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Asimov - An Exponentialist View
Bartlett - An Exponentialist View
Darwin - An Exponentialist View
Dawkins - An Exponentialist View
Drexler - An Exponentialist View
Ehrlich - An Exponentialist View
Malthus - An Exponentialist View
Sagan - The Secrets of the Universe
Savage - An Exponentialist View
Turchin - An Exponentialist View
Wallace - An Exponentialist View
Witting - An Exponentialist View

Malthus and Evolution
Malthusian Memes
Thomas Robert Malthus - Principle Of Population
Darwin on Malthus
Gigantic Inevitable Famine

New Malthusian Scale 
Population Doubling Mechanism 

External Links:
From the desk of Malthus: How the population debate began - National Academies Forum

Pop Malthus - a Malthus family blog

Reverend Thomas Robert Malthus - An Exponentialist View

"People at present think that five sons are not too many and each son has five sons also, and before the death of the grandfather there are already 25 descendants. Therefore people are more and wealth is less; they work hard and receive little."  HAN FEI-TZU 500 B.C.

Introduction

Malthus is most famous for his work An Essay On The Principle Of Population. However, it was due to this work that Malthus' biographer James Boner wrote of Malthus (Bonar, 1885) "He was the best-abused man of the age..." and goes on to say "...Malthus from the first was not ignored. For thirty years it rained refutations."

What did Malthus say to deserve so much attention?

Malthus' essay, first published anonymously in 1798, was a response to the popular optimistic vision of the day of endless human progress. It was a stark message (Malthus, 1798):

"The perpetual tendency of the race of man to increase beyond the means of subsistence is one of the general laws of animated nature, which we can have no reason to expect to change."  

Malthus also understood the dire eternal consequences of all of this for humanity (Malthus, 1798):

"The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction; and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague, advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world." 

Exponential Growth

What lead Malthus to his Principle Of Population, based on his model of exponential growth? Among others, Malthus might have been influenced by the writings of Aristotle (350BC), who said:

"...in the generality of states, if every person be left free to have as many children as he pleases, the necessary consequences must be poverty..."

In the preface to the second edition of his essay Malthus makes it quite clear who his influences were when he wrote the first edition of the essay (Malthus, 1826):

"The only authors from whose writings I had deduced the principle, which formed the main argument of the Essay, were Hume, Wallace, Adam Smith, and Dr. Price..."

Malthus then goes on to say (Malthus, 1826):

"In the course of this inquiry I found that much more had been done than I had been aware of, when I first published the Essay. The poverty and misery arising from a too rapid increase of population had been distinctly seen, and the most violent remedies proposed, so long ago as the times of Plato and Aristotle. And of late years the subject has been treated in such a manner by some of the French Economists; occasionally by Montesquieu, and, among our own writers, by Dr. Franklin, Sir James Stewart, Mr. Arthur Young, and Mr. Townsend, as to create a natural surprise that it had not excited more of the public attention."

Of particular note is the thinking of Benjamin Franklin and his 1751 essay "Observations concerning the Increase of Mankind, peopling of Countries, etc.," in which Franklin noted that the population doubling rate in the English colonies in America was 25 years. Assuming the current population there to be 1 million, Franklin observes (Franklin, 1751):

"This Million doubling, suppose but once in 25 Years, will, in another Century, be more than the People of England, and the greatest Number of Englishmen will be on this Side the Water."

This is an early example of what is now termed differential reproduction (caused in this case not by Natural Selection but by what I term Malthusian Selection), as explored in more detail by the later versions of Malthus' own essay. Franklin is saying that the English in their North American colonies will outbreed the English who remain in Britain. With a doubling time of 25 years, a population of 1 million will double four times in a century (1, 2, 4, 8, 16). Thus Franklin supposes that by 1850 there will be 16 million Englishmen living in North America, and fewer Englishmen living in Britain. Franklin wasn't far wrong (see Table A and Table B below), though in 1751 he would not have anticipated the struggle for independence which led to the formation of the United States Of America. 

But it was Malthus who was the first to effectively explore the tendency of populations to increase exponentially, and thus continuously outstrip their food supply (which he suggested only increased arithmetically). Having no reason to doubt the many statistical demographic sources available to him, nor any alternative but to use what was available, Malthus considers the rates of increase for populations around the globe. 

Population Doubling - The USA

In this example, he made use of the mechanism of population doubling to demonstrate his point (Malthus, 1798):

"In the United States of America, where the means of subsistence have been more ample, the manners of the people more pure, and consequently the checks to early marriages fewer than in any of the states of Europe, the population has been found to double itself in twenty-five years."

A population doubling rate of 25 years would require the equivalent of a constant growth rate of 2.8% for 25 years.

Year 1700 1725 1750 1775
Population (Millions) 1 1.5 2 3.25
Year 1800 1825 1850 1875
Population (Millions) 6 12 23.50 44
Year 1900 1925 1950 1975
Population (Millions) 76 115 150 210

Table A. The population of the United States Of America over three centuries.

Here and there we can see that the population of the USA did indeed double in 25 years and, though the population has continued to double, it is clear that the population doubling rate has not been constant. It should be noted that the United States Of America itself gained territory (and the inhabitants of that territory) over this time period, and also experienced enormous immigration.

