Rank Size Rule concept was propounded by P. K. Zipf. This is also a concept in urban hierarchy. The hierarchy is based on population size. Unlike primate city concept that focus only on the most dominant largest city and ignored the role of relationship of other small towns and villages in the settlement complex.
According to Zipf,
P1 = Population of the largest city
P2 = Population of the 2nd ranked city
Pn = Population of the nth ranked city
So, Pn ∝ (1/n) * P1
There is a relationship between the rank of a settlement and its population with respect to the largest city. Zipf found an exponential relationship between the population and rank of a city in a settlement.
If the relationship is plotted for the logarithmic function of the population, the graph is a straight line.
The following are the insights in the Rank Size Rule pattern.
The straight line of the log function is actually an ideal state. But in reality, there may be deviations. There are 2 possible deviations. Curve B depicts the primate city relationship where the largest city is much bigger and is a disproportionately large curve. Curve C depicts the possibility of more than one city comparable in size in the levels of upper hierarchy.
Big cities are very few and have considerable variation in their disproportionate sizes whereas smaller settlements, towns, and villages are numerous and maybe all of the comparable sizes.
Zipf himself didn't explain the reasons or the process in how the Rank Size Rule button results in reality and why do the settlements may acquire this relationship.
One of the interpretations in Rank Size Rule resolution is that it probably is a natural tendency and some empirical natural law that decides the ratio of population sizes. It is in accordance with the Fibonacci series and the rank-size rule obeys the Lucas sequence of the Fibonacci series.