The slowly renewable mini-model has two units in series (Figure II­-5a).

Inflows from an outside source into the system may accumulate in the first storage, becoming a reserve, which next supplies resource for growth of other units. After a large reserve storage exists, suppose a consumer unit is connected and draws from the resource tank using the resource to grow. The consumer units growth starts out like the mini-model #1 Exponential Growth with accelerating growth.

Figure II-5b shows the way the quantities in the reserve tank and the consumer unit rise and fall if one starts with a large accumulated reserve before the consumer starts to grow. The feedback from the consumer storage to pump more input is sometimes called "auto catalytic growth". As the storage of consumer unit grows, it pumps more and more from the reserve tank.

Because of the accelerating pumping by the consumer unit, the storage in the reserve tank is reduced to a low level. Consequently further growth of the consumer is not possible because the input no longer exceeds the depreciation (draining pathway).

Unlike the exponential case, growth slows down. The consumer unit may decrease its storage to a lower level. The reserve storage still receives a slow inflow from a renewable source but it is used by the consumer unit as fast as it inflows. A balance develops between the inflow and the use by the consumer unit.

This model resembles somewhat #4, the Renewable and Non­renewable Growth model. In both there is an initial growth that cannot be supported in the long run.

Examples of Slowly Renewable Growth

The arrangement of a tank and an "auto catalytic" consumer unit is found in many kinds of geological, chemical, biological, and economic systems. This mini-model is not a bad representation of the way resources are supplying our high energy civilization. The reserve tank represents the great storages of coal, oil, natural gas, soil, wood, and minerals available a hundred years ago. We have been in steep accelerating growth using up these reserves and are now slowing in growth. If our economic system follows this oversimplified model, our civilization will have to be reduced in quantity to be supported on the continuing input of the renewable sources.

Another example is the populations of fishes and other aquatic animals in a reservoir behind a new dam that drowns a forest. All the dead organic matter from the decomposing trees supports a very high level of fishes for a few years, but later the populations are less, living only on the regular inflow of organic matter from the tributary stream and local photosynthesis.

Another example is a town that develops around the cutting of a virgin forest, but later has to live on the regular, renewable growth of replanted trees, cutting them about as fast as they grow.

"What if" Experiments

Make the following changes in the program:

1. What happens if the reserve tank is initially zero? Change statement to E = 0. How does the quantity of consumer compare with the run with large initial reserve?
   


2. The level attained by the consumer in the long run is its "carrying capacity." What would happen to the carrying capacity if the regular inflow were doubled? Change to J = 4.
   


3. What would happen if there were no inflow? J = 0. Which minimodel already studied does this alternative resemble?

COMPUTER MINIMODELS AND SIMULATION EXERCISES FOR SCIENCE AND SOCIAL STUDIES

Howard T. Odum* and Elisabeth C. Odum+
* Dept. of Environmental Engineering Sciences, UF
+ Santa Fe Community College, Gainesville

Center for Environmental Policy, 424 Black Hall
University of Florida, Gainesville, FL, 32611
Copyright 1994

Autorização concedida gentilmente pelos autores para publicação na Internet
Laboratório de Engenharia Ecológica e Informática Aplicada - LEIA - Unicamp
Enrique Ortega
Mileine Furlanetti de Lima Zanghetin
Campinas, SP, 20 de julho de 2007