3. Competition of Two Populations in Exponential Growth (COMPETE)

There is a natural tendency for populations with unlimited food supplies to grow increasingly rapidly with exponential growth as we showed in Part II-1. As storage grows, the auto-catalytic feedback also grows accelerating growth.

In Figure III-3 two populations are shown, both growing from the same unlimited source. Even though resources are not in short supply, and even though there are no negative interactions, one population may become increasingly dominant. See Figure III-3b.

Some populations have individuals that work cooperatively in their production processes. Their growth is proportional to the interaction of its individuals. Its growth is proportional to the square of the population number. It is said to be "quadratically auto-catalytic”.


Examples of the rapid growth of populations on unlimited food resources are the early stages of growth of microorganisms in food, the growth of new plants when a field is abandoned, and the growth of new industries during human colonization of a new area.

Examples of the quadratic growth are the growth of fishes that school and birds that nest in colonies. The growth of the economy of the United states prior to 1973 was utocatalytically quadratic.

"What if" Experiments

  1. If the two populations have the same initial number of individuals, but the efficiency of growth is greater in one than the other, the first outdistances the other very rapidly as shown in Figure III-3b. Can you generate this result by setting the initial conditions for Ql and Q2 the same in lines 20 & 30 of the program and making the production coefficient larger? Did one population begin to outdistance the other?

  2. If the growth characteristics are the same, but one starts ahead of the other, it rapidly outdistances the one that starts out with fewer individuals (See the simulation run in Figure III-3b). Change the starting numbers for each population so that the other population starts out with more. How does the graph compare with that in Figure III-3b?

  3. To see the effect of having one population growth with quadratic feedback, substitute the following line:
    D1= K5 * R * Q * Q - K3 * Q
    Which population has the faster growth initially? Which one outdistances the other later?


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
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