The name is absent

and spread, including those where the invasion is governed by a non-convex biological growth function.
In particular, our model is consistent with invasions that follow a pattern of establishment, expansion,
and saturation as suggested by historical evidence.

Control of an invasive species takes the form of reducing the size of the invasion by chemical,
biological, manual, or other means. In this paper, control is an aggregate measure of the means used to
reduce the size of an invasion. Control costs are an increasing and convex function of the amount of
control. Control costs may also depend on the invasion size. The evidence from historical attempts to
eradicate invasive species indicates that it may cost as much to remove the last one to ten percent of an
invasion as it does to control the initial ninety to ninety-nine percent [Myers, et. al., 1998]. This means
that unit control costs can escalate as the size of an invasion is reduced and control costs may not be
jointly convex due to complementarities between the invasion size and control.

Together, control costs that depend on the invasion size and non-convex invasion growth have
important implications for the optimal control of an invasion. Under non-convex growth the optimal
amount of control may increase or decrease as the size of invasion grows, there may be multiplicities or
discontinuities in the optimal policy, and there are more likely to be corner solutions where there is no
control or complete eradication. When control costs depend on the invasion size an increase in the
current control has two opposing effects on future net benefits. It lowers future damages and it increases
future control costs. The latter creates an economic incentive to postpone control and can lead to
outcomes where the invasion follows a nonmonotonic time path under an optimal policy. The optimal
management of an invasion may exhibit cyclical or complex dynamics, as is the case when an invasion is
allowed to grow unchecked for a number of periods and only after it becomes large enough is it
controlled. When costs depend only on the amount of control, as with some forms of chemical control,
we show that the optimal invasion size is monotonic over time and convergent. If eradication is optimal
from one invasion size, it must necessarily be optimal for any invasion of a smaller size.

<<   3   4   5   6   7   8   9   >>

More intriguing information