# Malthusian growth model

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:

${\displaystyle P(t)=P_{0}e^{rt}\,}$

where

• 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.

## References

1. ^ "Malthus, An Essay on the Principle of Population: Library of Economics" (description), Liberty Fund, Inc., 2000, EconLib.org webpage: EconLib-MalPop.
2. ^ Turchin, P. "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.