A limiting factor flow may be one from outside the system as in Figure II-6. Such systems have limitations in the external source. Other limiting factor flows may come from within a system. In the production-­consumption system there is a recycle of materials that are required for the production process. If the recycle process is too slow, it can limit the production process so that an increase in factor I has a diminishing return.

Figure II-7 has the diagram and equations for simulating production as a function of the amount of material that is available to recycle. In this system TN is total nutrients and F*Q is nutrient in Q. F is the fraction of Q that is nutrient.

The simulation graph shown in Figure II-7b shows how production increases with increased I but with diminishing returns as I is increased further. Here the limit is in the recycle of the materials N regenerated from Q to the site available to production.

Examples of Recycle Limiting Factors

The recycle of nutrients in a balanced aquarium is one example of internal limiting factors. Another is the recycle of chlorophyll from state ready to receive light after which it becomes charged and has to go through a dark process being recycled for use again. One of the first examples ever studied as a simulation model was the process of using an enzyme in biochemistry.

In Figure II-7a the enzyme is N and the input "substrate" with which the enzyme is reacting chemically is 1. In economic production, the recycle of aluminum cans may be a recycle limiting factor N with diminishing returns curve (Figure II-7b) when other inputs I are increased.

"What if" Experiments

1. What is the effect of increasing the total materials TN available for recycle?
   After the simulation has run one curve, type CONT. The program increases the total materials in the system, TN, and another run is made. With more materials in the system, limitation is less and a higher level of production is reached. Many systems accumulate materials until they are not limiting.
   


2. What is the effect of increasing the coefficient K2 (the percent of the storage Q recycled per unit time)?
   


3. Consider a natural system you know well. Wath do you think is usually the internal limiting factor?
   If this is taken care of, wath do you think will then become limiting? Explain

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