If two species are using a common source of food, which is in short supply, the growth of one may deprive the other of its source of food. See Figure III-4a. Under some conditions the species that grows faster causes the other population to die out as in figure III-4b. This process is called competitive exclusion. For other values of their growth coefficients, the two species may coexist without competitive exclusion.

Whereas Figure III-4b shows the population numbers with the passage of time, Figure III-4c plots the numbers of one population as a function of the other. At first both populations increase. Then as population Q grows further, population Q2 decreases to zero.

Examples

An ecological example of competitive exclusion is competition between two species of grain beetles in a jar, which is supplied some grain each day. If a few of either species are put into the jar alone, the number of beetles increases up to a steady level as in the Logistic example (Figure III-2). However, if a few of both species are put into the jar together, they both increase at first, but soon the more efficient species consumes more of the food and the other species dies out.

An example from business is competition between two timber companies developing on a limited area of growing trees. The one that is more efficient with more production may drive the other out of business.

"What if" Experiments

1. Determine what happens if the two populations start with the same initial numbers, but one has a slightly higher growth rate. See the result in Figure III-4b and c. What is the effect of decreasing mortality rates (K3 or K4)?
   


2. Suppose one population has cooperative interactions represented by quadratic use as discussed in Section 4.3. Revise two lines in the program EXCLUS to read:
   130 R = I / (1 + K8 * Q * Q + K2* Q2)
   150 D1 = K7 * R * Q * Q - K3 * Q
   Can you explain the result?
   


3. By varying the growth rate and decay rate coefficients, can you find a set of coefficient values, which allows for coexistence?

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