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

Darwin's Views on Malthus

Evolution - An Exponentialist View

Population Doubling Mechanism 

New Malthusian Scale 

Board Not Bored Games:
Brief Demographic History Of Humanity

External Links:
The Internet Public Library

Darwin and Darwinism - Online archive on all matters Darwinian - from Human Nature

Charles Darwin - An Exponentialist View


At the outset I should make it clear that I am a latter-day Darwinian. Given the knowledge available in Darwin's day, I consider "Origin Of Species" to be one of the finest and most readable scientific works that I have read. By and large, it has stood the test of time both scientifically and as a brilliantly illuminating work. 

That being said, my purpose here is not to attack the great man, but merely to show (along with other examples based on other great writers) that exponential growth is consistently misrepresented throughout scientific literature. Also, I hope to show through this series of articles that it is a relatively simple thing to explain exponential growth more accurately, without losing your audience with scientific notation or mathematical formulae.

In considering the natural tendency of all creatures to breed exponentially, Darwin was deeply influenced by the first exponentialist, Reverend Malthus. Read my article Darwin's Views on Malthus for more. 

Exponential Growth - Three Examples

In 'Origin Of Species' (pages 117-119), The Struggle For Existence, Darwin introduces his views on exponential growth:

"There is no exception to the rule that every organic being increases at so high a rate, that if not destroyed, the earth would soon be covered by the progeny of a single pair. Even slow-breeding man has doubled in twenty-five years, and at this rate, in a few thousand years, there would literally not be standing room for his progeny. Linnaeus has calculated that if an annual plant produced only two seeds - and there is no plant so unproductive as this - and their seedlings next year produced two, and so on, then in twenty years there would be a million plants. The elephant is reckoned to be the slowest breeder of all known animals, and I have taken some pains to estimate its probable minimum rate of natural increase: it will be under the mark to assume that it breeds when thirty years old, and goes on breeding till ninety years old, bringing forth three pairs of young in this interval; if this be so, at the end of the fifth century there would be alive fifteen million elephants, descended from the first pair." 

Darwin has provided three examples of exponential growth. I shall explore all three in turn: Malthus, Linnaeus, Darwin.


Darwin first makes use of Malthus' twenty-five year doubling time for "slow-breeding man". See my articles Reverend Thomas Robert Malthus - An Exponentialist View, and Darwin's Views On Malthus for more on this example of exponential growth. 


Darwin then makes use of an example quoted from the great Swedish botanist, Carolus Linnaeus. In this example, a constant rate of exponential growth of 2 seeds per plant, per year, is assumed:

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

Table A. Using the Alphabet Option (constant rate) for New Malthusian Scale to explore Darwin's use of Linnaeus' example of exponential growth for plants

Note:  1 kilopop = 1024 pops

As you can see, each row allows for 10 population doublings. As a constant annual rate of doubling is assumed, each row represents 10 years. Hence, after 20 years there are 1024 kilopops (1024 x 1024 = 1,048,576) plants, which equates to Linnaeus' calculation. The great difficulty in considering Linnaeus' example is that it only considers each generation of seedlings, and does not mention the fate of any parent plants. Are they still alive, or dead? Also, can we assume that each seedling survives the full 20 years of Linnaeus' thought experiment?

This is an early example of what I have dubbed generational chauvinism. Perhaps the best known generational chauvinist is the great Italian mathematician, Leonardo of Pisa (who called himself Fibonacci, derived from filius Bonacci meaning son of Bonacci). In 1202AD Fibonacci  considered a population of immortal rabbits, starting with a breeding pair. The resulting Fibonnaci series (as it has become known) is actually a very handy method for counting immortal populations. For more on Fibonacci, take a look at Fibonnaci Numbers And Nature by Dr Ron Knott. 

Where Linnaeus goes wrong, like so many others since (including Darwin himself), is to think only in terms of generations of animals or plants. It is a perfectly understandable mistake, especially if like Darwin you are concerned with concepts such as heredity. Also, it is a deceptively inviting approach to modelling exponential growth. One leads to two, which leads to four, then eight, sixteen and so on. It's so easy, it has proven irresistible to generations of botanists and evolutionists.

