In earlier times, population growth was limited by the fact that the majority of children died before they were old enough to have children themselves. Illness and lack of resources has probably contributed greatly to the high childhood mortality. Today our technology is better, and so we are able to utilize the Earth’s resources more efficiently, and now, luckily, most people survive childhood. This has led to a population explosion. The greater number of people has led to faster technological progress, which is making room for still more people, and so on – a virtuous circle that helps to give human beings a better standard of living.
But as we have gotten better standards of living, the number of children we get has declined. Just during the last 50 years, the number of children born per woman (fertility rate) has more than halved from 4.9 to less than 2.4 worldwide:
If the average age at which women have children and the average life expectancy both remain constant, population figures will also remain constant if women have an average of two children – one boy, and one girl who grows up to have children of her own. In the above graph the value “2” on the y-axis is therefore an important separator (and thus emphasized with a different color).
If we do not develop life extension technology, there is a limit to how much the average life expectancy can increase, so if the number of children per woman (fertility rate) falls below 2, sooner or later the population figures will begin to decline. And not only will they decline, they will drop to 0 after a high enough number of generations. How fast the population figures drop depends on how far below 2 the fertility rate gets. A lot of people worry about overpopulation, but maybe it’s population decline we should worry about instead?
Especially if we manage to fight aging, ie if technology that can keep people alive and in good health indefinitely is developed, then many people are absolutely certain that the Earth will be overpopulated. But perhaps combating aging is precisely what is necessary for humankind not to die out?
How will population increase if people stop dying?
It is hard to say how many children it will be common to have in the future, but it does not seem unlikely that the fertility rate will drop below 2 some time during this century. Let me go through three different scenarios. In all cases we’re starting off with 9 billion people on Earth, and for simplicity there are as many people who are 0 years old as there are people who are 1 year old and so on up to and including 89 years of age. All women have their children when they are 30 years old. No one dies.
- Fertility rate is 2:
In that case 100 million children will be born in the first year. That’s the same amount of people that we assumed to be alive in all of the 90 different ages between 0 and 89 years. It will therefore continue to be born 100 million children every year indefinitely. Since no one dies, population increases linearly with 1 billion people every ten years. (A fertility rate above 2 will lead to an exponential increase.) - Fertility rate is 1:
Then 50 million children will be born each of the first 30 years. But after 31 years there will only be 50 million 30-year-olds, not 100 million as was the case for the previous 30 years. The number of children born after 31 years and the subsequent 29 years will therefore be 25 million. From year sixty 12.5 million children are born. And so on. The number of children born per year is halved each generation. When the fertility rate is 1, the population will increase every year, but never surpass 12 billion people. 1) - Fertility rate is 1.8:
90 million children are born each of the first 30 years. In the next generation 81 million children are born per year, then 72.9 million and so on. Also in this case the Earth’s population always increases, but it will never go past 36 billion people. 2)
How will the population figures change over time if everyone dies at 90 years?
Again, we start off with 9 billion people evenly distributed between 0 and 90 years of age and all women have their children when they are 30 years old. But instead of living forever, now everyone dies when they reach the age of 90.
- Fertility rate is 3:
150 million children are born each of the first 30 years, 100 million die, the population increases by 50 million per year. The next 30 years, 225 million children are born per year, 100 million people die, the population increases by 125 million per year. From the 90th to the 120th year 150 million people die per year (the same number of people as were born 90 years previously), but even though the number of people who die increases, the difference between the number who are born and die in the same year always increases, which means that the population increases faster every year. As with the case where no one died, this leads to an exponential increase of the population (even though life expectancy is not increasing). - Fertility rate is 2:
100 million children are born each year and 100 million die each year. The population figures remain constant. - Fertility rate is 1:
50 million children are born each of the first 30 years, 100 million die, the population will shrink by 50 million per year. The next 30 years 25 million children are born, 100 million people die, causing a reduction of 75 million per year. Then 12.5 million children are born, while 100 million people die. From year ninety 6.25 million people are born, and now the same number of people die as were born in the first generation, ie 50 million per year, so that the population will shrink by 43.75 million per year. The population will continue to decline in this manner, so if the fertility rate is less than 2 (and life expectancy remains constant), the population figures will go towards zero – the extinction of humankind.
