World Population Growth Projections

World Population, estimated, actual, and projected: 1800-2100

Some people look at the graph on the right and conclude that the population appears to still be in the midst of exploding, and there are wildly different projections for what the population will be in the near future.    Some probably assume they left off another curve that keeps rising even faster.

Is that what you see?  Is that what this graph really shows?  It is a nice graph, for what it shows, but it doesn’t really show a lot, and it is interesting to find out how others have interpreted it.  Let’s start with the most accurate interpretation first, which happens to be the first result of a Google search for this image.

This is a fair representation of what the graph shows, though it doesn’t specify the likelihood of each of the three projections by the UN, so you might assume they are equally likely, if you didn’t know otherwise.   More about that later.

Note also that it says there will be a “steady decline in the population growth rate”.  Can we see that decline in the graph? Only by noting that all three of the projections bend in the downward direction, or continue in a straight line, which could only happen if there is some decline in the rate of growth, as we’ll see below.

How do we know there must be some decline in the population growth rate?

What would happen to the graph if the growth rate was increasing?   That would mean that every year, a larger and larger fraction of the population would be added to the population, and that would cause the population line to curve upward.  But if the population line is straight, as it is for the red line in the graph, that means that the population would be increasing a constant amount every year, and therefore the fraction of the whole that it grows by is actually smaller each year.

You should also be aware that a non-zero growth rate still results in exponential growth.  Any growth rate that is greater than zero means that each year, the same size fraction of the whole is added, but because the whole grows, the fraction also grows.  So if the growth rate stays the same, then the population would, in fact, continue growing exponentially.

None of the three projections shown in the graph suggests that the growth rate is either increasing or staying constant, so the only other choice is that the growth rate will most likely be decreasing.

It is also interesting to note that if the growth rate was zero, then the growth would also be zero, and the population would stay the same.  The graph of the population would show a flat horizontal line, neither growing nor shrinking.  This is the goal of zero population growth.

So with a little deduction, we can tell from this graph that the population is no longer projected to be exploding exponentially.  The growth is no longer accelerating upwards; it is, in fact, decelerating.  Some people look at the still rising population curve and think that means the growth must be accelerating, but they forget to notice that the growth rate is actually slowing down.

World-Population-1000CE-2100

That’s not to say that the population wasn’t exploding in the past.  It certainly was exploding exponentially in the past, even more than exponentially, and if we take a longer look at history, as shown in the second graph (on the right), this rapidly accelerating growth is all the more apparent.  In this graph, the left axis is logarithmic, which means that a rising straight line here is actually showing exponential growth, and a line that is curving up is actually showing greater than exponential growth.

But what was true in the past doesn’t make it inevitable for the future.  People are fond of noting that the time to double the population has rapidly shortened for each doubling since 1800 when the population was about 1 billion.  It took 130 years to go from 1 to 2 billion, 40 years to go from 2 to 4 billion, etc.  But it also took about 40 years to go from 3 billion to 6 billion, and since the growth is slowing down, it appears the doubling from 4 billion to 8 billion will take 50-70 years, and possibly we will never double beyond that.

You should be asking yourself, what has changed recently to stop the explosion?  Alternatively, what could change to increase the growth rate so the population would again be exploding?  The answer to these questions is explored in another blog: World Population is Stabilizing

Another key thing to notice about both of these graphs is that the region in blue between 1950 and 2005 appears to be approximately straight, so you might assume that, if the conditions remain the same, the population would most likely follow along this same straight path, much closer to the high projection.   You can click on either graph to see it at full resolution, which makes the blue line much fatter, but it doesn’t show any more detail.  The next section will begin to look at this in more detail.

Next up, we will look at the argument made by Thomas Malthus, and more recently by Neo-Malthusians.

They argue that, given a mathematical model of how human population has grown in the past, this means it is likely to follow the same model in the future, and a population explosion beyond sustainability is all but inevitable, followed by a collapse to subsistence levels.  (Malthus actually tempered his opinion about the likelihood of overshooting and collapse, though many of his followers have not.)

A chart of estimated annual growth rates in world population, 1800-2005. Rates before 1950 are annualized historical estimates from the US Census Bureau. Red = USCB projections to 2025.

But does the recent data actually show the population is still growing (hyper-) exponentially?    In addition to showing the same graph of population projections included above, that same article includes the plot at the right showing the growth rate over the same period of time, with the following explanation (emphasis added):

The graph of annual growth rates does not appear exactly as one would expect for long-term exponential growth. For exponential growth it should be a straight line at constant height, whereas in fact the graph from 1800 to 2005 is dominated by an enormous hump that began about 1920, peaked in the mid-1960s, and has been steadily eroding away for the last 40 years. The sharp fluctuation between 1959 and 1960 was due to the combined effects of the Great Leap Forward and a natural disaster in China.[14] Also visible on this graph are the effects of the Great Depression, the two world wars, and possibly also the 1918 flu pandemic.

