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Tuesday, December 24, 2013

Breaking: Mankind Won't Go Extinct For Lack of Children

Many people worry about dropping birthrates and are concerned that one day mankind will become extinct for lack of children. For example, Hey Skipper recently wrote in the comments, "Self extinction is about 400 years off."

I've been meaning to do a population simulation for a long time. The simulation is fairly simple. Start with a population of 1,000,000,000 people. There are two types of "genes" in this population. The most common and also dominant gene is the "barren gene" and compels its individual to produce one child on average. Given that it takes two parents to produce a child, if this were the only "gene," the population would halve every generation and mankind would indeed go extinct in only a few hundred years.


The second "gene" is the "fruitful gene" and potentially compels its individual to have three children on average. However, since this "gene" is recessive, the individual is only compelled to have three children if he or she has two of these "genes." At the start of the simulation, only five-percent of the genes are of this type. So not only is it recessive, it's also rare.  If a double "fruitful" mates with a someone with at least one "barren gene", they split the difference and have two children.


The graph above shows the results of one run of the simulation (since it randomly combines each generation, the results are slightly different each time).  The population drops for 15 to 20 generations before turning the corner and recovering fully somewhere around the 40th generation. (If anybody wants the matlab code, let me know, I'll be happy to send it to you).

I think that this simulation is very pessimistic (i.e. the population will never drop that far).  I don't think the "fruitful gene" is fully recessive, I think it's more prevalent than five-percent, I think that "fruitful" people would seek each other out instead of mating randomly, and I think that the "fruitful gene" is probably more fruitful than just three kids.  For example: if the "fruitful" folk seek each other out instead of mating randomly, the population typically drops less than a factor of ten over 4 or 5 generations before recovering fully within 10; or when starting the simulation with 10% "fruitful genes" and having two fruitful parents produce four children, the population for only around 10 generations before recovering fully after 20.

The point of this is not to convince anybody, but rather to show why I'm highly skeptical of the claim that mankind will go extinct due to low birthrates.  I know too many highly educated, non-religious couples with access to birth control who have three or more children by choice.

The barren will go extinct, but not the fruitful.

14 comments:

Hey Skipper said...

There are two types of "genes" in this population.

Bret, you are assuming as true that which likely does not exist.

Pre-modern era, women could not control their own fertility. I am at a complete loss as to what evolutionary pressures would have selected for a gene that can count the number of pregnancies, and be satisfied at some specific number.

It certainly doesn't exist in other mammals, so presuming it in humans seems a real stretch.

What is clear is that when women are given a choice over how many children they will bear, that number is far less than they they can bear. Even Mormons, avowedly natalist, the TLF went from 4.4 to 3 in a generation.

This is what I mean:

The prediction that world population will soon begin to decline is based on almost universal human behavior. In the United States fertility has been falling for 200 years (except for the blip of the Baby Boom), but partly because of immigration it has stayed only slightly below replacement level for twenty-five years.

Obviously, if for many generations the birth rate averages fewer than 2.1 children per woman, population must eventually stop growing. Recently the United Nations Population Division estimated that 44 percent of the world's people live in countries where the fertility rate has already fallen below the replacement rate, and fertility is falling fast almost everywhere else. In Sweden and Italy fertility has been below replacement level for so long that the population has become old enough to have more deaths than births. Declines in fertility will eventually increase the average age in the world, and will cause a decline in world population forty to fifty years from now.


Annually, the US census bureau puts out population estimates for 2050. The 2012 estimate for 2050 is 39 million fewer than the 2008 estimate, almost half due to fewer births.

Perhaps definite trends should outweigh putative genes.

Hey Skipper said...

BTW, the article I linked to was written 14 years ago. Since then, every trend they cited has accelerated.

I'm in Japan today. Coincidentally, there is an article in the Japan Times that this year, for the first time, more adult than baby diapers were sold.

There is absolutely no sign of a 3 kid gene in this country.

Annoying Old Guy said...

Skipper;

Please observe Bret's graph, and note that it declines before increasing. That's consistent with your observations.

Bret is obviously taking a simplified view by encoding "willingness to have children" with his psuedo-genes, but I think the underlying point remains. Some people are still having children above replacement level and that's likely to be inheritable (genetically or culturally) and those people will eventually outnumber those who are not willing.

That is, breeders win.

P.S. Bret, have you ever read Taranto on his "Roe Effect" notion? Somewhat similar to what you write here.

Hey Skipper said...

... have you ever read Taranto on his "Roe Effect" notion? Somewhat similar to what you write here.

