## The concept of Rank-Size Rule or Rank-Size Distribution

The Rank-Size Rulewas revealed in both developed and underdeveloped countries when the cumulative frequency of cities with a population of greater than twenty thousand people was ranked against the size of a city on a log-normal scale.

The distribution of city sizes in terms of population in both underdeveloped and developed countries has recently come under close examination by specialist in many academic fields and under settlement geography. The advent of general systems theory has proved to be an invaluable analytical approach to the study of city size distribution, in that it incorporates stochastic growth theory, and the concept of entropy. The two aspects of general systems theory have been very useful in explaining some of the empirical regularities observed of city size distribution, especially the rank size distribution.

**For example: is there any significance in the fact that some cities have grown faster than other cities? What are the causes of his growth? What are the problems associated with differential growth and size of cities?**

Much of the work on urban problem has been done in relation to regional development programming in the United States and comparatively little research has been undertaken on the fundamental problems of defining an optimum size distribution of cities for developing countries. Any criteria for optimum population size involves implicitly and explicitly two elements: first the normative element, which places a positive or negative valuation in a particular situation and second a factual element which has the force of the statement of empirical relationships between variation in city size and variation in situation question.

**Related: **

Among the criteria that have been examined in relation to the optimum city size in both developed and developing countries is:

- City size and physical planning of cities with respect to the frequent demand that cities be small enough to enable ready access to the countryside and a reasonably moderate journey to work, i.e. transport problems.
- City size and health (mortality rate, incidence of disease etc).
- City size and public safety (crime rates, accident rates, fire hazards etc).
- City size and municipal efficiency.
- City size and education expenditure.
- City size and cost of living.
- City size and public recreation
- City size and retail facilities
- City size and family life.
- City size and miscellaneous psychological and social characteristics of urban life (community participation, social contentment).
- City size and associations.

## Factors affecting the Rank Size Rule

The factors like administrative organization, transportation linkages, industrial development and commercial spread play a major role in changing the rank-size relationship. The disproportionate development of these facilities causes variation in the centripetal forces involved in the growth of the settlements.

The population change in a centre within a certain time interval also changes the rank of a centre. The rank of any centre is dependent upon the hierarchical arrangement of the nodality value – which may be population size or an index based on different functions available at a place. The latter may depend upon the provision of administrative and transport facilities and the development of commerce and industry. The dissimilar and disproportionate development of these facilities causes variation in the centripetal forces involved in the growth of urban places.

This concept of close proximity has, however, changed today with the introduction of quick, mechanized transport, for example, people generally move from one village to another on foot which involves certain amount of time. The smaller enjoys the facility of buses so that the inhabitants can also move from one centre to another more quickly. The bigger towns have train facility for travel between them. The development of airways has connected one city level centre to another. Hence, travel by the various above means though involving money, does not consume much more time than the movement from one village to another on foot. The shows the expansion in the zone of influence and spatial pattern of an urban centre based on transport facilities, which also control the rank and number of different order of urban places. The larger centres are more widely spaced and are, therefore, fewer in number while the small towns are larger in number and more closely spaced. The regularity has proved that as the nodality/centrality of places increases, the number or urban places decreased according to the rank-size rule.

Dynamics of Rank Size Rule

#### The contribution of rank size rule in regional planning

- It helps in the interpretation of the relationship between rank and population size of settlements.
- It helps in analyzing the settlement networks.
- It explains settlements with respect to economic activities as increase in activities increase the population size.
- It explains the imbalance between the settlements due to rapid growth in population or activities.

**Rank-Size RuleAnd Developing Countries**

The most complete and comprehensive empirical study of the rank-size rulein developed and developing countries is that by Berry who analyzed city size distributions and their relationship to economic development in thirty-eight countries. He found that the distributions fall into two major categories namely the Rank Size Distribution and the Primate Distribution.

The Rank-Size Rulewas revealed in both developed and underdeveloped countries when the cumulative frequency of cities with a population of greater than twenty thousand people was ranked against the size of a city on a log-normal scale. Thirteen of the thirty-eight countries had log-normally distributed sizes.