The key to understanding the exponential growth of any population is to consider birth rates and death rates for a suitable time period, and from there calculate a percentage growth rate for that time period. From there it is then possible to extrapolate continued growth at that constant rate. Even this is a naive model of how exponential growth actually works in the real world, but it is still a valid tool for projecting exponential growth. Any attempt to model actual population growth must take account of variable rates of growth. This in turn leads to accepting variable doubling times for growing populations, or halving times for shrinking populations.

So, getting back to Linnaeus' plants, it is necessary to assume a birth rate and a death rate. Well, all we have is a birth rate (2 seedlings per year) and no death rate. That is the first, and most serious, error in this example. The second problem is that a constant rate (annual growth) is assumed. I have no problem with people assuming a constant rate, but it should always be made clear that real life populations do not work that way. I have not read Linnaeus' work, so I can't comment on how he worded this example himself. However, Darwin is guilty as charged.


Darwin's third example is his own, and he considers the "slowest breeder of all the animals", elephants. 

Pops 1 2 4 8   16 32 64 128 256 512 1024
kilopops 1 2 4 8   16 32 64 128 256 512 1024
Megapops 1 2 4 8 14.30 16 32 64 128 256 512 1024

Table B. Darwin's own example of exponential growth for elephants. 
A constant growth rate of 2 offspring per 20 years is assumed.

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

Darwin assumes an elephant has 6 offspring over a 60 year breeding period, or a pair each 20 years. It is not clear what his assumptions are regarding the sex of the offspring - are they all female? What is the ratio of females to males? Then, once again, this example falls foul to generational chauvinism. Once again, no death rate is mentioned. Once again, a constant rate of growth is used without signifying the naivety of such a population growth model.

In attempting to model Darwin's elephant example using my New Malthusian Scale, the over-riding parameters are 15 million elephants after 500 years from a breeding pair. Each row in Table B corresponds to 200 years (for 10 population doublings). The target population of 15 million elephants (14.30 Megapops) is actually reached during the 24th population doubling from 8 to 16 Megapops. This is between 460 and 480 years, slightly earlier than the 5 centuries mentioned by Darwin. Darwin's projection is even less accurate if we look at the population after 500 years (25 doublings) - the population would be 33,554,432 elephants (32 Megapops)

The only way to actually reach 15 million elephants after exactly 500 years, and reduce the number of doublings to 24, is to increase the population doubling time. To get an approximation, 500 years divided by 24 doublings = 20.834 years

Using a population doubling time of 20.834 years, we can bracket Darwin's 15 million elephants nicely. A starting population of 1 would reach 8 C-Pops (8,388,608 elephants) after 479.166 years, and 16 C-Pops (16,777,216 elephants) after 500 years. Clearly, the New Malthusian Scale provides a simple method to accurately demonstrate true exponential growth.

Darwin Extends Malthus' Principle Of Population

Although Malthus refers to his Principle Of Population as a one of the "...general laws of animated nature...", he focuses the attention of his reader on how that principle applied to humanity. Indeed, Malthus believed it was divinely and purposefully created for humanity on Earth. Malthus, a clergyman,  was deeply concerned with moral, ethical, social and religious matters. All of these are human concerns. 

So, Malthus was first and foremost a philanthropist (which, derived from the Greek, means "a friend of man"). History likes to record Malthus as a footnote in evolutionary theory, even though the basis of modern evolutionary theory effectively starts with Malthus and not with Darwin or Wallace. In a sense this is fair enough, for Malthus was not concerned with evolution, he was concerned about the fate of humanity. Still, though Malthus' contribution to modern evolutionary theory was unintentional, Darwin saw Malthus' Principle Of Population for what it was and not as Malthus might have intended it.

It is therefore Darwin who most effectively extended Malthus' Principle Of Population to all living creatures. The fact that this principle clearly does apply to all living creatures must surely weaken Malthus' assertions that God created this law solely for mankind. What would Malthus say of the morality of beasts? Or the morality of a virus? As Richard Dawkins has stated in "The Selfish Gene", all the virus wants to do is replicate. Strictly speaking, it doesn't even want to do it - it is blindly programmed to do it. There is no morality involved. However, none of this means that human beings are not moral and ethical creatures - we are. 

