Population Doubling Mechanism 

New Malthusian Scale 

External Links:

The Internet Public Library

Malthus, Thomas Robert, An Essay on the Principle of Population. J. Johnson. 1798. (1st edition) Library of Economics and Liberty.  

Malthus, Thomas Robert, An Essay on the Principle of Population. John Murray. 1826. (6th edition) Library of Economics and Liberty.

Malthus On Man - In Animals No Moral Restraint - Robert Young

Lyell, Charles, Principles Of Geology (1830) Electronic Scholarly Publishing

Natural Selection and Differential Reproduction - from Replicators: Evolutionary Powerhouses

Demographic Transition - Wikipedia

Darwin's Views On Malthus


In this article I will go beyond the usual brief explanation of Malthus' influence on Darwin, and explore Darwin's views on Malthus using Darwin's own writings and those of his son Francis Darwin.

Darwin Gives Malthus Credit

Most books on evolution briefly note that Darwin credits Malthus' essay as critical to his theory of Natural Selection. From Darwin's "Autobiography":

"In October 1838, fifteen months after I had begun my systematic inquiry, I happened to read for amusement Malthus on Population, and being prepared to appreciate the struggle for existence which everywhere goes on, from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The result would be the formation of a new species."

From Darwin's "The Variations Of Animals and Plants under Domestication":

"...I saw, on reading Malthus on Population, that natural selection was the inevitable result of the rapid increase of all organic beings..."

However, Darwin had a great deal more to say on Malthus than has been generally reported. 

Descent Of Man (1871) - Quotes

Once again, Darwin makes reference to Malthus' 25 year doubling time for the population of the United States Of America (citing the 6th edition of Malthus' essay, written in 1826):

"Civilised populations have been known under favourable conditions, as in the United States, to double their numbers in twenty-five years; and, according to a calculation, by Euler, this might occur in a little over twelve years. (57. See the ever memorable 'Essay on the Principle of Population,' by the Rev. T. Malthus, vol. i. 1826. pp. 6, 517.) At the former rate, the present population of the United States (thirty millions), would in 657 years cover the whole terraqueous globe so thickly, that four men would have to stand on each square yard of surface. The primary or fundamental check to the continued increase of man is the difficulty of gaining subsistence, and of living in comfort."

The reference to Euler is Swiss mathematician Leonard Euler (1707-1783). His name is used synonymously with that of Scottish mathematician John Napier (1550-1617) in describing the irrational number e (approximately 2.71828) as the Euler or Napier constant, as used in logarithms, calculus and differential equations. 

To rate of exponential growth required to satisfy Euler's projection would require the equivalent of a constant growth rate of 5.83% per annum for 12 years. Here I examine Darwin's use of Malthus' doubling rate of 25 years (which would mean a constant growth rate of 2.8%):

1 2 4 8 16 30 32 64 128 256 512 1024
kilopops 1 2 4 8 16   32 64 128 256 512 1024
Megapops 1 2 4 8 16   32 64 128 256 512 1024

Table A. Darwin uses Malthus to extrapolate exponential growth, assuming a constant rate of 25 years for a population of 30 million.

Note:  1 kilopop = 1024 pops, 1 Megapop = 1024 kilopops

Roughly speaking, if we take a population of 32 million and double it 26 times (for a total of 650 years), then Earth should be covered with people. Using the New Malthusian Scale to model such growth, this unfortunate event would occur when our population reached 1024 Megapops

Darwin later speculates on Malthus' views on the differential replication capabilities of barbarous and civilised races. 

"There is reason to suspect, as Malthus has remarked, that the reproductive power is actually less in barbarous, than in civilised races. We know nothing positively on this head, for with savages no census has been taken; but from the concurrent testimony of missionaries, and of others who have long resided with such people, it appears that their families are usually small, and large ones rare."

Today, this seems to be the opposite view of the First World's perception of the Third World. The Third World, we are told, suffers from the poverty trap with typically larger family size, younger age pyramid, and higher growth rate. The expectation is that such populations have not yet undergone the "demographic transition" which followed the introduction of modern medicine in the First World. This transition to slower growth rates would, it is hoped, be assisted by female emancipation, family planning and generally higher standards of living in the Third World. The anticipation is that, once through the demographic transition, the Third World will follow the First World's example and we should see slower rates of growth leading to global Zero Population Growth

My belief is that Darwin recorded the situation in his day accurately. Probably, with much higher infant mortality rates around the world in his day, most infants died as infants. This would result in the smaller families alluded to by Darwin. 

Today's Third World population has access to modern medical practices such as vaccination, without the luxury of being able to feed the large families which result. The First World, acting in this instance with the best possible humane intentions, effectively created the poverty trap suffered by the Third World. 

