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Malthusian growth model

From Wikipedia, the free encyclopedia

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.[1]

Malthusian models have the following form:


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.[5] It is widely regarded in the field of population ecology as the first principle of population dynamics,[6] with Malthus as the founder. The exponential law is therefore also sometimes referred to as the Malthusian Law.[7] By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics.[8]

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.

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The 1700s in Europe are often referred to as the Age of Enlightenment. It was a time, we'd come out of the Renaissance. We'd rediscovered science and reason and in the 1700s, we saw that come about with even more progress of society. As we exit the 1700s and enter into the 1800s, we start having the Industrial Revolution. And people saw the steady march of human reason, of human progress. And because of this, a lot of people were saying, hey, humanity will continue to improve. It will improve forever, to a point that poverty will go away. We will turn into this perfect utopian civilization without wars, without strife of any kind. And there was something to be said about that. You had significant improvements. In fact, you had even more dramatic improvements once the Industrial Revolution started. But not every one in the late 1700s was as optimistic. And one of the more famous not-so-optimistic people was Thomas Malthus, right over here. And I will just quote him directly. This is from his "Essay on the Principle of Population." "The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must, in some shape or other, visit the human race." Very uplifting. "The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction, and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and sweep off their thousands and tens of thousands. Should success still be incomplete, gigantic, inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world." So not so uplifting of a little quote right over here. But this was his general sense. He lived in a time where people were being very optimistic that progress, the march of progress, would go on forever until we got to some utopian civilization. But from Thomas Malthus' point of view, he felt that if people could reproduce and increase the population, they will, that there's no way of stopping them. So from his point of view, the way he saw it-- so let me on that axis-- let's say that that is the population, and that this axis right over here, let's say that that is time. So by his thinking-- and everything that he'd seen in reality up to that point would back this up-- that if people had enough food and time, they would reproduce, and they would reproduce in numbers that would grow the population. So in his mind, the population would just keep on increasing. It'll just keep on increasing, until it can't support itself anymore, until the actual productivity of the land can't produce enough calories to feed all of those people. So in his mind, there would be some natural upper bound based on the actual amount of food that the earth could support. So let's say that this is-- let me do that in a different color-- so in his mind, there was some upper bound, and once you get to that upper bound, then all of a sudden, the vices of mankind will show up. And if those don't start killing people, then all of these other things will, epidemics, pestilence, plague, and then famine. People are actually starving to death. So in his mind, once you got to this level, maybe you had a couple of good crops, people are feeling good about themselves, they overpopulate. But then, all of a sudden, you have a bad crop, or because you have a bad crop, people start fighting over resources, and wars happen. Or maybe the population is so dense that a plague develops. And then you have a massive wave of depopulation. And so you would just oscillate around this limit. And this limit some people refer to as a Malthusian limit, but it's just really the limit at which the population can sustain itself. And from Thomas Malthus' point of view, he did recognize that there were technological improvements, especially in things like agriculture. And that this line was moving up. He had seen it in his own lifetime, that this line had moved up. But from his point of view, however far you moved this line up, the population will always compensate for it and catch up to it, and eventually get to these Malthusian limit. And then the same not-so-positive things that he talks about would actually happen. And some people now say, oh Thomas Malthus, he was so pessimistic. He was obviously wrong. Look at what's happened. We have so much food on this planet right now. We've gone through multiple agricultural revolutions, and they are right. In the last 200 years, since Malthus, so since the early 1800s, we really have been able to outstrip population. So this line up here has been moving up much faster than even population. So right now, we actually do have more calories per person on the planet than we've had at any time in history. But it's not saying that Thomas Malthus was wrong, it's just saying that maybe he was just a little bit pessimistic in when that limit will be reached. Now the other dimension where you might say that he was maybe wrong was in this principle that a population will increase if it can increase. If there is food, and if there is time, people will reproduce. And a good counterpoint to that is what we've now observed in modern, developed nations. And so this right over here shows the population growth. I got this from the World Bank. But the population growth of some modern, developed nations. And you can see the United States is pretty low, but it's still positive. It's still over half a percent. But even that adds up when you compound it. But if you look over here, Japan and Germany-- and Japan and Germany have less immigration than the United States, especially Japan-- they are actually negative. So just this population left to its own devices, especially if you account for people not going across borders, just the population itself growing, they actually have negative growth. So there's some reason to believe that this is evidence that Thomas Malthus was wrong, or not completely right. He didn't put into account that maybe once a society becomes rich enough and educated enough, that they might not just populate the world, or have as many kids as they want, they might try to do other things with their time, whatever that might be. So I just wanted to expose you to this idea. Time will tell if Thomas Malthus, if we can always keep this line of food productivity growing faster than the population. And time will tell whether our populations can become, I guess we could say, developed enough, so that they don't inex-- I can never say that word. They don't always just keep growing. Maybe they do become a Japan or a Germany situation. And the world population, especially if we have a high rate of literacy, eventually does level off. So it never even has a chance of hitting up against that Malthusian limit. But I thought I would introduce you to the idea, and now you can go to parties and you can talk about things like Malthusian limits. And if you want to know what country is maybe closest to the Malthusian limit right now-- and we've talked about this before-- but a good case example is something like Bangladesh. They are, right now, the most population-dense country in the world. They have 900 people per square kilometer. And just to give you a sense of perspective, that's 30 times more dense than the United States is. So if you took every person in the United States, and turned them into 30 people in the United States, that would give you a sense of how dense Bangladesh is. And it's probably due to a certain degree that it's a very fertile land. The river delta of the Ganges essentially makes up the entire country. But they do, they have in the past, had famines. They've gotten a little bit beyond that. But still, you do have major problems with flooding and resources. So hopefully they'll be able to stay ahead of the curve.

See also


  1. ^ "Malthus, An Essay on the Principle of Population: Library of Economics"
  2. ^ Fisher, Ronald Aylmer, Sir, 1890-1962. (1999). The genetical theory of natural selection (A complete variorum ed.). Oxford: Oxford University Press. ISBN 0-19-850440-3. OCLC 45308589.CS1 maint: multiple names: authors list (link)
  3. ^ Lotka, Alfred J. (Alfred James), 1880-1949. (2013-06-29). Analytical theory of biological populations. New York. ISBN 978-1-4757-9176-1. OCLC 861705456.CS1 maint: multiple names: authors list (link)
  4. ^ Lotka, Alfred J. (1934). Théorie analytique des associations biologiques. Hermann. OCLC 614057604.
  5. ^ Turchin, P. "Complex population dynamics: a theoretical/empirical synthesis" Princeton online
  6. ^ Turchin, Peter (2001). "Does population ecology have general laws?". Oikos. 94: 17–26. doi:10.1034/j.1600-0706.2001.11310.x.
  7. ^ Paul Haemig, "Laws of Population Ecology", 2005
  8. ^ Ginzburg, Lev R. (1986). "The theory of population dynamics: I. Back to first principles". Journal of Theoretical Biology. 122 (4): 385–399. doi:10.1016/s0022-5193(86)80180-1.

External links

This page was last edited on 26 December 2020, at 06:28
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