For more on viral reproduction, see Viral Replication - An Exponentialist View. For more on Richard Dawkins, see Dawkins - An Exponentialist View.

The fact that Malthus' Principle Of Population applies to all living creatures, however base, is beyond dispute. Darwin even refers (in Origin Of Species) to some authenticated examples:

"... the numerous recorded cases of the astonishingly rapid increase of various animals in a state of nature, when circumstances have been favourable to them during two or three following seasons. Still more striking is the evidence from our domestic animals of many kinds which have run wild in several parts of the world: if the statements of the rate of increase of slow-breeding cattle and horses in South America, and latterly in Australia, had not been well authenticated, they would have been incredible. So it is with plants..."

The man credited as co-discoverer of the theory of evolution and Natural Selection, Alfred Wallace, came to the same conclusion (see Wallace - An Exponentialist View). 

Darwin himself concludes:

"Hence we may confidently assert, that all plants and animals are tending to increase at a geometric ratio, that would most rapidly stock every station in which they could any how exist, and that the geometric tendency to increase must be checked by destruction at some period of life."

In a sense then, to balance the injustice done to Malthus over the years, Darwin (and Wallace) should be mentioned in passing in any book relating to population growth. Perhaps just one entry in the index, for extending Malthus' great principle...

Reproductive Strategies and Differential Replication

Darwin later introduces the concept that has become known as reproductive strategy, and considers how this might affect another concept known as differential replication:

"The only difference between organisms which produce annually eggs or seeds by the thousand, and those which produce extremely few, is, that the slow-breeders would require more years to people, under favourable conditions, a whole district, let it be ever so large."

This sort of thinking is again tainted with a tinge of generational chauvinism. Without considering death rates, it is strictly not true to say that more offspring in each generation automatically ensures faster growth rates. Also, the population dynamics will depend greatly upon how dependant each species is on the other. Finally, assuming comparable growth rates, it is worth noting that larger creatures would have an advantage over smaller creatures in more quickly "peopling" any sized district. Size does matter.

I guess the key to understanding Darwin's meaning here is to consider exactly what he means by "under favourable conditions". If he means, as I suspect he does, that there are no checks (war, famine, pestilence, death or voluntary restraint) on population growth, then it is obvious that a reproductive strategy of having more offspring would be a key advantage (until the limits to growth were reached) over slower breeders. However, as Darwin well knew, Nature generally doesn't work like that. Darwin himself concludes:

"But the real importance of a large number of eggs or seeds is to make up for much destruction at some period of life; and this period in the great majority of cases is an early one....

....So that, in all cases, the average number of any animal or plant depends only indirectly on the number of its eggs or seeds."

Slow Breeders and Fast Breeders

Let us take two hypothetical species, Slow Breeders and Fast Breeders. Assume that there is no ecological interdependence between these two species. 

The reproductive strategy of the Slow Breeders is to produce 2 offspring every year. The reproductive strategy of the Fast Breeders is to produce 4 offspring every year. 

Slow Breeders
1 2 4 8 16 32 64 128 256 512 1024
Fast Breeders (thousands) 1 4 16 64 256 1024 4096 16384 65536 262144 1048576

Table C. Falsely proving Darwin's assertions on reproductive strategy 
and differential replication, by not using death rates.

Table C appears (incorrectly) to prove that having more offspring automatically ensures a win for the Fast Breeder in the race of differential replication. 

However, if we now factor in the respective death rates, the story could easily be different. Let's use some hypothetical birth rates and death rates. A 1,000-strong Slow Breeder population produces a total of 2,000 young per year (an average of 2 each). Suppose 1860 of these newborns die each year, then the net gain per year is 140 out of 2,000 or 70 for each 1,000. That's a growth rate of 7% per annum, which results in a population doubling roughly every 10 years.

