When will the world reach 'peak child'?

This is an interesting argument; thanks for sharing it. I didn't understand it right away and my intuition was that you must be incorrect. But after playing with some actual numbers I've come to understand. In an attempt to restate your claim in a way that's more intuitive to me:

If a group is reproducing above the replacement ratio, then they haven't hit peak child yet. So if only one subgroup remains that hasn't hit peak child, then that subgroup is also the only one that's growing (all others are shrinking). Assuming that trend continues (read: assuming subgroups have birth rates that reflect their culture, and that culture will be preserved in the next generation), this subgroup will grow without bound.

The pressure-release on a system like this (one which the article you linked points out in its conclusion) is that birthrate within a subgroup isn't fixed. The birthrate among the Amish appears to be declining slightly, perhaps influenced by economic forces in the US. In your example, while it's true that _tommorow_ there will be more Mormons and fewer Italians than today, that doesn't guarantee that eventually the world will be populated entirely by Mormons, because the birthrate in that subgroup isn't wholly 'inherited' (in the cultural sense) -- it may change in ways that we can't forecast today.

No, it just has to make less children than it did eighteen years before.

Not really, because subgroup membership is flexible: people can enter and leave a subgroup. But even ignoring that objection, calculating that the Amish will eventually outnumber everyone else is a crazy bad extrapolation, whereas predictions of world population are based on much more modest and justified extrapolations.

If you took some old population data you could perhaps extrapolate that Shakers were destined to increase exponentially, but what happened to them? I'd say that the destiny of a single religious group is typically a short-term and local phenomenon that doesn't much affect the long-term development of world population.

By the same token, if a certain group keeps reproducing at a high pace, but the majority of the world keeps having fewer and fewer children, the overall number of children will decrease, so the curve will be past the peak.

So we know the solution, whether the world or locals are willing to implement them are another question.

I don't think there is any way the world remains livable with 12 billion aspirational consumers.

[1]https://www.wired.com/2011/04/ff_vasectomy/

It's difficult to see now of course because Africa is more unstable and fragmented than East Asia. But a lot of countries in Subsaharian Africa are not worse off than China in the 1990s and have a promising gdp growth rate (not as big as China yet, though)

The West and the East will both be somewhat impoverished (relatively speaking, not in an absolute sense) by aging and shrinking workforces. They'll be desperate for workers from Africa.

In the poster boy of overpopulation, Bangladesh, the fertility rate dropped from 6.2 children to 2.1 children per mother (https://www.ft.com/content/f60e2ddc-0bbc-11e1-9861-00144feab...). No Asian country today has fertility rate above 2.5 AFAIK (except maybe the Philippines).

There's really no alternative path I can see. One could put it at urbanized, cosmopolitan women aren't interested in child birth unless there are positive options.

I mean, first people thought China's one-child policy was reducing childbirth but a close look and efforts to dial showed the decisions were fairly well set.

Brazil didn't have to have an education outreach program. Ordinary TV was enough to reduce the reproduction rate.

And a variety of nations are looking at their negative reproduction rates (Japan, Taiwan, Russia, France, China etc) and finding there's no easy reversal. It's more like high reproduction are an exception in society's transitioning out of peasantry but after that, it goes down and doesn't go up again.

I find this highly unlikely. There is huge selection pressure in favor of any population that is resistant to whatever is causing the general decrease in fertility.

One example is the Amish. For quite a while, now, their population doubles every 20 years. So far they've managed to maintain their fertility, where other notoriously high fertility populations who are less culturally isolated have not.

Think of it this way, given what you know of class dynamics and sexual selection in humans, if your child had the choice of selecting between one in a random assortation, without knowing which was which, which one would be advantaged and why?