Evolution - An Exponentialist View
Famous Exponentialists
Replicators - An Exponentialist View
A New Malthusian Scale
The Scales Of 70
Population Growth Models
Understanding Compound Interest
The Exponential Method
The Myth Of The Exponential Phase
An Exponentialist Glossary
What's New

BNBG - 6 Billion (The Cassandra Prediction - Exploding The ZPG Myth)

External Links:
Natural Selection and Differential Reproduction - from Replicators: Evolutionary Powerhouses


Who is an exponentialist? Here is my definition:

Exponentialist - An exponent of the exponent, with particular reference to the natural processes of replication.

Note that the first use of the word exponent is not intended as "advocate", or "proponent". Exponent also means "someone who explains", and that is how it is intended. The second use of the word exponent relates to exponential growth. Using the standard 'scientific notation', 23 = 8 (this is 2 x 2 x 2). 103 = 1,000 (this 10 x 10 x 10). In both cases, the 3 is the exponent. 

Hence, an exponentialist explains the significance of exponential growth with regard to all living things. 


I use the word "replication" in recognition of the work done by British zoologist Richard Dawkins in "The Selfish Gene", "The Extended Phenotype" and "A River Out Of Eden". In the latter work, Dawkins recognises the significance of humanity's role of enabling the "replication bomb" of life to "reverberate through deep space" from its fragile beginning on Earth.

For a definition of Dawkins' replicators, see What is A Replicator? from Replicators: Evolutionary Powerhouses. For Dawkins, Natural Selection ultimately works at the level of the gene and the gene is the basic unit of replication in the theory of Natural Selection. For the record, I agree with this point of view. This leads me to the exponentialist definition of a replicator:

Replicator - anything in the universe that is individually or jointly capable of causing a replication event.

A replicator should (literally speaking) only produce replicas (identical copies) whereas Natural Selection works in part due to mutation and non-identical copies. For all species which practice sex, sexual recombination during meiosis is a far greater source of genetic variation than mutation, resulting genetically unique individuals for Natural Selection to work on. Nonetheless, despite our apparent differences and uniqueness, all humans are still...human. Nature is capable of producing genetically unique individuals who are considerably less than 1% different genetically. Otherwise, each individual would belong to its own species!

A true replicator would have a fidelity of 100% (all copies are identical), making most species poor replicators (with fidelities somewhere between 99.9 and 100%). Personally, I'm not going to quibble over values of less than one tenth of a percent. Even poor replicators produce pretty good copies, good enough to ensure that you and I are members of the same species!

If you don't like to see the word replication used in regard to human populations, then by all means stick with reproduction. For species which practice sex, reproduction is, after all, what drives evolution through genetic variability (by comparison, mutation is a minor factor). Yet the virus, for example, cannot be said to reproduce, though it clearly replicates. At the end of the day, reproduction and replication both usually result in the same thing - more individuals belonging to the same species as the original "reproducers" or "replicator".

Similarly, rather than use the common term "cell division", I prefer to unify the terminology by referring to "cell replication". Also, "birth rate" becomes "replication rate". Finally, I prefer to use the term "differential replication" over "differential reproduction".

Replication is also the word Eric Drexler ("Engines Of Creation") uses for the Holy Grail of  molecular nanotechnology (MNT) - a self-replicating assembler. Potentially, a new form of life. 

Even without MNT, John von Neumann suggested long ago what has become known as the von Neumann machine. Any self-replicating machine, whether endowed with artificial intelligence or not, could be viewed as a replicator.


From the exponentialist point of view, all populations capable of  exponential growth are seen as populations of replicators. Hence, an exponentialist views all living creatures as replicators. This includes viruses and bacteria. 

An exponentialist can consider any discrete population, so long it as it remains meaningful to classify a population as discrete. Therefore, the exponentialist sees nations as discrete populations, as are the contents of many a Petri-dish. Hence, the exponentialist view considers populations within a species as well as the entire population of a species.

An exponentialist also recognises the reductionist view of life presented through cell replication, and can even consider discrete populations of differentiated cell populations within the same body (see Cell Replicators - An Exponentialist View). Thus, the exponentialist view can ignore the concept of a species altogether if it is meaningful to do so.

Growth Rates

The exponentialist view can be said to be Malthusian, in that it regards all populations as having a replication rate and death rate. Consequently, all populations of replicators can be said to have a growth rate for any stated time period.

