> "The world as a whole is headed for a relatively gentle flattening of population growth"
You know something that's really weird to think about? In 1950 Africa's population was 227m! [1] The US at the time had about 160m, nearly as many people as the entire African continent! Fertility rates are hard to intuit because they're not only exponential, but systems where the effect is delayed from the cause by several decades, but then once it starts - it starts rocketing off uncontrollably, be that in loss or gain of population.
The world's population may start to level off at some point, but sub-replacement rates will cause Western nations to start losing population at an exponential rate. It will be the equal but opposite of what happened to Africa over the past century. And this doesn't level out or even slow down, except when people start having children again. So for instance many people know Japan now has > 10% of its population over 80, but I think a lot of us have this sort of concept that 'Well sure, but as they start to die off - then things will probably start to look a bit more sane.'
In reality, it's the exact opposite. As this group dies off, they're going to be replaced by an even larger group of 80+ year olds, leaving Japan in an even worse state, as one can immediately see just glancing at Japan's population pyramid. [2] Right now Japan's losing about 1 in 200 people per year, and this will never stop until either they go extinct or they start having children again. And it will actually get substantially worse until they hit their 'fertility equilibrium point' where all living generations have/had comparable fertility rates (picture the sides of the population pyramid having a constant slope). And that's what's waiting for the entirety of the Western world, if we don't turn things around.
And this is also likely a vicious cycle because as age ratios and demographics get all screwed up, economies will start to collapse, which will make it even more uncomfortable to have children.
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[1] - https://www.worldometers.info/world-population/africa-popula...
[2] - https://en.wikipedia.org/wiki/Demographics_of_Japan#/media/F...