Common scaling laws for city highway systems and the mammalian neocortex

A variety of scaling laws are known for the mammalian neocortex relating gray matter volume, total number of synapses [1, 2], white matter volume [3–9], number of neurons [6, 10–12], surface area [4, 5, 13–16], axon caliber [1, 17], and number of cortical areas or compartments [18]. These neocortical scaling laws appear to be a consequence of selection pressure for a sheet-like structure (namely, gray matter) to economically maintain a high level of interconnectedness [1, 2, 19, 20]. We might therefore expect to find similar scaling laws for any sheetlike structure under similar selection pressures, in which case the neocortex would be just an instance of a more general kind of structure. Here, we investigate city highway systems as a potential kind of network which may be driven by similar principles as the neocortex. In contrast to neurons, which are conduits for information-related signals on which brain computations rely, highways are conduits for physical materials and people. But from the perspective of the city as a whole, the materials and people that highways transport are crucial to the large-scale function carried out by the city, and are, in a sense, signals—that one signal is electric and the other physical may not matter in regards to the fundamental principles governing them. In addition to the prima facie analogy between city highway networks and the brain’s neural connections, there are several other reasons we chose to examine city highway networks. First, the organization of city highway networks tends to be driven by political and economic forces over decades, rather than being planned in advanced following known principles of highway engineering [21]—i.e., city highways systems are a result of an evolution-like mechanism. Second, cities are under selection pressure to efficiently interconnect via highways and roads. Third, because cities lie on the land they are approximately a surface, or a sheet. Fourth, highway network data are readily available (and our data set consists of 60 U.S. cities varying in population from 10 to nearly 10, see Table 2 for raw data). Finally, the organization of city highway systems is interesting in and of itself: nearly half of Earth’s 6.6 billion people now live in cities, and cities are becoming ever larger and densely populated. The proper functioning of a city requires that people and materials be quickly moved throughout it. This is a very difficult design problem, one that is magnified by the fact that city population tends to grow much faster than city surface area, and cities tend to increase in population over time, so that the efficient highway network must constantly evolve from the pre-existing one. Identification of scaling laws governing how highway organization scales with city size could potentially lead to better highway systems, and more efficiently running cities. MARK A. CHANGIZI AND MARC DESTEFANO