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).

Impossible to answer ...

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?

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.

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 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
$$
Pcdot0.9^{frac{x}{65}}
$$
Where $x$ is age and $P$ is the population aged 0-65. Therefore, the total population is
$$
Pint_0^infty0.9^{frac{x}{65}}dx
$$
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.