Wednesday, August 31, 2005

Population Growth

Dinner party conversation last night raised a point I’d never thought about. That population growth (or shrinkage) is related not only to the number of children the average woman bears, but also to her age when she gives birth. Meaning, let’s say that women have, on average, two kids. The effect on population growth will be completely different if they have them at age 20 (in which case population growth will be higher) or if they have them at age 40 (population growth will be lower).

I’d love to figure out the equation that governs this, but let’s take a simple example. For simplification we’ll trace only female lineage, but if you think about it you’ll see that this doesn’t change the essential results:

Let’s say life expectancy is 85. A woman has two children at age 20 (boy and girl). When she’s 40, her daughter has two kids (boy and girl). When she’s 60, her grandaughter has two kids (boy and girl). When she’s 80 her great grandaughter has two kids. That means that when she dies at age 85, there are eight people alive that are offspring of herself or of her direct female descendants.

Now let’s assume that she gives birth at age 40. When she’s 40 she has two children. When she’s 80, her daughter has two kids. When she dies at age 85, there are only four people alive that are her offspring, or offspring of her female descendants. Meaning, the difference within this period of 85 years is a factor of two. Double the population just because of the earlier age of childbearing.

I find this particularly interesting since we tend to talk about the replacement rate – the rate of birth that’s required to keep a population steady (not declining), and it’s usually quoted at about 2.1 births per woman. But in fact, this rate is tightly tied to the age of childbearing, and changes in that age can change population sizes dramatically, even if the number of children per woman remains constant.

Of course the specific example of interest is today’s phenomena of women having children later in life. With new methods that allow freezing of eggs for later use, this age is likely to get even higher. The conclusion is that this change can cause population decline even if the ultimate number of births per woman doesn’t change.


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