This paper examines conditions for extinction when the net benefits from a renewable resource are a nonlinear function of the harvest rate. As in the linear case, extinction depends on the size of the interest rate relative to the growth potential of the species. Here, however, the size of the initial resource stock is also crucial. It is shown that extinction is optimal if the interest rate is greater than the growth potential of the species, but only for small initial stocks. Indeed, if the initial stock is sufficiently high, extinction need not be optimal even if the interest rate is infinite.