Growth (cont.)
NRR and growth
If the NRR is the average number of daughters to a woman, it can be interpreted as the ratio of one generation to another. If the length of the generation is G, then we can express this as:
NRR = PG / P0
If the initial population size is P0 and time is t, the exponential growth formula tells us that:
Pt = P0 . e rt
It follows that:
Pt / P0 = e rt
If we substitute generation length G for time = t, it follows that:
NRR = e rG
This means that we can express the NRR in terms of exponential population growth. If we knew the value for G (average generation length), we could solve the equation for r and find the annual growth rate using the following steps:
ln NRR = rG
r = ln NRR / G
Exercise: If we know the NRR, what further measure do we need to use the NRR to estimate annual growth?