While I think Taranto is brilliant, in this regard I think he has presumes too much.

Since essentially all women have many fewer children than they can potentially bear, having an abortion will only effect the timing, not the absolute number, of births. Asserting that women who are inclined to have abortions are also inclined to have fewer children amounts to a claim of correlation without any information about causation.

Some people are still having children above replacement level and that's likely to be inheritable (genetically or culturally) and those people will eventually outnumber those who are not willing.

Of course some women are having more than two children, but you make a huge leap from there to the presumption that their daughters will inherit that inclination in the future in a way that is glaringly absent in the present.

It certainly isn't working that way in Japan, or much of the rest of Asia, or Europe, or even in the US. Absent the birth rate of recent immigrants, the US would also be below replacement TLF.

And culture doesn't help your cause, because that is precisely where the finger points as the cause of plummeting birth rates.

In our brave new world, children have significant opportunity costs. Women are not automatons.

Annoying Old Guy said...

Skipper;

Because of women's "biological clock" affecting the timing of births can also affect whether there is a birth at all.

I don't think you can presume daughters won't be influenced by their mother's attitude toward reproduction. For one example, religion - it's clear that religious people have more children and that is certainly culturally inherited. You can say "it's not that large an effect" but that's precisely the kind of small differential that evolution uses to make large differences over time. For your thesis to be true, there must be no genetic / cultural combination that encourages reproduction. Because as long as there is a at least one, it will in time dominate.

While children may be opportunity costs, women may also believe children have some positive aspects, and the latter can IMHO be influenced both genetically and culturally.

Bret said...

Hey Skipper wrote: "It certainly isn't working that way in Japan..."

Isn't it? Let me know if they still have falling birth rates after 16 generations as in the simulation. :-)

Hey Skipper wrote: "It certainly doesn't exist in other mammals..."

Variants do. Many mammals adjust litter size based on food supply and environmental stresses.

Also, to emphasize AOG's point, many highly religious sects have very high birthrates. For example, ultra-orthodox jews in israel have 6 to 8 children per couple. Still. And, in fact, the ultra-orthodox will become a sizeable chunk of the Israeli population in another couple of generations because of this impressive fertility.

Will that trend continue? I doubt it as they'll probably be nuked by Iran after a bit. But some combination of genes and culture will take root, probably multiple times, in the next several hundred years that sustains a more than replacement fertility rate and those groups will inherit the earth.

The time frame we're considering is a really long time. That's more-or-less from the end of the middle ages to the modern era. An LOT can happen in that period of time.

Hey Skipper said...

I don't think you can presume daughters won't be influenced by their mother's attitude toward reproduction.

I'm not; quite the opposite. I’m certain that influence exists.

However, so far as I can tell, that influence only extends to somewhat lagging the overall trend. Mormon Total Fertility Rate (TFR*) has gone down at least as fast as the rest of the US. While it is still above replacement, the trend is still down.

But even taking maternal and religious attitudes as read, the clear trend is for fewer people to consider religious dogma as being literally true.

For your thesis to be true, there must be no genetic / cultural combination that encourages reproduction.

Not quite. For my thesis to be true, there only has to be no specific genetic component that programs women to want to have a specific quantity of children. Clearly women have a deep desire to have children, but the degree to which that desire is requited depends on the number of children. One child does so infinitely more than none, but each additional child does so far less than the one previous. That has to be so, or women would have as many children as their fertility would allow; clearly, that isn’t the case.

The evolutionarily unprecedented ability to control fertility means that at some point, the opportunity cost outweighs the positive aspects of an additional child.

So the only things required for my thesis to be true is that more women reach that point at two or fewer children than do so at three or more, and that there is no inheritable quantity tendency.

IMHO, modernity’s consequences have already caused the former, and there is no evidence for a heritable tendency towards family size.

If my thesis is correct, the longer a society is modern, the more its TFR will trend towards 1.2 - 1.8. AFAIK, there aren’t any exceptions.

Interestingly, the UN population projections I have looked at over the last couple days presume, without justification, that TFR will rebound to replacement rate. That doesn’t jive particularly well with their own data for population replacement rates.**

Currently, the global replacement TFR is 2.33, and the TFR is, at 2.36, scarcely past that. As more countries get wealthier, and more women gain control over their fertility, that rate is bound to go down. The native born US population has a sub-replacement TFR. The total EU TFR is 1.6.

The existence of females with power to control their fertility is not a product of evolution; therefore, it is far from necessarily the case that humans are evolutionarily adapted to this, or can adapt in the very short time that might be available. That right there might be the answer to the Fermi Paradox.

