zipf's rank size rule and the primacy concept i an important topic for geographers and town planners.

1. RANK SIZE RULE AND PRIMATE CITY
DEMOGRAPHY AND URBANISATION
PRESENTED BY
TRYAMBAKESH SHUKLA
BP/463/2008
SCHOL OF PLANNING AND ARCHITECTURE
NEW DELHI

2. •IN 1950: 29% OF 2.5 BILLION PEOPLE
LIVED IN CITIES AND TOWNS.
•BY 2005: 50% OF 6.5 BILLION PEOPLE
WILL LIVE IN URBAN AREAS.
•BY 2025: 60% OF 8.3 BILLION PEOPLE
WILL LIVE IN URBAN AREAS.

3. • FORM, GROW, CHANGE, AND SOMETIMES
DISAPPEAR
• INCREASINGLY CONCENTRATE PEOPLE,
RESOURCES, AND ENTERPRISES IN SMALL
AREAS THE WORLD OVER
• ARE DYNAMIC, HIGHLY PRODUCTIVE,
INTERACTIVE OPEN ECOSYSTEMS (INVOLVING
GEOGRAPHY, ENERGY, PEOPLE, INFORMATION,
PRODUCTION)
• CREATE COMPLEX HIERARCHAL NETWORKS OF
PROXIMITY, INFRASTRUCTURE, MIGRATION,
COMMUNICATION, AND COMMODITY
EXCHANGE
URBAN AREAS

4. RANK SIZE RULE
ZIPF’S OBSERVED THE SIZE AND
NUMBER OF SETTLEMENTS IN VARIOUS
COUNTRIES. HE NOTICED A COMMON
CHARACTERISTIC WHICH HAS BEEN
CALLED THE RANK-SIZE RULE. HAVING
OBSERVED THIS ORDER IN THE REAL
WORLD, HE THEN SOUGHT TO EXPLAIN
IT. THE RANK-SIZE RULE IS AN EMPIRICAL
REGULARITY.

5. MAIN AIM OF RANK SIZE RULE
THE MAIN AIM OF THE RANK-SIZE RULE IS
TO FIND REGULARITIES CONCERNING THE
CHARACTERISTICS OF SETTLEMENTS IN
VARIOUS COUNTRIES, AND TO FIT A
GRAPHICAL DESCRIPTION TO THE SIZE
DISTRIBUTION OF CITIES .

6. THE RANK SIZE RULE
• THE SETTLEMENTS WITHIN A DEFINED AREA
ARE RANKED IN DESCENDING ORDER
ACCORDING TO THE SIZE OF THEIR
POPULATION
• THE SIZE OF A PARTICULAR TOWN CAN BE
PREDICTED BY OBSERVING ITS RANK AND
THE SIZE OF THE LARGEST CITY IN THE AREA
• THE TOWN’S POPULATION IS DERIVED BY
DIVIDING THE LARGEST CITY’S POPULATION
BY THE TOWN’S RANK

7. THE RANK SIZE RULE
• PR P1/R OR PR=P1(R )-1
WHERE P IS THE POPULATION
R IS THE RANK
P1 IS THE POPULATION OF THE FIRST-
RANKED CITY
PR IS THE POPULATION OF THE RTH
RANKED CITY

8. THE RANK SIZE RULE
• PR P1/R OR PR=P1(R )-1
WHERE P IS THE POPULATION
R IS THE RANK
P1 IS THE POPULATION OF THE FIRST-
RANKED CITY
PR IS THE POPULATION OF THE RTH
RANKED CITY

9. THE RANK SIZE PATTERN
IT IS USUALLY POSSIBLE TO RELATE THE RANKS
AND SIZES OF THE CENTRAL PLACES IN COUNTRY
BY USING A REGRESSION ANALYSIS
LOG PK = LOG P1 - B LOG K
P1 = POPULATION OF LARGEST CITY OR TOWN
PK = POPULATION OF THE Kth TOWN
B = COEFFICIENT WHICH MUST BE ESTABLISHED
EMPIRICALLY FOR EACH INVESTIGATION.

