where r is the discount rate for the project. The summation over AWs+t in Eq. (3) is the value associated with keeping alive the option of being able to use existing uncollected PGRFA that would be lost without the investment plus the value of new PGRFA that are developed due to the investment.

Eq. (3) can be maximized in a discrete time current value Hamiltonian framework that accounts for the uncertainty and irreversibility effects. Given 1 ..., J in situ conservation regions, maximizing the equation with

respect to Ij, subject to a budget constraint,-^

/(I + r)' <1, produces the first-order condition for the marginal value of incremental increase in conservation expenditures

T-s-t dNW V 1 dA w, t+s+k dl*jt k=0 (1 +r)t+s+k dAJt

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