# Is Malthusian theory of population growth being realized?

You probably are familiar with Malthus' Theory of Population Growth.

If you are not, Malthusian model has the following mathematically form:

$$P(t) = P_0e^{rt}$$

A basic graphic representation is:

Note that population is growing in a exponential form where as the resources are growing only linearly. By resources, I do not only mean food resources, but they also include water, energy, land and anything else that support the continuation of expansion of human societies.

Malthusian theory of population growth has been subjected to criticism, mostly, IMHO, a reaction for the theory being too pessimistic.

But let's have a look at the real population growth for the past couple of thousand years:

Now, let's smooth the graph out:

Do you see what I see?

Still not convinced? Let's zoom in for the more recent times (vertical axis is in billions):

Those are the figures from wikipedia, on which I have calculated percentage change per five years:

Note that even at the current stage, we are still at an above the average trend for over the past 211 years (since 1804 when the world population hit 1 billion):

$$1.0095^{211} = 7.35$$

There are, currently 7.35 billion people on earth.

The average of annual population increase is 0.95% per year, but we are increasing at a rate of more than 1% per year.

Is Malthusian theory of population growth being realized? If this is true, are we going to hit the point of crisis soon because of the limited resources?

If not, why not?

Please support it with number and figures, I would appreciate a more scientific than opinion based discussion.

• Lots of good answers, choose one? – Thorst Oct 13 '15 at 13:45

The annual growth rate of the global population has been in decline since about 1967 (five decades ago).

The absolute annual growth peaked in 1987 (three decades ago).

Malthusians claim that:

1. population growth is geometric or higher; and
2. food production growth is arithmetic or lower.

If either of those do not hold, then Malthusian theory does not hold. And it turns out that neither of them hold:

1. Population is not growing geometrically (not even arithmetically); and
2. food production turned out to be capable of greater than arithmetic leaps in growth: food production per capita grew by 45% between 1961 and 2013 (source: UN Food & Agriculture Organization FAOSTAT Food Production Indices for the world, element code 434, domain code QI, Area code 5000, Item code 2051, Agriculture (PIN);)

Some relevant factors: cheap, reliable, ubiquitous contraceptives; education and emancipation, particularly for women; cheap and plentiful crop fertilisers; mechanisation of farming; and selective crop breeding, by taking the old practice of eating the best of each crop and sowing the worst, and doing the exact opposite.

Here are two charts, using the global historic data from the US Census organisation for 1800-1950, and the UN data for 1950-2014.

• You don't base your answer on historical data, but on projections that are based on certain bias? That's what half of those graphs/numbers are. @denesp – TelKitty Oct 12 '15 at 10:55
• @chmod711telkitty denesp is not the answerer, I am. Please do look at the numbers. The observations, not the projections. You'll see they confirm exactly what I've written. If you didn't want the truth, why did you ask the question? – 410 gone Oct 12 '15 at 11:03
• You're wrong, at least for the first claim. The annual growth rate has always been over 0.5% since 1825. It means that the population has been growing faster than 1.005**year, which is geometric. So indeed, "population growth is geometric or higher". The population has been growing slower than 1.02**year, but it is irrelevant for Malthus claim. – Eric Duminil Jul 28 '19 at 16:32
• @EricDuminil one quick way to check whether a time series shows geometric growth or higher, is to look at the trend in annual differences. A geometric time series has an increasing trend in annual differences, and the increase in the difference gets greater each year. An arithmetic time series has a constant series of time differences. The data shows that population growth hasn't been geometric for a long time. Malthus's theory was broken from the beginning, and is still broken now. Someone will have to do a lot more than mere numerology to find any merit in it. – 410 gone Jul 29 '19 at 1:38

The Malthusian crisis has two parts. The first is exponential population growth. As others have noted, there is a trend for declining fertility once countries achieve an advanced state of development. Here's another figure showing this fact:

Note that fertility (number of children per adult female) is decreasing essentially everywhere, and is forecast to be only slightly above replacement level worldwide by the middle of the century. Here's the source.

It also turns out that Malthus greatly underestimated the importance and potential of technological development for agriculture.

Here's the amount of wheat produced from one hectare of land in the developing world (where most population growth takes place; figure source):

The consequence for food producting is shown in the following figure, which shows an index of food production per-capita (source):

It's increasing, meaning that the rate of growth in agricultural productivity has actually exceeded the rate of population growth over the last half-century (despite this being the period of fastest recorded population growth).

• the importance and potential of technological development for agriculture is mostly linked to cheap and plentiful oil (e.g. with heavy machinery, pesticides & fertilizers). Which is a non-renewable resource. – Eric Duminil May 11 '19 at 9:47
• Land is also a non-renewable resource. I heard somewhere (so unreliable) that half of the Earth's farmable land is currently being farmed. Which means we're in for a mass famine at 16 billion. (if the conversion of land to farms hasn't depleted the oxygen first) – user253751 Oct 21 '20 at 12:27

I think the answer of @EnergyNumbers covers most of the important points but I would like to emphasize something else. When setting up a model you should not give the same weights to data from 500 years ago as you give to the data of last year. Since circumstances can change a lot in that time the trends may change as well. For example world population was nearly constant between 1000 and 1300 but it did exhibit significant growth in the last two centuries. There was perhaps geometric growth in the 19th and 20th century as modern medicine spread to all parts of the world but this process is now over (most places have basic forms of modern medicine) and the current growth may be better described by a linear curve. Who knows, maybe in a year the shape of the curve will change again. I would not bet on this though.
To highlight the importance of changing circumstances here is an anecdote (which is not proof of anything):

In 1894, the Times of London estimated that in under 60 years, every street in the city would be buried nine feet deep in horse manure. Similarly, a New York prognosticator in the 1890s predicted by 1930 the citizens of that not-so-fair city would see that selfsame horse excrement rise three stories high if nothing were done.

The other excellent answers provided data - mine will provide a simple look into at what stage we are, if Malthusian Theory holds.

I replicate here the first graph of the OP:

For the graph to be meaningful, "resources" in it must be measured in "number of people that can be sustained by existing resources". To the degree that the amount of resources needed to sustain one person have not really changed -we are talking about survival here, not "good living"-, this normalization does not affect the remarks that follow.

Contemplating the above graph, we realize the following: there is an "initial period", during which the growth rate of resources is larger than the growth rate of the population. Then the exponential growth of population starts to show, and its growth rate becomes greater than the growth rate of resources (which is assumed in the Theory to remain constant). And these happen before the "Point of Crisis".

What is the implication of this? That there is an initial period where "resources per capita" grow, and then we enter a second stage where "resources per capita" fall as we start to approach the "point of crisis". Note that this has nothing to do with how resources are distributed among humans.

So, according to the Malthusian Theory itself, a clear sign that we have started to approach the point of crisis, will be the observation that "resources per capita" start to exhibit a downward trend.

This is a general conclusion, even if we assume that resources do not grow linearly but may exhibit exponential growth (albeit weaker than that of the population).

Now, the OP reminded us that the rise in population during the 20th century, was immense. Looking at the (excel) figures provided by the OP, in the period $1960-2010$ population rose from 3 bill to 7 bill, i.e. by 134%.

On the other hand, as @EnergyNumbers' answer reports, food production per capita grew by 45% between 1961 and 2013. But this means that food production itself grew by 235%: the "resources per capita" figure still grows comfortably.

So to the question

"Is Malthusian theory of population growth being realized?"