* I had used the wrong acronym previously
**http://en.wikipedia.org/wiki/Total_fertility_rate#Replacement_rates” Why is blogger suddenly throwing fits over links in comments?

Annoying Old Guy said...

Skipper;

You think there is no genetic component to how much women want to have children, which in turn will influence how many that have despite control of fertility?

Hey Skipper said...

That is an interesting question.

I don't think there is a genetic component to, say, homosexuality, but there it is, nonetheless.

I certainly don't think there is a genetic component to raw numbers of children. It is an extraordinary claim that there is a gene that programs some brains to be happy with one baby, others with two, and yet still others with more.

Clearly, there is some genetic component. It is called "maternal instinct" for a reason. But just as clearly, that instinct is very elastic; otherwise, there is simply no accounting for plummeting birth rates in response to changing opportunity cost considerations.

That means that beyond the certainty that post-industrial economy opportunity cost considerations cause a collapse in TFR, it is arguable that the proclivity to have children doesn't have enough variation to eventually overcome below-replacement TFR.

Which means the link between how much women want to have children, and how many they want to have, is far from ironclad.

The answer to the question might lie in twin studies looking at TFR. I don't know of any.

(BTW, Taking Bret's graph as read, the human population drops to 100,000 before increasing. His entering argument is that 5% of the female population has an inherited tendency to satiate their maternal instincts at three children. What if he is right in general, but wrong in the specifics? What is the minimum if instead 4.9% has that gene?)

Bret said...

Hey Skipper,

AOG asked you a "yes" or "no" question. It doesn't look to me like you answered it in your many paragraph response. If you did answer it, I'm guessing your answer to his question is "no." Is that correct?

You asked: "What is the minimum if instead 4.9% has that gene?"

About the same. It's not quite that sensitive, though 5% was getting near the edge. However, that's without those wishing to have more children seeking each other out. If fruitful folk seek each other out, the population doesn't get below 100,000,000 and starts recovering after 4 or 5 generations. Also when fruitful folk seek each other out, extinction is avoided as long as there is at least one "fruitful" couple (though they'll get fairly interbred).

Hey Skipper said...

That was my way of saying the answer is unknowable, but on balance I don't think it likely there is a gene that inclines it's bearer to a specific number of children.

As for seeking out, I think you are wishing away some real information problems.

So, sure there might be such explicit genetic programming. But what if there isn't?

Bret said...

Hey Skipper,

Good point - it was really a yes, no, maybe, or don't know kind of question, so "don't know" is a perfectly good answer. But once we get to maybe and/or "don't know," aren't statements like "self extinction is about 400 years off" a little too certain?

You wrote: "I don't think it likely there is a gene that inclines it's bearer to a specific number of children."

Not a specific number of children, just like genes don't make you an exact height. But my observations show me that there's a range of intensity around sex-drive, baby-hunger, etc., each of which is ultimately going to affect number of offspring, and each of which look to me to have a significant genetic component.

One more thing to consider (I almost added this to the original post). Let's say the population drops to 1 million. At that point, I don't think there'd be sufficient capacity for specialization to manufacture birth-control pills, condoms, etc. At some level of population, there wouldn't even be enough resource to protect women against rape. I think that the population wouldn't drop below that point.

Annoying Old Guy said...

Let me re-iterate Bret in that the genetic factor I am asking about is the psychological reward of having children, which shifts the average number of children but is obviously not as deterministic as Skipper seems to think. It also seems very likely (if not outright undeniable) that women liking children and raising them would be a strong contributor to genetic success.

Hey Skipper said...

[Bret:] But my observations show me that there's a range of intensity around sex-drive, baby-hunger, etc ...

[AOG:] It also seems very likely (if not outright undeniable) that women liking children and raising them would be a strong contributor to genetic success.


I agree that the desire to have children is distributed just like other characteristics are. And it is impossible to both believe in evolution and deny that wanting to have and raise children is a huge contributor to fitness.

The question you are assuming the answer to is variance around the mean. If the variance is high, then there will be a lot more women whose desire to have children is significantly greater than the mean.

If it is low, then very few women will be far from the mean.

You are presuming the former, but I'm not aware of any evidence one way or the other.

Let's say the population drops to 1 million. At that point, I don't think there'd be sufficient capacity for specialization to manufacture birth-control pills, condoms, etc.

Excellent point, and one which invalidates my assertion that extinction due to low birth rates is over the top.