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The World model

In the end of the 1950ies, Jay Wright Forrester suggested a sort of graphical user interface for the simulation of interactions between objects in dynamic systems, called Systems Dynamics. He further developed and applied this method in his books Industrial Dynamics (1961) and Urban Dynamics (1969), which sparked debates on the feasibility of modeling social, economic and ecological problems in an even broader context. In consequence, in 1971 he published the book World Dynamics containing the first so called World model, dealing with complex interactions of the economy, the population and the ecology of the World. 

Commissioned by the Club of Rome and founded by the Volkswagen Foundation in 1972, students of Forrester, among them Donella and Dennis Meadows, published the highly influential book Limits to Growth, which also bases its insights on the simulations of Forrester's  World model. This first World model was relatively simple and mainly interested in possibilities to analytically grasp the broad behavior modes of population-resource-capital interactions. However, the book had enormous impact and so had its methodology (see here for one review).

Meadows D., Meadows D.l., Randers J., Behrens W. (1972). The Limits to Growth. A Report to The Club of Rome's Project on the Predicament of Mankind, New American Library. Universe Books.

The model considers the interaction of three large spheres of dynamics, summarized as "Population Food", "Capital Quality of Life" and "Pollution Resources" in a time span from the year 1900 to 2100. It builds on about 250 equations, using the methods of causal loop diagrams and of stock and flow analysis, allowing to test different scenarios based on different assumptions about availability of resources and rates of population growth and consumption. The following image depicts the model's Population & Food sphere and in the plots to the the right corresponding predictions about the development of population and food resources up to the year 2100. A version of the model, from which this diagram is taken, can be found in the model library of Vensim-PLE (most probably in the folder: ...\Vensim\help\models\Sample\EXTRA).

World model 1

One important new approach in the model was the notion of exponential (instead of static) reserves, considering reserves in their dynamics, that is, as changing and not as static entities. For example, if the known reserves of any resource would be 100 million metric tons of which 2 millions are mined annually, the simple calculation of \(\frac{100}{2}\) yields a static index of resources lasting for 50 years. If however, the rate of consumption grows with 2% annually (mining increases with 2% each year), the resource would instead last for \(\frac{ln(0.02*\frac{100}{2} + 1)}{0.02}=34.56\) years only. This method hence does not consider constant usage, but constant growth rates of usage (which of course do not need to be constant all the time in their turn).

The model was heavily criticized at the time, but overly important for the further development of the methodology of Systems Dynamics and of systems sciences in general. Several improvements and upgrades for the model were suggested, such as the World2 and World3 models by Forrester and his team mates, the Mesarovic/Pestel Model, the Bariloche Model, the MOIRA Model, the SARU Model, the FUGI Model or the UN World Model. As a consequence, the models became increasingly complex considering more and more interacting dynamics. The 1975 World model by Mihailo Mesarovíć and Eduard Pestel ("Menschheit am Wendepunkt", 1974) for instance, considered already more then 100000 equations, several subsystems, and 10 different World regions.

The World3 model of 2003

Repeatedly, the team of Forrester suggested updates for the World model. In 2003, a model was suggested as a 30-Year Update to the one used in Limits to Growth. This model is known as the World3-2003 model and also included in Vensim's model library (at ...\Vensim\help\models\Sample\WRLD3-03). The following plot shows an output scenario from this model.

World model 3

An online-javascript implementation, generated by Brian Hayes, can be tested here

Meadows D., Meadows D.l., Randers J., et al. (2004). The Limits to Growth: The 30-Year Update. Chelsea Green Publishing Company

Turner, G. (2008). "A comparison of the Limits to Growth with 30 years of reality". Global Environmental Change 18 (3): 397–411.