Generative models of scale-invariant systems of cities: Do they agree with or contradict theoretical and empirical expectations?

Cities around the world differ greatly in size and in their social and economic characteristics. Yet quantitative regularities can be observed when considering systems of cities. Quite often, rank-size distributions of cities are approximately scale-invariant and scaling laws relate the size of cities to some particular socio-economic variables. These scaling regularities are worth investigating once acknowledged their deviations to strict scale-invariance and their spatial and temporal variations. One research objective is to devise models incorporating generative processes that are thought to be crucial to the emergence of these empirical patterns, and then to test whether the models can reproduce them accurately. The aim here is to provide a critical cross-disciplinary overview of such models. Three disciplines are covered: economics, geography and physics. Models are examined and compared with respect to the explanatory processes they incorporate, with a focus on the role of space, the diversity of the entities modelled and the dynamics that the models can or cannot simulate. From this examination, recommendations are provided for building generative models of scale-invariant systems of cities that are really relevant.