Hence, I would add the growth rate for a given time span as an attribute of any replicator population, such as 1% per annum, or 2% per day. Given that any population of replicators can be said to have a replication rate and a death rate, it follows that all populations of replicators can only ever be in one of 3 states for a stated time period: 

It is worth repeating that Positive Population Growth leads to exponential growth, which allows us to calculate population doubling times. Similarly, Negative Population Growth rates allow us to calculate population halving times. Populations with Zero Population Growth can be said to persist at a constant number.

The following table uses the Rule of 70 to approximate the doubling and halving times for typical non-zero population growth rates (divide the growth rate into 70 to get the period):

Positive Growth Rate

1% 2% 3% 4% 5% 6% 7%
Doubling Period 70 35 23.3 17.5 14 11.6 10

Negative Growth Rate

1% 2% 3% 4% 5% 6% 7%
Halving Period 70 35 23.3 17.5 14 11.6 10

Table A: Crude doubling and halving times derived using the Rule Of 70.

Clearly, for a given rate, the period is the same regardless of whether the rate is positive or negative. For human populations, the time unit normally used is one year. For bacteria, the time unit is typically an hour or less. Hence, 35  would be 35 years for a human population, or 35 hours for a bacterial population which doubles every hour.

Growth Models

The exponentialist view is that the Couttsian Growth Model, derived from the Malthusian Growth Model, represents a scientific law. See Population Growth Models for more.

Differential Replication

Differential replication is the principle of the comparative success of replication between competing populations. Broadly speaking, for a given time period, there are 5 possible results of differential replication:

For each population, the starting population size and the growth rate for a given period are the key factors in the assessing the comparative success of a population. This is especially true if the populations being compared represent varieties of the same species, or discrete populations of the same variety. In such cases, it is possible to point the finger and label one population "fit" and another "unfit".

However, in considering the comparative success of populations of different species, one should consider Darwin's wedge analogy where the long-term success of one population requires the failure of one or more other populations (see Darwin - An Exponentialist View for more). After all, today's populations of living creatures are all competing within the same limited resource pool - Earth. So far, only humans have dared dip their toes the next (massive) resource pool - our Solar System.

Also, it is possible to project extinction for any population which experiences long-term Negative Growth, and a Malthusian disaster for overly successful populations which grow for too long. Clearly, the trick seems to be to grow within the available limits and then stop growing before your population is too many. If an opportunity for further growth then presents itself, evolution will favour whichever species uses that opportunity to grow some more.

This is the exponentialist view of the survival of the fittest. 

Natural Selection 

Natural Selection is the principle by which some populations are favoured due to inherent genetic traits, including instinctive behavioural factors. The typical view is that evolution is deemed to be a combination of Natural Selection and Differential Replication. However, there are other factors to consider.

Malthusian Selection

Malthusian Selection is proposed as the principle by which some populations are favoured due to environmental considerations. 


Malthusian Selection also includes its share of non-instinctive behavioural factors. See Malthus - An Exponentialist View for more. 

It is further proposed that differential replication results from a combination of both Natural Selection and Malthusian Selection. Hence, under similar environmental circumstances, Natural Selection can still favour one competing population over another. Similarly, assuming populations with similar genetic traits, Malthusian Selection can still favour one competing population over another.

Artificial Selection

Artificial Selection is the manipulation of natural material (DNA) by artificial means. For millennia, humanity has created new varieties of plants and animals through selective breeding. This is a form a genetic engineering so familiar to us that it almost seems natural. 

Artificial Selection has been used to create all manner of esoteric variations, not all of which directly affect the reproductive success of the new variety of creature. However, should the traits of the new variety come into great demand then the reproductive success of the new variety can be said to have been indirectly affected by the traits for which it is desired. 

Thus, Artificial Selection has played its part in the differential replication of numerous species favoured by humanity.

 Unnatural Selection

Some people have used the term Unnatural Selection to describe genetic engineering and cloning. I prefer to extend this term to include MNT, artificial intelligence, and all forms of artificial life. After all, genetic engineering and cloning still rely upon genetic material with which to work. In this sense, they can really be considered an extension of Artificial Selection. 

