Urban Primacy,the Primate City and Rank Size Rule

Urban Primacy is when one city is dominantly large in a group of cities. Usually when a largest city is over twice as large as the next city, this would constitute urban primacy. Other measures are more rigorous whereby a city is only primate when it is at least 3 times larger than the next two cities combined. Primacy is almost always calculated using this kind of population-size ratio. Ideally metropolitan level populations are used so as to avoid dividing the largest city by an adjacent centre.

The idea of primacy was first introduced by mark Jefferson in 1939. His proposition was that nationalism crystallizes in primate cities which are super eminent in both size and national influence. He assessed the degree of primacy by computing the ratio of the size  of the second and third ranking cities to that of the largest one. He found that in the forty-six countries of the world the largest cities were two or three times as large as the next largest city. The ratio of the population of the three largest cities approximated the sequence 100:30:20  ( i.e. the third largest is one-fifth the six of the largest). According to him there are various reasons for a city to exceed its neighbors in size, but once it did so the process became cumulative giving it an impetus to grow and draw away from all other cities in character as well as size. The particular ratio sequence has been later ignored, though the concept of the primate city and primacy is widely used.

primate city is the largest city in its country or region, disproportionately larger than any others in the urban hierarchy. A primate city distribution is a rank-size distribution that has one very large city with many much smaller cities and towns, and no intermediate-sized urban centers: a King effect, visible as an outlier on an otherwise linear graph, when the rest of the data fit a power law or stretched exponential function. The law of the primate city was first proposed by the geographer Mark Jefferson in 1939. He defines a primate city as being “at least twice as large as the next largest city and more than twice as significant.” Aside from size and economic influence, a primate city will usually have precedence in all other aspects of its country’s society, such as being a center of politics, media, culture and education and receive most internal migration.

The Rank-Size Rule

The rank-size rule says that ‘when ranks of cities, arranged in descending order, are plotted against their populations (rank 1 being given to the largest, and so on) in a doubly logarithmic graph, a rank-size distribution results’ (Das and Dutt 1993: 125), or to put it in much simpler words: ‘In an ordered set of cities representing a given country, the product of the rank and size of a city is constant’ (Dziewonski 1972: 73). The rank-size rule is also commonly referred to as Zipf’s Law because the model describing a constant relation between the size of an event and its rank was at first developed by G. Zipf. In the case of cities distribution by population, when the natural logarithms of the rank and of the city size (in terms of the number of people) are calculated and represented graphically, a remarkable log-linear pattern is attained, which is called the rank-size distribution. If the slope of the line is equal or close to -1 (a straight line), the relationship is known as Zipf’s Law.

Zipf’s has probably the best presentation of the empirical findings on rank and size of the cities. The rank size rule states that for a group of cities, usually those exceeding some size in a particular country, the relationship between size and rank of cities is given by:

Pr = P1/r

Where Pr = population of the largest city ranked r

P = population of the largest city

r = rank of city r

Rank Size Rule is a simple model which states that population size of a given city tends to be equal to the population of the largest city divided by the rank of the given city.

Rank-size rule analysis and ancient cities

The Rank Size Rule applies to the modern cities but when we try to apply the same law to the older cities we face difficulty in correlating the theory. The geographers try to correlate the data with the population datum which we don’t have in case of ancient cities and ancient city were characterized by city walls or fortifications but the settlement was never within the city walls, it always exceeded. The population of the city will depend on the city area. A larger city will have larger population.

Rank Size Rule

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I am Rashid Aziz Faridi ,Writer, Teacher and a Voracious Reader.
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