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We derive the explicit solutions to singular stochastic control problems ofthe monotone follower type with (a) an expected discounted criterion, (b) anexpected ergodic criterion and (c) a pathwise ergodic criterion. These problemshave been motivated by the optimal sustainable exploitation of an ecosystem,such as a natural fishery. Under general assumptions on the diffusioncoefficients, the discounting rate function, the running payoff function andthe marginal profit of control action, we show that the optimal strategies areof a threshold type. We solve the three problems by first constructing suitablesolutions to their associated HJB equations, which take the form ofquasi-variational inequalities with gradient constraints. In the cases of theergodic control problems, we also use a suitable new variational argument.Furthermore, we establish the convergence of the solution of the discountedcontrol problem to the one of the ergodic control problems as the discountingrate function tends to 0 in an Abelian sense.

Singular stochastic control problems motivated by the optimal sustainable exploitation of an ecosystem