10. THE RANK SIZE PATTERN
• 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.).

11. THE RANK SIZE PATTERN

12. INTERPRETING ZIPF’S GRAPH LINES
• DISTANCE FROM ORIGIN = TOTAL URBAN
POPULATION
• SLOPE: AN INTEGRATED SCALING FACTOR
• CURVES (VIOLATE ZIPF’S LAW)
–CONCAVE
–CONVEX
• TAILS (A PROBLEM FOR POWER LAWS)
–UPPER (A FEW BIG CITIES)
LOWER “FAT” (MANY, MANY SMALL CITIES)

13. INTERPRETING ZIPF’S GRAPH LINES
• SLOPE OF THE LINE (AMT OF
DROP FOR 1 UNIT ON THE
HORIZONTAL AXIS)
• E.G.1.0 =
• E.G. 2.0 =
• HIGH = EVEN DISTRIBUTION OF
URBAN POPULATIONS
AMONG ALL CITIES
• LOW = URBAN POPULATION
CONCENTRATED IN
CERTAIN SIZE CITIES

14. WHAT DOES THE CURVE TELL US?
• CONVEX (SEE RIGHT):
BIG CITIES MAY BE
LIMITED IN SIZE,
POPULATION IN MANY
MEDIUM SIZE CITIES
• CONCAVE: FEW
MEDIUM SIZE CITIES,
BIG CITIES OR SMALL
CITIES MAY ACCOUNT
FOR LARGE SHARE OF
URBAN POPULATION
US CENSUS DATA 2000, n = 448

15. EXAMPLES NOT FITTING THE RULE
• IN AUSTRALIA, THERE IS A LARGE GAP
BETWEEN THE “PRIMATE” OR LARGEST
CITY AND LOWER RANKED CITIES. THERE
IS A DEVIATION FROM THE IDEAL
STRAIGHT RANK-SIZE LINE.THIS IS
BECAUSE IN AUSTRALIA, THE STATE
CAPITALS DOMINATE EACH STATE’S
TERRITORY

16. THE LAW OF A PRIMATE CITY
• A PRIMATE CITY IS ONE WHICH FAR
OUT-RANKS ALL OTHER CITIES OF THE
COUNTRY IN WHICH IT IS LOCATED,IN
TERMS OF POPULATION, COMMERCIAL
ACTIVITIES, INDUSTRIAL OUTPUT AND
POLITICAL INFLUENCES.

17. THE LAW OF A PRIMATE CITY
• THE LAW OF THE PRIMATE CITY IS MAINLY
APPLICABLE TO AGRICULTURAL BASED,
DEVELOPING COUNTRIES.IT WILL SHOW
FOLLOWING CHARACTERISTICS:
- SMALL TERRITORIAL EXTENT
- RELATIVELY HIGH POPULATION DENSITIES
- LOW PER CAPITA INCOME

18. THE LAW OF A PRIMATE CITY
• IDEA OF PRIMACY WAS FIRST INTRODUCED
BY MARK JEFFERSON IN 1939. HE STUDIED 46
COUNTRIES OF THE WORLD AND FOUD THAT
THE LARGEST CITIES WERE TWO OR THREE
TIMES AS LARGE AS NEXT LARGEST CITY.
• FRYER ISOLATED THE MILLION CITIES OF
SOUTHEAST ASIA AND ANASLYSED THEIR SITE,
MORPHOLOGY AND PATEREN OF GROWTH.
• MURPHEY TRACED THE GROWTH OF CAPITAL
CITIES OF ASIA.

19. FACTORS GIVING RISE TO PRIMATE CITY
• SPREAD OF COLONIALISM
• STRONG CENTRALIZED GOVERNMENT
• ECONOMIC FACTORS
• INDUSTRIAL AGGLOMERATION
• RURAL-URBAN MIGRATION
• EFFICIENCY OF MODERN TRANSPORT

20.  SILIGURI IS THE ONLY PRIMATE CITY IN THE REGION. IT IS 6 TIMES LARGER THAN THE 2ND LARGEST URBAN CENTER (JALPAIGURI).
 POPULATION IS CONCENTRATED IN SILIGURI.
 PRESENCE OF ONLY 1ST & 4TH ORDER OF URBAN CENTERS. MISSING LINK OF 2ND , 3RD ORDER URBAN CENTERS.
EXAMPLE OF RANK SIZE RULE IN INDIA
Siliguri Jalpaiguri Mal Mainaguri
Uttar
Bagdogra
Bairatal
Actual Population 1258256 213713 45288 44254 38505 8205
rank size rule
expectation(Pn=P1/n)
1250000 625000 416667 312500 250000 208333
0
200000
400000
600000
800000
1000000
1200000
1400000
POpulation
Projected Population 2031
0.00
1.00
2.00
3.00
4.00
5.00
Towns
Towns
PRIMACY INDEX = POPULATION OF THE SUBJECT TOWN/
POPULATION OF THE NEXT LARGER TOWN IN THE
REGION

21. RANK SIZE DISTRIBUTION OF CITIES IN
EASTERN INDIA