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I was interested in an easy way to figure out how population could change over time at different replacement rates. I haven't come across any ready formulas, so decided to make my own (and sorry if it doesn't read so easily without subscripts and superscripts):
The main concern is population, so let X be any given population. To track changes over time in one year increments, we can make our starting point X0, the one year point X1, two years X2 and so on. X1 will then most simply equal the effect of births - deaths on X0, so we can use the customary birth and death rates as percentages and say X1=X0 +X0(birth rate – death rate)). If we take a potentially attainable number, using the 2008 numbers from Italy, for instance, with a birth rate of .00836 and a death rate of .01061, the formula becomes X1=X0+X0*-.00225. This only gives us the change over one year, though, and we need to apply the changes of each year to the next year's number to get anywhere past X1, which gets a little more complex or repetitive.
Fortunately its about the same thing as calculating compound interest, so rather than puzzling it out I just borrowed that formula. The problem can be stated simpler, then, as X1=X0(1+-.00225), or X1=X0(.99775). Then X2=X0(.99775) to the power of 2, X3=X0(.99775) to the power of 3 and so on.
Moving on, the question that would be the whole reason for the math is: how doomed are we? Or are our population problems intractable to the point that starvation and war are inevitable, given peak oil and climate change.
If the current population of the planet attained the longevity and birth rate of Italy, which is considered to be at the forefront of the European population decline attributed to affluence and education, at "X100", or 100 years from now, our population would only naturally drop to 5.4 billion or so. It would take more than 500 years for the population of the planet to drop naturally to the 2 billion mark which has sometimes been offered as the planet's carrying capacity...
Having gone over the numbers pretty well myself, I think, I was just posting this in case someone can find an error or something I've missed.
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