The primate distribution which was characteristics of fifteen out of thirty-eight countries examined is observed, when a stratum of small towns and cities is dominated by one or more very large cities and there are deficiencies in the number of cities of intermediate size. Berry study tended to support the hypothesis that Primate City Distributions are associated with over-urbanization and superimposed colonial economies in underdeveloped countries or with political administrative controls in indigenous subsistence and peasant economies. Furthermore it has been argued that primate cities have paralytic effects upon the development of smaller urban places and tend to be parasitic in relation to the remainder of the national economy.

**Related: Rural urban fringe: Concept, History, Reasons, Issues**

Nine out of thirty-eight countries examined had distributions intermediate between log-normal (rank size) and the primate distribution.

## 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.

**Pattern as per rank-size rule **

Settlements in a country may be ranked in order of their size. The ‘rule’ states that, if the population of a town is multiplied by its rank, the sum will equal the population of the highest ranked city. In other words, the population of a town ranked *n* will be 1/*n*th of the size of the largest city—the fifth town, by rank, will have a population one-fifth of the first.

It is usually possible to relate the ranks and sizes of the central places in country by using a regression analysis

log *P _{k}* = log

*P*–

_{1}*b*log

*k*

where P_{1} is the population of the largest city or town, P_{k} is the population of the *k*th town by rank, and *b* is a coefficient which must be established empirically for each investigation. The greater the value of *b*, the steeper the slope, and the greater the primacy of the largest city or town. Many developing countries show a sharp fall from the largest, primate city to the other cities, and this is known as the primate rule.

The theoretical rank size rule pattern is a straight line.

In urban primacy, a single city dominates and is much greater than the next large center (primary pattern).

In Binary pattern two or more cities are larger than the predicted size.

In Stepped order pattern there are series of levels and steps (conurbations, cities, towns etc.).

**Related: Burgess model or concentric zone model**

### 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.

**Related: Central Place Theory (CPT) by Walter Christaller (1933)**

## FAQs

### What is rank-size rule by zipf? ›

If this power is equal to one, Zipf's law collapses into what is commonly called the rank-size rule. This implies that in the case of cities, **the second largest city is one-half the size of the first and the third largest city is one-third the size of the largest and so on**.

### What does the rank-size rule explain? ›

According to the rank-size rule, **there should be a larger number of small cities than bigger cities**. Also, this rule predicts that the larger a city's population is then the fewer number of cities there should be in the surrounding area with a similar population.

### How does rank-size rule explain the pattern of urban settlement? ›

The population of urban settlements (towns, cities) will be inversely proportional to the rank in the urban Hierarchy. That means a larger population has a smaller rank in the urban hierarchy. The pattern of the rank-size rule was created by George Zips in 1949, it is also known as Zipf's law.

### Who defines rank-size rule theory? ›

Mark Jefferson studied 51 countries where he found that. In 27 countries the population of largest city is more than twice than the 2nd rating city. In 18 countries the population was more than three times.

### Why does the rank-size rule not apply in all countries? ›

Why does the rank-size rule not apply in all countries? **Because some countries have one dominant city where they concentrate all of their wealth** (such as the capital city), bolstering that city and its population above the rest of the cities in the state.

### Which of the following is rank-size rule associated? ›

**Zipf's general theory** known as the rank-size rule was presented to explain the regularity regarding the population of a town and its rank in relation to the largest town which is assigned number 1 in the hierarchy.

### What cities follow the rank-size rule? ›

Some countries have some cities that fit in the rank size rule but other cities populations in the top 10. In the United States, **New York City is largest, then Los Angeles, then Chicago, then Houston, then Phoenix, then Philadelphia**, etc.

### When was the rank-size rule created? ›

In **1949**, George Zipf devised his theory of rank-size rule to explain the size cities in a country. He explained that the second and subsequently smaller cities should represent a proportion of the largest city.

### In which year the concept of rank-size rule was proposed? ›

The Rank Size Rule was first observed by F. Auerbach in **1913**.

### Does the United States follow the rank-size rule? ›

The United States has a large population, a large area, and a long history of urbanization. Thus, it has none of the three characteristics used to generate primate cities. In fact, **the United States follows the Rank-Size Rule.**

### How can the problem of urban sprawl be solved? ›

**Revitalization of existing urban centers and towns** helps to preserve the existing natural environment, thereby reducing urban sprawl. New urbanism seeks to turn existing communities and neighborhoods into diverse districts, cleaning up polluted and dilapidated areas.