Each 1,000 Fast Breeders produce 4,000 offspring each year (an average of 4 each). Let's assume a death rate of 3960 out of each 4,000 offspring per year, or 990 out of each 1,000. That's still a net annual gain of 10 per thousand (a 1% growth rate), and results in a population doubling time of 70 years:

Years   10 20 30 40 50 60 70 80 90 100
Slow Breeders (thousands) 1 2 4 8 16 32 64 128 256 512 1024
Years   70 140 210 280 350 420 490 560 630 700
Fast Breeders (thousands) 1 2 4 8 16 32 64 128 256 512 1024

Table D. Disproving Darwin's assertions on reproductive strategy 
and differential replication, with death rates factored in.

Thus, much like the moral from Aesop's fable of the Hare And The Tortoise ("Slow and steady wins the race"), it is entirely possible for a Slow Breeder to win the race of differential replication against the Fast Breeder.

Of course, the false assumption in the above table is that any offspring which survive their first year are then immortal. Only the infant mortality rates were considered. This is easily remedied by assuming the same adult death rate for both Slow Breeders and Fast Breeders. For this example, you can try any adult mortality rate per 1,000 between 1 and 9 individuals (any more and you start having to consider zero or negative population growth). The result will be the same, in that the Slow Breeders will out-breed the Fast Breeders.

So, to derive the true (Malthusian) definitions of Slow Breeder and Fast Breeder it is a simply a matter of comparing the percentage growth rates for an identical time period. To summarise, here are 2 definitions of the same populations from table D:

Darwinian Definition Malthusian Definition
Slow Breeders - 2 offspring per year Fast Breeders - 7% per annum (doubles every 10 years)
Fast Breeders - 4 offspring per year Slow Breeders - 1% per annum (doubles every 70 years)

Table E. Comparison of definitions for Slow Breeders and Fast Breeders.

If the two species are interdependent, such as rabbits and foxes, or some bacterial disease and its host human population pool, then things get a little more complicated. Of course, Nature is (see the full quote from Darwin below) "a tangled bank", and is far more complex than pairs of interdependent species.

In the case of predator and prey, a regular cycle of positive and negative growth rates will typically ensue for each species. When there are few foxes, the rabbit population will boom. A booming rabbit population encourages population growth in the fox population. A booming fox population causes the rabbit population to crash. A crashing rabbit population causes the fox population to crash... and so on. This very common natural state is known as dynamic equilibrium.

In the case of a bacterial disease and its host human population pool, if the Fast Breeder bacteria is too successful, it can kill an individual host before it escapes the current limit to growth (the current human host). In this case, if the host dies, so does the bacterial population. Or, if the bacteria manages to get over that particular hurdle and spreads successfully throughout the human population pool, it could still prove overly successful if the entire host population dies off quicker than it can reproduce. Again, a Fast Breeder reproductive strategy can result in a lose-lose situation. Such Fast Breeders are destined for extinction. Today's microbial Fast Breeders are the survivors of past differential replication races, in which more subtle reproductive strategies ensured their own (and their host populations') survival.

To conclude, Darwin should at least be credited with considering how the reproductive strategy of a species would affect its differential replication comparative with other species. In case this sounds like any sort of argument against Darwinism, rest assured that it is not. All I am questioning is the wording that Darwin used, in the hope that the reader will understand the Malthusian principles behind differential replication.

Homo philoprogenitus (lover of many offspring)

Apparently (Lovelock, 1979) the term Homo philoprogenitus derives from C.G Darwin, grandson of Charles Darwin who studied with the great New Zealand physicist Ernst Rutherford. 

So, Darwin's grandson has provided a label for a Fast Breeder population of humans, able to out-breed their slower cousins, Homo sapiens. This would be true whether the advantage was genetic, environmental, or cultural. 

Darwin's Wedge

From 'Origin Of Species' (pages 117-119), The Struggle For Existence):

"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."

Should anybody doubt the accuracy of Darwin's opening sentence in the above quotation, consider the following 3 hypothetical species:

Years   10 20 30 40 50 60 70 80 90 100
1 2 4 8 16 32 64 128 256 512 1024
ZPG (thousands) 1 1 1 1 1 1 1 1 1 1 1
Unfit (individuals) 1000 930 864 804 748 695 646 601 559 520 483

Table F. The survival of the fittest, from an exponentialist view.

