Malthusian growth model

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A Malthusian Growth Model, sometimes called a simple exponential growth model, is essentially exponential growth based on a constant rate. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most influential books on population.[1]

Malthusian models have the following form:

 P(t) = P_0e^{rt} \,


  • P0 = P(0) is the initial population size,
  • r = the population growth rate, sometimes called Malthusian parameter,
  • t = time.

This model is often referred to as the exponential law.[2] It is widely regarded in the field of population ecology as the first principle of population dynamics,[3] with Malthus as the founder. The exponential law is therefore also sometimes referred to as the Malthusian Law.[4]

It is generally acknowledged that populations can not grow indefinitely. [5] Joel E. Cohen has stated that the simplicity of the model makes it useful for short-term predictions, but not of much use for predictions beyond 10 or 20 years.[6]

The simplest way to limit Malthusian growth model is by extending it to a logistic function. Pierre Francois Verhulst first published his logistic growth function in 1838 after he had read Malthus' essay.

See also


  1. "Malthus, An Essay on the Principle of Population: Library of Economics" (description), Liberty Fund, Inc., 2000, webpage: EconLib-MalPop.
  2. Peter Turchin, "Complex population dynamics: a theoretical/empirical synthesis" Princeton online
  3. Turchin, P. "Does Population Ecology Have General Laws?" Oikos 94:17–26. 2000
  4. Paul Haemig, "Laws of Population Ecology", 2005
  5. Cassell's Laws Of Nature, James Trefil, 2002 – Refer 'exponential growth law'.
  6. Cohen, J. E. How Many People Can The Earth Support, 1995.

External links