Differential Reproduction - An Exponentialist View
Malthus and Evolution

Malthusian Selection (available for peer review) - Academic Publishing Wiki


External Links:

Natural Selection and Differential Reproduction - from Replicators: Evolutionary Powerhouses

The World At Six Billion - United Nations


Differential Reproduction - An Exponentialist View


Differential reproduction is typically linked with the evolutionary process of Natural Selection. However, in this article I will examine how differential reproduction can be usefully linked with an earlier concept I have termed Malthusian Selection. To do so I will focus, as Malthus did, on human populations. The intent of this article is to supplement the usual explanation of differential reproduction. Note that I usually use the term differential replication in preference to differential reproduction, but for this article decided to use the more commonly used term.

Evolution and Differential Reproduction

From Engines Of Creation, nanotechnology visionary Drexler discusses the universal nature of replicators and the implications of differences in the rate of replication, also known as the Malthusian Parameter (Drexler, 1990):

"In the terminology of Oxford zoologist Richard Dawkins, things that give rise to copies of themselves are called replicators. In this environment, RNA molecules qualify: a single molecule soon becomes two, then four, eight, sixteen, thirty-two, and so forth, multiplying exponentially...."

"Biochemists have found that differing RNA molecules replicate at  differing rates, depending on their lengths and subunit patterns. Descendants of the swifter replicators naturally grow more common.  Indeed, if one kind replicates just 10 percent more rapidly than its  siblings, then after one hundred generations, each of the faster kind gives rise to 1,000 times as many descendants. Small differences in exponential growth pile up exponentially."

In The Blind Watchmaker Dawkins (1986) states that Natural Selection is "...all about the differential success of rival DNA...". In The Selfish Gene Dawkins argues that there is at least one law of biology that applies to all life, throughout the universe. I call this Dawkins' Law  (Dawkins, 1976):

"This is the law that all life evolves by the differential survival of replicating entities."

In  What Is Evolution? Mayr argues that differential reproduction is largely due to chance (Mayr, 2001):

"Much of the differential survival and reproduction in a population are not the result of selection, but rather of chance."

What Mayr refers to as chance is often called stochastic processes by evolutionists. However, I argue that a more useful way of thinking about the differential reproduction of human populations has existed for some time.

Malthusian Selection and Differential Reproduction

In An Essay On The Principle Of Population Malthus argues that human populations grow at different rates for specific reasons (Malthus, 1798)

"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;"

Darwin speculates on Malthus' views on the differential replication capabilities of barbarous and civilised races (Darwin, 1871). 

"There is reason to suspect, as Malthus has remarked, that the reproductive power is actually less in barbarous, than in civilised races."

In an interview fellow evolutionist Wallace proclaims (Wallace, 1912)

"The theory propounded by Malthus," he said, "is the greatest of all delusions. As man develops towards a higher type; as he becomes more refined and more civilised, so his fecundity decreases. Low down in the scale of life, birth is only limited by available sustenance. But the higher grows the type, the less is the fecundity."

These days, Wallace's argument seems to make sense. However, allowing for the times in which they wrote, I believe that Malthus (and Darwin) were correct and Wallace was wrong. See Wallace - An Exponentialist View for more. However, the main point of these quotes is to illustrate early opinion on the causes of differential reproduction in humans.

Carl Sagan has argued that the human cultural adaptation of agriculture (a central feature of civilised human populations) is a key reason for the explosion of human populations in the last ten thousand years (Sagan, 1997):

p.18 "Exponentials are also the central idea behind the world population crisis. For most of the time humans have been on Earth the population was stable, with births and deaths almost perfectly in balance. This is called a "steady state". After the invention of agriculture ... the human population of this planet began increasing, entering an exponential phase which is very far from a steady state. Right now the doubling time of the world' population is about 40 years. Every forty years there will be twice as many of us. As the English clergyman Thomas Malthus pointed out in 1798, a population increasing exponentially - Malthus described it as a geometrical progression - will outstrip any conceivable increase in food supply. No Green Revolution, no hydroponics, no making the deserts bloom can beat an exponential population growth."

Perhaps the only true role for natural selection in human populations in recent millennia is our grimly acquired immunity to disease (pp 195-214, Guns, Germs and Steel - Diamond, 1997).  Diamond has famously and some say controversially explored the spread of civilized populations at the expense of indigenous populations. Yet Diamond does not attribute the guns and the steel elements of his argument to natural selection. These are human cultural adaptations, but not evolutionary adaptations. Diamond also considers the relative population densities of hunter gatherers and civilisations. Clearly civilised societies can support much greater population densities, but again this is due to cultural adaptation and not any physical superiority earned by civilised humans by natural selection.

