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

External Links:

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

Exponentialist Blog

Welcome to the Exponentialist homepage

Twice two equals four: 'tis true, 
But too empty, and too trite.
What I look for is a clue
To some matters not so light.

W. Busch, from "Schein and Sein" (1909). 
Translation by Karl Popper.


This web site is dedicated to exploring all aspects of the exponential growth and exponential shrinkage of replicator populations. This could include any life form based on cells, and biological viruses. It can include genes and memes, Von Neumann machines, artificial life, computer viruses, and molecular nanotechnology assemblers. It can also include loans (e.g.. mortgages) and investments (e.g.. stock market shares, bank accounts). Thus, Exponentialist theory applies equally to the worlds of population ecology, population dynamics, demography, evolutionary theory, and finance. 

The approach taken is to make extensive use of population doubling, just as Malthus did, and to combine that with population halving via my own New Malthusian Scale

Malthusian Views Versus Exponentialist Views - Summary

However, there are differences between the Malthusian argument and the Exponentialist argument. See the following table for a summary of the main differences between Malthusian and Exponentialist views on population growth and food supply:

Assertion Malthusian Exponentialist
Population grows exponentially Yes, if unchecked

Assumes a constant rate,
with a focus on
positive growth rates.
Yes, checked or not

Assumes variable rates,
allowing for negative and
positive growth rates.

(equivalent to variable rate compound interest)

It is possible to sustain exponential growth at a constant rate in the real world Yes, if unchecked (in theory)

But checks always apply

Limits to growth apply (e.g. the Earth) Yes Yes
Sustained exponential population growth is impossible due to limits to growth Yes Yes
Food supply grows linearly Yes No - Food grows exponentially (also at variable rates)
Population outstrips food supply due to power of exponential growth over linear growth Yes No
Checks on population include infanticide, murders and accidental death, war, famine, pestilence, environment, natural disaster, infertility, moral restraint (abstinence / late marriage) Yes

Opposed to other factors such as contraception, abortion and homosexuality

If the other checks on population fail then population growth will outstrip food supply and global famine will result No No
If the other checks on population fail then population growth will periodically outstrip food supply and localised famine will result Yes Yes
Sometimes population outstrips food supply due to imbalance of exponential growth in population and food supply (and sometimes food supply outstrips population for the same reason). No Yes
This is a universal law of nature, and applies at all times to all populations of all species Yes

But with a focus on human populations


It's also worth noting that Malthus believed that species were created by God, whereas the Exponentialist view is that species evolved. Ironically, both co-founders of evolutionary theory came independently to the theory only after reading Malthus on population (See Charles Darwin - An Exponentialist View, and Alfred Russel Wallace - An Exponentialist View, for more).

What did Malthus actually say?

I believe Malthus, between 1798 and 1830, presented a flawed vision of a scientific law for population growth. Malthus described population as growing geometrically (the term used these days is exponentially). The Malthusian Growth Model is universally taken to mean exponential growth at a constant rate. In his essay, Malthus stated (Malthus, 1798):

"Population, when unchecked, increases in geometric ratio.( my bolding)

So, the geometric (exponential) growth model was only intended as a law of nature governing unchecked population growth. Much of the rest of Malthus' essay is an exploration of those factors which check growth

And here, in A Summary View (1830), Malthus clearly understood that population growth rates and population doubling times vary:

"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."


"It may be safely asserted, therefore, that population, when unchecked, increases in a geometrical progression of such nature as to double itself every twenty-five years. This statement, of course, refers to the general result, and not to each intermediate step of the progress. Practically, it would sometimes be slower, and sometimes faster."

Malthus also described the food supply as adhering to an arithmetic, or linear growth model. This was confusing and unnecessary, given Malthus' proposed universal law of exponential-like population growth. After all, food grows in populations. Contradicting his own assertion that food supply grows linearly, Malthus himself even gave examples of food growing exponentially - see Malthus on Grain and Malthus on Sheep.

Despite these flaws in Malthus' vision of a universal law of nature for population growth, his Exponential Law is widely regarded as an approximate law of nature.

Exponentialist views - some details

My revision of the Malthusian Growth Model I call the Couttsian Growth Model which assumes variable rate compound interest and allows for positive population growth and negative population growth. To get a feel for how this works in the real world read my  Scales of 70 which is an extension of the Rule of 70, and combines Malthus' use of population doubling with population halving. However, unlike the Malthusian Growth Model, it is not limited to constant rate growth and allows for variable rates of growth (including positive and negative rates).

I find that the Couttsian Growth Model can be applied to all populations of any species, across any time period. That certainly sounds like a scientific law to me, so let me know if you think differently. 

