The name is absent

marginal costs of control, or the marginal costs of control evaluated at their limiting values of a = 0 and y

= 0. Similarly, damages increase exponentially with the size of the invasion that remains at the end of

the period, and γ represents intrinsic marginal damages, or marginal damages from an incrementally
β. Hence, the optimal policy governing the invasion size is monotone if a > β, while if β > a the optimal
invasion size is governed by a decreasing policy on the interior of Ω. Table 1 summarizes the conditions
for eradication or noneradication, given exponential cost and damage functions and any invasion growth
function satisfying A.1-A.5.

The condition for both the Corollary to Proposition 1 and Proposition 2 is independent of β so it
is essentially the same condition that applies if control costs are independent of the invasion size.
Further, the condition applies regardless of whether a > β or β > a. This means that in the case of
exponential costs and damages, the efficiency of eradicating small invasions does not depend on the
monotonicity of the optimal policy.

It is relatively straightforward to extend these results to other cost and damage functions. For
example, what is important in most of the results are the marginal damages from an arbitrarily small
invasion (either directly or because D_x(0) is a lower bound on marginal damages from larger invasions).
In Table 1, the conditions for Propositions 1, 2, 4, 5.a and 6 apply much more generally to any convex
damage function where D_x(0) = , including the case of linear damages, D(x) = x.

7. Conclusion

The results of this paper can provide the foundation for both a normative and a positive analysis
of invasive species control. For example, they may help explain why some observed efforts to control
invasive species involve a repeated process where periods of inaction are followed by intervals of

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