Population through time

Population, be it of a sector, a square kilometer, an entire region, or even only of a single structure or room, is a quantity. Analyzing population change through time is therefore simply a matter of tracking the increases and decreases of this quantity as it pertains to a particular unit of analysis. The most convenient way to do this - since the time periods used in this study are of unequal length - is by calculating for each phase an annual rate of population growth relative to the previous phase. This is done using the following equation ([Hassan 1981]: 139):

  
$r=\frac{1}{T}\ln \frac{P_{f}}{P_{i}}$ 




where $r$ = annual rate of population change 


		 		 $T$ = number of years 


		 		 $P_{i}$ = initial population index value 


		 		 $P_{f}$ = final population index value

Multiplying the derived value of $r$ by 100 yields an annual percentage rate of population growth. This is the figure which I will use in this study to measure rates of population growth or decline, since growth rates seem often to be reported in terms of annual percentage rates (e.g. [Hassan 1981]: 140). Cross-cultural comparisons and archaeological studies have shown that an annual growth rate of approximately 0.1% characterizes non-industrial agricultural village populations worldwide ([Hassan 1981]: 220, 234; also [Carneiro and Hilse 1966,Cowgill 1975]). This accords almost perfectly with the population growth rates calculated for the various Taraco Peninsula phases.