The World3 model was a computer simulation of interactions between population, industrial growth, food production and limits in the ecosystems of the Earth. It was originally produced and used by a Club of Rome study that produced the model and the book The Limits to Growth. The principal creators of the model were Donella Meadows, Dennis Meadows, and Jørgen Randers.

The model was documented in the book Dynamics of Growth in a Finite World. It added new features to Jay W. Forrester's World2 model. Since World3 was originally created it has had minor tweaks to get to the World3/91 model used in the book Beyond the Limits and later was tweaked to get the World3/2000 model distributed by the Institute for Policy and Social Science Research.

The model consisted of several interacting parts. Each of these dealt with a different system of the model. The main systems were

Criticism of the model:
There has been quite a bit of criticism of the world3 model. Some has come from the model creators themselves, some has come from economists and some has come from other places.

One of the major criticisms of the model is that it simply has not reflected the reality of the world since the 1970s when the model was first published. This criticism is in general false, since most of the predictions of doom or collapse do not begin to occur until around 2015 in the reference run. The model predicted that humanity would run up against the fundamental limits to economic growth about a century after the publication of the book: i.e. 2072, with extremely serious ecological problems only beginning to become obvious in the 2030s and 2040s. Moreover, some of the other runs in the model had even later dates for the beginning of the collapse. The 1992 book, Beyond the Limits, describes several values of the model that were revised to fit what had happened. None of those changes were sufficient to change the general qualitative conclusions reached by the Meadows group.

Since the modelers that created the model are most familiar with it, their criticism is most relevant. In the book Groping in the Dark: The First Decade of Global Modelling (Page 129), Donella Meadows, states:

We have great confidence in the basic qualitative assumptions and conclusions about the instability of the current global socioeconomic system and the general kinds of changes that will and will not lead to stability. We have relatively great confidence in the feedback-loop structure of the model, with some exceptions which I list below. We have a mixed degree of confidence in the numerical parameters of the model; some are well-known physical or biological constants that are unlikely to change, some are statistically derived social indices quite likely to change, and some are pure guesses that are perhaps only of the right order of magnitude. The structural assumptions in World3 that I consider most dubious and also sensitive enough to be of concern are:

Of course, since Donella Meadows was very closely associated with the model, she would be unlikely to see problem in the basic qualitative assumptions, so outside criticism needs to be looked at.

The most detailed criticism of the model is in the book Models of Doom: A Critique of the Limits to Growth.

Both Julian Lincoln Simon and Bjørn Lomborg have discussed the assumptions that the model makes.

The first assumption that they criticize is the assumption of finite natural resources. Since the model has a hard limit and no method of switching to substitutes, this is probably a valid complaint about the model. They also state that the limits on agriculture are invalid since they are based on the limit of the amount of land. However, this is incorrect, since the model does allow more food to be grown with the same amount land but with increases of other agricultural inputs (such as fertilizer).

Vaclav Smil disagreed with the combination of physically different processes into simplified equations:

But those of us who knew the DYNAMO language in which the simulation was written and those who took the model apart line-by-line quickly realized that we had to deal with an exercise in misinformation and obfustication rather than with a model delivering valuable insights. I was particularly astonished by the variables labelled Nonrenewable Resources and Pollution. Lumping together (to cite just a few scores of possible examples) highly substitutable but relatively limited resources of liquid oil with unsubstitutable but immense deposits of sedimentary phosphate rocks, or short-lived atmospheric gases with long-lived radioactive wastes, struck me as extraordinarily meaningless. ——Energy at the Crossroads.

He does however consider continuous growth in world GDP a problem:

Only the widespread scientific illiteracy and innumeracy -- all you need to know in this case is how to execute the equation y = x * e^rt-- prevents most of the people from dismissing the idea of sustainable growth at healthy rates as an oxymoronic stupidity whose pursuit is, unfortunately, infinitely more tragic than comic. After all, even cancerous cells stop growing once they have destroyed the invaded tissues.——Energy at the Crossroads
The authors of the book Surviving 1,000 Centuries consider some of the predictions too pessimistic, but some of the overall message correct.

"...[W]e come to the well-known study, Limits to Growth, published under the sponsorship of the 'Club de Rome' - an influential body of private individuals. A first attempt was made to make a complete systems analysis of the rapidly growing human-biological-resource-pollution system. In this analysis the manifold interactions between the different parts were explicitly taken into account. The conclusion was that disaster was waiting around the corner in a few decades because of resource exhaustion, pollution and other factors. Now, 35 years later, our world still exists, ... So the 'growth lobby' has laughed and proclaimed that Limits to Growth and, by extension, the environmental movements may be forgotten. This entirely misses the point. Certainly the timescale of the problems was underestimated in Limits to Growth, giving us a little more time than we thought. Moreover, during the last three decades a variety of national or collaborative international measures have been taken that have forced reductions in pollution, as we shall discuss. A shining example of this is the Montreal Protocol (1987) that limited the industrial production of fluorocarbons that damage the ozone layer and generated the 'ozone hole' over Antarctica. The publication of Limits to Growth has greatly contributed towards creating the general willingness of governments to consider such issues. Technological developments have also lead to improvements in the efficiency of the use of energy and other resources, but, most importantly, the warnings from Malthus onward have finally had their effect as may be seen from the population-limiting policies followed by China and, more hesitantly, by India. Without such policies all other efforts would be in vain. However, the basic message of Limits to Growth, that exponential growth of our world civilization cannot continue very long and that a very careful management of the planet is needed, remain as valid as ever." ——Surviving 1,000 Centuries ISBN 978-0-387-74633-3 pg 4-5 Roger-Maurice Bonnet and Lodewijk Woltjer.

