The phrase “All roads lead to Rome” shows in five words how important roads are to important cities. Yet when we think about what has caused some cities to continue and grow and others to decline and be forgotten, we often think primarily of cultural and political events, climate, land productivity, and geography. As a consequence, most current scientific models of how cities develop treat roads as a by-product or exogenous factor, and need large amounts of socio-economic data to be able to reproduce the location of cities.
In the article published in Scientific reports, Takaaki Aoki of Kagawa University, Naoya Fujiwara of Tohoku University, Toshiyuki Nakagaki of Hokkaido University and Mark Fricker of Oxford University found that all they needed to explain the distribution of cities in Italy was, first, a small set of mathematical equations, which explain how the population of Italy places and the connections between them interact; second, a map containing the topography of the landscape in question. They emphasized: “Landscape alone is insufficient to explain population distribution as a form of geographic determinism, but requires an interdependent dynamic feedback between population and the transportation network that occurs in parallel.”
The computational model built by Aoki and his colleagues is based on a grid of cells, each with terrain and slope, as well as population. In each round of the model, the computer estimates how the road network between each point on the map and every other point grows or shrinks based on how popular the endpoints are; and vice versa, how each cell’s population changes as a result of how well it is connected to all other cells. The landscape is included in the calculation through a network of roads through different types of terrain that are more or less attractive. While these conditions alone already produce results quite similar to the distribution of cities in the real world, the researchers could further improve accuracy by incorporating “history” into their model, starting the simulation with a population distribution similar to that of ancient Roman times and increasing typical journey lengths over time.
However, the model developed by the researchers can by no means completely accurately reproduce the distribution of modern cities, with some cities in the model being larger or smaller than in reality, and their locations do not always match perfectly. The researchers acknowledge that there are many important details, such as small-scale landscape features or historical events, that will greatly increase the accuracy of their model. But they argue that it still “provides a basic reference tool for predicting the expected population distribution when it is limited solely by topography.” It is all the more remarkable that in many alternative models the relief of the natural landscape is not even clearly taken into account.
The researchers say that by using their model as a “complex null model,” future work can quantify the importance of socioeconomic, environmental, and other factors responsible for deviations from real data. In this way, they hope to pioneer a “new direction of deconstruction of the complex phenomena of human civilization, which involve many natural and social factors.”