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. " — Thomas Malthus, 1798. An Essay on the Principle of Population. Chapter I. 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. (Wikipedia).
Introduces logistic equation by discussing Malthusian growth model and Verhulst equation. Solves logistic equation by separating variables. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: h
From playlist Differential Equations
8. Demographic Transition in Europe; Fertility Decline
Global Problems of Population Growth (MCDB 150) Prior to Malthus, population growth was seen as good for the power and wealth of a country. The rapid population growth of America was crucial in expelling England (via the Revolution) and France (via the Louisiana Purchase) from the US. B
From playlist Global Problems of Population Growth with Robert Wyman
Logistic Growth Function and Differential Equations
This calculus video tutorial explains the concept behind the logistic growth model function which describes the limits of population growth. This shows you how to derive the general solution or logistic growth formula starting from a differential equation which describes the population gr
From playlist New Precalculus Video Playlist
Introduces notation and formulas for exponential growth models, with solutions to guided problems.
From playlist Discrete Math
Logistic function application | First order differential equations | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/integral-calculus/ic-diff-eq/ic-logistic-models/v/logistic-function-application Differential Equations on Khan Academy: Differential equations, separable equation
From playlist Differential equations | AP Calculus BC | Khan Academy
How Populations Grow and Change: Crash Course Geography #33
Is the world overpopulated or underpopulated? While we worry about there being too many people for the planet to support, we can also worry about how fewer people in a given place may affect the economy, what may happen when there are more elderly people who need care than there are health
From playlist Geography
Demographic transition | Society and Culture | MCAT | Khan Academy
Created by Sydney Brown. Watch the next lesson: https://www.khanacademy.org/test-prep/mcat/society-and-culture/demographics/v/globalization-theories?utm_source=YT&utm_medium=Desc&utm_campaign=mcat Missed the previous lesson? https://www.khanacademy.org/test-prep/mcat/society-and-culture
From playlist Society and culture | MCAT | Khan Academy
The Mathematics of Population Growth Using Linear Models
Introduce implicit and explicit population models and their notation. Solve guided problems involving population models and their applications.
From playlist Discrete Math
Alison Etheridge: Spatial population models (4/4)
Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In these lectures, we focus on some of the models which arise when we try to model the interplay between the forces of ev
From playlist Summer School on Stochastic modelling in the life sciences
Lec 9 | MIT 21L.448J Darwin and Design, Fall 2010
Lecture 9: Malthus and the Compound Interest World Instructor: James Paradis View the complete course: http://ocw.mit.edu/21L-448JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 21L.448J Darwin and Design, Fall 2010
Thomas Malthus and population growth | Cosmology & Astronomy | Khan Academy
Thomas Malthus's views on population. Malthusian limits. Created by Sal Khan. Watch the next lesson: https://www.khanacademy.org/science/cosmology-and-astronomy/life-earth-universe/humanity-on-earth-tutorial/v/land-productivity-limiting-human-population?utm_source=YT&utm_medium=Desc&utm_c
From playlist Cosmology and astronomy | Physics | Khan Academy
Alison Etheridge: Spatial population models (3/4)
Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In these lectures, we focus on some of the models which arise when we try to model the interplay between the forces of ev
From playlist Summer School on Stochastic modelling in the life sciences
Alison Etheridge: Spatial population models (1/4)
Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In these lectures, we focus on some of the models which arise when we try to model the interplay between the forces of ev
From playlist Summer School on Stochastic modelling in the life sciences
Population regulation | Ecology | Khan Academy
Keep going! Check out the next lesson and practice what you’re learning: https://www.khanacademy.org/science/ap-biology/ecology-ap/population-ecology-ap/a/mechanisms-of-population-regulation Learn the difference between density-dependent and density-independent factors that affect populat
From playlist Ecology | High school biology | Khan Academy
Alison Etheridge: Spatial population models (2/4)
Abstract: Mathematical models play a fundamental role in theoretical population genetics and, in turn, population genetics provides a wealth of mathematical challenges. In these lectures, we focus on some of the models which arise when we try to model the interplay between the forces of ev
From playlist Summer School on Stochastic modelling in the life sciences
Population, Sustainability, and Malthus: Crash Course World History 215
In which John Green teaches you about population. So, how many people can reasonably live on the Earth? Thomas Malthus got it totally wrong in the 19th century, but for some reason, he keeps coming up when we talk about population. In 1800, the human population of the Earth passed 1 billio
From playlist World History 2
Lec 10 | MIT 21L.448J Darwin and Design, Fall 2010
Lecture 10: Malthus and the Compound Mind Instructor: James Paradis View the complete course: http://ocw.mit.edu/21L-448JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 21L.448J Darwin and Design, Fall 2010
10g Machine Learning: Isotonic Regression
Lecture on isotonic regression. Introduces the idea of a piece-wise linear model with monotonic constraint. Follow along with the demonstration workflow: https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/SubsurfaceDataAnalytics_IsotonicRegression.ipynb
From playlist Machine Learning
25. Cases IV: Hyper and Mega-urbanism
MIT 4.241J Theory of City Form, Spring 2013 View the complete course: http://ocw.mit.edu/4-241JS13 Instructor: Julian Beinart This lecture focuses on urbanism in the Global South. Discussion targets how to deal with population growth, the residue of colonialism, the tradition of tribalism
From playlist MIT 4.241J Theory of City Form, Spring 2013