If a population of microbes grows on a constant-pressure source, it increases exponentially, as in model II-1. But, if the death rate is increased because of more interactions and crowding which cause stress and toxicity, then the population levels off. Even though there is all de the nutrients the microbes can use, crowding causes increased deaths until the deaths equal the births and the population reaches a steady state.

In the diagram (Figure III-2) the outflow is proportional to times Q (K4*Q*Q). This is called a self-interactive or quadratic drain.

Examples of Logistic Growth Models

An example is an experiment with mice. Several males and females were put into a large cage with sawdust and nesting sites and constantly-available food and water. They ate and ran, and reproduced exponentially. After several months the researchers noticed that some of the females were no longer producing babies and some of those who did moved their babies from place to place until they died. The population leveled. The cage did not look full, but the mice were responding to crowding.

This may also true of populations of people, especially in cities. Think of New York, Miami, and Cairo. Population grows exponentially until crowding of houses, streets and cars to increase the negative factors of dirt, noise, crime and pollution. The more the population builds up, the greater the negatives until people move out and the growth of the city levels off.

"What if" Experimental Problems

1. In the example of the city, what would happen if you increased E: start with a greater availability of food, electricity, and housing? Does the population grow faster, at the same rate, or slower? Does it level at the same size? Does it take longer or less time to level? Why? Change E to 3 and run the graph again.
   


2. If you put many more mice in the cage at the beginning of your experiment, would they all survive or would the population decrease?
   Try starting with Q = 160.
   


3. If you tried the mice experiment with another species, which was less sensitive to crowding, which variable would you change? How would that affect the final population level?

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