Of course, a population with any positive growth rate should be classified Fit, and a population with any negative growth rate should be classified Unfit. The growth rates above are just an example. Long-term fitness then depends upon being consistently more Fit than Unfit. This kind of blind, mathematical fitness results in a contest of differential replication of populations in the struggle for life.

Evolution does not treat the Unfit kindly - they tend to go extinct, sometimes locally...sometimes globally. Evolution favours the Fit but, thanks to the Malthusian limits to growth (e.g. the Earth), eventually they could become victims of their own success. See Reverend Thomas Robert Malthus - An Exponentialist View for an example of limits to growth using humanity. So, it is possible to be too Fit for too long.

Hence, it is no surprise that all species (even the Unfit) are at least theoretically capable of being Fit and capable of "striving to the utmost"  towards exponential growth. Why is this no surprise? Because by increasing birth rates, and decreasing death rates, all Unfit species in existence today could, "under favourable conditions", be transformed from Unfit to Fit. Similarly, of those that are currently classified Fit by virtue of their positive growth rate, some will eventually prove Unfit. 

To paraphrase George Orwell from "Animal Farm": 

"All surviving creatures are made Fit, though some are more Fit than others." 

As for the ZPG population, 1,000 individuals is a dangerously low population to walk that particular evolutionary tightrope. That is when a larger population proves to be an advantage to the fitness of that population. If a catastrophe struck the Earth, there is a better statistical chance of survivors from a population of 1 million individuals, and even more chance of survivors for 1 billion individuals. 

However, there is always a chance (however remote) that a catastrophe will do more harm to the ZPG population's competitors or predators. In which case, the 1,000 ZPG individuals would suddenly find Fitness thrust upon them, and their population would explode. Such an event apparently occurred some 65 million years ago, ending the age of the dinosaurs and resulting in the age of the mammals. The fossil record shows that many such events have occurred. In each case, as numbers grew, so genetic variation grew statistically more likely (through mutation and sexual recombination). Natural Selection did the rest.

Finally, as in the classic example of rabbits and foxes, it is worth repeating that ecosystems typically reach a state of dynamic equilibrium. This means that birth rates and death rates even out over time, with populations that fluctuate up and down resulting in fairly stable populations. Therefore, it is common for such populations to oscillate between being Fit, and Unfit, giving every appearance of a passive ZPG population.

Many people interpret this state of affairs to mean that it is incorrect to assert that all populations (of all species) are striving towards exponential growth. Nothing could be further from the truth. 

Bubbling madly in the pressure cooker, under the enormous power of exponential growth, any population will explode outwards the moment the lid is off. Such is the true state of dynamic equilibrium. 

For more this kind of mathematical "fitness", read Evolution - An Exponentialist View.

As to interpreting what Darwin's wedge analogy (above) means, there are many possibilities. I like to picture each wedge with the exponential population doubling series running out from the thin end of the wedge (1, 2, 4, 8 etc):

The thickness of any particular wedge depends upon where that population currently is on the New Malthusian Scale. Therefore, I apply Darwin's analogy to populations and not just to species. Of course, if you consider the global population of each species, then you are effectively talking about species anyway. Therefore, even though this is Darwin's analogy, it is Malthus' Principle Of Population which runs at its heart. 

To understand how Darwin's Wedge illustrates Natural Selection, you need to understand what Malthus had to say about exponential growth and the competition for resources in the Struggle For Existence. Darwin did understand Malthus, and knew for a certainty that Malthus had discovered the true nature of the struggle. The wedge for a Fit species gets fatter and fatter as it is driven in with exponential force, and it moves up the New Malthusian Scale. The wedge for an Unfit species gets thinner and thinner as it is driven out by competing wedges, and its population moves down the New Malthusian Scale.

Any wedge which is too successful will face the Malthusian limits to growth. Our species is good at pushing those limits back, sometimes on a grand scale (e.g. the Agricultural Revolution, the Industrial Revolution and the Green Revolution). Eventually of course, if our population continues to grow, we will face the indisputable limit to growth posed by the Earth itself. Only the colonisation of space can take us beyond that particular limit.