It is interesting to note that the American Declaration Of Independence, published on 4th July 1776 (Malthus, living in England, would have a boy about 10 years old), contains the following Injury amongst the many such Injuries said to have been perpetrated by King George III of Britain against the people of his thirteen American colonies (National Archives, 1776):

"HE has endeavoured to prevent the Population of these States; for that Purpose obstructing the Laws for Naturalization of Foreigners; refusing to pass others to encourage their Migrations hither, and raising the Conditions of new Appropriations of Lands."

It is interesting to reflect what population doubling times would have resulted in these former colonies had they not won the War Of Independence (1775-1781).

As to the effects of the expanding European population on the native American population, Malthus himself commented in the Preface to the 2nd edition of his essay (Malthus, 1826):

"If the United States of America continue increasing, which they certainly will do, though not with the same rapidity as formerly, the Indians will be driven further and further back into the country, till the whole race is ultimately exterminated, and the territory is incapable of further extension."

Note Malthus' explicit mention of an anticipated decline in the rate of increase for the population of the USA. Clearly, even though Malthus and those who read him (such as Darwin) made extensive use of 25-year population doubling period for the USA, Malthus appreciated that this was an approximation.

Population Doubling - The British Isles

Malthus then considers his own island nation, Great Britain (which in those days included Ireland), and projects the same hypothetical doubling rate. He dismisses the possibility that food supply could quadruple after the population doubles twice and so only allows the food supply to increase arithmetically every twenty-five years  with enough each time for 7 million more people (Malthus, 1798):

"The population of the Island is computed to be about 7 millions, and we will suppose the present produce equal to the support of such a number. In the first twenty-five years the population would be 14 millions, and the food being doubled also, the means of subsistence would be equal to this increase. In the next twenty-five years the population would be twenty-eight millions, and the means to subsistence only equal to the support of twenty-one millions. In the next period, the population would be fifty-six millions, and the means of subsistence just sufficient for half that number. And at the conclusion of the first century the population would be one hundred and twelve millions and the means of subsistence only equal to the support of thirty-five millions, which would leave a population of seventy-seven millions totally unprovided for."

Years (from 1800AD approx.)  0 25 50 75 100
Population (Millions) 7 14 28 56 112
Absolute increase of population 0 7 14 28 56
Available Food Supply 
(for population in millions)
7 14 21 28 35
Absolute increase of food supply 0 7 7 7 7
Shortfall in Food Supply
(for population in millions)
0 0 7 28 77

Table B. Malthus' projected population of British Isles from 1800 to 1900 with food shortfall. The linear growth of the means of subsistence (food supply) fails to keep up with a population growing exponentially.

Clearly, Malthus is saying that the shortfall in the food supply will prevent the population from doubling as projected. Malthus states this belief quite clearly in the conclusion to Chapter VII (Malthus, 1798):

"That the increase of population is necessarily limited by the means of subsistence."

Time has again proven Malthus correct, as these actual population figures for the British Isles show. 

Years 
(from 1800AD approx.)
 0 25 50 75 100
Population (Millions) 7 14 28 34 42

Table C. Actual  population of British Isles from 1800 to 1900.

It's interesting to note that Malthus' projection is spot on for the first 50 years. Then, as Malthus expected, the rate of population growth slowed and did not double as projected. Nonetheless, the population still managed to double from 28 million to 56 million by the 1960s (doubling in roughly 110 years, rather than the projected 25 years).

Population Doubling - The Earth

Malthus then rightly attempts to avoid the confusion of national immigration and emigration figures on natural increase. To do so, he proposes to model population growth for the whole Earth. First, in a roundabout way, Malthus introduces the concept of the limits to growth imposed by Earth itself (Malthus,1798):

"But to make the argument more general and less interrupted by the partial views of emigration, let us take the whole earth, instead of one spot, and suppose that the restraints to population were universally removed. If the subsistence for man that the earth affords was to be increased every twenty-five years by a quantity equal to what the whole world at present produces, this would allow the power of production in the earth to be absolutely unlimited, and its ratio of increase much grater than we can conceive that any possible exertions of mankind could make it."

Malthus is saying that, taking the whole Earth, it is unrealistic to assume a continued increase in food supply to support an exponentially growing population. He continues (Malthus, 1798):

"Taking the population of the world at any number, a thousand millions for instance, the human species would increase in the ratio of - 1,  2,  4,  8,  16, 32, 64, 128, 256, 512, etc. and subsistence as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 etc. In two centuries and a quarter, the population would be to the means of subsistence as 512 to 10: in three centuries as 4096 to 13, and in two thousand years the difference would be almost incalculable, though the produce in that time would have increased to an immense extent."

Years (from 1800AD approx.)  0 25 50 75 100 125 150 175 200 225 250 275 300
Population (Billions) 1 2 4 8 16 32 64 128 256 512 1024 2048 4096
Absolute increase of population 0 1 2 4 8 16 32 64 128 256 512 1024 2056
Available Food Supply  1 2 3 4 5 6 7 8 9 10 11 12 13
Absolute increase of food supply 0 1 1 1 1 1 1 1 1 1 1 1 1
Ratio of Population to Food Supply 1:1     2:1   4:1   16:1  

512:10

    4096:13

Table D. Malthus' projected population of Earth from 1800 to 2100 with food shortfall. The linear growth of the means of subsistence (food supply) fails to keep up with a population growing exponentially. 