If population growth is not limited by the available resources, the number of human beings will go towards infinity if the fertility rate remains above 2, something that applies regardless of whether we live forever or whether the average life expectancy remains constant. This clearly illustrates that Max More is right when he writes:
If we want to slow population growth, we should focus on reducing births, not on raising or maintaining deaths.
The number of children per woman has declined sharply in recent decades and even threatens to drop below 2 this century. If that happens, the average life expectancy must always increase lest population will begin to decline towards zero. To have an ever-increasing life expectancy is only possible if effective life extension technology is developed.
I’m not going to take a position on what is the optimal number of people on Earth, but if we can prevent people from getting sick and dying, that is obviously a good thing. And as we have seen, that does not necessarily mean that the population will grow beyond all bounds. Depending on how many children it will be common to have in the future, developing life extension technology may actually be necessary – humankind may risk dying out if we don’t!
1) Here we get a geometric series where the first term, a = 30 x 50 million, with quotient k = 0.5. The number of births when the time (number of generations) goes to infinity, then becomes:
If we add 9 billion people, which was what we started off with, we find that world population will never surpass 12 billion people.
However, the formula presupposes that the number of people can be a decimal number, which it obviously cannot. So in practice population will stop increasing (ie no more people will be born) when all individuals in the youngest generation (maybe it’s 1-5 individuals) are boys.
2) Geometric series with a = 30 x 90 million and k = 0.9:
Adding 9 billion, gives a total of 36 billion people after an infinite number of generations.
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Great post! I would just add the point that the fertility rate is ALREADY below 2 in many countries, especially in Europe (Eastern Europe more drastically), Japan, and Russia. Even now, 44% of the world?s population live in 83 countries and territories where fertility is below replacement levels.
Actually; extending peoples lives is the problem, there is too many people, living too long. All the diseases are simply natures way of keeping our population in check, just like with other animals, there is no reason we need to continue bending the laws of nature because we want to achieve the impossible of never dying. Simply put; in our world, there is not enough to go around, nor the room, cities are holding more than they’ve been designed to do, countries, suxh as Japan, are holding more people than they should, not enough jobs, or money, or places to live, too much traffic, crowds, et cetera. We don’t need to be curing every disease, trying to live to be 200 years old, what we need to do is embrace death, as hard as it sounds. Most of the [first] world problems would go away once there isn’t so many people, crazy or not,the things that kill us, are here to kill us. Our population has been out of check for a long time, we think ourselves the best on this planet, as we invade on other animals living space, because ours is “running out,” no, which is another thing; once oir numbers are where they should be, the numbers of other animals will also increase, once some of their land returns to them, which is real good for endangered animals. No need for everybody to live, much less live “forever.”
I’m all for life extension, but this is an example of the limitations of mathematical thinking without sufficient context. From a standpoint of quality of life (for humans) and the health of most other species, a reduction in human population is clearly desirable. It would also increase available resources, which would tend to increase population growth, or at least decrease the rate of population decline. These trends are regularly observed in both human and animal populations. So while mathematical models can reasonable predict that the human population will peak at 11 billion, there is no reason to expect that it will ever decline past a point of comfortable resource equilibrium.
It is actually in the best interest of humans to reduce birth rates to <2/woman until a comfortable and ecologically sustainable population level is reached, and then seek equilibrium. And, if we succeed in conquering the aging process, it becomes all the more important that we reduce population growth, because otherwise the equation changes and we replace death by aging with death by starvation.
Fortunately, even without aging or disease, people will still die, so a steady state population is still possible without a zero birth rate.