Where are we headed? Mark Lewis Baldwin.

Where Are We Headed?

The world population has been growing exponentially for as long as history has been recorded. Without constraint, it would continue to do so, but there are constraints on our world system. There are limited amounts of land, food, and other natural resources. Even now, as we approach these limits, the world population shows signs of breaking its growth trends.

Jay W. Forrester presented this concept to the world over ten years ago in his book World Dynamics. He described a world dynamics computer model which predicted the breakdown of the growth patterns and showed how a breakdown in certain cases could be catastrophic. The implications of this model were further explored in the better known work Limits to Growth.

The world dynamics model was originally written in Dynamo by Dr. Forrester at MIT. The entire computer model has now been written in Atari Basic, so that anyone may experiment with the capabilities of the model.

Dr. Forrester's model treats the world as a closed continuous system, and models each important parameter in the system. Variables which measure levels, sometimes known as state variables, in this model include population (P), natural resources (NR), capital investment (CI), pollution (POL) and the fraction of capital devoted to agriculture (CIAF).

Each of these state variables affects the change of the other state variables through a set of relationships. It is the definition of these relationships which reflects both the accuracy of the model and its actions. Small changes in a relationship between two states could cause vast changes in the action of the model.

Let us examine a small portion of the model. The population of the earth is affected directly by two factors, the death rate and the birth rate. If we were modeling a smaller system such as a country, we would also have to include immigration and emigration.

The birth rate in the world is approximately 4 percent per year. In the model, this value is BRN for Birth Rate Normal. Likewise, the death rate (DRN) is at 2 percent. These rates are approximations based on the year 1970 and include the entire world, not just the United States.

If these rates stayed the same, we would be able by simple integration to predict the world population at any future time, but these rates vary for many reasons. If the available food (Food Ratio, FR) decreases, the death rate varies in some inverse proportion until no food at which point the death rate becomes 100 percent. On the other hand, if an infinite food supply is available, the death rate does not drop to zero but asymptotically approaches some value that it less than what currently exists today.

Figure 1 shows the relationship between food and death rate incorporated into the model. This table appears on line 8290 in the program. Other factors which influence the death rate include crowding (CR), pollution (POLR), and the material standard of living (MSL). All of the other rates in the model are controlled by the same types of considerations.

The model then integrates the values over time and we have our world simulation. The Basic version uses only a first order integration scheme with a step size of one year. Better integration schemes could be used but it seemed impractical considering the original approximations in the model.

What happens when we incorporate all of these factors? Figure 2 is a plot produced on an Atari showing some of the important variables and how they change with time. Variable values plotted include population, pollution, capital investment, food, natural resources, and the quality of life.

If the model is accurate, it shows that if the world continues on its current path, the population will peak in the year 2020. At the same time, the quality of life (Q) will decrease significantly. One of the important detrimental factors will be a large scale increase in pollution and a drop in natural resources (NR).

Can we do something about this? One of the most common suggestions is to control the birth rate. This is simple to test by inserting the following statement: 1495 IF TIME>1980 THEN BRN=.03

What we have done is decrease the birth rate by 25 percent to 3 percent starting in 1980. Figure 3 shows the results of this experiment. The change in birth rate helped some temporarily, but in the long run seemed to have little effect.

What else we try? Well, the government is always asking us to conserve our resources. Let's try cutting the consumption of natural resources by 75 percent. This is easily done by adding the following line:

1495 IF TIME> 1980 THEN NRUN= .25

Look at Figure 4 for the results. A policy of reducing natural resource usage alone could be catastrophic to the world, by the year 2060, cutting our population by 80 percent. Here is an example of an obvious solution doing the opposite of what anyone would expect. Thought and analysis need to go into the decisions made by our world leaders.

That is where this model and more detailed variations of it are important. It allows us to examine and experiment with systems which are complex in nature without destroying what we are testing. That is the real value of any computer model. The Basic program is shown in Listing 1. Table 1 lists all of the variables. For simplicity, the variable names are the same as those used in the original model.

Four of the subroutines in the program are specific to the Atari as they enable the computer to plot the results. Subroutine 10000 initializes the plotting routine for the screen while 12000 does the same for an Epson MX-80 printer. Routines 11000 and 13000 plot the data on the screen and printer respectively.

The rest of the program should be easily translatable into other Basics, so you need only write your own output routines.

A large number of simplifications and assumptions were required in the original model. Although there has been a great deal of argument in academic circles about the accuracy of Forrester's model, it is a first attempt at solving and describing a complex system, and it does provide some insights into the problem.

Don't just run the program, experiment with it. Vary the parameters and see what you can do with the world in your computer.

References

Forrester, Jay W., World Dynamics (Cambridge: Wright-Allen Press, 1971).

Meadows, Donella H.; Meadows, Dennis L.; Randers, Jorgen; and Behrens, William W. III, The Limits To Growth, A Report For The Club Of Romes Project On The Predicament Of Mankind (New York; Universe Books, 1972).

Table: Figure 1. Death-rate-from-food multiplier vs. food ratio.

Table: Figure 2. The world on its current path.

Table: Figure 3. The world with a 25% reduction in birth rate.

Table: Figure 4. The world with a 75% reduction in the usage of natural resources.

Table: Micro-World Dynamics Variables

Table: