On Rank-Size Distributions of Cities: An Ecological Approach

Abstract

Models of City Size Distribution Two quite different empirical regularities relating rank and size of cities in an area have been noted throughout the literature. Jefferson advanced the observation that the largest city in a country frequently is far greater than the second one and proposed the so-called "law of the primate city." 1 On the other hand, apart from some earlier attempts, Zipf called widespread attention to the fact that in many countries the distribution of all cities by rank and size is such that the population of any city multiplied by its rank is a constant.2 This regularity, the so-called "rank-size rule," has been studied in recent years by Simon and Ward, among others, who have tried to derive it as the outcome of stochastic processes operating in a system under steady state.3 It can be observed that primacy and rank-size rule are not mutually exclusive models. Rather, a perfect fit to the rank-size rule of all cities in an area except the largest is compatible with a high level of primacy. Therefore, it can be expected that the conditions associated with the fulfillment of each model derive from quite different characteristics of the area under study. The present report concerns the analysis of the rank-size distribution of cities-over time as well as for subareas at one fixed point in time-in one specific country, Argentina, in which sufficiently reliable census data exist for five different dates throughout a period of nearly one hundred years (1869-1960). The basic assumption is that neither primate cities nor the rank-size rule can be expected in any area, whatever the criterion established to delimit it.4