Human Populations Do NOT Grow Exponentially
[This is part of my series on Thomas Malthus’ “Essay on the Principle of Population,” first published in 1798. You can find an overview of all my posts here that I will keep updated: “Synopsis: What’s Wrong with the Malthusian Argument?”]
In my previous post, I have explained why Thomas Malthus’ has no argument that “subsistence increases in an arithmetical ratio” (cf. I.18), ie. the food supply grows linearly over time. He only asks his readers to grant him a rule that it does, and then he concludes that, indeed, it does. But that is just a simple logical fallacy known as “begging the question” (assuming what you want to prove).
In my next post in this series, I will look into Malthus’ discussion of why “population, when unchecked, increases in a geometrical ratio” (cf. I.18), ie. it grows exponentially over time. The argument is very hard to pin down because Malthus does not develop it explicitly. He only gives some hints and makes it sound as if the proof were obvious.
But then, on closer inspection, the argument is also a case of “begging the question.” Malthus just assumes that a population “when unchecked” not only can have, but must have maximum fertility and minimum mortality. In as much as these are constants of human nature, this is equivalent to saying that it grows exponentially at the maximum rate possible. But then the conclusion is only a reformulation of the assumption.
Note that Malthus’ exact claim is only for a population “when unchecked,” something he concedes has never been the case. However, he treats it as if the same also applied for actual populations that are not “unchecked” and have leeway because they have not yet reached the maximum size possible for a given food supply. Of course, if that were so, the Malthusian end-game follows: Any human population will grow until it cannot go on.
I would say that Malthus believed this and not the cautious claim about a population “when unchecked,” which is rather meaningless because it never applies by his own admission. Of course, Malthus also knows that the general assertion is not true in concrete cases. But he tries to handle this by supplying adhoc explanations that these are some slight perturbations of the ideal case. The deviations appear to him only like a mist that lies over a reality that is captured well by his sweeping claim.
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You can fault Malthus for many things, but rhetorically he was a master. The takeaway from his essay for many readers has been exactly that: There is always “population pressure,” human populations can just not stop growing until they hit a binding constraint from the food supply that stops them at the maximum size possible. They are practically always on the brink of starvation.
This is basically what I would call the Malthusian worldview. It has become a part of our culture and is so ubiquitous that even critics of the Malthusian argument take it for granted. Challenging this worldview hence feels like getting a tattoo: “I am a certified crackpot.” Even I cannot escape this feeling.
But then my point is this: It is not true.
Human populations do NOT grow exponentially when they can, not even close. There is no “population pressure,” and all this is simply not the appropriate model for what humans do.
If you wonder, I will present a rough explanation of what human populations really do. It is not as handy as an exponential function. But then who says everything has to be very simple? That is only an unfounded assumption with Enlightenment thinkers, of which Malthus is one despite all his criticisms.
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In this post, I would like to tackle two central claims of the Malthusian worldview. The first is that human populations can just not stop growing unless a binding constraint from the food supply stops them. And the second is the prediction that they will hence always grow to the maximum size possible.
Let’s begin with the question whether human populations just grow at a fixed rate once they have enough food. As anyone in a modern industrial society knows: This is clearly false. But then that does not have to faze those who believe in the Malthusian worldview. There are perhaps some extraordinary conditions now that humans were not made for, they have a “false consciousness” and have lost touch with their true human nature, etc. But up until about 1800 or 1600 or whatever, it was always so. It was a “Malthusian world.” Proof: Everybody calls it that.
However, this is not true.
I take my data from the Maddison Project database in its current version, which provides population sizes on the current territory of the respective (pre-1990) countries for the dates 1 AD, 1000 AD, and 1500 AD. You have to be careful here because such estimates are inherently imprecise to a large extent. It is appropriate to add huge errors bars around every data point mentally. Still the argument I will make is, as they say, so safe you can drive a truck through.
