On the set of robust sustainable thresholds

In natural resource management, or more generally in the study of sustainability issues, the objective often consists of maintaining the state of a given system within a desirable configuration, typically established in terms of standards or thresholds. For instance, in fisheries management, the procedure for designing policies may include maintaining the spawning stock biomass over a precautionary threshold and ensuring minimal catches. With the evolution of some natural resources, under the action of controls and uncertainties, being represented by a dynamical system in discrete time, the aim of this paper is to characterize the set of robust sustainable thresholds. That is, the thresholds for which there exists a trajectory satisfying, for all possible uncertainty scenarios, prescribed constraints parametrized by such thresholds. This set provides useful information to users and decision-makers, illustrating the tradeoffs between constraints. Using optimal control, maximin and level-set approaches, we characterize the weak Pareto front of the set of robust sustainable thresholds and derive a numerical method for computing the entire set, as we show with a numerical example relying on renewable resource management. Recommandation for Resource Managers For biological, ecological or social systems, identifying robust sustainable thresholds that it is possible not to exceed over time regardless of uncertain future scenarios, is a fundamental challenge to operate in a sustainable way. The set of robust sustainable thresholds provides useful information to users and decision-makers, illustrating the tradeoffs between constraints. The computation of the weak-Pareto front of the set of sustainable thresholds provides a tool for the management and visualization of multiple objectives related to sustainability that can be accomplished in a robust manner, allowing to observe the (in)compatibility of multiple objectives and their tradeoffs.