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Concept
Malthusian growth model
Summary
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.
Malthusian models have the following form:
where
P0 = 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:
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:
"Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand. ... The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in the course of a few thousand years. Necessity, that imperious all pervading law of nature, restrains them within the prescribed bounds. The race of plants, and the race of animals shrink under this great restrictive law. And the race of man cannot, by any efforts of reason, escape from it. Among plants and animals its effects are waste of seed, sickness, and premature death. Among mankind, misery and vice.
Official source
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Related concepts (6)
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 in geometric progression (so as to double every 25 years) while food production increased in an arithmetic progression, which would leave a difference resulting in the want of food and famine, unless birth rates decreased.
Human overpopulation
Human overpopulation (or human population overshoot) describes a concern that human populations may become too large to be sustained by their environment or resources in the long term. The topic is usually discussed in the context of world population, though it may concern individual nations, regions, and cities. Since 1804, the global human population has increased from 1 billion to 8 billion due to medical advancements and improved agricultural productivity. Annual world population growth peaked at 2.
Population dynamics
Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, although over the last century the scope of mathematical biology has greatly expanded. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model.