 

The Limits to Growth is a 1972 book modeling the consequences of a rapidly growing world population and finite resource supplies, commissioned by the Club of Rome. Its authors were Donella H. Meadows, Dennis L. Meadows, Jørgen Randers, and William W. Behrens III. The book used the World3 model to simulate the consequence of interactions between the Earth's and human systems. The book echoes some of the concerns and predictions of the Reverend Thomas & Robert Malthus in An Essay on the Principle of Population (1798).

Five variables were examined in the original model, on the assumptions that exponential growth accurately described their patterns of increase, and that the ability of technology to increase the availability of resources grows only linearly. These variables are: world population, industrialization, pollution, food production and resource depletion. The authors intended to explore the possibility of a sustainable feedback pattern that would be achieved by altering growth trends among the five variables.

The most recent updated version was published on June 1, 2004 by Chelsea Green Publishing Company and Earthscan under the name Limits to Growth: The 30-Year Update. Donnella Meadows, Jørgen Randers, and Dennis Meadows have updated and expanded the original version. They had previously published Beyond the Limits in 1993 as a 20 year update on the original material.

In 2008 Graham Turner at the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Australia published a paper called "A Comparison of `The Limits to Growth` with Thirty Years of Reality". It examined the past thirty years of reality with the predictions made in 1972 and found that changes in industrial production, food production and pollution are all in line with the book's predictions of economic and societal collapse in the 21st century.
The purpose of The Limits to Growth was not to make specific predictions, but to explore how exponential growth interacts with finite resources. Because the size of resources is not known, only the general behavior can be explored. The authors state in a subsection titled The Purpose of the World Model:

In this first simple world model, we are interested only in the broad behavior modes of the population-capital system. By behavior modes we mean the tendencies of the variables in the system (population or pollution, for example) to change as time progresses. A variable may increase, decrease, remain constant, oscillate, or combine several of these characteristic modes. For example, a population growing in a limited environment can approach the ultimate carrying capacity of that environment in several possible ways. It can adjust smoothly to an equilibrium below the environmental limit by means of a gradual decrease in growth rate, as shown below. It can overshoot the limit and then die back again in either a smooth or an oscillatory way, also as shown below. Or it can overshoot the limit and in the process decrease the ultimate carrying capacity by consuming some necessary nonrenewable resource, as diagrammed below. This behavior has been noted in many natural systems. For instance, deer or goats, when natural enemies are absent, often overgraze their range and cause erosion or destruction of the vegetation.

A major purpose in constructing the world model has been to determine which, if any, of these behavior modes will be most characteristic of the world system as it reaches the limits to growth. This process of determining behavior modes is "prediction" only in the most limited sense of the word. The output graphs reproduced later in this book show values for world population, capital, and other variables on a time scale that begins in the year 1900 and continues until 2100. These graphs are not exact predictions of the values of the variables at any particular year in the future. They are indications of the system's behavioral tendencies only.

The difference between the various degrees of "prediction" might be best illustrated by a simple example. If you throw a ball straight up into the air, you can predict with certainty what its general behavior will be. It will rise with decreasing velocity, then reverse direction and fall down with increasing velocity until it hits the ground. You know that it will not continue rising forever, nor begin to orbit the earth, nor loop three times before landing. It is this sort of elemental understanding of behavior modes that we are seeking with the present world model. If one wanted to predict exactly how high a thrown ball would rise or exactly where and when it would hit the ground, it would be necessary to make a detailed calculation based on precise information about the ball, the altitude, the wind, and the force of the initial throw. Similarly, if we wanted to predict the size of the earth's population in 1993 within a few percent, we would need a very much more complicated model than the one described here. We would also need information about the world system more precise and comprehensive than is currently available.

Exponential reserve index
One key idea that The Limits to Growth discusses is that if the rate of resource use is increasing, the amount of reserves cannot be calculated by simply taking the current known reserves and dividing by the current yearly usage, as is typically done to obtain a static index. For example, in 1972, the amount of chromium reserves was 775 million metric tons, of which 1.85 million metric tons were mined annually (see exponential growth). The static index is 775 / 1.85 = 418 years, but the rate of chromium consumption was growing at 2.6% annually (Limits to Growth, pp 54–71). If instead of assuming a constant rate of usage, the assumption of a constant rate of growth of 2.6% annually is made, the resource will instead last

(note that the book rounded off numbers).