All too often, these wedges are linked together in their fate. Think of some prey species growing exponentially, thus encouraging the growth of its main predator. Sometimes, the growth of the population of one species will "drive out" the wedge for another. Think of an expanding viral population, decimating a human population. 

All too often, some environmental factor (e.g. the seasons, a flood, a volcano, an earthquake, continental drift etc) will separate a population into two or discrete populations. In such circumstances, a new species can arise over time, and a new wedge is added. Occasionally, whole collections of wedges are wiped out in global catastrophes, making room for the rapid growth of any remaining populations. 

Primitive Man and Contemporary Savages

In the "Descent Of Man", Darwin compares the rates of differential replication for early man with those of savages living at his time:

"If we look back to an extremely remote epoch, before man had arrived  at the dignity of manhood, he would have been guided more by instinct and less by reason than are the lowest savages at the present time. Our early semi-human progenitors would not have practised infanticide or polyandry; for the instincts of the lower animals are never so perverted as to lead them regularly to destroy their own offspring, or to be quite devoid of jealousy. There would have been no prudential restraint from marriage, and the sexes would have freely united at an early age. Hence the progenitors of man would have tended to increase rapidly; but checks of some kind, either periodical or constant, must have kept down their numbers, even more severely than with existing savages. What the precise nature of these checks were, we cannot say, any more than with most other animals...

...No doubt, in this case, and in all others, many checks concur, and different checks under different circumstances; periodical dearths, depending on unfavourable seasons, being probably the most important of all. So it will have been with the early progenitors of man."

Readers should not be distracted by Darwin's use of the term "savages". Such was the terminology of the day. In today's language, we might prefer to call such people "hunter-gatherers". 

I examine the relative rates of differential replication of hunter-gatherers with agrarian peoples, and then agrarian peoples with industrial peoples, in my articles on the Mechanism Of Population Doubling and the Brief Demographic History Of Humanity. Darwin might just as easily, and reasonably, have considered the relative differential reproductive rates for Cro-Magnon man and Neanderthal man in Europe (a race which the Neanderthals lost).

In all such cases, when considering the fates of disparate peoples with varying levels of sophistication, it is those newcomers most capable of sustaining higher levels of population growth that have inevitably eclipsed the original populations. Agrarian societies have displaced hunter gatherer societies, industrial societies have replaced agrarian societies, and hi-tech societies are replacing industrial societies. Often this process entails warfare and colonisation. This is a sad fact of history, with one salutary lesson. Populations which embrace scientific progress are generally more successful than those which favour tradition. This is because much scientific progress either increases birth rates or, more often, decreases death rates. Plus, scientific progress has (so far) allowed humanity to push back the limits to growth, and has allowed us to support our ever increasing numbers. 

Of course, most people don't think of scientific progress in terms of birth rates, death rates and growth rates. In the West, there is certainly a drive to use science to lower birth rates and reach Zero Population Growth. So, cultural factors are also relevant in determining how science is used in relation to population growth. But only a minority of people, even in the West, consciously work towards the goal of ZPG. Regardless, such ZPG populations will become marginalised (in an evolutionary sense) by those populations capable of growth. Any populations capable of sustaining growth must embrace scientific progress. For more, see The Cassandra Prediction - Exploding The ZPG Myth.

However, the special danger of today's world is the ability that such scientific progress - whilst offering so much - has the ability to destroy all such progress to date. For an example of a new technology which could compete with humanity (indeed, the whole of Nature) in a battle of differential replication, read Grey Goo - An Exponentialist Explanation. Nonetheless, I remain hopeful of humanity's future.

Contemporary Savages and Nature

Again, in the "Decent Of Man", Darwin makes a comparison which involves Man and alludes to rates of differential replication:

"Man in the rudest state in which he now exists is the most dominant animal that has ever appeared on this earth. He has spread more widely than any other highly organised form: and all others have yielded before him. He manifestly owes this immense superiority to his intellectual faculties, to his social habits, which lead him to aid and defend his fellows, and to his corporeal structure. The supreme importance of these characters has been proved by the final arbitrament of the battle for life."

