An efficient algorithm for Nash equilibria when harvesting interacting living resources

Natural ecological communities exhibit complex mixtures of interspecific biological interactions, which makes finding optimal yet sustainable exploitation rates challenging. Most fisheries management advice is at present based on applying the Maximum Sustainable Yield (MSY) target to each species in a community by modelling it as if it was a monoculture. Such application of single-species MSY policies to strongly interacting populations can result in tragic overexploitation. However, the idea of "maximising the yield from each species separately" can be extended to take into account species interactions using a multispecies or ecosystem model and determining a Nash Equilibrium (NE), where the yields of each species taken in isolation are simultaneously maximised. Here we present nash, an R package that streamlines the computation of NE reference points for fisheries and other systems represented by a user-defined multispecies or ecosystem model. We present two real-world fisheries management applications alongside performance benchmarks. Satisfactorily search results are shown across models with an approximate factor 15 increase in performance when compared to the expensive round-robbing sequential optimisation algorithms used by other authors in the literature. We believe that the nash package can play an instrumental role in fully implementing ecosystem-based management policies worldwide. Open Research statementThis submission uses novel code, which is provided, per our requirements, in an external repository to be evaluated during the peer review process via the following link https://github.com/ThomasDelSantoONeill/nash