### What was the most important religious reason for the origin of settlements? ›

Question | Answer |
---|---|

The most important religious reason for the origin of settlements was a place to do what? | Bury the dead |

The most important political reason for the origin of settlements was a place to do what? | Protect the group's assets |

### Is rank-size rule applicable in India? ›

So, **the rule will not apply**. RANK-SIZE RELATIONSHIP IN INDIA. The rank-size relationship is absent in India at the national level as the population size of Mumbai, Kolkata and Delhi is very close to each other. Moreover, a great majority of states in India also do not conform to the rank-size rule.

### Does England follow the rank-size rule? ›

In the case of the United Kingdom, **the rank size rule does not apply**.

### Does France follow the rank-size rule? ›

**The Rank Size Rule is proven invalid in France**. Since Paris contains more than two times the people as Marseille, it does not follow this rule.

### Does Japan follow the rank size rule? ›

**The rank size rule is invalid based upon the populations of Japan's five largest countries**. Tokyo and Osaka, being the two largest cities in Japan, do not follow the rank size rule.

### Does Canada follow the rank size rule? ›

**Each cities actual population is close to the estimated population of the rank size rule**. It has been proved valid towards the city of Vancouver. The rest of the other cities have proven the Rank Size Rule valid. The percent of urban population in Canada is 80.7%.

### When comparing rank-size rule and primate city rule What do the two patterns imply? ›

When comparing rank-size rule and primate city rule, what do the two patterns imply? **Ranks size rule indicates the society is sufficiently wealthy to justify the provision of goods and services to consumers throughout the country.**

### What is the population of the fourth largest city in a country where the rank-size rule applies if the largest city is one million in population? ›

Which of the following is the best example of a central place with a large hinterland? What is the population of the fourth largest city in a country where the rank size rule applies if the largest city is one million in population? a. **250,000**.

### How does rank-size rule relate to Mexico's urban geography? ›

The rank-size rule states that the nth largest city of a country has 1/n the population of the largest city. This doesn't apply to Mexico because **several cities in Mexico have similar population sizes, and don't follow the rank-size rule**. Therefore, this rule cannot be applied to Mexico.

### What is an example of a rank-size rule city? ›

Rank-Size Rule: n th-largest settlement is 1/n the population of the largest settlement. In other words, 2nd largest is 1/2 the size of largest. Another Example: **4 ^{th} largest city is ¼ the population of the largest city**. Works best in most developed countries that have full distribution of services.

### Does Russia follow the rank-size rule? ›

Top 5 Most Populous Cities in Russia

**Russia's cities do not follow the rank size rule**. For example Novosibirsk should have around 3.8 million people, but in reality it has around 2 million less. This makes Moscow a primate city because it is disproportionatly larger than all the other cities.

### Why are primate cities important? ›

Primate cities, because of their sheer size and the economic activities concentrated in them, **serve as magnets to migrants from rural areas and smaller cities or towns**. Many are attracted by the promise of better economic opportunities and lives in the primate cities.

### Does Australia follow the rank-size rule? ›

**Australia technically does follow the rank-size rule**, although Melbourne is not half the size of Sydney. However the third fourth, and fifth largest cities do follow the rank size rule with being 1/3, 1/4, and 1/5 the size of Sydney.

### Which of the following occurs when the cities in a country follow the rank-size rule and the country has a primate city? ›

Which of the following occurs when the cities in a country follow the rank-size rule and the country has a primate city? **The largest city is two times the population of the next-largest city**.

### What is an example of a primate city? ›

**Mexico City** is an example of a primate city because it is disproportionately larger than other Mexican cities and dominates the country.

### What are examples of primate cities? ›

**Mexico City, Paris, Cairo, Jakarta, and Seoul** have been described as primate cities in their respective countries. Sub-national divisions can also have primate cities.

### Does the US have a primate city? ›

Los Angeles is the second-largest city in the United States with a population of 16 million. This means that **the United States lacks a primate city**. This isn't surprising given the geographic size of the country. Even cities within the country are larger in size than that of an average European city.

### Does Mexico follow the rank-size rule? ›

**Mexico does not follow the rank-size rule**. The largest city has 20 million people while the second largest has 1.6 million which is not half of 20 million.