Potentially, MNT could create true replicators with 100% fidelity. Evolution by Natural Selection would not occur for such hypothetical species, though Malthusian Selection would still apply to populations of such creatures as they compete for their wedge of Darwin's pie (see Darwin - An Exponentialist View for more). However, whatever its guise, Unnatural Selection will be analogous to Natural Selection in terms of its effect on Differential Replication. Then, should Unnatural Selection take up the reins from Natural Selection, Malthusian Selection will apply equally well alongside Unnatural Selection.

MNT replicators could have population doubling times comparable with bacteria (which can double in as little as 20 minutes). Such replicators would be capable of massive and rapid growth on an unprecedented scale. See Grey Goo - An Exponentialist Explanation for a disaster scenario involving MNT. 

Graphical Overviews

For a graphical exponentialist view of evolution click on the image below:

For a graphical exponentialist view of differential replication click on the image below:

Darwin's wedge (see Darwin - An Exponentialist View for more):

Like a mythical ouroboros which eats its own tail, populations on the Malthusian Wheel cycle endlessly up and down the standard doubling series:

Wheel.gif (11205 bytes)

This is a variant on my New Malthusian Scale. With the wheel, you can track (with tokens) any sized population as it doubles or halves over time. Add a token to your stack (or increment the value of a token by 1) each time you double from 512 to 1024. Your tokens will now be on the 1 space. Remove a token (or decrement the value of a token by 1) each time you drop from 1 to 512. 

Or imagine a single token moving clockwise around the wheel. As it doubles from 512 (to 1024), so it becomes 1 on the next leg of its journey. A simple colour key could denote whether the token represents Pops, Kilopops, Megapops and so on. 

The population in this example starts at 1 and effectively doubles 30 times (the equivalent to increasing along three rows of the New Malthusian Scale.


It should be noted that the exponentialist view does not seek to explain the "Origin Of Species" as Darwin did. The exponentialist view is more concerned with populations rather than species. Hence, regardless of how a species originated, and regardless of why a species might change, the exponentialist view seeks to explain what then happens to all discrete populations of that species.

The exponentialist view extends beyond the species, to any population of replicators. This includes DNA, viruses, computer viruses, artificial life, nano-life, von Neumann machines, animals, plants, fungi, cells and bacteria. It might also be possible to include memes. All populations of replicators are subject to Malthus' unifying Principle Of Population. All replicator populations, by their very nature, take every opportunity to grow exponentially. This principle inevitably pits life against life, in an eternal struggle for existence

Checks On Populations

All replicator populations face involuntary checks which increase their death rate and slow their growth. All too often, these involuntary checks can be traced to the actions of another replicator population. Of the Four Riders Of The Apocalypse, War and Pestilence can be directly attributed to the actions of other replicator populations. Death often comes to the prey in the form of the predator or the hunter. Herbivores and parasites also cause Death for their more passive victims. For humans, we use words like murder, infanticide, execution and assassination. Death can even come by accident. In the end, Death waits for us all.

Infertility is an example of an involuntary  natural check on the replication rate. Humans are adept at finding ways around this check (IVF, cloning etc). 

Humans are capable of showing various means of restraint to voluntarily reduce their replication rate. Measures such as sterilisation, contraception, abortion, sexual abstention, and "moral restraint" on the frequency of copulation and number of offspring. Homosexual orientation (voluntary or involuntary) can also reduce the replication rate, as can the option for heterosexuals to have children later in life.

Some human voluntary checks affect the death rate and can thus be attributed to Death - suicide, euthanasia and hunger strike for example. 

All replicator populations must face the Malthusian limits to growth imposed by unchecked exponential growth (or Couttsian Growth). Famine, the last of the Four Riders Of The Apocalypse to be considered, is the ultimate check which awaits such populations. 

None of this changes the reality of life but does, hopefully, put the precarious balancing act of Nature into perspective. Nature constantly juggles millions of replicator populations (each comprised of thousands, millions, billions or even trillions of individuals) whilst at the same time managing to walk a narrow tightrope.

You have to respect that.

From Kate Stafford (2001) of Replicators: Evolutionary Powerhouses:

"The idea of seeing evolution in terms of competing populations struggling within Malthusian limits is one of a very few viable concepts that approximate "higher-level selection" - in this case, competition between populations. I think that's a meaningful achievement - providing a framework in which this sort of competition can be seen as an evolutionary level in its own right, rather than a sort of derivative property that comes from individuals' struggle for survival (which of course can be reduced still further, to the level of the genes)."

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Copyright 2001 David A. Coutts
Last modified: 05 June, 2009