Stephen Hawking argues that the exponential phase of human population growth is even more recent  - roughly the era of the Industrial Revolution (Hawking, 2001):

"In the last two hundred years, population growth has become exponential; that is, the population grows by the same percentage each year. Currently, the rate is 1.9 percent a year. That may not sound like very much, but it means that the world population doubles every forty years..."

If we consider human populations over these timeframes it is reasonable to assert that we as a species have barely evolved at all. It is also clear that environment itself is a factor in human differential reproduction, as the relative lack of human population in the Saharan desert or Arctic proves.  I have termed this combination of cultural and environmental factors Malthusian Selection. Malthusian Selection could in principle apply to any population of any species, but is most easily illustrated using Malthus' favourite topic - human populations. 

Darwin's Wedge

Darwin compared the "face of nature" to "ten thousand sharp wedges" being driven in against one another. This is a useful analogy for the principle of differential reproduction. From 'Origin Of Species' (pages 117-119), The Struggle For Existence (Darwin, 1859):

"In looking at Nature, it is most necessary to keep the foregoing considerations in mind - never to forget that every single organic being around us may be said to be striving to the utmost to increase in numbers; that each lives by a struggle at some period of its life; that heavy destruction inevitably falls either on the young or old, during each generation or at recurrent intervals. Lighten any check, mitigate the destruction ever so little, and the number of the species will almost instantaneously increase to any amount. The face of Nature may be compared to a yielding surface, with ten thousand sharp wedges packed close together and driven inwards by incessant blows, sometimes one wedge being struck, and then another with greater force."

The World At Six Billion

The following graph is based on figures from Table 2 of The World At Six Billion (United Nations):

United Nations Population Division - Population Of The World and Its Major Areas, 1750-2150

For any given year, using a pie chart to express percentages, we can see a demonstration of Darwin's wedges applied to human populations:


As the total population increases over time, both the North American and South American / Caribbean populations are expanding as a percentage of the total, and both the European and Asian populations are shrinking as a percentage of the total. Note that the Asian total includes the world's two population powerhouses, India and China.

A sobering thought is that as the global human population increases its percentage of the total biomass so many other species are going extinct.

A New Malthusian Scale

Inspired by Malthus' use of the common doubling series to explain exponential growth (see Malthus - An Exponentialist View for more), I created the New Malthusian Scale. Here I have mapped the populations of Europe, USA, India, China and Australia I have mapped the populations over time to my New Malthusian Scale (1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and 1024 millions):

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 1860   1901   1986 ?          
Australia Population (Millions) 1 2 4 8 16 32          
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

Roughly based on figures from "Atlas Of World Population History" by Colin McEvedy and Richard Jones. Years in red are my guesses. Populations with two dates indicate population collapse and recovery.

As predicted in Nature magazine (Population Set To Decline, 2nd August 2001), by 2100 only North America and South America will continue to experience positive growth rates. Refer Human Replicators - An Exponentialist View for more. Is this because the human populations in these continents are somehow "fitter", and thus favoured by Natural Selection? No - humans in these continents are in evolutionary terms the same as humans everywhere. Yet evidence of differential reproduction of human populations is beyond doubt. I suggest therefore that Malthusian Selection is a more appropriate term to explain the causes of that differential reproduction as it implies differential reproduction without natural selection and without the implication that any populations are evolving. Thus, Malthusian Selection and Natural Selection go hand in hand in explaining the principle of differential reproduction particularly in the case of human populations.


Darwin, Charles. Origin of Species, 1859

Darwin, Charles. Descent Of Man, 1871

Dawkins, Richard, The Selfish Gene. Oxford University Press. 1976, 1989.

Drexler, K. Eric. Engines Of Creation - The Coming Era of Nanotechnology. Oxford University Press. 1990.

Hawking, Stephen. The Universe In A Nutshell. Bantam Spectra. 2001

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

Mayr, Ernst. What Evolution Is. New York: Basic Books. 2001

McEvedy, Colin; Jones, Richard. Atlas Of World Population History.Viking.1978

Sagan, Carl. Billions and Billions: Thoughts on Life and Death at the Brink of the Millennium. Headline Publishing, 1997

United Nations, The World At Six Billion

Wallace, Alfred Russel. The Last of the Great Victorians - Special Interview with Dr. Alfred Russel Wallace by Frederick Rockell. 1912. The Alfred Russel Wallace page from Professor Charles Smith

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Copyright 2008 David A. Coutts
Last modified: 27 June, 2012