Long Story Short: The Malthusian Argument and Its Main Problems

[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?”]

My last post was rather long because I had to explain a few concepts and go into a fine-grained discussion. However, the gist is rather simple. Please recall (or else refer to the long version for an explanation) that I defined two quantities:

• Excess fertility: Fertility minus two. How many children more are born than are necessary to stabilize the population if there were no mortality.
• Attrition: The product of fertility and mortality. The number of children born who do not survive to fertile age. I use this as a proxy for mortality (but it also changes with fertility), so I can plot it in the same graph as excess fertility.

When I have excess fertility and attrition in one graph with population size on the horizontal axis (or for a fixed area: population density), the distance between the two lines is proportional to population growth per generation. Where the two lines intersect, population growth is zero, ie. the population stabilizes.

Malthus’ intuition is that fertility is not responsive to population size or only minimally so, and that it is at the maximum possible. That’s the blue line in this graph, which is a constant:

The red line (hidden below the yellow line on the left) is for the case that mortality is also unresponsive to population size until the population hits a binding constraint for the food supply. Since there is a fixed distance between the two lines, we have growth by a fixed percentage per generation or exponential growth on a continuous time-scale. Mortality eventually explodes when the population reaches a constraint for the food supply. Mortality becomes so hight that attrition equals excess fertility, ie. the population stabilizes. That means maximum fertility becomes replacement fertility for this high mortality.

Malthus thinks that there can be also other factors that raise mortality already before a binding constraint for the food supply is reached. He falsely insinuates that they are all driven by the constraint for the food supply although that need not be the case. Population size itself could be the driver.

This case is the yellow line. Mortality and with it attrition increases already earlier on, but the result is practically the same: So many people have to die that maximum fertility becomes replacement fertility. The only difference is a smaller eventual size for the population and more people now die also from other causes, not from starvation alone. In both cases, for the red and the yellow line, the population grows to the maximum size that is possible. It just cannot grow any further. For the red line, the constraint for the food supply determines the eventual size. For the yellow line, that may or may not be the case.

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Malthus considers also factors that might lower fertility. He again falsely insinuates that these are all driven by the constraint for the food supply although he gives examples where this cannot be the case, eg. people of higher status fretting about the social status of their children, not the food supply. That would be driven by population size alone. But in any way, Malthus assumes for no reason that any reduction in fertility has to be inessential, and so the situation remains almost the same as above. The implicit assumption is that the poor are too stupid or inconsiderate to control their fertility in a meaningful sense.

However, once Malthus concedes that the population can also lower its fertility, he cannot stop the conclusions where he wants. At this point anything becomes possible because population growth is determined by only fertility and mortality if there is no migration. When both are variable, any population dynamics are possible. Of course, this is convenient to explain examples away that run counter to the Malthusian argument. You interpret actual fertility as maximum fertility with the “preventive check,” and actual mortality as minimum mortality with “postive checks.” However, that proves too much.

Here is what can happen with control over fertility:

The green line is excess fertility, ie. fertility minus two. The population reduces it from some point on. That might have to do with effects from a constraint for the food supply, but that need not be the case. The population can do this at any size and for any reason.

The yellow line is again attrition: the product of fertility and mortality. It only decreases here because fertility does. Mortality is fixed in this example. That means, for now fixed mortality, the population reduces its fertility to the corresponding replacement level and stabilizes. In the case above, it was the other way around: Mortality increased to turn fixed fertility into replacement fertility.

Obviously, modern industrial societies are examples where population growth comes to a halt although no hard constraint is in sight. But there is no reason to exclude that also preindustrial societies could do this. Even if mortality played some role, it might be only a minor one because fertility adjusts to it, not the other way around. The eventual population size can be anything up until the maximum size possible. There is still a constraint from the food supply, but it may be inessential because the population never grows to it. In addition, when the population stabilizes, it still has leeway on the upside. It can grow further if it raises its fertility. So it is not stopped by a hard constraint anymore.

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The crucial question is whether the first case or the second case are typical for how actual populations behave. The Malthusian idée fixe is that populations are not able to lower their fertility materially. However, that cannot have been so even in preindustrial societies. Typical mortality until fertile age fell around 50% and seems to be more of a constant for preindustrial life. That holds for hunter-gatherers, forager-horticulturists, acculturated foragers, and was also true before the Industrial Revolution, for example in Sweden in the 18th century, cf. Gurven & Kaplan: Longevity among hunter-gatherers, a cross-cultural examination.

However, mortality around 50% until fertile age corresponds with replacement fertility of about four. If four children are born per two people and half of them die, then there will be two who survive to the next generation, ie. stabilization. Hence if you observe such societies over the longer run and they stabilize, they must have had a fertility of about four on average. If you observe only slow growth, fertility must have come close to four. But maximum fertility for humans is much higher. Actual population have had fertility of eight or more for some time. In principle, it could go even beyond ten.

Now, if actual fertility fell around four, then these populations must have had the necessary control over their fertility to achieve stabilization, and we are in the second case above, not in the Malthusian case where a population cannot stop growing until something stops it the hard way. If a population can stabilize, it can stabilize at any size up until the maximum size possible. The eventual population size may be determined by a constraint for the food supply when it has an effect already before mortality begins to rise, but that need not be the case.

All this shows that Malthus’ intuition about population dynamics is false for humans (and as I will argue also for many other species). The mistake in the Malthusian argument is that you are led to believe that the first case above, and even the red line with skyrocketing mortality at the last minute captures population dynamics up to a small perturbation. And that’s why you can keep all the conclusions in this case also for actual populations. However, these conclusions — growth to the maximum size possible, rising mortality as the mechanism that stops growth, and a constraint for the food supply as the driver — do not carry over once a population has the power to control its fertility and stabilize at any size.

The normal situation for populations is not maximum fertility and extreme mortality, but replacement fertility corresponding to rather stable mortality. Malthus anchors the intuition of his readers at the wrong level and reinforces this with a gripping account that captures the imagination. When he discusses societies that are far away or in the remote past, he concludes from his theory that they must have had the dynamics he assumes. That is then used as proof although it is circular. However, when Malthus has to address actual societies he and his readers know about, he makes his theory so flexible that his conclusions in the ideal case no longer carry over. It is easy to miss this because he glosses over the problem that poses for his argument and most of his exposition turns around circular explanations that support his case.