Graphed, Malthus' comparison of arithmetic (linear) growth and geometric (exponential) growth looks like this:

Graph A. Malthus' comparison of arithmetic (linear) growth and geometric (exponential) growth

Here are the historical figures for our global population from 1800, with a conservative estimate of when we will reach 8 billion:

Year  1800 1930 1974 2040?
Population (Billions) 1 2 4 8
Actual doubling time (years) - 130 44 66

Table E. Actual world population with real doubling times, and projection for 8 billion.

So, despite Malthus' projected 2 to 1 ratio of population to food supply by 1875, it appears that our global population currently continues to double. Clearly then, Malthus' projection does not hold true. Indeed, skeptical environmentalist Bjorn Lomborg argues that things have actually got better (Lomborg - 2001):

"Although there are now twice as many of us as there were in 1961, each of us has more to eat, in both developed and developing countries."

Although this does invalidate the principle of linear growth for food supply, this does not invalidate Malthus' Principle Of Population. Malthus himself stated (Malthus, 1798):

"That population does invariably increase when the means of subsistence increase."

Malthus lived at the time of the Industrial Revolution. Like the Agricultural Revolution before it, the Industrial Revolution did increase the means of subsistence, and on a global scale. 

The medical sciences also made great advances during this time, further fuelling our continued global population growth. For example in 1798, the year that Malthus published his famous essay, fellow countryman and physician Edward Jenner (1749-1823) published his paper (after successful trials) on vaccination against smallpox, which would lead to an eradication of that disease. Other such medical discoveries then followed.

However, it is a mathematical certainty  that the Earth cannot sustain the continued exponential growth of its human population. If you think that our global population can continue doubling beyond the 4096 billion projected in Table D, then consider Malthus' projection for 2,000 years, up to 3800 AD.

New Malthusian Scale

Using my New Malthusian Scale to explore Malthus' projection of constant global population doubling, the early landmarks (see Table D) are 512 A-Pops (512 billion people) and 4 B-Pops (4,096 billion people). 

Each row in the table below shows 10 population doublings. Using Malthus' constant doubling rate of 25 years, that means that each row represents 250 years and 4 rows represent 1,000 years. Hence, after 2,000 years, the population is 1,024 H-pops (10247 x 109 people). The food supply would have increased arithmetically 80 times, and would thus be capable of feeding only 80 A-Pops (80 x 109 people). Thus the "almost incalculable" ratio can be declared to be:

 10247 to 80 (1208925819614629174706176 to 80).

A-Pops
(billions)
1 2 4 6 8 16 32 64   128 256 512 1024
B-Pops 1 2 4   8 16 32 64   128 256 512 1024
C-Pops 1 2 4   8 16 32 64   128 256 512 1024
D-Pops 1 2 4   8 16 32 64   128 256 512 1024
E-Pops 1 2 4   8 16 32 64 67.98 128 256 512 1024
F-Pops 1 2 4   8 16 32 64   128 256 512 1024
G-Pops 1 2 4   8 16 32 64   128 256 512 1024
H-Pops 1 2 4   8 16 32 64   128 256 512 1024

Table F. Global population doubling every 25 years using the Alphabet Option (constant rate) of The New Malthusian Scale from 1800AD to 3800AD. Current global population is approximately 6 A-Pops.

Note:  1A-pop = 1024 pops, 1B-pop = 1024 A-pops, 1 C-pop = 1024 B-pops etc. 

Given that 1 A-Pop equals 1 billion people and, taking the average weight of a human to be 80 kg, then 1 A-Pop would have a mass of 80 kg x 109

Object Mass (Scientific notation) Mass (New Malthusian Scale)
Earth 5.98 x 1024  kg 67.98 E-Pops

Table G. Converting the mass of the Earth into people

So it is clear that the mass of our global human population would soon exceed (between 2925AD and 2950 AD) that of the Earth should it continue to double every 25 years. Even if it takes longer for our population to double, the maths is still the same. From our 4 billion in 1974 it would take only 45 more population doublings for our human population to weigh more than the Earth itself. 

Given that the available food supply has to match our population, and we need somewhere to live other than just a writhing ball of humanity and its food supply, I'd suggest that we could easily wipe 30 population doublings off the true Earth-bound limit to growth. Even then, only the most bigoted technophile could expect us to be able to sustain 15 more population doublings to 128 B-Pops (131,072 billion people) on Earth. 

We cannot continue to double our numbers, however slowly, if we remain on Earth. Logically then, if restricted to the Earth, there must come a point when our population ceases to double (voluntarily, or otherwise). This is irrespective of any technological advance whatsoever. 

The only scenario which allows the total human population to continue doubling is the human colonisation of space. Even then, humanity will continue to face limits with each planet, or each solar system, colonised. 

Plants and Animals

Neatly summarised in the introduction to the Penguin Classics 1883 edition of An Essay On The Principle Of Population are quotes from Malthus such as (Malthus, 1798):

"In taking a view of animated nature, we cannot fail to be struck with the prodigious power of increase in plants and animals."

and (Malthus, 1798):

"Elevated as man is above all other animals by his intellectual faculties, it is not to be supposed that the physical laws to which he is subjected should be essentially different from those which are observed to prevail in other parts of animated nature..."

and (Malthus, 1798):

"...all animals, according to the known laws by which they are produced, must have a capacity of increasing in geometrical progression."

Clearly then, Malthus knew that his Principle Of Population applied to all life. It is curious, therefore, that he chose to model food production using an arithmetic model (1, 2, 3, 4, 5, etc) rather than a geometric (1, 2, 4, 8, 16 etc) one. This error in Malthus' argument is frequently taken as a falsification of his Principle Of Population, but it is far from it.

