A continuous hockey stick stock–recruit model for estimating MSY reference points

With political commitment to restore stocks to levels where they can produce maximum sustainable yield (MSY), fisheries managers request evaluations of management plans that include options for an FMSY policy. The procedure to estimate FMSY with dynamic-pool, stock assessment models is well established for common stock-recruitment relationships (S-RR). In this paper, we extend this capacity to another S-RR, a piecewise function known as the hockey stick, which is frequently assumed when the data do not support more elaborate functions. However, the hockey stick is not continuous, which makes it problematic for this application, where differentiable functions are required. The bent-hyperbola model proves to be an adequate continuous equivalent to the hockey stick for estimating FMSY.