Sustainable management of fisheries: an illustration of viability concepts and methods

Indicators and their associated reference points are key elements of current fisheries management advice, as well as of the developing ecosystem approach to it, especially in the International Council for the Exploration of the Sea precautionary approach. However, although sustainable management is claimed to be a guide for decision making, no general and long term objectives are explicitely stated. In this talk, we show how viability may help both giving a framework for setting decision making, and computing operational policies. We define ``desirable configurations of the system'' as a set of sustainable objectives (een ecologic, economic and/or sociologic requirements. Formulating the problem as one of control of nonlinear systems in the presence of state and control constraints for discrete time dynamics, the viability kernel is known to play a basic role for the analysis of such problems and the design of viable control feedbacks. Unfortunately, this kernel may display very non regular geometry and its computation is not an easy task in general. We show how monotonic properties of both dynamics and constraints allow for relevant analytical upper and lower approximations of the viability kernel through weakly and strongly invariant sets. Computations are performed, using scientific software Scilab, to test viability of current practices and to propose others. In particular, we examine how an economic requirement of minimal yearly fish yield could be incorporated in the International Council for the Exploration of the Sea precautionary approach.