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:

P(t) = P_0e^{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

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

External links

Malthusian Growth Model from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota
Logistic Model from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota
Laws Of Population Ecology Dr. Paul D. Haemig
On principles, laws and theory of population ecology Professor of Entomology, Alan Berryman, Washington State University
Introduction to Social Macrodynamics Professor Andrey Korotayev
Interesting Facts about Population Growth Mathematical Models from Jacobo Bulaevsky, Arcytech.

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Malthusian growth model

See also

References

External links