use the results to compute the net reproductive rate, the mean length of a
generation, and the growth rate. Is the growth rate what you would expect?
14.12. For a carrying capacity K, what population, N, would result in a specific growth
rate that is one-half of the max imum?
14.13. Both the logistic equation and the Monod model produce sigmoidal growth curves.
(a) Why do we not use the logistic model for microorganism growth in wastewater
treatment plants? (b) Conversely, why not use the Monod model for ecological
population modeling?
14.14. (a) How many possible pairwise interactions are there among nine species? (b)If
each species has, on average, only two interactions, how many interactions will
there be in this case?
14.15. As of the year 2005, the human population exceeds 6 billion people vs. 3.5 billion
in 1950 and 1.6 billion at the start of the twentieth century. Find the values of r and
K that make the logistic equation fit these data. According to this, what is the
carrying capacity of Earth? How does this compare with the estimates given in the
text? What are possible explanations for the discrepancy?
14.16. In the Lo tka–Volterra predator–prey model, the period of the oscillations depends
on the initial conditions. But in the vicinity of the steady-state solution given in
Section 14.4.1, it approaches 2pðadÞ
1=2
. Thus, a decrease in the host growth rate
or the predator death rate would increase the period. Can you explain in words
why this is so?
14.17. Suppose that someone were to enter a large temperate-zone hardwood forest and
harvest all of the trees in a 100-ft circle. Describe the changes that might occur at
the site if it were left undisturbed for the next 100 years.
14.18. Compute the Simpson and Shannon–Weaver diversity indices and Pielou’s
evenness index for a community consisting of four species that each comprises
one-eighth of the organisms and a fifth species that comprises the other 50%.
Which species distribution in Table 14.9 does this community mos t resemble?
REFERENCES
Berner, E. K., and R. A. Berner, 1987. The Global Water Cycle: Geochemistry and Environment,
Prentice Hall, Englewood Cliffs, NJ.
Brown, L., C. Flavin, H. French, et al,, 1997. State of the World 1997, W.W. Norton, New York.
Krebs, C. J., 1994. Ecology, HarperCollins, New York.
Mattson, C. P., and N. C. Vallario, 1975. Hackensack Meadowlands Development Commission report.
Murray, J. D., 1993, Mathematical Biology, Springer-Verlag, New York.
Odum, E. P., 1987. Basic Ecology, Saunders College Publishing.
Odum, E. P., 1993. Ecology and Our Endangered Life-Support Systems, Sinauer Associates,
Sunderland, MA.
Prigogine, Ilya, 1972. Introduction to Nonequilibrium Thermodynamics Wiley, New York.
Prigogine, Ilya, 1978. Time structure and fluctuations, Science, Vol. 201, pp. 777–785.
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