Here is the average growth for the 43 countries with data from 1 AD to 1000 AD per generation of 25 years (if it had been regular exponential growth):
The first ten countries here are: Greece, Italy, Turkey, China, Algeria, Albania, India, Switzerland, and Romania where you had shrinkage or practically no growth. The last ten countries are: Canada, Denmark, Ethiopia, Finland, Mexico, the United Kingdom, Japan, Poland, South Africa, and Mozambique. Some of them were only settled at the time, so part of the explanation can also be immigration into a new territory.
And here is the chart for the same 43 countries from 1000 AD to 1500 AD:
The bottom ten are now: Iraq, Algeria, Morocco, Egypt, Tunisia, Iran, Turkey, Greece, Albania, and Libya (talk about Muslim fertility!), and the top ten: Czechoslovakia, Romania, Hungary, Austria, the Netherlands, Poland, Mozambique, Germany, Belgium, and Finland.
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Now, to put this in perspective: Malthus claims that population growth “when unchecked” means a doubling per quarter century or more, ie. an increase by 100%. Over the longer run, none of these countries came even remotely close. The highest increase is only somewhat more than 10% per generation of twenty-five years, most fall well below it.
So the vision in the Malthusian worldview that populations basically behave as “when unchecked” up to minor perturbations is as off as it could be. There were even many countries that saw almost no growth for half or a whole millennium. The population of Greece halved from 1 AD to 1000 AD, as did the population of Iraq from 1000 AD to 1500 AD.
Malthusians will be unfazed by this: Of course, these countries were not “unchecked” and so their population growth was kept down by something. But still, if that was so on a regular basis for all countries we have data for, why take supposed “unchecked” growth as a reference point that up to small deviations captures most of reality?
And then this cannot be true. Countries like Greece or Iraq could have grown back to their initial size in just a quarter century with one doubling. But they failed to do that for centuries.
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Let’s work through this in more detail:
Mortality until adulthood (age 30) in pre-industrial societies fell quite regularly into a range from 40% to 50% barring extreme events and plus or minus a few percent. If I take the upper percentage and fertility of eight, which is basically what Malthus assumes “when unchecked,” then this means a doubling per generation of twenty-five years: a couple has eight children of whom four survive to the next generation. That is exactly Malthus’ claim.
Now, the historical data are nowhere near this ideal case by far. Malthusians will not be surprised and will tell you for each country about catastrophes that led to very high extraordinary mortality on top of an already high baseline mortality of 50% until adulthood (age 30). To push population growth down from 100% to only 10% or even close to 0% per generation, though, that would mean that extraordinary mortality would have had to wipe out almost half the population on average in each generation!
Intuitive thinking is very sloppy and needs only the semblance of an argument: A Malthusian might tell you about the horrors of the Black Death, and that probably explains it then. But the plague “only” killed 30% to 60% of the European population once, and it was an outlier. From 1000 AD to 1500 AD catastrophes on a par with it would have had to strike the population every quarter century to explain these growth rates, not once, twenty times.
There should be some records of what these events were that kept population growth down by that much. It is not enough to show that such catastrophes could lead to a massive decrease, that is understood. But you also have to explain why they could have the right order of magnitude and frequency. If you are arguing from a worldview, though, just the association is good enough. It looks like a proof, so it probably is one. Because you already know that it must have been so. Or it was something else. But it was so.
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Let’s just ignore the extraordinary mortality for the moment. As I said, “ordinary” mortality of 50% until adulthood (age 30) is already rather high as an assumption for pre-industrial societies. Everything is already baked into it that happens on a regular basis: deaths that result from malnutrition, frequent undernutrition, ubiquitous diseases, homicides, etc. But then mortality of 50% until adulthood means that replacement fertility was only four, far below the eight or more that are possible. You have four children per couple, two of whom die before they can have children of their own, and so the population remains stable.
