Death from old age has stopped, but fertility window is the same. What is the new population equlibrium?

I'm imagining a near-future world where a process can be undergone that will halt all future aging of the body, but the approach causes infertility. Those undergoing it will not have (biological) children afterwards. This means that the long life does not lead to exponential growth in population, as the number of new children per generation has not increased by the extended life span. In fact since some may choose to undergo the anti-aging process when younger, to ensure they live their life in a younger more youthful body, the choose to self-sterilize by going through anti aging process may in fact drop the total birth rate per generation slightly.

These no longer aging adults will obviously not die of old age. Our medical technology will also increase and so death from health issues like heart disease or cancer will also decrease by a good amount (though some will still happen). However, death by accidental, homicide, suicide, etc will still occur slowly leading to the adults with expanded life span still eventually dying.

I'm wondering how much this will expand the total world population relative to today. Obviously with so many people living longer our total population will go up. However, at some point we would still hit equilibrium, where the number of deaths via non-age related causes will still equal the number of births.

I'm looking primarily at first world nations when it comes to population growth and total population size. Keep in mind many first world nations of today already have stable or decreasing population size if one ignores immigration, ie they don't birth as many children as adults die.

For now I want to assume that the increased population does not lead to a significant resource limitation putting constraints on birth rate or survival; ie were not all fighting over limited food/space caused by doubling our population. I'll be considering resource limitations in future questions based off of the answer to this one. However, Our population has time and time again doubled past what people thought would be an unsustainable population thanks to technology allowing more efficient production of food and usage of resources etc so it's possible our technology alone will be able to sustain the increased population well, but I'm also not beyond adding limited emigration to new worlds to make up for a situation where the population is just too high.

I'd also mostly like to ignore options such as freezing eggs prior to undergoing the anti-aging process or similar approaches to work around the infertility issues. I'll address such potential later, it may even be that such approaches are outlawed (or heavily regulated/taxed) by governments to help ensure sustainable populations.

I'm looking for hard science answers, if you can actually point to studies to back up claims on things such as birth rates and death rates I'd love it (though I don't require it).

• what about adoptions? are there also outlawed/regulated? – Kepotx Mar 11 '19 at 16:13
• I think you could likely ignore things like people choosing the process younger or IVF as far as worldbuilding goes. They're small numbers anyway and we have people who don't want kids now or can't have them and use IVF. I don't think it would make much of a difference. – Andon Mar 11 '19 at 16:14
• @Andon in this setting we may have a large number of people who want kids, but can't have them. – Alexander Mar 11 '19 at 16:24
• What do you mean by not dying of old age? Nowadays in civilized countries nobody dies of old age, everybody dies of some medical condition. Only in poor countries is old age still a valid cause of death. To take a specific example, a 93 year old man dies of a heart attack; did he die of old age (which would have been the case until about 40 years ago), or did he die of a heart attack (as it would be considered today)? – AlexP Mar 11 '19 at 16:25
• @AlexP very good point, but, if speaking stictly, nobody ever died just of an old age :) – Alexander Mar 11 '19 at 16:49

People do not simply die of general old age, they die of specific causes which become more common with age. Cancers, organ failure, any time mankind minimized one problem another one becomes the new number one.

Grabbing a random life table from an industrialized nation, about 0.2% of 40-year-olds die before they become 41. Or to look at it the other way around, 99.8% survive to the next year.

So one person should live $$\sum_{n=1}^{\infty} 0.998^{n}$$ more years, which a handy online site says is 500 years. That gives 540 years total.

For simplicity, assume that each couple has two children at age 40, counted as one child per person. By the time a first-generation immortality recipient dies, there are 12.5 generations of descendants around. From that point, this model is in a steady state.

The result is a 13.5-fold increase of population if the "one child" and "0.2% death rate" assumptions hold. Less if there are fewer children, of course, or more if the average couple has more than one child.