Populations of all living things tend towards exponential growth, and are only prevented from continued exponential growth by Malthusian positive checks. Thanks to the ability some life-forms (such as plants, algae and bacteria) to harness the energy of the Sun, or the Earth itself (bacteria in particular), virtually all human food is derived from such creatures or those that feed upon them. Malthus understood the special power of mankind over nature (Malthus, 1798):

"The main peculiarity which distinguishes man from other animals, is the means of his support, is the power which he possesses of very greatly increasing these means."

Given a helping hand from humanity, as Malthus points out in these next two examples, crops and livestock can be actively encouraged to grow at a faster exponential rate.

Malthus on Grain (A Summary View, p.224, Penguin Classics)

In considering various reports from around the world regarding the variable rates of growth in the farming of wheat, Malthus projects a modest rate of growth which would quickly cover all available land (Malthus, 1830):

"Now supposing that in any one country during a certain period, and under ordinary cultivation, the return of wheat was six grains for one, it would be strictly correct to say. that wheat had the capacity of increasing in a geometrical ratio, of such a nature as to sextuple itself every year. And it might be safely calculated hypothetically, that if, setting out from the produce of one acre, land of the same quality could be prepared with sufficient rapidity, and no wheat were consumed, the rate of increase would be such as completely to cover the whole earthly surface of our globe in fourteen years."

The equatorial radius of the Earth is 3,963.3 miles. To calculate the surface area of a sphere, we must use the following formula:

4 x pi x r2

Hence, Earth's surface area is 197,468,818 miles2 

Malthus uses acres in his calculations. To convert, 1 mile2 = 640 acres. Therefore Earth's surface is (197468818 * 640) acres = 126,380,043,520 acres. 

Seven tenths of the Earth's surface is either submerged by water, or covered with ice. In his example, Malthus is only interested in the land available for the growth of wheat. Therefore, for his example using grain (and the next example using sheep), the unassailable limit to growth is reached at (126,380,043,520 * 0.3) acres = 37,914,013,056 acres.

Malthus states that 1 acre of wheat would sextuple every year, and thus reach the calculated limit to growth in just 14 years. Is he right?

Acres of wheat 6 36 216 1296 7776 46656 279936
Acres of wheat 1679616 10077696 60466176 362797056 2176782336 13060694016 78364164096

Table H. Malthus' sextupling population of wheat from 1 original acre.

Yes, Malthus is right. 37,914,013,056 acres falls between the 13th and 14th sextupling of the wheat population. 

This example is fairly unique for Malthus. It is a rare example in which he applies the Principle Of Population to any species other than humanity. It shows that he was perfectly aware of the validity of considering rates of growth other than doubling. It clearly indicates that Malthus understood natural limits to growth other than the whole Earth. It is also an interesting example of measuring population growth through a measurement for area! 

Personally, I find it a useful example of the unsuitability of sextupling over doubling. The numbers in the series quickly exceed the comfort zone for mental arithmetic for most people (including me).

Malthus on Sheep (A Summary View, p.224, Penguin Classics)

Perhaps that's why Malthus preferred to use the doubling series, which he returns to in his next example, this time using sheep (Malthus, 1830):

"In the same manner, if it be found by experience, that on land of a certain quality, making allowance for the ordinary mortality and accidents, sheep will increase, on average, so as to double their numbers every two years, it would be strictly correct to say, that sheep have a natural capacity of increasing, in geometrical progression, of which the common multiple is two, and the term, two years; and it might be safely said, that if land of the same quality could be provided with sufficient rapidity, and no sheep consumed, the rate of increase would be such, that if we were to begin with the full number which could be supported on an acre of land, the whole earthly part of the globe might be completely covered with sheep in less than seventy-six years."

A-Pops
(acres)
1 2 4 8 16 32   64 128 256 512 1024
B-Pops 1 2 4 8 16 32   64 128 256 512 1024
C-Pops 1 2 4 8 16 32   64 128 256 512 1024
D-Pops 1 2 4 8 16 32 35.3 64 128 256 512 1024

Table I. Global sheep population doubling every 2 years using the Alphabet Option (constant rate) of The New Malthusian Scale.

Note:  1A-pop = 1024 pops, 1B-pop = 1024 A-pops, 1 C-pop = 1024 B-pops etc. 

Each row on the table equates to 20 years worth of population doubling. Therefore, we should expect to find Malthus' projection proven before the 6th doubling on the bottom row ("...less than seventy-six years"). This would place his projected population between 32 and 64 D-Pops.

Using the New Malthusian Scale, it is a simple matter to divide the limit to growth (37,914,013,056 acres) by 1024 (then divide the result by 1024, and so on) until any number between 1 and 1024 is reached. This happens after only 3 divisions, and the resultant figure is 35.3 D-Pops. Malthus' projection is proven. 

Again, Malthus has applied his Principle of Population to a non-human species, and uses acreage as a novel (but valid) measure of population growth. It is perhaps worth reflecting that food production per acre must have increased dramatically over the years to support Britain's actual population growth (see Table C)- sustained exponential growth of produce doesn't seem to have been a situation which Malthus considered likely to be sustained. In fact, in considering the British mainland, Malthus uses the word impossible (Malthus, 1798):

"If I allow that by the best possible policy, by breaking up more land and by great encouragements to agriculture, the produce of this Island may be doubled in the first twenty-five years, I think it will be allowing as much as any person can well demand.