Increases by a few percent per generation look perhaps impressive, but if you look at it as average fertility, the differences are hard to spot. Here is the graph for the 43 countries from 1 AD to 1000 AD assuming this level of mortality:
The replacement level is four by assumption, and the range goes only from 3.93 for Greece to 4.18 for Mozambique. All these countries had almost the replacement level with a very high precision over a millennium.
Now, you could come with the catastrophes again. But that would only mean that the replacement level was actually somewhat higher. The general pattern would be scaled up, but should remain practically the same.
And here is why catastrophes cannot explain it: Suppose that these populations actually had fertility of eight. Now, to achieve this pattern across 43 countries around the world, all these specific catastrophes would not only have had to wipe out about half the population per quarter century, but even with extreme precision. In Greece, they would have added up together with ordinary mortality for the extra four children above the replacement level to a reduction by 4.07, and in Mozambique by 3.82 on average. Either this is a very weird coincidence, or it is not true.
Here is the graph for the time from 1000 AD to 1500 AD:
The range is slightly larger from 3.86 for Iraq to 4.42 for Finland. That is about half a child per generation between the extremes. Again, these populations hit the replacement level with very high precision. And if the explanation were some unknown catastrophes on a regular basis, the reductions over half a millennium would have had to add up to 3.58 to 4.14 including ordinary mortality. Again, a remarkable coincidence if it were so.
Malthusians would be unfazed by that, too: There are also the preventive checks that lead to lower fertility and that explains it. But then think about what that means: If mortality, neither ordinary nor extraordinary, did the trick to produce this pattern, then the control over fertility must have been remarkable.
These populations could have had fertility of eight or more, but then lowered this to practically four with extreme precision. Obviously, if they could do this, they could also go for replacement fertility itself, and many did. But once a population can do this, inevitable population growth, so-called “population pressure” is out the window. The population might never grow at all, and it might even shrink sometimes!
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The only reasonable interpretation of these data is that all these populations across the world targeted the replacement level and they did it via fertility because they had hardly any control over mortality, neither ordinary nor extraordinary. Even more: These population certainly did not have exactly the same mortalities over half and a whole millennium. So they also adapted their fertility in a way that brought it close to a moving replacement level.
Of course, this sounds unbelievable. But I will show in a further post that a population can do this quite easily if it has control over its fertility. Only very simple inputs are needed and a simple rule to react to them. Once you concede that a population can have this level of control over its fertility, “population pressure” is not inevitable.
The baseline was hence certainly not a doubling every quarter century as Malthus has made us believe, but a stable population. There was some growth on average (around 1% per generation), so a Malthusian might feel vindicated that populations just barely missed the replacement level and that produced “population pressure.” But then why should that be so? If you can see to it that you don’t have eight children on average, but only like 4.04, why not 4?
All it takes as an explanation is this:
In the first place a population targets a certain population size — probably indirectly via population density or area per capita because its size is not directly observable. Since there can be shocks from mortality because of catastrophes or general shifts in the level, there will be some deviations. But if the population does not target the replacement level, but the population size, it can react to that by changing its fertility.
The replacement level is not the target itself, only an outcome when a population stabilizes its size under constant conditions. As already announced, I will show in a later post how this can work. It is not even particularly hard once you grant that a population has control over its level of fertility. And it certainly explains the observed pattern while the Malthusian argument cannot do that.
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But then there was some population growth? Does this not show there is an inherent drive to have exponential growth?
Well, no. Only if you are obsessed with the idea that population growth can only be exponential growth. But if you don’t buy into this, there is no problem with the idea that a population might remain stable for a long time, and then grow for some time and stabilize again. If growth is the exception, it might even be rather strong when it comes, and still the overall increase could be quite small. The objection is the Malthusian worldview at work: If a population starts to grow, it cannot stop because it must be exponential growth, which goes to infinity. But who says that?
What would be the explanation why a population sometimes grows then?