It remains to be seen whether the optimistic talk of demographic transitions for the Third World is justified. It is just as likely that plagues like HIV / Aids will enforce such a growth-rate slow down through typical Malthusian positive checks.

To understand who Darwin calls barbarous, and who is civilised, it is necessary to consult Malthus' "Essay On The Principle Of Population". In the 6th edition of An Essay On The Principle Of Population, Malthus classifies European countries and the newly formed United States Of America as civilised. Amongst those 'ancient nations' still around in Malthus' day, China was one of those that Malthus considered less civilised. Darwin, as the next quote will show, is thinking of India. Ignoring any national slurs inferred by either writer, what are the demographic facts? The following table compares the rates of population growth for Europe, the United States Of America, China and India:

Year 5000BC 3000BC 2000BC 1000BC 400BC 900 1250
1725 1825 1950 ?
Population (Millions)
1 2 4 8 16 32 64 128 256 512 1024
Year 1700 1750 1775 1815 1830 1860 1890 1930 2000 ?
Population (Millions)
1 2 4 8 16 32 64 128 256 512
Year 4000BC 3000BC 2000BC 1100BC 700BC 450BC 800 1575 1875 1950 2000
Population (Millions)
1 2 4 8 16 32 64 128 256 512 1024
Year 5000BC 4000BC 3000BC 1500BC 700BC 350BC 200
1525 1725 1910 1985
Population (Millions)
1 2 4 8 16 32 64 128 256 512 1024

Table B. A comparison of national population growth rates over time, roughly based on figures from "Atlas Of World Population History" by Colin McEvedy and Richard Jones. Figures in red are my educated guesses. Populations with two dates indicate population collapse and recovery.

Clearly, the USA is catching up fast, aided and abetted by the influx of migrants often from Europe, India and China! 

Darwin freely admits the lack of evidence available to him (on the relative "reproductive powers" involved) either way, but offers several observations. Here, he rightly considers the effects of recent medical advances such as vaccination on population growth rates:

"Notwithstanding that savages appear to be less prolific than civilised people, they would no doubt rapidly increase if their numbers were not by some means rigidly kept down. The Santali, or hill-tribes of India, have recently afforded a good illustration of this fact; for, as shewn by Mr. Hunter, * they have increased at an extraordinary rate since vaccination has been introduced, other pestilences mitigated, and war sternly repressed.

* The Animals of Rural Bengal, by W. W. Hunter, 1868, p. 259."

Darwin observes that the savages are quite capable of a Malthusian style of moral restraint (i.e. late marriage):

"Savages almost always marry; yet there is some prudential restraint, for they do not commonly marry at the earliest possible age."

Ironically for Malthus' case in attempting to prove divine revelation through his own Principle Of Population, I suspect these "savages" were unlikely to be Christian. Therefore, would they expect to be rewarded, as Malthus stated, "...in this life as well as  the next" as a good Christian would?

Darwin then catalogues a list of the usual Malthusian suspects which act as positive checks on populations of savages:

"With savages the difficulty of obtaining subsistence occasionally limits their number in a much more direct manner than with civilised people, for all tribes periodically suffer from severe famines. At such times savages are forced to devour much bad food, and their health can hardly fail to be injured... They are then, also, compelled to wander much, and, as I was assured in Australia, their infants perish in large numbers... Savages, when hard pressed, encroach on each other's territories, and war is the result; but they are indeed almost  always at war with their neighbours. They are liable to many accidents  on land and water in their search for food; and in some countries they  suffer much from the larger beasts of prey. Even in India, districts  have been depopulated by the ravages of tigers."

My own observation is that only three population doublings separate a population of 128 million people from becoming a population of 1024 million people. Realistically, that could happen in as little as 105 years at a mere 2% growth rate per annum. Therefore, any seeming deficiency in the reproductive power of populations of such size (China in Malthus' time, and India in Darwin's) is all too quickly "remedied".


Darwin then goes further, and is not afraid to consider some of the more unpleasant ways in which human societies have, and still do, voluntarily keep their populations in check. Darwin rarely criticises Malthus, but here he does so (though rather gently): 

"Malthus has discussed these several checks, but he does not lay stress enough on what is probably the most important of all, namely infanticide, especially of female infants, and the habit of procuring abortion."

On the topic of infanticide Malthus, writing of the Chinese and other 'ancient nations', had mentioned:

"...the custom of exposing children, which, in times of distress, is probably more frequent than is ever acknowledged by Europeans. Relative to this barbarous practice, it is difficult to avoid remarking, that there cannot be a stronger proof of the distresses that have been felt by mankind for want of food, than the existence of a custom that thus violates the most natural principle of the human heart. It appears to have been very general among ancient nations, and certainly tended rather to increase population."