In the next twenty-five years, it is impossible to suppose that the produce could be quadrupled...."

So in the end it would seem that Malthus has directly contradicted himself. On the one hand, he argues that the "means of subsistence" will increase through linear growth and will thus fall short of the exponential growth of our human population (refer Table B). On the other hand, Malthus claims that all animal and plant populations can increase exponentially. Malthus also claims humans have the peculiar ability to actively encourage that exponential growth (through farming). Thus humans obtain their means of subsistence from these exponentially growing populations!

As Malthus' projections for our global population show (see Table D and Table F), continued exponential growth would mean that our global human population would weigh more than the Earth! The same is true for any replicator population, and the same is true for the sum of all replicator populations. Thus, for now, the Earth represents the ultimate reality check for all exponential population growth. Each replicator population competes for its slice of the Earth pie in a perpetual struggle for existence.  Should we break free, life will be able to spread throughout our solar system and beyond into the Milky Way galaxy (Malthus, 1798):

"The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in the course of a few thousand years."

However, what is clear is that our human population can only continue to grow exponentially if our food supply also grows exponentially. Look what happens when exponentially growing food supply fails to keep up with an exponentially growing population:

Year  0 25 50 75 100 125 150 175 200 225 250 275 300
Population (Billions) 1 2 4 8 16 32 64 128 256 512 1024 2048 4096
Available Food Supply  1   2   4   8   16   32   64
Ratio of Population to Food Supply 1:1   2:1   4:1   8:1   16:1

 

32:1   64:1

Table J. Population doubling every 25 years, and food supply doubling every 50 years. Thus, even using a simple exponential growth model, it is possible to demonstrate why populations can face starvation through inadequate food supply, droughts, crop failures etc. 

This Exponential Vs Exponential comparison is a much better representation of reality than that proposed by Malthus in 1798 (see Table D). However, the best representation of reality is only achieved by allowing for variable rates of compound interest, which lead to the variable doubling and halving periods that we see in nature.

Variable Rates Of Growth

In considering the growth of a population, Malthus always considers birth rates and death rates to derive his growth rate, as this extract from A Summary View on The Principle of Population makes clear (Malthus, 1830):

"The immediate cause of the increase of population is the excess of the births above deaths; and the rate of increase, or the period of doubling, depends upon the proportion which the excess of the births above the deaths bears to the population."

This is the basis of the my New Malthusian Scale, and it is also the basis of the Malthusian Growth Model used in population dynamics. Malthus is not simply stating his opinion - he is stating a law of nature as mathematical fact. As extended by my Couttsian Growth Model, this law applies to all populations of replicators. See The Mechanism Of Population Doubling for a quick explanation of how variable rates of compound interest lead to variable doubling and halving periods.

Even though Malthus made regular use of constant growth rates in his projections, he was aware that real-world growth rates vary with circumstances (Malthus, 1798):

"The greatest check to the increase of plants and animals, we know from experience, is the want of room and nourishment; and this experience would direct us to look for the greatest actual increase of them in those situations where room and nourishment were the most abundant."

Refer to Malthus' analysis of the "Proportions of Births to Deaths" of Prussia/Lithuania, Pomerania, Brandenburg, and Magdeburg in the early 18th century (Malthus, 1798). Malthus concludes that the average growth rates vary so much every 5-10 years that they are "...an inadequate criterion of the real average increase of population." His analysis of various birth and mortality figures around the globe in A Summary View (Malthus, 1830) provide yet more evidence that Malthus was fully aware that the growth rates varies per any given population over time, and varies between populations at any given time.

Let's examine another hypothetical situation involving a population and its food supply, this time allowing for variable rates of compound interest: 

Years   1800 1930 1974 2040 2100 2200 2250 2300
Doubling or Halving Period   130 44 66     210 50
Population (Billions) 1 1 4 8 10 10 16 8
Available Food Supply  1 2 4 8 10 10 16 8
Ratio of Population to Food Supply 1:1 1:1 1:1 1:1 1:1 1:1 1:1 1:1

Table K. Starting with historical figures for 1800, 1930 and 1974, Table K shows our global stabilise as predicted around 2100, then double again (perhaps thanks to some new food technology) then collapse (perhaps due to a food monoculture collapse / environmental catastrophe). This is hypothetical only, not my prediction of future events.

Historically, global food supply has matched global population, allowing the population to grow. In the future, demographic transition is supposed to stabilise global population growth - see Human Replicators - An Exponentialist View for more. 

An important point to note is that, whatever happens, our global human population and its available food supply can be expected to stay fairly close to 1:1. Why? Because, as the agricultural and industrial revolutions and the green revolution have taught us, we are highly capable as a species of increasing the means of our own subsistence. Yet as already noted this does not mean that we can go on increasing indefinitely on Earth, otherwise our population and food needed to supply it would weigh more than the Earth itself (clearly impossible if we are restricted to Earth). In the meantime, if there is a collapse in the food supply or the population, the ratio would soon balance out at roughly 1:1 again. 

Historically, population doubling times and available food supply have kept pace with each other and have done so at variable doubling periods. Whatever happens, it is certain that we can expect our global population and its food supply to obey the same universal law of nature that they always have. Namely, growth (or shrinkage) comparable to exponential growth (or shrinkage), but based on variable rates of compound interest not any constant rate of growth (or shrinkage). Hence, doubling periods (and halving periods) will also be variable.

