Dynamic decentralization of harvesting constraints in the management of tychastic evolution of renewable resources

This study proposes a new framework to tackle the uncertainty that prevails in the exploitation of renewable resources. It deals with the question of how to guarantee both a minimum multi‐species harvest and the renewal of resources when their evolutions are uncertain. The problem is twofold: to decentralize a global constraint (on a multi‐species harvest) into local constraints (on the resources of the different species) and, then, to use a ‘tychastic’ approach necessitating only the forecasts of the lowers bounds of the resource growth rates. This study, formulated as a ‘tychastic’ regulated system with viability constraints, departs from stochastic approaches generally used to deal with uncertain situations. It provides the time dependent harvesting rule allowing to always comply with a minimum harvest objective and resources replenishment thresholds whatever happens and a tychastic measure of risk viability in terms of minimum resources initially required. To solve this problem involving global and local constraints a new method that decentralizes the constraints has been devised. An example is presented whose numerical results are obtained thanks to a dedicated software using mathematical and algorithmic tools of viability theory.