An evolutionary theory for interpreting urban scaling laws

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.