This is what the Couttsian Growth Model explains, when looking at the history of any population of any species. This is what the Couttsian Growth Model predicts for the future of any population of any species.

Darwin Conducts An Experiment

Without specifically having Malthus' assertions on the greatest checks on population of "want of room and nourishment" in mind, Darwin actually tests this theory (see the chapter "The Struggle For Existence" from Origin Of Species, 1859) by planting 357 seeds in a plot of ground, 3 feet long by 2 feet wide, "...dug and cleared, and where there could be no choking from other plants...". Each seed had been marked, and Darwin was able to determine that 293 of the seeds were destroyed by slugs and insects. 

Even though Darwin does not provide a comparative study in which the seedlings are choked by other plants, I would conclude that Darwin has proven Malthus wrong in asserting which is the "greatest check". The greatest check to life is...life. Life is consumed by other life. 

Still, nobody would argue that "want of room and nourishment" are insignificant checks. The most important point, to reiterate, is that rates of growth vary. Malthus understood that. Generally speaking, he would also be right in assuming that higher rates of growth would accompany locations with a greater supply of sustenance. 

Viewing Darwin's experiment from the perspective of the slugs and insects, Malthus' assertion  makes more sense. Both the slugs and insects would find themselves in a situation where both room and nourishment (the plant seeds) were abundant. Static plant seeds being much easier to count than slugs and insects, Darwin only provided figures for the plant seeds. Unfortunately then, we don't know what effect Darwin's experiment had on slug and insect numbers.

Differential Replication

In considering what I term differential replication, Malthus wrote (Malthus, 1830):

"Taking countries in general, there will necessarily be differences as to the natural healthiness in all gradations, from the most marshy habitable situations to the most pure and salubrious air. These differences will be further increased by the employments of the people, their habits of cleanliness, and their care in preventing the spread of epidemics. If in no country was there any difficulty in obtaining the means of subsistence, these different degrees of healthiness would make great difference in the progress of population;

...But as the actual progress of population is, with very few exceptions, determined by the relative difficulty of procuring the means of subsistence, and not by the relative natural powers of increase, it is found by experience that, except in extreme cases, the actual progress of population is little affected by unhealthiness or healthiness..."

Malthus wrote these lines in an age when vaccination against smallpox was in its infancy, and so was not well placed to judge the effect of medical advances on both birth rates and death rates. However, what these lines do prove is that Malthus clearly understood that many factors would play a part in producing the growth rate for any particular population, and that these factors would vary from population to population. This, he foresaw, would lead to variable growth rates. Although Malthus is discussing human populations in this passage, most of what he said would also apply to any life-form.

Malthus believed in the God-given immutability of species, and would have firmly believed (along with most of his contemporaries) that "All men are created equal...". With the human genome now revealed, and the genetic nature of some diseases understood, few people would now literally hold this Truth to be self-evident any more.

Malthus lived a long time before knowledge of heredity or genetics became available. These days, differential replication is normally attributed to genetic factors. The mutability of species allow them to gradually adapt (over vast stretches of time) to their environment, and gain (or lose) a reproductive edge over competitors - this is Natural Selection. Those which gain an advantage will increase in number, and those which lose an advantage will decrease in number (and be driven to extinction). Differential replication ranks alongside Natural Selection in modern evolutionary theory.  

The existence of variable rates of growth, regardless of the cause of the variation, leads to the principle of differential replication. Differential replication essentially boils down to a competition between populations with different growth rates. 

So, whilst Malthus was incorrect (due to his ignorance of knowledge yet to be discovered) to assert that the "...relative natural powers of increase..." are insignificant, he may have a very good point regarding "...the relative difficulty of procuring the means of subsistence..." Surely we must consider the effects of the environment, behaviour and habit on reproductive success? 

I assert that, whether you believe in Creationism, or Evolution, differential replication must still be explained. This is something which is very lightly explored in most defences of evolutionary theory, which mostly focus on natural selection rather than differential replication. Creationists do not even use the explanation provided for them by Malthus. Both camps could learn something about differential replication from Malthus.

For the moment, regardless of your preconceptions, forget all the arguments. Assume that all species simply exist, with no need to explain why. Now it still remains to explain why some populations increase, some remain stable, and some decrease (and eventually go extinct). 

Malthusian Selection

It might surprise some Creationists to realise that Malthus, an English clergyman, provided the only common ground they inevitably share with Evolutionists. There was no Wallace or Darwin to argue against the fixity of species. Lamarckism was, even in Malthus' day, unconvincing. Therefore, in Malthus' day, all species were imagined to be created as they are and unchanging. 

If all humans were identical genetic clones (hence no genetic cocktail mixed via sexual recombination) with no possibility of genetic mutation, then differential replication would still apply simply due to the variable environmental circumstances of distinct populations. 

In our hypothetical situation, some populations would have adequate water and food, and some would not. Depending upon available shelter and the local weather, some might suffer from too much heat, or not enough. Some might get too wet. Some would suffer local plagues. Some clone populations would be more successful at waging war on other clone populations. Consequently, some populations will grow faster than others, some will remain stable, and some will decline. Recorded human history would certainly confirm that populations living close to fresh water grew so rapidly that civilisation was often the result.

