Exponentialist homepage

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

Reverend Malthus and Evolution

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

Some Related Wikipedia Links:

Thomas Robert Malthus
Population Dynamics

Evolution - An Exponentialist View


The exponentialist view of evolution is not an entirely traditional view. Where exponentialists and evolutionists would agree is that natural selection favours those populations capable of sustaining higher rates of positive population growth. Both would agree that such populations must ultimately face limits to growth.

Through a principle commonly known as differential reproduction, which I call differential replication, it is possible to demonstrate the effect of different rates of growth on a population. More on this later.

 The key difference between the exponentialist and traditional views of evolution is that the exponentialist is not concerned with the origin of species, whereas this is the cornerstone of the theory of natural selection. This is not to deny the validity of the theory of natural selection, so far as it goes. Also, given what Darwin wrote concerning artificial selection, most people would agree that humanity is entirely capable of improving the rates of growth of favoured species, and reducing the rates of growth for those species that are not favoured. However, it is the exponentialist view that factors other than natural selection and artificial selection are just as significant in producing differences in the growth rates of rival populations. I refer to these other factors as Malthusian Selection, whereas evolutionists refer somewhat vaguely to stochastic processes. 

Above all, the exponentialist view of evolution is concerned with populations and population growth. The study of human population growth is known as demography. For the study of populations in general we have population dynamics.

I want to highlight the universally exponential nature of all population growth and all population shrinkage as explained through the Couttsian Growth Model extension of the Malthusian Growth Model. I use population doubling and population halving through the New Malthusian Scale to keep this as simple as possible.

I want to illustrate the incredibly fast pace of such growth (and shrinkage) compared to the commonly held perception of evolution working at a snail's pace across geological ages. I want to show how dynamic any state of dynamic equilibrium must be. Nature only manages to keep things in balance by playing exponential forces against exponential forces. The geological record is full of explosions of life, and the more famous mass extinctions. In considering explosions of life, Darwin stated (Darwin, 1859):

"Lighten any check, mitigate the destruction ever so little, and the number of the species will almost instantaneously increase to any amount."

The correct model for a growing population is one which uses variable rates of compound interest. This leads to the Couttsian Growth Model which can be readily demonstrated through the use of the New Malthusian Scale. As Malthus stated (A Summary View - 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."

The correct model for extinctions is also one which uses variable rates of compound interest. However, in this case, the growth rates are negative (Whitfield , 1993, p. 182):

"The extinction of a species does not usually involve the sudden death of all its individual members. Rather, it is a function of the dynamics between rates of birth and death. Species will persist when their overall birth rate equals or exceeds their death rate. But if the latter exceeds the birth rate for a long enough period, replacement of one generation by the next ceases to exist. If no new factor intervenes then the species will go extinct."

Thus, Malthus' earlier statement can be turned on its head to provide an argument for exponential population shrinkage:

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

This fusion of population studies and evolution that I call exponentialism.

Differential Replication

In An Essay On The Principle Of Population Malthus argues that human populations grow at different rates for very 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;"

Although he did not use the phrase, essentially Malthus was arguing that the differential replication of human populations is due to environment and cultural factors. From the second edition onwards of his essay on population Malthus went on the prove his case. In the process he effectively founded the modern field of demography (Peterson, 1979). Malthus never wrote on evolution (he was a creationist, believing in the fixity of species). Nonetheless, in his work he clearly identified factors that affect the growth rate of human populations. See Malthus - An Exponentialist View and Reverend Malthus and Evolution for more on Malthus.

The image above shows three different populations (assume the figures are in millions), growing at different annual rates. This is of course a simplification, because for most populations an annual rate is not appropriate. Very fast replicators include bacteria, cells (see Cells - An Exponentialist View for more), viruses (see Viruses - An Exponentialist View for more) and nanotechnology assemblers (see Drexler - An Exponentialist View for more). 

Nonetheless, the principle of differential replication applies to all replicator populations. An annual rate of growth is appropriate for measuring differential replication between rival human populations, so let us consider three very different populations. I use the Rule Of 70 to quickly extrapolate approximate population doubling and halving times (at 7% a population doubles every 10 years, at negative 1% a population halves every 70 years).

The population growing at 7% might be taking advantage of every conceivable technological advantage (cloning, genetics, exo-wombs, IVF, robotics, biotechnology, nanotechnology, solar energy etc) to colonise space. One might argue how human they would remain, but nonetheless 1 million such "humans" growing at this rate would become 1024 million in just 100 years. 

