Why would you keep having more and more children when you didn't have to? I have it on good authority that most women aspire to do other things than just pop out as many as they can.
There are plenty of neighborhoods and even countries that might give you pause. There are plenty of people for whom having children is their only goal, their only live purpose, and the only meaningful thing they do in their life besides living.
In any population, there are sub-populations with higher and lower fertility.
Over time, because of differential reproduction, these sub-populations will eventually come to dominate, and form the majority of the whole population.
At that point, overall population increase begins and accelerates indefinitely until it hits a Malthusian wall of scarcity.
This process is the same regardless of what distinguishes the higher-fertility subgroups. It could be religion, or genes, or culture, or any combination of these. In any case, those characteristics will eventually dominate.
So one way or another, we will overpopulate and be forced to stop, unless we stop the process of high-fertility subgroup domination using some sort of long-term planning. In the end the only permanent solution may be some fixed-proportion guided reproduction regime, or perhaps a fixed genome mix that we maintain at all times. No natural gene recombination may be allowed, no natural mutations may be allowed to persist.
The current reprieve from this Malthusian tautology is the temporary result of the Industrial revolution and associated cultural shifts colliding with old-time cultural constructs. It couldn't last more than a century or so. Already, differential fertility of massive and obvious. Fertility of very conservative people is 2.35, of the most liberal it is 1.6. Subgroups like Amish, orthodox Jews, and conservative Muslims, and low-IQ people are rapidly growing in the population.
The Amish population doubles every 20-25 years; a simple calculation reveals they'll be hundreds of millions of people within a couple centuries, and billions a couple decades after that. They will grow until something stops their reproduction. The only question is what that something will be.
Evolution will win out in the end. Life finds a way. And it has all the time in the universe to do so.
When someone shows me a picture of exponential growth I always ask whether they're sure it isn't a sigmoid curve. In the case of population, extrapolations such as yours rest on the implicit assumption that motivating factors will never change.
For example, I was a bit surprised about your mention of the Amish population doubling, and went to read a few articles to learn more about that. Consider this quote from one in a Lancaster County, PA paper (which seems like a well-informed source since it sits in the middle of Amish country):
Ben Riehl, an Amish farmer, said the local settlement is growing “as fast or faster than it ever has.” However, he thinks families are getting somewhat smaller. A family may have five children these days, rather than nine or more.
He attributes that to the shift away from farming, a vocation that lends itself to large families.
Demographics are just not a one-way street. Certainly there are strong incentives and traditions to pop out lots of children in some contexts. But those incentives change, and do people's behaviors. We're going to be overrun by _________!' is a common anxiety that has been refuted over and over again by anthropological studies. It only makes sense in models where you assume everyone acts independently and populations and individuals don't really interact with each other.
Well, there's nothing that says the Amish are homogeneous or must stay that way.
Even among Amish, there will be some sub-groups where fertility falls, and others where it stays the same or rises.
So, the Amish who reduce fertility (like those you quoted) will eventually be outnumbered by those other groups of Amish who continued to reproduce at higher rates.
Even if the differential is tiny, and the high-population group is initially a single individual, it will eventually dominate. Heck, even with zero high-fertility sub-population, one will eventually mutate into existence and then dominate. This is evolution.
Maybe it'll be 50 years, or 150, or 1,000 years. What you're saying could affect the timing of the wheat-and-chessboard outcome, but it doesn't change that outcome.
>Demographics are just not a one-way street. Certainly there are strong incentives and traditions to pop out lots of children in some contexts. But those incentives change, and do people's behaviors.
You're still imagining that the base "rules" like human nature are invariant. For example, you're talking about "incentives", as though people respond to incentives in fixed ways.
But they don't. Even if the incentives change to encourage low populations, some subgroup will quasi-irrationally ignore those incentives any over-reproduce anyway. Eventually, that subgroup and their quasi-irrational characteristics will dominate.
>We're going to be overrun by _________!' is a common anxiety that has been refuted over and over again by anthropological studies. It only makes sense in models where you assume everyone acts independently and populations and individuals don't really interact with each other.
Well first, you seem to be making some implied xenophobia accusation. Nothing in my comment identified any "we" nor any "_blank_" that "we" would be overrun by. This has nothing to do with fear. I simply said something about population dynamics that applied to all organisms of all species everywhere.
In addition, usually the identity lines aren't that clear and my point doesn't require them to be. I clearly talked about sub-populations who come to dominate their identity group, which is different from one identity group dominating another. Both can occur.
I'd ask that you please don't imply in some accusation of irrational immoral xenophobia on my part, and don't attribute emotions like xenophobic "anxiety" to me without me stating them. It's just not productive.
Regarding your narrow point, 'We're going to be overrun by _________!' has not been refuted. Quite the opposite - historically, it's come true many, many times: Native Americans got overrun by fast-breeding Europeans. Ainu were overrun by fast-breeding Japanese. Berbers were overrun by Arabs. Many ancient tribes overran other tribes (e.g. Zulu overran many other tribes). And so on.
>When someone shows me a picture of exponential growth I always ask whether they're sure it isn't a sigmoid curve.
I agree in general. But here's why I'm sure this isn't a sigmoid curve: Life began on Earth 3.8 billion years ago and population has always been exponential for every species, anywhere, ever.
The only major exception I can think of is humans since the industrial revolution, and evidence shows that this is temporary. I'd be happy to hear about other examples (though I suspect they'd also be temporary or very strange exceptions that prove the rule).
If we want it to be a sigmoid curve, we must choose to make it a sigmoid curve using policy.
Also - If you think the Flynn effect (measured increases in average IQ over time) contradicts the hypothesis that low-IQ people have more kids, you're confused. Both can be true at the same time, if the Flynn effect is due to environmental changes and not eugenic breeding (which seems to be scientists' tentative conclusion right now).