Without actually using the term "clone", this is still pretty much what Malthus thought. This form of differential replication is what I call Malthusian Selection. It is environmental and behavioural selection on the reproductive success of a population. It is a much more short-term form of selection than Natural Selection, but constantly applies. One way to think of my argument is like the nature / nurture debate for individuals, which most people rate ay 60/40. I hesitate to put a figure on Natural Selection / Malthusian Selection, but would suggest 60/40 might not be a bad starting position.

What Wallace and Darwin realised, which Malthus did not, was that variability within a species also played a huge role in providing small advantages and disadvantages within a species, and even between competing species (e.g. predator and prey). Though genetics was undiscovered at the time, they both also realised that such variability was hereditary. Hence, species would gradually evolve into new species. Both men realised that old and new species would then face a survival of the fittest contest, over time, which would frequently result in the extinction of either the old or new species. Both men therefore realised that this slow process would favour changes which improved a species in the contest of differential replication.

The First Exponentialist

Malthus introduced the concept of considering discrete populations at different locations (e.g. the USA, Britain, and the Earth). He introduced the concept of a natural trend towards exponential growth for the human species, simply and accurately illustrated through the standard exponential population doubling series (and population doubling times). He briefly explored the exponential growth of non-human species. He postulated non-exponential growth rates for food production within the limited resources of the different locations used. In essence, he introduced the concept of Limits To Growth. He insists that this natural state has always existed, and always will (Malthus, 1798):

"...this constantly subsisting cause of periodical misery has existed ever since we have had any histories of mankind, does exist at present, and will for ever continue to exist, unless some decided change takes place in the physical constitution of our nature." 

His thinking didn't extend beyond Earth, and identify the true limits to growth. These are the Kardashev Levels - Planet, Solar System, Galaxy (that will be the subject of another article).

Malthus failed to recognise the role of science and technology in not just sustaining a population, but causing that population to grow exponentially.

Although he did consider human life-span extension in his essay, he failed to explore any of the possibilities whereby "...some decided change takes place in the physical constitution of our nature." Today, such examples are easy to come by - nanotechnology, artificial intelligence, human-computer cyborgs, genetic engineering and cloning.

Some of these oversights are perhaps due to the fact that he was a man of his age. Few people then considered the possibility of colonising space, or changing our physical constitution, as anything more than a fantasy. 

Malthus does not take the usual generational view of populations so common to most writers on the subject before or since. Virtually every exponentialist since Malthus has ignored this salutary lesson, and instead they fall into the trap of considering population growth from one generation to the next. I have dubbed this failing in other exponentialists as generational chauvinism. Just read some of the articles on other exponentialists and you will get my point. Malthus was a pioneer in this sense, rarely matched.

Malthus, like so many others since, used a simple model of exponential growth which used a constant growth rate. Today, we know that any positive rate of growth (however variable from year to year) will result in the exponential growth of the population in question. Variable growth rates therefore result in variable population doubling times. This more sophisticated population growth model is known as The Couttsian Growth Model

I therefore feel justified in claiming that Malthus was the first true exponentialist.

The Finest Minds

Here, Malthus philosophises about the nature of original thinking, and the finest minds (Malthus, 1830):

"The finest minds seem to be formed rather by efforts at original thinking, by endeavours to form new combinations, and to discover new truths, than by passively receiving the impressions of other men's ideas. Could we suppose the period arrived, when there was not further hope of future discoveries, and the only employment of mind was to acquire pre-existing knowledge, without any efforts to form new and original combinations, though the mass of human knowledge were a thousand times greater than it is at present, yet it is evident that one of the noblest stimulants to mental exertion would have ceased; the finest feature of intellect would be lost; everything allied to genius would be at an end; and it appears to be impossible, that, under such circumstances, any individuals could possess the same intellectual energies as were possessed by a Locke, a Newton, or a Shakespeare, or even by a Socrates, a Plato, an Aristotle or a Homer."

I would add Malthus to that list of original thinkers. His was one of the finest minds.

Malthus - An Influential Person

Michael Hart, in his book The 100  - A Ranking Of The Most Influential Persons In History (Hart, 1978,1992), ranks Malthus at number 80. That's really not bad, considering all those who might be on such a list. Of course, as Hart states, the list is his personal assessment and he invites the reader to create his or her own list.

Part of Hart's justification is that Francis Place (1771-1854) was so influenced by Malthus' essay that he wrote the first book advocating contraception in 1822. Hart correctly notes that Malthus himself did not advocate contraception, but preferred to advocate his own suggestion of "moral restraint". It should be noted that both are important checks on population. 

Hart also discusses Malthus' influence in the field of economics. Indeed, on my pilgrimage to the site of Malthus' burial at Bath Abbey, a German couple arrived at the same time as me to pay homage to the great economist. They were unaware of the recognised significance of Malthus' Principle Of Population in the field of demography, and of its use in mathematical population growth models.

Hart, like so many others, only briefly mentions Malthus' influence on Darwin and Wallace and their founding of modern evolutionary theory. 

Darwin and Wallace

Charles Darwin is ranked at number 16 for his theory of Natural Selection. Yet modern evolutionary theory, including Darwinism, is underpinned by the Malthusian Principle Of Population. Still, though it is tempting to think of "promoting" Malthus from number 80, it is clear that few people except Darwin were able to grasp the true significance of Malthus' Principle Of Population and then take it and express it anew, and with such conviction. See Darwin - An Exponentialist View and Darwin's Views On Malthus for more.

Alfred Russel Wallace, co-founder of modern evolutionary theory, is only mentioned in passing under the entry for Darwin in Hart's top 100. Perhaps then, Malthusians should be grateful that Malthus is listed at number 80? 