The population at Zero Population Growth might be Earth-bound adherents of the ZPG lobby. They would hope to remain at 1024 million forever. 

The population slowly declining at negative 1% could be our European and Japanese populations, plus a few others currently at negative rates of growth. A population of 1024 million which sustains a 1% negative growth rate will be reduced to 1 million individuals in just 700 years.

For human populations it is easy to prove that nations around the world experience different rates of population growth - try the online CIA World Fact Book. All the indications are that this situation will continue, as explored in Human Replicators - An Exponentialist View.

Thus I have demonstrated the principle of differential replication for these hypothetical human populations. Unlike the usual explanation of differential replication, Natural Selection and Artificial Selection fail to fully explain why human populations might grow at different rates, either over time or between rival populations. 

See Differential Reproduction - An Exponentialist View for more on differential replication.

Malthusian Selection

Malthusian Selection is proposed as the process by which some populations are favoured due to environmental considerations and non-instinctive behavioural factors. Note that both Natural Selection and Malthusian Selection include environmental factors:


Natural Selection includes the concept of environmental factors through the Malthusian Parameter, which is defined as the fitness of the genome relative to the environment. But this is looking at the world through the genome in order to explain the origin of species. From a population perspective all that matters is the effect on the Malthusian Parameter (the growth rate). The exponentialist view is that the question of the fitness of the genome is secondary to the question of the growth rate of the population. The concept of fitness should relate primarily to the population, and not the genome. Why, you may ask. For one thing, population growth happens on a much faster timeframe than the evolution of species and is therefore a more immediate problem. In a human lifetime billions of people can be added to the world's population with little change in human evolution (with the possible exception to inherited immunity to viruses such as AIDS). For example, the human global population doubled from 3 billion in 1960 to 6 billion in 1999 in just 39 years. The imperative is to understand populations and population growth first and the evolution of species second.

The differential replication of discrete human populations at any time of history, or of the same human population over history, is largely explained by Malthusian Selection and not Natural Selection. Yet differential replication is seen, quite rightly, as an evolutionary process. How can both views be true? The answer is that differential replication results from a combination of both Natural Selection and Malthusian Selection. When considering populations, it is fair to say that the concept of differential replication includes Natural Selection rather than saying that the concept of Natural Selection includes differential replication. So, under identical environmental circumstances but with unequal genomes, Natural Selection will favour one competing population over another. Similarly, assuming populations with identical genomes, Malthusian Selection will favour one competing population over another.

Malthus' focus was on human cultural factors, and generally the non-instinctive behavioural factors in question are human. Malthusian Selection then relates to the affect of non-instinctive behavioural factors on the growth rate of human populations. For example, hygiene, medicine, technology, industry, agriculture, science, education (including family planning), sexual preference (heterosexual or homosexual), warfare, murder and so on. Compare the phenomenal and sustained growth rates of human populations since the move towards civilisation and living in cities. Evolutionary theory, and natural selection, do not explain the affect of these human cultural factors on human population growth rates, whereas Malthusian Selection does provide an explanatory framework.


Artificial Selection is a special case in which human cultural factors indirectly affect the genome of other species (through animal husbandry, hybridisation, and other farming and gardening techniques) and Unnatural Selection is another special case in which human cultural factors directly affect the genome of other species (through genetic engineering) or directly affect any other mechanism for self-replication (for example, through molecular nanotechnology). Hence both Artificial Selection and Unnatural Selection are caused by human cultural factors, but relate to the selection pressure on the genome (or other self-replication mechanism, in the case of molecular nanotechnology). Typically then, Artificial Selection and Unnatural Selection affect the genome of non-human populations.

The exponentialist view is that Natural Selection, Artificial Selection, Malthusian Selection and Unnatural Selection all contribute to the rate of growth for a population  - the Malthusian Parameter - and thus each influences differential replication.


Darwin, Charles, Origin Of Species. 1859.

Fisher, R. A. The Genetical Theory of Natural Selection -  (1930, 1958) - A Complete Variorum Edition - Oxford University Press. 1999, 2003.

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

Peterson, William, Founder Of Modern Demography, Malthus. Transaction Publishers. 1979, 1999

Whitfield, Philip, From So Simple A Beginning - The Book Of Evolution. MacMillan Publishing Company. 1993.

Back to Top

Send email to exponentialist@optusnet.com.au with questions or comments about this web site.
Copyright 2001 David A. Coutts
Last modified: 13 December, 2009