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.