Exponential growth and carrying capacity

Watch it happen — see the populations of major cities grow in these animated maps that reveal in 60 seconds how cities have exploded in size over the last 130 years

Al Bartlett, Professor Emeritus of Physics, University of Colorado, Boulder, Colorado toured universities around the world to explain exponential growth, his excellent videos are here: Arithmetic, Population, & Energy

Al Bartlett. Science 1 November 2002: 981-987In their comprehensive review of advanced technology paths to global climate stability, Hoffert et.al. (1) open with a clear statement of the origin of the problem: “In the 20th century, the human population [of the earth] quadrupled and primary power consumption increased 16-fold” (2). If these rates were to persist through the 21st century, Earth’s population would be 16 times larger than in 1900, and the primary power consumption would be 256 times that in 1900. Even without the greenhouse problems, the obvious impossibility of continuing these growth rates would lead rational people to say that the present declines in the growth rates of U.S. and world populations are too slow and that the world’s first order of business should be to stop the growth of populations and the growth of per capita primary power consumption. Instead of advocating the obvious, the authors paint a picture of all manner of technological fixes which, at enormous expense, may provide some answers to the need to stop the growth in emissions of greenhouse gases that are associated with energy production. As is so often the case, technological fixes are offered without being reviewed in the light of Eric Sevareid’s Law: “The chief cause of problems is solutions” (3, 4). One can be sure that each technological solution will create new problems that are not indicated by calculations, equations, and technical speculations.

The article makes it clear that achieving global climate stability won’t be easy, but it ignores the first and easiest thing we should do. We should follow the lead of the countries of Europe that all have population growth rates that are presently near or below zero. These countries are making real strides toward sustainability as is indicated in the First Law of Sustainability: “Population growth and/or growth in the rates of consumption of resources, cannot be sustained” (5).

More exponential growth examples

1) Chapter 8 of Hardin’s Living within Limits:  Assume 2 grams of gold grows at 5% compound interest.  In 2,000 years, this would grow to the equivalent of 4.78 x 1042 grams of gold, more than the mass of the earth — 5.983 x 1027 grams – or the equivalent of 800 Trillion earths.

2) Evar Nering, in “The Mirage of a Growing Fuel Supply”: In my classes, I described the following hypothetical situation. We have a 100-year supply of a resource, say oil — that is, the oil would last 100 years if it were consumed at its current rate. But the oil is consumed at a rate that grows by 5 percent each year. How long would it last under these circumstances? This is an easy calculation; the answer is about 36 years.

Oh, but let’s say we underestimated the supply, and we actually have a 1,000-year supply. At the same annual 5 percent growth rate in use, how long will this last? The answer is about 79 years.

Then let us say we make a striking discovery of more oil yet — a bonanza — and we now have a 10,000-year supply. At our same rate of growing use, how long would it last? Answer: 125 years.

If you want to play around with exponential growth rates, check out an Exponential Growth Calculator.  To convert an exponential number to decimal, use a Scientific notation to decimal converter.

3) M. King Hubbert has an excellent article on exponential growth I highly recommend reading:

Hubbert, M.K., 1993. Exponential Growth as a Transient Phenomena in Human History, in: Daly, H., Townsend, K. (Eds.), Valuing the Earth: Economics, Ecology, Ethics. MIT Press, Cambridge, pp. 113-125.


My comment: When we’ve gone back to the age of Wood after fossil fuels go away, our agricultural system is so dependent on fossil fuels we won’t be able to support over 300 million people.  Systems ecologists, who study the carrying capacity of the United States, have estimated that without fossil fuels, the USA can provide food for between 100 million (Pimentel), 150 million (Erlich), and 250 million (Smil 2000).

Matters will be made even worse by how far people live to where the food is grown — more than half of us live near the coasts, but must of the food is grown in the middle of the country.  The Ogalla aquifer which provides about a third of our food over the ten high plains states is also drying up.

Any population increase, however small, will eventually saturate the Earth. It doesn’t matter if Egyptian women have gone from having 7 to 3 children. That’s still way too many children. The population needs to drop down to carrying capacity quickly, even one child per woman might be too many given the carrying capacity of Egypt and the decline rate of oil in the future.  Egypt is way past their carrying capacity now. They relied on exports of fuel to pay for food, now they are importing oil.

Fossil fuels enabled the human population to grow at a rate of 2.0% for a while –133 times higher than the .00015 rate before fossil fuels and an overall average of 0.833% for the past 300 years, or 55 times higher than the growth rate of homo sapiens for millions of years before that (Hardin):

  • Initial human population: 600,000,000 in 1700
  • Growth rate .00833 (.833%)
  • Time unit: 300 (years)
  • Final amount: 7.3 Billion people

If we continue to grow at a .833% rate there’ll be 15 billion people in 2100.  Cut that in half, and you’ve still got 10.5 billion people.

We need a negative growth rate of 1 child per woman or less world-wide to stay under the depletion curve of oil and other fossil fuels.   It’s too late to do that.  It would have never worked anyhow, since capitalism depends on endless growth, businessmen need more customers, religious leaders want more followers, and nations more children to out-reproduce their enemies to win battles.  And ultimately it’s part of our biological nature to consume and reproduce at maximum possible levels, like all the other creatures on the planet from algae to elephants.

Alice Friedemann at energyskeptic


1. M. I. Hoffert et al., Advanced Technology Paths to Global Climate Stability: Energy for a Greenhouse Planet, Science 298, 981 (2002).

2. It must be stressed that these enormous increases are consequences of negligibly small annual growth rates; of population of 1.386%, of per capita primary power consumption of 1.386%, and of total primary power consumption of 2.77%.

3. E. Sevareid, CBS News, December 29, 1970; quoted in T.L. Martin, Malice in Blunderland (McGraw-Hill, New York, 1973).

4. For instance, when the problem was the need for more electric energy, a solution was nuclear power. But nuclear power has presented a whole new set of problems, each of which, it is said, can be solved by more technology.

5. A. A. Bartlett, “Reflections on Sustainability,” Population & Environment, Vol. 16, No. 1, September 1994. Renewable Resources Journal, Vol. 15, No. 4, Winter 1997-98, Pgs. 6-23

Garrett Hardin. 1995. Living Within Limits: Ecology, Economics, and Population Taboos. Oxford    University Press

Pimentel, D. et al. 1991. Land, Energy, and Water.  The Constraints Governing Ideal U.S. Population Size. Negative Population Growth.

Smil, V. 2000. Enriching the Earth: Fritz Haber, Carl Bosch, and the Transformation of World Food Production.  MIT Press.

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2 Responses to Exponential growth and carrying capacity

  1. Jonathan says:

    Fertility rate isn’t the only variable to play with here. To get a good picture you need to consider the death rate and longevity too.

    My guess is we’ll see much higher death rates until some kind of balance is restored between our resource demands and what can actually be sustainably provided. The average life span is going to shorten and the standard deviation is going to increase enormously. Back to the old r-selection strategy…

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