A Malthusian growth model, sometimes called a simple exponential growth model, is essentially
exponential growth
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast ...
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
The book ''An Essay on the Principle of Population'' was first published anonymously in 1798, but the author was soon identified as Thomas Robert Malthus. The book warned of future difficulties, on an interpretation of the population increasing ...
'' (1798), one of the earliest and most influential books on
population
Population is a set of humans or other organisms in a given region or area. Governments conduct a census to quantify the resident population size within a given jurisdiction. The term is also applied to non-human animals, microorganisms, and pl ...
.
["Malthus, An Essay on the Principle of Population: Library of Economics"]
Malthusian models have the following form:
:
where
* ''P''
0 = ''P''(0) is the initial population size,
* ''r'' = the population growth rate, which
Ronald Fisher
Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962) was a British polymath who was active as a mathematician, statistician, biologist, geneticist, and academic. For his work in statistics, he has been described as "a genius who a ...
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 be written in the form of a differential equation:
:
with initial condition:
''P''(0)= ''P''
0
This model is often referred to as the exponential law. It is widely regarded in the field of
population ecology
Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment (biophysical), environment, such as birth rate, birth and death rates, and by immigration an ...
as the
first principle
In philosophy and science, a first principle is a basic proposition or assumption that cannot be deduced from any other proposition or assumption. First principles in philosophy are from first cause attitudes and taught by Aristotelians, and nuan ...
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 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
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation
f(x) = \frac
where
The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L.
...
.
See also
*
Logistic function
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation
f(x) = \frac
where
The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L.
...
for the mathematical model used in
Population dynamics that adjusts growth rate based on how close it is to the maximum a system can support
*
Albert Allen Bartlett – a leading proponent of the Malthusian Growth Model
*
Exogenous growth model – related growth model from
economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
*
Growth theory – related ideas from
economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services.
Economics focuses on the behaviour and interac ...
*
Human overpopulation
Human overpopulation (or human population overshoot) is the idea that human populations may become too large to be sustainability, sustained by their environment or resources in the long term. The topic is usually discussed in the context of wor ...
*
Irruptive growth – an extension of the Malthusian model accounting for population explosions and crashes
*
Malthusian catastrophe
Malthusianism is a theory that population growth is potentially exponential, according to the Malthusian growth model, while the growth of the food supply or other resources is linear, which eventually reduces living standards to the point of tr ...
*
Neo-malthusianism
*
The Genetical Theory of Natural Selection
References
External links
Malthusian Growth Modelfrom 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 ecologyProfessor of Entomology, Alan Berryman, Washington State University
Introduction to Social MacrodynamicsProfessor
Andrey Korotayev
Andrey Vitalievich Korotayev (; born 17 February 1961) is a Russian anthropology, anthropologist, economic history, economic historian, comparative politics, comparative political scientist, demography, demographer and sociology, sociologist ...
Ecological OrbitsLev Ginzburg, Mark Colyvan
{{modelling ecosystems, expanded=none
Empirical laws
Mathematical modeling
Population
Population ecology
1798 in economic history