early human history r (%) = 0.002%We already saw that the human rate of natural increase ("r") has increased over our history. That is, the human population has grown at a faster and faster per capita rate with time (largely because of decreases in d). Following are estimates of the global human "r" (expressed as a percentage) for various times in the past:
early human history r (%) = 0.002%
1650-1750 = 0.3%
1750-1850 = 0.5%
1850-1950 = 0.8%
Current = 1.2%
We can also see this increasing rate by looking at changes in estimated doubling times. The doubling time is just what it sounds like; it is the number of years it would take for the population to double its current size if "r" remained constant.
prehistoric - a mill yrs or so
in 1650 we were at 500 mill
by 1850 were at 1 bill -- took 200 yr to double from 1650
by 1930 were at 2 bill -- took 80 yr to double from 1850
by 1975 were at 4 bill -- took 45 yr to double from 1930
current estimated world doubling time is ~ 58 yrs (if the current
rate of growth continued)
Strikingly, most of the increase in the human population has taken place in less than one tenth of 1% of our history!!
The increase in the absolute growth rate (G) for humans has been driven by two things.
The first is that r is growing (as we just saw), driven mainly by decreases in d.
The second force driving the increase in G is related to this.
Assume for the moment that r is constant; that the human r is now maximal at its current 0.012 (or 1.2%, adding 1.2 people for each 100 at each time step). If that percentage remains constant from year to year, does that mean that the same number of people will be added each year?
That is, will G be constant if r is constant?
No, a constant, positive r gives rise to a curve that looks like this:
The slope of this curve (which is G) is getting steeper and steeper; more and more people are being added at each time step. Why is this, if r is constant?
The answer is that N is getting bigger and bigger at each time step, and we are applying a constant multiplier (r) to a larger and larger base number. While the per capita rate (r) is constant, there are more and more people to apply that rate to!
This is directly analogous to compound interest in the bank. "r" is the fixed interest rate (remember, not as a percentage here!), and the interest itself earns interest (people added to the populations produce more people, just like your interest gets added to the principal and earns interest).
So, the second factor that has caused the growth rate of the human population (G) to increase over time is that N has grown rapidly as well! (Remember, the other important, and related, factor was the historical increase in r.) G = r * N, and both r and N have been increasing.
(Click ">>" box to move to the next section (on exponential growth) now; "<<" box to move to preceding section, "Contents" box to return to master directory for the BI301 web site. Or, use "Navigate .")
Page maintained by Patricia Muir at Oregon State University; last updated Oct. 21, 2008.