Here is an idea: If opportunities arise (first!), eg. new land becomes available or wealth creation gets a boost from some technological advance, like the domestication of animals and plants, then a population can react to that. It would then grow into the opportunity. And if the opposite happens, as for Italy and Greece when the Roman Empire came to an end, a population shrinks into less opportunity. The mental block here is only the Malthusian worldview with its idée fixe that populations cannot do this. But then as the historical data show, it is hard to deny that populations have the required control over their fertility and can adjust it with precision.
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A Malthusian might not be impressed by all this. Couldn’t the explanation also be that slow growth of the food supply results in such slow growth? As already explained above, this is at odds with reasonable assumptions for mortality. But then this is another part of the Malthusian worldview that is hardy: Human populations are assumed to be almost always close to the maximum size for the food supply. And so its increase determines population growth.
Here is why this is not true. It also blocks an attempt to move the “Malthusian world” further back in time, like things were different already from 1 AD on. But before that, it was always so.
The argument is so simple that you can do the calculations on an envelope. Here are the relevant inputs:
The initial population that we are all descended from 100,000 years ago had probably a size of some 300,000 or so. They lived only in Africa. Later they branched out and settled the whole world. By 10,000 BC, the size of humankind was perhaps 3 million people (sources here). In between humans had mastered fishing, though, which is attested by our spread along the shorelines during the early expansions. Apart from that they were all hunter-gatherers up until this time. Of course, you have to add large error bars, but then a truck can drive through. Until 1800, with traditional agriculture, humankind had reached a size of somewhat less than a billion. Now it stands at about 7.5 billion people.
Here are rough estimates for population densities: Hunter-gatherers cannot go beyond about 1 per square kilometer. But it can also be 0.1 or below depending on the environment. I take a conservative estimate of 0.1 for them. Primitive agriculture can raise this to perhaps 10 per square kilometer, traditional agriculture to 100, and modern agriculture to 1,000 (all on the lower end of estimates). As further inputs I need land area: Africa has an area of about 30 million square kilometers, the world an area of about 150 million square kilometers.
So, 300,000 people in Africa at a population density of 0.1 would need 3 million square kilometers, or about 10% of the total area in Africa. 3 million people in the world and again at a density of 0.1 would need 30 million square kilometers or 20% of the total area. But then fishing perhaps allowed for higher population densities, so 0.1 might be too low, and hence the area needed could also have been less. 1 billion people at a density of 100 would need 10 million square kilometers or less than 10% of the total area of the world. And 7.5 billion poeple at a density of 1,000 would need 7.5 million square kilometers or about 5% of the total area of the world.
Of course, much of Africa or the world is not suitable for hunting and gathering, traditional or modern agriculture: the Sahara, arctic regions, sometimes the Ice Age, etc. Still, it would seem that like 80% or maybe 90% of all the land would have to be inhospitable for humans at all times to make the case that humankind has ever grown to carrying capacity. I don’t think that is plausible. You have a lot of leeway here also in other regards. Maybe the estimates for population densities are too high. But you would have to explain a large factor that is at least not obvious at first glance.
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All in all, my point in this post is this: Central claims of the Malthusian worldview are dubious: Humankind has apparently never grown to carrying capacity, and has not even come close ever.
Actual growth rates have been much lower than just a slight deviation from Malthus’ ideal case “when unchecked.” With reasonable assumptions about mortality in pre-industrial societies, fertility must have been very close to the replacement level on average over long periods of time and across the world.
Not exponential growth should be the baseline, but stable population sizes. Fast growth must have been the exception and should have connected plateaus that lasted over long periods of time. There was no mechanism that led to growth that could just not stop. And the probable causality was that first opportunities arose and then populations grew into them, and if those opportunities faded away they shrank back to a lower level.
If this account is only moderately in line with reality — and the available evidence supports such a case — the central tenets of the Malthusian worldview are completely false. And so are all conclusions that are built on them.