I suspect that Darwin would have happily conceded the barbarity of this practice, but not that it would tend to increase population. How could it? Any death only increases the death rate of a population and thus must either slow positive growth or speed negative growth. Malthus is not being true to his own Principle Of Population. Still, given Malthus' position in the Church, it is perhaps no surprise that Malthus did not stress these matters to Darwin's satisfaction! 

Origin Of Species (1859) - Quotes

Here Darwin clearly shows his Malthusian colours:

P.67 - "In the next chapter the Struggle for Existence amongst all organic beings throughout the world, which inevitably follows from their high geometrical powers of increase, will be treated of. This is the doctrine of Malthus, applied to the whole animal and vegetable kingdoms. As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected. From the strong principle of inheritance, any selected variety will tend to propagate its new and modified form."

Again Darwin openly gives Malthus due credit, and makes it perfectly clear how exponential growth actually works in the natural world:

P.116 - "Hence, as more individuals are produced than can possibly survive, there must in every case be a struggle for existence, either one individual with another of the same species, or with the individuals of distinct species, or with the physical conditions of life. It is the doctrine of Malthus applied with manifold force to the whole animal and vegetable kingdoms; for in this case there can be no artificial increase of food, and no prudential restraint from marriage. Although some species may be now increasing, more or less rapidly, in numbers, all cannot do so, for the world would not hold them."  

The Life and Letters of Charles Darwin's - Vol 1 
- Edited by Darwin's son Francis Darwin

Here is what Darwin's son, Francis, had to say about the effect of Malthus' essay on Darwin's theory of natural selection:

"He has mentioned in the Autobiography that it was not until he read Malthus that he got a clear view of the potency of natural selection. This was in 1838--a year after he finished the first edition (it was not published until 1839), and five years before the second edition was written (1845). Thus the turning-point in the formation of his theory took place between the writing of the two editions."

Again Malthus is credited as providing "the key to the idea of natural selection":

"In writing on the Table of Contents of the 1844 MS. that it was sketched in 1839, I think my father may have intended to imply that the framework of the theory was clearly thought out by him at that date. In the Autobiography he speaks of the time, "about 1839, when the theory was clearly conceived," meaning, no doubt, the end of 1838 and beginning of 1839, when the reading of Malthus had given him the key to the idea of natural selection."

The Life and Letters of Charles Darwin's - Vol 2
- Edited by Darwin's son Francis Darwin

J.D. Hooker (Sir Joseph Dalton Hooker, English botanist and explorer). Malthus is called a "great philosopher" (no less) by Darwin, as indeed he was:

Letter to J.D. Hooker 5th June, 1860

"What has -- done that he feels so immeasurably superior to all us wretched naturalists, and to all political economists, including that great philosopher Malthus? This review, however, and Harvey's letter have convinced me that I must be a very bad explainer. Neither really understand what I mean by Natural Selection. I am inclined to give up the attempt as hopeless. Those who do not understand, it seems, cannot be made to understand."

C. Lyell (Sir Charles Lyell, English geologist). Here Darwin infers that Malthus' Principle Of Population is "the plainest case" and would accuse anyone who cannot understand it as incapable of understanding "common reasoning":

Letter to C. Lyell, 6th June, 1860

"...It consoles me that -- sneers at Malthus, for that clearly shows, mathematician though he may be, he cannot understand common reasoning. By the way what a discouraging example Malthus is, to show during what long years the plainest case may be misrepresented and misunderstood."

Darwin is consoled by the inability of people to understand Malthus.

A.R. Wallace is, of course, Alfred Russel Wallace, co-discoverer of the theory of evolution. Here Darwin bemoans the fact the term Natural Selection is a faulty label for a meme, and humorously uses the newly suggested phrase "survival of the fittest" to suggest that memes must compete in an evolutionary sense. Of course, Darwin didn't know the word meme, but I'm sure Richard Dawkins (who invented the term in his book "The Selfish Gene" in 1975), would approve of Darwin's thinking here:

Darwin to A.R. Wallace, 5th July 1866 (Letter 191)

"The term Natural Selection has now been so largely used abroad and at home, that I doubt whether it could be given up, and with all its faults I should be sorry to see the attempt made. Whether it will be rejected must now depend "on the survival of the fittest." As in time the term must grow intelligible the objections to its use will grow weaker and weaker. I doubt whether the use of any term would have made the subject intelligible to some minds, clear as it is to others; for do we not see even to the present day Malthus on Population absurdly misunderstood? This reflection about Malthus has often comforted me when I have been vexed at the misstatement of my views."

