Robust Viable Analysis of a Harvested Ecosystem Model

The World Summit on Sustainable Development (Johannesburg, 2002) encouraged the adoption of an ecosystem approach. In this perspective, we propose a theoretical management framework that deals jointly with three issues: (i) ecosystem dynamics, (ii) conflicting issues of production and preservation, and (iii) robustness with respect to dynamics uncertainties. We consider a discrete-time two-species dynamic model, where states are biomasses and where two controls act as harvesting efforts of each species. Uncertainties take the form of disturbances affecting each species growth factors and are assumed to take their values in a known given set. We define the robust viability kernel as the set of initial species biomasses such that at least one harvesting strategy guarantees minimal production and preservation levels for all times, whatever the uncertainties. We apply our approach to the anchovy-hake couple in the Peruvian upwelling ecosystem. We find that accounting for uncertainty sensibly shrinks the deterministic viability kernel (without uncertainties). We comment on the management implications of comparing robust viability kernels (with uncertainties) and the deterministic one (without uncertainties).