Bent Hockey-Stick Stock-Recruitment Function

The hockey-stick is a simple and widely applicable stock–recruitment function. One drawback is its non-differentiability at the breakpoint, which can be especially problematic when using state-space models for stock assessment. Here, we develop a new bent hockey-stick model that retains the desirable properties of the original hockey-stick function while providing a differentiable breakpoint. We also propose a new algorithm for estimating MSY under multiplicative process stochasticity in the stock–recruitment relationship. Simulation studies demonstrate the utility of these approaches, which can substantially enhance the robustness and sustainability of fisheries management.