John G. Wilson, an Australian descendant of Alfred Wallace, has recently (2000) written a moving and compelling case to restore Wallace's contribution to modern evolutionary thinking to its rightful place. He notes that the Linnaean Society of London only recently (28th May, 1998) unveiled a portrait of Wallace alongside that of Charles Darwin. 

Wallace also grasped the true significance of Malthus' Principle Of Population, and this fact is usually noted in most works on evolution. See Wallace - An Exponentialist View for more. However, without belittling Wallace's overall contribution, I believe Wallace's treatment of exponential growth (and Malthusian theory) is cursory compared to Darwin's. 

Conclusion

I am grateful to John G. Wilson for his book, and his efforts to restore the reputation of Wallace. I am not descended from the Reverend Malthus, and have no family honour to restore in the case for Malthus. Nonetheless, I hope that the series of articles that I have written for the Exponentialist web site will have a similar effect in restoring the scientific reputation of a reluctant scientist - the Reverend Thomas Malthus. 

I call Malthus a reluctant scientist because, even though he greatly admired men of science, and his Principle Of Population is a law of nature, he sought to use his theories to advance the cause of religion. In the conclusion to his Summary View, in answering the critics of his day, Malthus wrote (Malthus, 1830):

"It has been thought, that a tendency in mankind to increase beyond the greatest possible increase in food which could be produced in limited space, impeaches the goodness of the Deity, and is inconsistent with the letter and spirit of the scriptures. If this objection were well founded, it would certainly be the most serious one which has been brought forward;"

Malthus' concluding arguments which followed on from the above are weak, not worth repeating here, and certainly not scientific. That does not mean that his Principle Of Population is unscientific. Subsequently, I believe that Malthus' scientific contribution has been relegated beneath its rightful place, due to his religious beliefs. It is not good science to ignore the contribution of a scientist because of his beliefs. It is not sufficient for other writers to simply mention Malthus in a passing comment from Darwin, or Wallace. Nor is it right to pretend that such a man as Malthus is not a scientist. Malthus deserves much more recognition as a scientist than he has been given, and I would encourage all writers on evolutionary theory and exponential growth to make the effort and read Malthus.

My motivation in advancing the case for Malthus is simple - I wish to make my own small contribution to the advancement of science. In a very real sense this is quite an irony, for Malthus was such a man of faith. As Darwin put it (Darwin, 1880):

"I am a strong advocate for free thought on all subjects, yet it appears to me (whether rightly or wrongly) that direct arguments against christianity [sic] & theism produce hardly any effect on the public; & freedom of thought is best promoted by the gradual illumination of men's minds, which follows from the advance of science. It has, therefore, been always my object to avoid writing on religion, & I have confined myself to science. I may, however, have been unduly biassed [sic] by the pain which it would give some members of my family, if I aided in any way direct attacks on religion."

Darwin, of course, did not intend this passage for publication but it is now widely quoted.

I agree with Darwin that the advancement of science is the best way to promote freedom of thought. I therefore conclude by asking the reader, especially those scientists among you, to reconsider the Principle Of Population as a law of nature, and Malthus' essay as a work of science. 

Already Malthus' Exponential Law is widely recognised as an approximate law of nature, and all it takes to turn it into a genuine law of nature is to recognise that all population growth of all species is based on variable rate compound interest.

References

Bonar, James. Malthus and His Work (2004 reprint). Kessinger Publishing. 1885.

Darwin, Charles. Letter to E. B. Aveling. Darwin Correspondence Project. 1880. Web site accessed 7th August, 2012.

Franklin, Benjamin. Observations concerning the Increase of Mankind, peopling of Countries, etc., Google Books. 1751

Hart, Michael.  The 100  - A Ranking Of The Most Influential Persons In History. Simon & Schuster. 1978,1992.

Lomborg, Bjorn, The Skeptical Environmentalist - Measuring the Real State of the World. Cambridge University Press. 2001

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. Note: The 6th edition includes the preface from the 2nd edition (which was written in 1803).

Malthus, Thomas Robert. A Summary View. 1830. (included with Penguin Classics 1983 edition of the 1st edition of Malthus' essay).

National Archives (USA). Declaration of Independence (transcipt). 1776. Web site accessed 7th August, 2012.

 

Bibliography

The Forgotten Naturalist In Search Of Alfred Russel Wallace - John G. Wilson

Atlas Of World Population History - Colin McEvedy and Richard Jones

Physics For Scientists and Engineers (Fourth Edition) - Serway

Influences on the first edition of 'An Essay On The Principle Of Population' quoted by Malthus in the preface to the second edition:

Political Discourses - David Hume (1711-76)
(Google Book Results)

An inquiry into the Nature and Causes of the Wealth of Nations - Adam Smith (1723-90)
(Google Book Results)

A Dissertation on the Numbers of Mankind in Ancient and Modern Times (1753), Characteristics of the Present State of Great Britain (1758), and Various Prospects of Mankind, Nature and Providence (1761) - Robert Wallace (1697-1771)
(Google Book Results)

Essay on the Population of England from the Revolution to Present Time (1780), Evidence for a Future Period in the State of Mankind, with the Means and Duty of Promoting it (1787) - Richard Price (1723-1791). 
(Richard Price Papers from American Philosophical Society)

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Copyright 2001 David A. Coutts
Last modified: 22 August, 2012