A stock rebuilding algorithm featuring risk assessment and an optimization strategy of single or multispecies fisheries

Gröger, J. P., Rountree, R. A., Missong, M., and Rätz, H-J. 2007. A stock rebuilding algorithm featuring risk assessment and an optimization strategy of single or multispecies fisheries. – ICES Journal of Marine Science, 64: 1101–1115. We present a simple but flexible stock-rebuilding algorithm model that features ideas of risk assessment, with all constraints set up explicitly, and with clear optimality for controlling fishing effort (or fishing mortality) and maximizing landings (or economic value). In contrast to the conventional approach, our approach does not predict future stock development from historical stock dynamics, but provides directly optimal annual F values and associated optimum catch quotas for a given planning horizon. Hence, the F values are not estimated retrospectively, but are realizations of a control variable created through the optimization process. The optimal solution is based on maximization of a non-linearly constrained objective function for catch or yield, whereas the constraints inter alia include biomass targets, F limits, and stable catch. We present the basic theory together with selected model variants, such as inclusion of biological interactions and integration of elements of risk assessment. The optimization procedure outlined here is not only “risk averse” but a risk minimization procedure in itself. It can be applied in a deterministic or stochastic decision-making process as well as within a single or multispecies context. We illustrate the approach with a simplified (deterministic) multispecies fisheries management and a (stochastic) single-species risk assessment example.