Couttsian Growth Model

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Introduction

Whilst evolutionists generally accept the Malthusian (constant rate exponential) nature of population growth, others such as Dawkins (1996) sometimes point out that an exponential growth model (for example, when applied to local doubling of cell populations) is naive. However, even Dawkins (1996) does not always qualify his (typically Malthusian) explanation of exponential growth:

"It is the nature of a replicator that it generates a population of copies of itself, and that means a population of entities that also undergo duplication. Hence the population will tend to grow exponentially until checked by competition for resources or raw materials. ...Briefly, the population doubles at regular intervals, rather than adding a constant number at regular intervals. This means that there will soon be a very large population of replicators and hence competition between them."

Demographer Joel E. Cohen (1995) went further, arguing that:

"Surprisingly, in spite of the abundant data to the contrary, many people believe that human population grows exponentially. It probably never has and probably never will."

Cohen then examines a number of other population models (the logistic curve, the doomsday curve, and the sum-of-exponentials curve). He then uses a semi-log plot to examine world population history for the last two thousand years. He confidently concludes:

"...Population growth was not exponential during these millennia, whatever Malthus and others may have thought."

Cohen is equally critical of the Logistic Growth Model, too, pointing out the frequency of failed predictions by Verhulst and others. He concludes:

"In any event, the available simple models do not describe human population history"

Cohen presents Egypt's demographic history as a classic example of intractible population modelling complextiy.

So does population grow exponentially, or not? Does a simple but universal physical law of population growth exist, or not?

Re-examining Malthus

Malthus typically considered the growth rate (dubbed by Fisher as the Malthusian parameter), and from that deduced the population doubling time. From 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.

Thus:

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.

There is more to Malthus that he has been given credit for.

Scales of e

Taken together, as demonstrated by the Exponentialist Scales of e, these statements indicate that variable positive rates of population growth result in variable population doubling periods. Conversely, it has been shown that variable negative rates of population growth result in variable population halving periods. Yet, such growth is more akin to Malthus' geometric (or exponential, constant rate) model of population growth rather than any arithmetic (or linear) model.

The Scales of e takes the concept of the Rule of 70, or the Rule of 72, and expands it to cater for any mixture of positive and negative rates of variable compound interest. Variable rates of compound interest result in variable population doubling and population halving times. The timeframes involved are entirely comparable to those for fixed rate compound interest. This explains the demographic history of Egypt, and does so simply.

To avoid confusion with the existing Malthusian Growth Model, I call this revised model the Couttsian Growth Model. Linguistically, all it takes is one word to change fixed rate compound interest (Malthusian Growth Model) to variable rate compound interest (Couttsian Growth Model).

Two Centuries of Exponential Growth (a fallacy)

Conceptually, it has taken over two centuries to make this simple leap. Even the US Census Bureau, who acknowledge that rates of population growth vary from year to year, do not see the simple population growth model of variable rate compound interest.

No less a person than Stephen Hawking (2001) is one of many luminaries who get confused on this point:

"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..."

So the population grows exponentially, and the rate is currently 1.9%. But it wasn't a constant rate of 1.9% for those two centuries!

Paul Ehrlich (1990) is another one that promotes the concept of the exponential nature of human population growth, and notes:

"Exponential growth occurs when the increase in population size in a given period is a constant percentage of the size at the beginning of the period. Thus a population growing at 2 percent annually or a bank account growing at 6 percent annually will be growing exponentially."

Yet he also states:

"The slowdown has only been from a peak annual growth rate of perhaps 2.1 percent in the 1960s to about 1.8 percent in 1990. To put this change in perspective, the population's doubling time has been extended from thirty-three years to thirty-nine. Indeed, the world population did double in the thirty-seven years from 1950 to 1987"

The self-styled Club Of Rome (1972) wrote:

"A quantity exhibits exponential growth when it increases by a constant percentage of the whole in a constant time period. A colony of yeast cells in which each cell divides into two cells every 10 minutes is growing exponentially."

Discussing the slowdown in growth rates, and with no hint of self-contradiction, they concluded:

"Thus, not only has the population been growing exponentially, but the rate of growth has also been growing."

Carl Sagan (1998) puts the exponential phase of human population growth back to the time of the agricultural revolution:

"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."

