cities. From an evolutionary theory built upon the observation of networks of cities in different parts of the world and over long time-periods, it has been possible to identify stylised facts that characterise their main features and properties. This paper presents data-oriented simulations of two kinds of system: in early settled countries (Europe, 1300—2000) and in countries more recently settled (the United States, 1650—2000). The model can simulate properly the general dynamics of urban systems, at different scales of observation (general configuration and trajectories of individual cities). The simulations help to identify some dynamic properties that are shared by both systems: a general growth trend and spatial expansion (produced through interurban competition which generates emulation towards innovation that explain the persistency of the hierarchical configuration); a dramatic increase of contrasts in city sizes since the first industrial revolution linked to the increase of communication speed; and, a differentiation of urban economic functions produced through interactions between cities and innovation cycles, as industrial revolution. The model also puts forward the necessary integration of a new urban function in the model, which represents the early emergence of global cities. Yet, beyond these similarities in the evolution of all urban systems, when they are fully integrated, the model also measures to what extent the observed peculiarities in their contemporary spatial and functional configuration depend on differences in the early space-filling process between the two kinds of system.

Pour construire une théorie géographique du changement qui ne se limite pas à la simple spatialisation d’une théorie de l’histoire ou des transformations sociales, on propose de formaliser les observations de l’évolution des systèmes spatiaux à l’aide des concepts et des méthodes élaborés par les sciences de la complexité. Au cours des trente dernières années, des avancées des théories physiques de l’auto-organisation, des théories de l’évolution du vivant ou des systèmes cognitifs adaptatifs ont renouvelé notre conception de la dynamique des systèmes, en interrogeant notamment les conditions d’émergence de la nouveauté. La géographie pourrait ainsi proposer une interprétation de la formation et de l’évolution d’entités localisées qui, à côté d’autres réseaux intermédiaires comme les groupes ou les institutions, structurent les interrelations entre les individus et le monde.

For the first time the systems of cities in seven countries or regions among the largest in the world (China, India, Brazil, Europe, the Former Soviet Union (FSU), the United States and South Africa) are made comparable through the building of spatio-temporal standardised statistical databases. We first explain the concept of a generic evolutionary urban unit (“city”) and its necessary adaptations to the information provided by each national statistical system. Second, the hierarchical structure and the urban growth process are compared at macro-scale for the seven countries with reference to Zipf’s and Gibrat’s model: in agreement with an evolutionary theory of urban systems, large similarities shape the hierarchical structure and growth processes in BRICS countries as well as in Europe and United States, despite their positions at different stages in the urban transition that explain some structural peculiarities. Third, the individual trajectories of some 10,000 cities are mapped at micro-scale following a cluster analysis of their evolution over the last fifty years. A few common principles extracted from the evolutionary theory of urban systems can explain the diversity of these trajectories, including a specific pattern in their geographical repartition in the Chinese case. We conclude that the observations at macro-level when summarized as stylised facts can help in designing simulation models of urban systems whereas the urban trajectories identified at micro-level are consistent enough for constituting the basis of plausible future population projections.