### What impact does urban sprawl have on the environment? ›

Urban sprawl can **reduce water quality by increasing the amount of surface runoff**, which channels oil and other pollutants into streams and rivers. Poor water quality is associated with a variety of negative health outcomes, including diseases of the gastrointestinal tract, kidney disease, and cancer.

### How does urban sprawl affect the economy? ›

Sprawl has two primary impacts: it increases per capita land consumption, which displaces other land uses, and it increases the distances between activities, which increases per capita infrastructure requirements and the distances service providers, people and businesses must travel to reach destinations.

### How does urban sprawl affect people? ›

Urban sprawl has been correlated with **increased energy use, pollution, and traffic congestion and a decline in community distinctiveness and cohesiveness**.

### What are the 4 types of settlements? ›

The four main types of settlements are **urban, rural, compact, and dispersed**.

### What are the 3 types of settlement? ›

Settlement Types

There are generally three types of settlements: **compact, semi-compact, and dispersed**. Each is based on its population density.

### What are the 3 main patterns of settlement? ›

The three main patterns of settlement are **dispersed, nucleated and linear**.

### Does China follow the rank-size rule? ›

**China does not follow the rank size rule** but does not have a primate city/mega ctiy either. The largest city in China is Shanghai with a population of 23 million. The second largest city in China is Beijing with a population of 18.079 million.

### What city is megalopolis? ›

Rank | Megalopolis name | Major cities |
---|---|---|

1 | Mega Manila | Manila, Calamba, Angeles City, Baguio, Batangas, Dagupan, Olongapo, Bacoor |

2 | Southeast Economic Zone | Đồng Nai, Bình Dương, Ho Chi Minh City, Bà Rịa–Vũng Tàu province, Long An, Tiền Giang |

### What is called a settlement with less than a population of 100000? ›

**Township or Subdistrict** – a medium town which has a population between 1,000 and 10,000. Suburb or Locality – a small mixed-use town or residential area, existing either as a part of a city or urban area or as a separate residential community within commuting distance of a city.

### What does rank-size rule mean? ›

According to the rank-size rule, **there should be a larger number of small cities than bigger cities**. Also, this rule predicts that the larger a city's population is then the fewer number of cities there should be in the surrounding area with a similar population.

### How many Super cities are there? ›

Today the world has **28** megacities, according to the United Nations, and that figure is projected to increase.

### What do you mean by primate city? ›

A “primate city” is a city that serves as by far the biggest city in the country that it inhabits. It's population is exponentially greater than the population of the next largest city in that country.

### Why does the rank-size rule not apply in all countries? ›

Why does the rank-size rule not apply in all countries? **Because some countries have one dominant city where they concentrate all of their wealth** (such as the capital city), bolstering that city and its population above the rest of the cities in the state.

### How do you find the rank-size rule? ›

The 'rule' states that, **if the population of a town is multiplied by its rank, the sum will equal the population of the highest ranked city**. In other words, the population of a town ranked n will be 1/nth of the size of the largest city—the fifth town, by rank, will have a population one-fifth of the first.

### Is Nigeria a rank-size rule? ›

**The rank size rule does not apply in Nigeria's case**. It did not predict the largest city in Nigeria. It is close when it predicted the population of Port Harcourt. Lagos is the primate city and the mega-city because its population is greater than 10 million.

### Does Mexico follow the rank-size rule? ›

**Mexico does not follow the rank-size rule**. The largest city has 20 million people while the second largest has 1.6 million which is not half of 20 million.

### Does South Korea follow the rank-size rule? ›

**The rank size rule is proven invalid in South Korea**. In order for South Korea to be under the rank size rule, Busan's population would have to be 1/2 the population of Seoul.

### Does Australia follow the rank-size rule? ›

**Australia technically does follow the rank-size rule**, although Melbourne is not half the size of Sydney. However the third fourth, and fifth largest cities do follow the rank size rule with being 1/3, 1/4, and 1/5 the size of Sydney.

### Does Brazil follow the rank-size rule? ›

The rank size rule was off about one million for the first and second largest countries, however it was only about 300,000 off for the fourth and fifth largest countries. Overall, **Brazil follows the rank size rule**.