Malthusian Growth Model

A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. 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."Malthus, An Essay on the Principle of Population: Library of Economics"

Malthusian models have the following form:
:$P(t) = P_0e^$
where

* ''P''₀ = ''P''(0) is the initial population size,
* ''r'' = the population growth rate, which Ronald Fisher called the ''Malthusian parameter of population growth'' in The Genetical Theory of Natural Selection, and Alfred J. Lotka called the ''intrinsic rate of increase'',
* ''t'' = time.

The model can also been written in the form of a differential equation:

:$\frac = rP$

with initial condition:
P(0)= P₀

This model is often referred to as the ''exponential law''. It is widely regarded in the field of population ecology as the first principle of population dynamics, with Malthus as the founder. The exponential law is therefore also sometimes referred to as the ''Malthusian Law''. By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics.

Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources:

A model of population growth bounded by resource limitations was developed by Pierre Francois Verhulst in 1838, after he had read Malthus' essay. Verhulst named the model a logistic function.

See also

*Albert Allen Bartlett – a leading proponent of the Malthusian Growth Model
*Exogenous growth model – related growth model from economics
*Growth theory – related ideas from economics
*Human overpopulation
*Irruptive growth – an extension of the Malthusian model accounting for population explosions and crashes
*Malthusian catastrophe
*Neo-malthusianism
*The Genetical Theory of Natural Selection

References

External links

Malthusian Growth Model
from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota

from Steve McKelvey, Department of Mathematics, Saint Olaf College, Northfield, Minnesota

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
Ecological Orbits
Lev Ginzburg, Mark Colyvan

{{modelling ecosystems, expanded=none

Empirical laws
Mathematical modeling
Population
Population ecology
1798 in economics