In today's politically correct world, readers might prefer the use of the term humanity to Man. However, such sensitivities make little difference to Darwin's argument. Using Darwin's wedge analogy, humanity's population is growing exponentially and thus forcing out numerous other wedges (species). 

To get an idea of our global impact on life, consider an example from "The Atlas Of The Living World" (1989), edited by David Attenborough (now Sir David Attenborough), in which it is estimated that humanity makes use of 27% of the Earth's plant production for our own purposes. 

A Tangled Bank

In the conclusion to "Origin Of Species", Darwin clearly understands the significance of the law of Nature which Malthus revealed with his Principle Of Population. It is this law which is responsible for the "Struggle for Life", and consequently drives Natural Selection.

"It is interesting to contemplate a tangled bank, clothed with many  plants of many kinds, with birds singing on the bushes, with various  insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent upon each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; Inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the conditions of life and from use and disuse: a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms. Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being evolved."


Darwin was always openly full of praise for Malthus, and his Principle of Population. Yet today Malthus usually only merits a brief mention in most books relating to evolution, none of which explore Malthus' Principle Of Population in any detail. Malthus deserves more. Darwin would shake his head in dismay at today's understatement of Malthus' contribution to modern evolutionary theory.

Darwin was a Malthusian, and Darwinism is based on Malthusian principles..

Added 11th June, 2004:

Nanotechnology and Darwin's Wedge

On the topic of Darwin's wedge, I once posed a question to father of nanotechnology Eric Drexler through his ex-wife Chris Peterson, and got a one word answer (via email, 16th May, 2001):


My question to Eric is: "Taking Darwin's wedge analogy, do you agree that life (in the broadest sense) operates according to the Principle Of Population, which therefore proves that life is (in at least one sense) a zero sum game?" Eric wrote to this: "yes". [Chris Petersons' additional comments]: However, I'd suggest that this not be quoted without a great deal of context. It's a bad idea to spread the meme that life is a zero sum game. But I get the impression you know that! Note that even if life is a zero sum game, it can still be extremely rewarding and fun for the individual concerned! 

I'm happy to say I agree with Chris' additional comments.

How is this relevant to Eric's much publicised rejection of the Grey Goo scenario? Well, taking the Darwin's wedge analogy, population is driven by Malthus' Principle Of Population, and an exponentially expanding population in a limited environment (such as an island or a planet) inevitably displaces other populations, which then decline. Grey goo was never really the real problem with nanotechnology. Nanotech-enhanced species (including humans and other mammals, bacteria, insects or plants via Freitas' various nanomedicines), will inevitably out-compete existing natural species. Together with biotech, genetic engineering, repro-genetic technologies (Refer Lee M Silver), AI (refer Ray Kurzweil), robotics etc etc....all of these will add up to enhanced and new species which will easily out-compete any existing species. Some might regard this as the Unnatural versus the Natural, and will fight against it. Others have accepted it as natural because it's simply evolution at work. I'll repeat a quote from Eric's Engines Of Creation which I believe still holds true even after Eric's recent and supposedly newsworthy rejection of the grey goo scenario:

 "'Plants' with 'leaves' no more efficient than today's solar cells could out-compete real plants, crowding the biosphere with an inedible foliage. Tough, omnivorous 'bacteria' could out-compete real bacteria: they could spread like blowing pollen, replicate swiftly, and reduce the biosphere to dust in a matter of days. Dangerous replicators could easily be too tough, small, and rapidly spreading to stop - at least if we made no preparation. We have trouble enough controlling viruses and fruit flies.

Forget grey goo (except for some entertaining science-fiction stories), it was never really the threat. Our ability as a species to alter the direction of evolution for any and all existing Earth species...this power of ours is only going to increase. The blind watchmaker may not be dead, but he's certainly getting his sight back.

See also Grey Goo - An Exponentialist Explanation

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Copyright 2001 David A. Coutts
Last modified: 02 July, 2012