In general, the formula for calculating the amount of time left for a resource with constant consumption growth is :

;
where:

y = years left;
g = 1.026 (2.6% annual consumption growth);
R = reserve;
C = (annual) consumption.
The authors list a number of similar exponential indices comparing current reserves to current reserves multiplied by a factor of five:

		Years
Resource	Consumption growth rate, annual	Static index	Exponential index	5 times reserves exponential index
Chromium	2.6%	420	95	154
Gold	4.1%	11	9	29
Iron	1.8%	240	93	173
Petroleum	3.9%	31	20	50

The static reserve numbers assume that the usage is constant, and the exponential reserve assumes that the growth rate is constant. For petroleum, neither the assumption of constant usage or the assumption of constant exponential growth was correct in the years that followed.

Whether intended or not, the exponential index has often been interpreted as a prediction of the number of years until the world would "run out" of various resources, both by environmentalist groups calling for greater conservation and restrictions on use, and by skeptics criticizing the index when supplies failed to run out. For example, The Skeptical Environmentalist (page 121) states: "The Limits to Growth showed us that we would have run out of oil before 1992." What The Limits to Growth actually has is the above table, which has the current reserves (that is no new sources of oil are found) for oil running out in 1992 assuming constant exponential growth.

The Limits to Growth attracted controversy as soon as it was published. Yale economist Henry C. Wallich labeled the book "a piece of irresponsible nonsense" in a Newsweek editorial dated March 13, 1972. Wallich's main complaints are that the book was published as a publicity stunt with great fanfare at the Smithsonian in Washington, and that there was insufficient evidence for many of the variables used in the model. According to Wallich, "the quantitative content of the model comes from the authors' imagination, although they never reveal the equations that they used." Considering that the detailed model and Meadows' et al. justifications were not published until 1974 (two years after The Limits to Growth) in the book Dynamics of Growth in a Finite World, Wallich's complaint about "the peculiar presentation of their work and by their unscientific procedures" had merit at the time.

Similar criticisms were made by others. Robert M. Solow from MIT, complained about the weak base of data on which The Limits to Growths predictions were made (Newsweek, March 13, 1972, page 103). Dr. Allen Kneese and Dr. Ronald Riker of Resources for the Future (RFF) stated:

"The authors load their case by letting some things grow exponentially and others not. Population, capital and pollution grow exponentially in all models, but technologies for expanding resources and controlling pollution are permitted to grow, if at all, only in discrete increments."

Writing for the Michigan Law Review, Alex Kozinski, a United States judge appointed by Ronald Reagan, discussed The Limits to Growth at length at the beginning of his review of The Skeptical Environmentalist, calling the authors 'a group of scientists going by the pretentious name "The Club of Rome"'.

As described in the exponential reserve index section, it is claimed that The Limits to Growth predicted oil running out in 1992 among other natural resources. It came out that this conclusion was claimed to be in the book by Richard Bailey, who found this figure in a scenario table, dedicated to a very particular variable configuration. The book's real conclusion was that it was very unlikely that resources would end in 1992. The 1992 date was extrapolated out of context by critics dedicated to demolish "Limits" work, and is still present in common knowledge.

It should be noted, that the authors of the report accepted that the then-known resources of minerals and energy could, and would, grow in the future, and consumption growth rates could also decline. The theoretical expiry time for each resource would therefore need to be updated as new discoveries, technologies and trends came to light. To overcome this uncertainty, they offered an upper value for the expiry time, calculated as if the known resources were multiplied by two. Even in that case, assuming continuation of the average rate of consumption growth, virtually all major minerals and energy resources would expire within 100 years of publication (i.e., by 2070). Even if reserves were two times larger than expected, ongoing growth in the consumption rate would still lead to the relatively rapid exhaustion of those reserves. On the other hand, reserves may continue to grow, considering the large amounts of minerals in the planet Earth.

In 1976, Gerard O'Neill, published The High Frontier: Human Colonies in Space which proposed to sidestep the near term limits described by the Limits to Growth by developing use of non-terrestrial materials through practices like asteroid mining. That approach never got serious consideration by policy analysts in Western countries-where is was largely assumed that if NASA projects couldn't achieve the hoped for economies of launch systems, it couldn't be done. In Japan, development of non-terrestrial materials is still regarded as potentially important-that sentiment behind initiatives such as the recent proposals to develop a space elevator.

Expansion of Recycling is sometimes proposed as another means around the problems described in The Limits to Growth. This was developed a theme by Eric Drexler in Engines of Creation.

In 2008 researcher Peter A. Victor wrote, that even though D.H. Meadows et al. probably paid too little attention for price-mechanism's role in adjusting, their critics have paid too little. He states that Limits to Growth has had a huge impact on how we still think about environmental issues and notes that the models in the book were meant to taken as predictions "only in the most limited sense of the word" as they wrote.