As far as Darwin's comment on Malthus goes, I agree with Darwin that Malthus is still not properly understood...even in our new millennium. Darwin once again expresses the comfort he gains in knowing Malthus is so poorly understood. 

However, the exponential growth of populations is such a poorly presented phenomenon throughout scientific literature on evolution that it I personally find it hard to find any consolation from such a lack of understanding. The confusion arises over Malthus' Exponential Law, which is widely recognised as only an approximate law of nature. The Exponential Law is, effectively, based on an understanding of population growth based on fixed rate compound interest. To turn this approximate law of nature into a true law of nature, it is necessary to consider population growth based on variable rate compound interest - refer Couttsian Growth Model for more.

More Letters Of Charles Darwin - Vol 1

Edited by Darwin's son Francis Darwin, and A.C Seward

Letter 71 to A.R. Wallace, 6th April, 1859

"You are right, that I came to the conclusion that selection was the principle of change from the study of domesticated productions; and then, reading Malthus, I saw at once how to apply this principle. Geographical distribution and geological relations of extinct to recent inhabitants of South America first led me to the subject: especially the case of the Galapagos Islands."

Asa Gray (American botanist). Once again Darwin would accuse anyone who does not understand Malthus as being incapable of reason:

Letter 104 to Asa Gray, 8th June, 1860

"A review in the last Dublin "Nat. Hist. Review" is the most unfair thing which has appeared,--one mass of misrepresentation. It is evidently by Haughton, the geologist, chemist and mathematician. It shows immeasurable conceit and contempt of all who are not mathematicians. He discusses bees' cells, and puts a series which I have never alluded to, and wholly ignores the intermediate comb of Melipona, which alone led me to my notions. The article is a curiosity of unfairness and arrogance; but, as he sneers at Malthus, I am content, for it is clear he cannot reason. He is a friend of Harvey, with whom I have had some correspondence. Your article has clearly, as he admits, influenced him. He admits to a certain extent Natural Selection, yet I am sure does not understand me. It is strange that very few do, and I am become quite convinced that I must be an extremely bad explainer."

Was Darwin an "extremely bad explainer"? Clearly not as, one by one, all alternate theories to Natural Selection either become extinct or turn out to reinforce Darwinism. At worst, I would accuse Darwin of presenting a naive view of exponential growth. His generational chauvinism led to unwieldy assumptions of "immortal" populations. This, together with his unqualified (and naive) assumption of constant growth rates, are both now hopefully laid to rest by the renaissance of the Malthusian Principle Of Population and the introduction of the New Malthusian Scale.

My sincere hope is that the mathematical nature of Malthus' Principle Of Population will be seen as indisputable proof of the nature of all replicators (to use Dawkins' term) - all replicators are capable of exponential growth, all replicators will tend towards exponential growth if given the chance to do so, all replicators face their own Malthusian limits to growth, and all populations of replicators actively compete with other replicator populations through the principle of differential replication. 

The Struggle For Existence

Malthus, Darwin and Wallace all referred to the struggle for existence. However, for Malthus, species were immutable and so his struggle for existence was based on environmental and behavioural factors. To Malthus, the struggle was for resources - principally food and water. Some populations would still fare better than others, and therefore grow more quickly. I call this Malthusian Selection, which compliments Natural Selection in driving differential replication. It does not replace the theory of Natural Selection. How could it? It does not even attempt to explain genetic variation (through mutation, or sexual recombination via meiosis) and nor does it attempt to tackle heredity! 

Both Darwin and Wallace understood the principle of heredity, even though genetics was unknown in their day. To them, the Malthusian struggle for existence drove Natural Selection, forcing variation on species.

The exponentialist view is that the struggle for existence is one of differential replication. All factors which affect replication rates and death rates will affect growth rates. As competing populations will sustain different growth rates, the result is differential replication. Hence, some population flourish, some go extinct, and some merely persist. 

The exponentialist view is a Malthusian view. This view blurs the edges at which level evolution works, for Malthusian principles work on populations. Remember, a population could be a species, or any arbitrary sub-set of a species. Hence, Malthusian principles work both between species and within species.

I see the exponentialist view as reinforcing Darwinism, whilst at the same time elevating Malthus' unintentional contribution in the field of evolution to its rightful place. Perhaps the exponentialist view could best be described as Malthusian Darwinism. Judging from Darwin's view of Malthus, I don't think Darwin would have minded this view. Darwin, to his credit, was able to see beyond the sanctimonious moralising in Malthus' essay to understand the scientific nature of the law which Malthus had so clearly uncovered. Darwin time and again openly places Malthus' writings at the core of his own.

Darwin was a Malthusian Darwinist.

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Copyright 2001 David A. Coutts
Last modified: 08 November, 2009