• Many people in industrialized nations are waiting with their children until they are in stable economic circumstances. If your immortality society is worried about insufficient birth rates, they could subsidize childbearing by young couples, in time to get the treatment before they are middle-aged.
• Counting parents, grandparents, great-grandparents, uncles, ... you get an amazing ratio of adults to children. Are you aware of the term professional aunt, no kids?
• I have every intention to consider the professional aunt situation. In fact I've already mostly written the question about how society will change due to most adults being infertile, before I put it on hold by realizing I should first get a better estimate of what the population distribution would look like before asking anything else. – dsollen Mar 11 '19 at 18:21

A few things that I would like to point out are that in the "Developed World" birth rates are dropping, and most of the new population growth will come from Africa and Asia. An anti-aging procedure would almost certainly cost a fortune, and would most likely only be available to affluent people living in the "Developed World". The overall population effects of an anti-aging procedure, might be a lot less than what you imagine as the procedure it will likely only be available to a select few. It might stabilize population levels in the "Developed World", but it would not likely have much effect in the rest of the world.

• The article you linked does not sustain your affirmation that birth rates are expected to increase greatly in developing countries. What the article says is that in the next 10 years most of the population growth will come from developing countries, which is a bit obvious given that no developed country is significantly above replacement level. – AlexP Mar 11 '19 at 17:15

The stable population would be huge

As a rough estimate, 4.25 trillion

Today, your chances of dying before the age of 65 are about 30%. After that, most deaths will be aging-related. Let's say, in the future, that number decreases to 10% as healthcare becomes more widely accessible throughout the world.

So, as a very rough estimate, a given population of ageless humans decreases by 10% every 65 years. Just to be clear: that is crazy. Once the population stabilizes at that death rate, 1.738% of people will be above the age of 2500. That's crazy long life!

That means that, for every 9 living 65-year-olds, there's 1 dead one. It also means that the population by age is given by $$P\cdot0.9^{\frac{x}{65}}$$ Where $$x$$ is age and $$P$$ is the population aged 0-65. Therefore, the total population is $$P\int_0^\infty0.9^{\frac{x}{65}}dx$$ Which is $$-\frac{65P}{ln(0.9)}$$ or $$616.929P$$ So the population would stabilize at roughly 617 times the population aged 0-65. Currently, that's about 91.5% of the population, or 6.89 billion. So if we started right now, the stable population would be around 4.25 trillion. The birth rate to keep that population stable would be 106 million births per year. That's about 15 births per thousand people today, or about 25 births per million people once the population stabilizes at over 4 trillion.

Now, that number is definitely wrong. This was a very hacky way to do the math, and it made a bunch of assumptions about how humans are born (namely, in the same quantity every year, exactly) and die (efficiently and at a constant rate). It also assumes that the human population exactly turns over every 65 years, with 100% of people being gradually replaced with new ones. It assumes that our current population is stable (it isn't – we're facing massive overpopulation).

But as a very rough estimate, this is the kind of number we'd be looking at.

Let's make some brutal simplifications to make the problem easier to solve.

• First, we note that men don't count. In general, for first order approximations of demographic evolution, men can be safely ignored; they don't make children, and no nation has ever taken a demographic hit because it didn't have enough men -- as long as there are a few men around, they will do their demographic job without complaining.

• Let's assume that the initial population pyramid has a uniform distribution for women from 0 to 49 years of age; this is a reasonable approximation for a civilized country with excellent healthcare and total fertility around replacement rate, for example, France.

• To fix some numbers, let's assume that there are 400,000 females for 0 years of age, 1 year of age, 2 years of age, and so on to 49 years of age. This is also a good approximation for France.

• We discount people 50 years old or older at the start of the exercise; they don't count, because they don't make children.

• Let's assume that with nobody dying of plain old age, the average age at death is 150 years.

Now, with those assumptions, we notice that there are 400,000 women crossing the threshold from 49 to 50 years of age each year. Since they will live on the average to the age of 150, it means that in the steady state there will be $$(150 - 50) \times 400\,000 = 40\,000\,000$$ of them. Since the number of women 0 to 49 years of age doesn't change, the total number of women will be $$40\,000\,000 + 50 \times 400\,000 = 60\,000\,000$$.

In conclusion, if the reproductive habits of the French don't change, and the average age at death is increased to 150 years, the population of France will stabilize at around 120,000,000 people, a little less than double the present value of about 68,000,000 people.

