  We consider the problem of optimal singular control of a stochastic partial
differential equation (SPDE) with space-mean dependence. Such systems are
proposed as models for population growth in a random environment. We obtain
sufficient and necessary maximum principles for such control problems. The
corresponding adjoint equation is a reflected backward stochastic partial
differential equation (BSPDE) with space-mean dependence. We prove existence
and uniqueness results for such equations. As an application we study optimal
harvesting from a population modelled as an SPDE with space-mean dependence.