This scientific law, once unmasked, reveals something I call Malthusian Selection. My hypothesis is that Malthusian Selection compliments Natural Selection in terms of its impact on the differential replication of populations in the struggle for existence. In the case of human populations, it is probably more significant than Natural Selection (see Human Replicators - An Exponentialist View for more). My hypothesis is likely to be a rude awakening for many demographers, who seem to distance themselves from Malthus by crudely dismissing the Malthusian Growth Model on the basis that it only supports constant rates of positive growth (and all that follows from that assumption).

I argue that both Cornucopians and Malthusians (including Neo-Malthusians) typically have errors in their arguments, but that with my revision of Malthus' work it is clear that the Malthusians are closer to the truth than the Cornucopians. See Paul R. Erhlich And The Prophets Of Doom - An Exponentialist View, Albert Bartlett - An Exponentialist View and Carl Sagan - The Secrets of the Universe for more.

My Exponentialist views include a definition of a living entity, which includes the key concept of the replication event.

A living entity is the result of a replication event by one or more replicators, and is encoded with the instructions of its own assembly.

I therefore rule out what I call cellular chauvinism (the view that the cell is the smallest unit of life), as this would exclude (for example) the virus.

My hypothesis may require a correction to the definition of the term exponential growth as found in most dictionaries and encyclopaedias, and possibly a re-evaluation of the assumptions of limits to growth in the logistic growth model. Mathematicians  - a call to arms from a logician (but not a mathematician). 

What Darwin and Wallace did intuitively was to recognise Malthus' scientific law (even if it is unrecognised as a scientific law today), and then they independently came up with Natural Selection. Since then, Natural Selection (with Artificial Selection) is often depicted (incorrectly) as the key contributor to differential replication. I argue that Malthusian Selection is also a key contributor to differential replication. I believe my hypothesis will put the record straight in restoring Malthus to his rightful place as the effective author of what could now be called The Origin Of Populations (rather than An Essay On The Principle Of Population). It will also help to illustrate the pace at which populations grow, and the true mechanism which drives that pace. This in turn will facilitate an examination of the pace of evolution, which depends so very much on the often obscurely explained process of differential replication as part of the theory of evolution.

The fitness of a population is measured via the Malthusian Parameter (the growth rate). However, the greater this is the more unsustainable it becomes, due to limits to growth. This is true for both constant rate growth and variable rate growth. The ultimate Malthusian catastrophe has to be prolonged human global population growth which would result in Human Global Ecophagy as our human population pushes our ecosystem to the limit.

The creationist arguments against "the survival of the fittest" will also need to be re-examined, now that differential replication can be made so obvious as the process continues with or without Natural Selection (thanks to Malthusian Selection)!


Evolutionists might also want to finally ditch their naive generational approach to population modelling in favour of the Couttsian Growth Model (see Dawkins - An Exponentialist View). Also, note that differential replication applies equally well to populations of genes, viruses, bacteria, grass, trees, humans, fish, whales, beetles and in short any living thing. So, just like the theory of evolution, Malthus' scientific law of population removes us from centre stage and puts us with every other living thing. However, as already noted, Malthusian Selection (and indeed Artificial Selection and Unnatural Selection) may well put us right back into centre stage.

Evolutionists might take this opportunity to re-examine the level at which evolution works. There is higher-level selection at work via both Malthusian Selection and Natural Selection, via the overarching process of the differential replication of populations.

Finally, futurists and pro-space lobbyists might appreciate my examination of K. Eric Drexler's work on molecular nanotechnology (MNT), or Marshall T. Savage's exploration of our future in space (without MNT).

So, there's something for everyone.

The aim is to keep it simple. So far, there are few fancy graphics, just some original views. All external links should be working, though only a core of internal pages has been published yet. Most articles have already been reviewed before being published, but please feel free to provide your own feedback. Most articles are still considered draft. 

You will find an exploration of various Growth Models, Replicators and Famous Exponentialists amongst other assorted articles.

As a further caveat, I would add that the only professional qualification I hold is a Certified Software Test Professional (CSTP) certification. My exponentialist web site is the result of passionate interest, nothing more.


Professor Don Roper (February 2003) has provided the following comments:

"Good luck with your work. I did look at the pages you recently sent me -- it's excellent pedagogy. But I find your work more interesting cause you're tackling a knotty issue and you're on the right track, seems to me."

More comments by Professor Roper on my Scales Of 70 page.

If you have any constructive criticism on this article, email me.

Send email to exponentialist@optusnet.com.au with questions or comments about this web site.
Copyright 2001 David A. Coutts
Last modified: 11 July, 2012