• "We discount people 50 years old or older at the start of the exercise; they don't count, because they don't make children." I am descended from a great great grandfather whose father was 50 when he was born. And that father was 60 when his youngest daughter was born and she married and had children. – M. A. Golding Mar 11 '19 at 18:16
• @M.A.Golding: Both of them were men... So they don't count for rough and dirty demographic estimations. While women past 50 do sometimes have children, this is rare enough to be ignored in such back-of-the-envelope calculations. – AlexP Mar 11 '19 at 18:39

When biology is altered to this point, you treat it as a sociology problem

There are several science fiction novels that deal with the changes that the removal of death does to society. The example that first comes to mind is Kim Stanley Robinson's Mars trilogy longevity treatments that, in theory, can make you almost immortal, or Cory Doctorow's Down and out in the magic kingdom memory storage that, coupled with cheap printing makes trivial to avoid dead (you'll lose the memories up until the last backup) or the more cynical take of the same concept in Richard K. Morgan Altered Carbon series.

All of them are recommended lectures because they tend to explore the concept on how longevity affects society.

But you asked for hard science.

When a space becomes crowded, our social behaviour changes

In a series of studies conducted between the 40 up to the 70's ethologist John B. Calhoun coined the term "Behavioural sink" to describe the societal collapse in animal societies as a result of extreme overcrowding.

It's most famous experiment is the "Mouse Utopia", in which he created an ecosystem for mice in which water and food escalated accordingly to the population but the space remained the same. In all cases once the population of mice reached a threshold of overcrowding they started to exhibit abnormal behaviours:

• Dominant male's aggressiveness response where heightened
• The female mice aggressiveness was also increased
• The young mice were expulsed from cadres before weaning occurred
• The non-dominant male started to behave non-reactively, even when attacked or hurt

Also of note, this behavioural changes didn't revert once the population decreased, eventually causing a complete collapse of the colony.

This already happened in animal colonies

There are several documented examples of isolated animal colonies collapsing, but the one that I was able to recall was the one of St. Matthew Island. The humans introduced 29 reindeer in 1944 as a source of food, and then left the island. The colony of reindeers had no natural predators and abundand food and rose up to 6000 in 1963, to suddenly collapse to about 42 speciments in about 2 years, and dissapearing from the island by the 80's.

Even if we attribute the crash to the harsh winters of 1963-64, the fact that the population never recovered even when the island could sustain them.

This already is happening in human colonies

Birth rates are declining in developed countries where the life expectancy is longer. A good study case is Japan, which has one of the highest life expectancies and one of the lowest birth rates.

The case of Japan has long been studied because it sports a lot of differences on how the rest of countries have adapted to the societal changes brought by overpopulation:

• Japan has upheld a very tight immigration control, meaning there's a limited influx of immigrants from poorer countries. This has a double effect, as these migrants tend to be more willing to have early offspring.
• Japan has doubled down on traditional roles, which means that unlike the rest of developed countries, the number of births outside marriage has not increased.

There are several more factors (like a collapsing job market) but the general picture is: Japan has to change or it is doomed.

And as for the rest of the countries, we are more or less compensating our lack of willingness to reproduce with migrants, but this is just a patch: once migrants are integrated in our society, they adopt our rules, including our unwillingess to reproduce. And at some point we will run out of space for more.

If we become immortal, society as we know it is doomed

If we don't change as a society to adapt to this (and this will be VERY hard), the choice we will have is that if our society will destroy itself or if we will run out of resources before that. And if we use the animal colonies as example, if we collapse, we probably won't rise again.

(In fact, I am of the opinion that even if we don't become immortal, we still have to deal with this, but that's outside of the scope of the question)

If we survive, we will probably not be humans anymore

To survive inmortality, we will probably have to change so much that we will look back at how humans were in the 20th century and they will be as alien as cavemen if not dinosaurs.

If the society wants to survive, fertility will be irrelevant because you'll want the population to stop growing. Reproduction will be done in vats and will be carefully planned. Male and Female will have their genes (sperm and ovulums) extracted and frozen before being treated with the anti-age serum, and they will be treated as soon as they end puberty.

(At that respect I recommend the lecture of Louis McMaster Bujold's Miles Vorkosigan saga, which talks a lot about reproduction, reproductive rights, and gene modification in several of the books)

• This would be a great answer if I had asked about the repercussions of the option, which I did not. I will be addressing all this later, but this question was specifically about numbers and asked for hard science to back it up. This answer is off topic for the question asked. – dsollen Mar 12 '19 at 17:18
• @dsollen fair enough. I tend to ramble too much anyway. In any case, my conclusion is we already are overpopulated and your technology will cause the collapse, so the new population equilibrium will be 0 :) – Stormbolter Mar 13 '19 at 9:17