Again, the idea that there can be a "phase" of exponential growth implies a separate growth model (and thus a separate physical law of nature) applied during our hunter-gatherer days. Furthermore, Sagan needlessly reinforces the (Malthusian) delusion that a separate growth model applies to food which, after all, grows in populations too. There is only one universal growth model needed - the Couttsian Growth Model.

Sagan rather poigniantly states:

"If you understand exponentials, the key to many of the secrets of the universe is in your hand.""

Modern day Malthusian, Albert Bartlett has lectured on Arithmetic, Population, and Energy over 1,500 times. He too uses the classic (constant rate) exponential growth model for human populations, thus unfortunately allowing his critics to easily dismiss his prophecy of doom as human populations don't grow exponentially. Ironically, Bartlett has stated:

"The greatest shortcoming of the human race is our inability to understand the exponential function."

Universal Physical Law

Today the Malthusian growth model bears Malthus' name, and is nonetheless widely recognised as an approximate physical law of population growth.

If the Malthusian Growth Model is an approximate physical law, then the Couttsian Growth Model is an actual physical law that applies to all populations of all species for all time. Just four words - variable rate compound interest.

Note that variable rate compound interest is simply consecutive periods of fixed rate compound interest (constant rate exponential growth), at variable rates. This makes sense, for all examples of actual exponential growth are at best temporary periods of growth at a constant rate. Sustained exponential growth at a constant rate is logically and practically impossible, due to Malthusian limits to growth.

A classic example of the Couttsian Growth Model in action is the population doubling of the human world population from 3 billion in 1960 to 6 billion in 1999. Each year of growth represents classical (averaged) exponential growth at a constant rate for all 12 months. Yet each year, the global growth rate varies. Consectuve periods of exponential growth, yet the growth rate varies every year.

Malthusian population thinking is the key to understanding a simple but universal physical law of population growth. According to Wikipedia, such a simple law of population growth is not supposed to exist (from the Malthus article):

...it is widely acknowledged that population growth is almost never exponential, but instead influenced by so many factors that no simple mathematical model can describe it.

Conclusion

Malthus' Principle of Population is finally brought up to date. The arithmetic (or linear) model of the growth of food can be dropped altogether. The geometric nature of population growth remains, but is is based on variable rate compound interest rather than fixed rate rate compound interest.

The concept of Malthusian catastrophe is founded on a misinterpretation, or misrepresentation, of Mallthus' position. Malthus himself noted:

"...this constantly subsisting cause of periodical misery has existed ever since we have had any histories of mankind, does exist at present, and will for ever continue to exist, unless some decided change takes place in the physical constitution of our nature.

Most interpretations emphasise Malthus' assertion that food supply cannot keep pace with population. It is estimated that the Chinese have experienced at least 1,800 famines. The Indians have not fared much better. Famine is definitely a factor. Yet human history is rife with infanticide, murder, droughts, floods, fires, epidemics, pandemics, and warfare. This is what Malthus explained:

"The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction; and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague, advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world."

The Couttsian Growth Model is proposed as a universal physical law. Thus, all populations of all species are always subject to Couttsian Growth, or Couttsian Shrinkage, as per the model.

The periodical misery of which Malthus spoke is caused by occasional but inevitable localised imbalances of the complex and powerful exponential forces of Couttsian population growth. Limits to growth still apply, but populations are not compelled towards them by Couttsian Growth Model (unless they sustain variable and positive rates of population growth).

Einstein referred to compound interest as the most powerful force in the universe. Sure it exists in the world of finance. However, most significantly, compound interest is a force of life and is latent in all populations of all species.

See Also

Malthusian Selection

References

• Club of Rome (1972), The Limits to Growth.
• Joel E Cohen (1995), How Many People Can The Earth Support?. Norton. ISBN 0-393-31495-2
• Richard Dawkins (1996), Climbing Mount Improbable. Penguin Group. ISBN 0-14-026302-0
• Paul R. Ehrlich (1990), The Population Explosion.
• Stephen Hawking (2001), The Universe in a Nutshell.
• Carl Sagan (1998), Billions and Billions.
• Wikipedia Malthus article

External Links

• Scales Of e - Exponentialist article
• US Census Bureau - Incorrect Use Of The Exponential Method - Exponentialist article
• Laws of Population Ecology Dr. Paul D. Haemig