Viable harvest of monotone bioeconomic models

Some monospecies age class models, as well as specific multi-species models (with so-called technical interactions), exhibit useful monotonicity properties. This paper deals with discrete time monotone bioeconomic dynamics in the presence of state and control constraints. In practice, these latter " acceptable configurations " represent production and preservation requirements to be satisfied for all time, and they also possess monotonicity properties. A state x is said to belong to the viability kernel if there exists a trajectory, of states and controls, starting from x and satisfying the constraints. Under monotonicity assumptions, we present upper and lower estimates of the viability kernel. This helps delineating domains where a viable management is possible. Numerical examples, in the context of fisheries management, for the Chilean sea bass (Dissostichus eleginoides) and Alfonsino (Beryx splendens) are given.