We study the optimal sustainable
harvesting of a population that lives in a random environment. The
novelty of our setting is that we maximize the asymptotic
harvesting yield, both in an expected value and almost sure sense, for a
large class of harvesting strategies and unstructured population
models. We prove under relatively weak assumptions
that there exists a unique optimal harvesting strategy characterized by
an optimal threshold below which the population is maintained at all
times by utilizing a local time push-type policy. We also discuss,
through Abelian limits, how our results are related to the optimal
harvesting strategies when one maximizes the expected cumulative present
value of the harvesting yield and establish a simple connection and
ordering between the values and optimal boundaries. Finally, we
explicitly characterize the optimal harvesting strategies in two
different cases, one of which is the celebrated stochastic Verhulst
Pearl logistic model of population growth.