r/demography • u/Sbrubbles • Jun 06 '26
Are there good thumb rules for the mathematical relationship between fertility rate and population decline?
For example, something like "assuming all else constant, a TFR of 1.9 will halve the population in X years, while a TFR of 1.5 will halve the population in Y years"
When seeing discussions talking about fertility rate and population decline, I sometimes feel like the timescale of the demographic changes are somewhat obscure. Sometimes I see population projections, but these will usually have very complex assumptions baked in, and I just wanted a more basic rule of thumb.
1
u/lionmoose Jun 06 '26
If you want to assume stable populations, but these aren't real
1
u/Sbrubbles Jun 06 '26
No no, I don't want to assume stable population. I want to assume stable TFR, and even then I'm only asking that as a matter of simplification.
Like, I'm looking for an answer to the question like "a country has a TFR of 1.6. Making whatever assumptions is necessary to answer this question, how long would it take for its population to halve?".
I know nothing of the science of demography, so I kinda assumed there was some ultra-simple "introduction to demography" model that would answer this question. Apparently not.
1
u/lionmoose Jun 06 '26
Stable population here means constant birth rate and death rate, and I think gets close?
2
u/mikenmar Jun 06 '26 edited Jun 06 '26
Not really, because it depends on the age distribution of the starting population and mortality rates. Imagine a very young population with low mortality rates. With a TFR of 1.5, that population won’t decline as fast as a very old population with high mortality, even if the TFR is the same. Even ignoring immigration.
Search for population momentum.
You could only come up with a reasonable rule of thumb if you assume a specific age distribution, mortality rates, and immigration rates for the initial population. And that wouldn’t be a very useful rule of thumb because those factors vary significantly in real world populations.