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is to figure out what that strategy is and how it operates. We are able to show that
some plants act as though they know when to optimally switch from vegetation
to seed production
2
. Here we assume that insects might employ a similar kind of
optimal strategy in switching egg maturation times to maximize the number of eggs
produced.
Consider two forms of a particular insect whose life cycle was described in
Chapter 3.1: EGGS and ADULTS. As before, let them each have an experimen-
tal survival fraction and an average maturation time and let the ADULTS have a
particular egg-laying rate. Start the model with no adults and 50 eggs. Now suppose
that the life span of these adults was only 24 days and suppose that they could some-
how adjust the egg average maturation time. Think of the insect species as originally
having a variety of maturation rate responses to a given temperature. Assume that
the most successful insect subspecies is the one whose average egg maturation time
maximizes the number of eggs at the end of the 24-day adult life period. What is
this optimum average egg maturation time?
We set up a sensitivity analysis and vary T to find the largest egg clutch in 24
days. The optimal average egg maturation time for our imagined insect species is
1.54 days (unrealistically short, except perhaps for certain mosquito species), as
one can find in the table with the actual model. That such an optimal T exists for
this model when the remaining parameters are fixed leads us to ask if that species
has evolved to an optimal T. We would be assuming that the model structure was
accurate and that the parameters were accurately measured. If not, then our model
could be wrong or the insect might have another goal. In any case, it should be clear
that such a model allows us to address very interesting questions about the insect,
questions that could not be framed without such modeling.
Still another value of the average maturation time may someday be found in a
model. Suppose that an insect was a link in a disease transmission. We could study
the effect of introducing genetically modified insects such that the disease link is
broken by extended or shortened average maturation time. In this way, the modified
insect would occupy the critical ecological niche but produce an under- or over-
supply of eggs, restricting the spread of the disease.
3.3 Two-Age Class Parasite Model
Now that we have modeled in more detail the dynamics of an insect population,
let us turn to the spread of disease within different cohorts of an insect popula-
tion, such as asexually reproducing aphids, consisting of two life stages—nymphs
2
Cohen, D. 1971. Maximizing final yield when growth is limited by time or by limiting resources,
J. Theo. Biol.
33, 299-307.
Chiariello, N. and J. Roughgarden. 1984. Storage allocation in seasonal races of an annual
plant: optimal vs. actual allocation,
Ecology
65-4, 1290-1301.
Kozlowski, J. and R. Wiegert. 1986. Optimal allocation of energy to growth and reproduction,
Theo. Pop. Biol. 29, 16-37.
Hannon, B. 1993. The optimal growth of Helianthus Annus, J. Theo. Biol. 165, 523-531.