Obviously, a lot more is going on with the population than the almost straight smooth blue line in the first World Population graph would suggest.  That’s not to say that the steady decline in growth rate will continue as projected, but the growth rate is at least not increasing at this time.

Where did this graph of the growth rate come from?

As the caption says, estimates were made from earlier data.  But the basic calculation is to start with the population data for each year and subtract the population in the prior year, which results in the population growth.  To get the growth rate, we then divide the population growth by the total population.  This growth rate number gives us a good indication of how fast the population is changing independent of how large the population is.

Why should we expect the growth rate to continue declining as projected by the red line in this graph?   After all, the growth rate has changed directions several times in the last century.   And which of the three projections of the total population does this projection of the growth rate correspond to?   These are important questions that we will get to, but first I want to return to focusing on interpretations of the first graph, and moreover, what else is it not saying?

Why are there three alternative projections of population?

What is the reason that the first graph shows three alternative projections of the population?  Note that the low and medium alternative projections are distinctly different from the high projection, so you should wonder what goes into these projections such that the result might vary so much.  We really can’t tell from this graph alone how the alternative projections were arrived at, or which is more likely to come about.  Is the middle alternative more likely just because it is in the middle?  We don’t really know.   To answer that, we will have to look at more detailed data.

It turns out that the alternative projections are shown because the largest uncertainty that makes a significant difference, and that we have a choice in changing, is the number of children that each woman has.  We don’t have as much choice about the death rate, and the average length of life, and the maximum lifespan, partly because we always want to reduce the death rate as much as possible and increase our lifespans, as long as we maintain our quality of life at the same time.

Estimated and projected world population according to different variants, 1950-2100 (billions)

Here is a plot from the source of the data that shows the three projections (high, medium, and low) and a couple more, identifying that these alternatives are based on varying the assumptions about fertility.

According to the source of the data, the 2010 Revision of the World Population Prospects of the United Nations Department of Economic and Social Affairs (UNDEP press release):

Small variations in fertility can produce major differences in the size of populations over the long run. The high projection variant, whose fertility is just half a child above that in the medium variant, produces a world population of 10.6 billion in 2050 and 15.8 billion in 2100. The low variant, whose fertility remains half a child below that of the medium, produces a population that reaches 8.1 billion in 2050 and declines towards the second half of this century to reach 6.2 billion in 2100.

Average annual rate of change of the world population by projection variant (percentage)

So which of these alternatives is more likely to be correct?  To answer this question, it may help to look at why the fertility would change, and how much change is required for each variant.

We’ll get to that soon, but first, lets look more closely at how the population is changing.  The next plot shows the same set of variants, but it shows the rate of change in population rather than the total population. (This is similar to the plot of growth rate above.)

Note that if we extend the curve from the actual population change before 2010 in the white area out into the light gray area showing projections after 2010,  the closest match in terms of the direction of the curve seems to be the middle alternative,  if not the “constant fertility” alternative at the top.   It seems reasonable to guess that whatever is causing the decline in growth rate up until 2010 would most likely continue.

Now, to finally address the question of which alternative is more likely to be accurate, we find the following explanation about Probabilistic Projections in the section titled “Why do we use probabilistic forecasting methodology?“:

The common way to forecast future population is based on the assumptions of “variants” (low, medium and high variants). These variants are said to cover a “plausible range of future population trends.” The medium variant is usually the best “guess” of what will happen.

Well, that answers that question, but we should read on to find out how good this guess is:

This approach is imprecise in the sense that it does not tell the user what “plausible” means. And this approach is incomplete because it ignores uncertainties in mortality, fertility, and migration assumptions. And it is statistically deficient, because when high or low variants for world regions are computed by adding up the low or high variants of the country projections, the likelihood that all countries follow the same variant paths simultaneously is implausible.

Hmm, so is there a better way?  Read on…

The population projections presented here avoid these problems of the “variant approach” because they are explicit in stating probabilities; they fully incorporate uncertainties in fertility, mortality and migration; and they scale up from regions to the world in a statistically consistent manner.

So there are varying ways to analyze the data, and even if we use the best known analysis, there is a fair amount of uncertainty in the data itself, and the further we try to project into the future, the less likely we are to be correct.  It is more appropriate to consider not just three alternatives but many alternatives in a range of possibilities, which the bands in this graph suggest.

Average Population Growth Hides Births and Deaths

Since population growth is the number of births minus the number of deaths, if we only look at the average population growth, the result of that difference, then we can’t tell how many births or deaths are involved.  There might be a low or high number of births and deaths, but we only know the difference between the births and deaths.