We consider sustainable management issues formulated within the framework of
control theory. The problem is one of controlling a discrete--time dynamical
system (e.g. population model) in the presence of state and control
constraints, representing conflicting economic and ecological issues for
instance. The viability kernel is known to play a basic role for the analysis
of such problems and the design of viable control feedbacks, but its
computation is not an easy task in general. We study the viability of nonlinear
generic ecosystem models under preservation and production constraints. Under
simple conditions on the growth rates at the boundary constraints, we provide
an explicit description of the viability kernel. A numerical illustration is
given for the hake--anchovy couple in the Peruvian upwelling ecosystem
