This is a model of daily production and consumption (Figure II-8). A common example is the photosynthesis and respiration in a forest. The sunlight (J) increases and then decreases each day, with none coming to earth at night.

The nutrients (N) are used up by the photosynthesis in the daytime and released by respiration at night. The quantity of organic matter (Q) produced goes up with photosynthesis in the daytime and down as it is consumed by respiration at night. Q could also represent oxygen, which is produced by photosynthesis and used by respiration.

It is important to realize that respiration is occurring both day and night. In the daytime the quantities of organic matter and oxygen produced by photosynthesis are greater than those used in respiration; at night respiration uses organic-matter and oxygen. In most plants there are excess organic matter and oxygen available to animal consumers.

In Figure II-8b the top section shows the daily variation of the sun, the second the nutrients and the bottom the organic matter.

A sine wave is used for the sunlight input for each day. The sine wave puts into the program an increasing and then decreasing quantity (J), in a pattern very close to the sun's regular daily increasing and decreasing of light. The equation for J is a sine wave which goes up and down from the zero line in 12 hours:

J = 40 * SIN (T/15.9)

We cut off the next 12 hours of the sine wave which would be negative. The equation says, if the sunlight (J) is less than zero then it is zero:

IF J < 0 THEN J = 0

In this model total nutrients in the forest system is TN. N is the nutrients in the soil available for photosynthesis. K3 is the proportion of the organic matter that is nutrients. Organic matter in the forest consists of the organic matter in the living and dead trees (including roots), plants, and animals. The amount of inorganic nutrient chemicals, which are part of that organic matter, is K3*Q. Therefore, the nutrients in the soil (N) are the total nutrients (TN) minus the nutrients that are part of the dead and living components of the forest. The equation is:

N - TN - K3*N

The change in organic matter (DQ) is the increase in organic matter by photosynthesis minus the decrease by respiration. Photosynthesis is proportional to the available sunlight (JR) and the soil nutrients (N): (Kl*JR*N). Respiration is proportional to the quantity of living and dead matter in the forest (K2*Q). Therefore, the equation is:

DQ - KI*JR*N K2*Q

You get a graph (Figure II-8b) when you run the program. The daily variation, dependent on the sun, is striking.

Examples of Models of Production and Consumption

This is an accurate model for any natural ecosystem: the plants and animals in a pond or the ocean where the nutrients are dissolved in the water, a coral reef where most of the photosynthesis is in the coral algae, and even in a tiny drop of water in antarctic ice.

It is also a model for a self-sufficient economic system with the time seasons or years. Goods are built up, used, and then the broken pieces and wastes are recycled into new goods. If this were a primitive economy, the energy source would be the seasonal sun and rain. If it is a modern island economy, it could be dependent on intermittent ship deliveries of oil to stimulate its production. Since this system has no inflow or outflow of materials, it is not a model for an economy which imports and exports.

"What if" Experiments

1. How would the growth of the forest be different if acid rain reduced the total available nutrients? Decide how you think the graph of Q and N would change. What will you change in the program to decrease the total nutrients? Try it and see if your prediction was right.
   


2. What will happen to the economy dependent on oil if the fuel tankers brought in 25% more fuel at each delivery? Change and run the program to see.
   


3. If this system was a pond with algae and small fish, what would the changes be if you started with a larger consumer fish? Try doubling the proportion of Q eaten by consumers (K2). How would this change the quantity of algae (Q) and the available nutrients in the water (N)?

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