An alternative stock-recruitment function for age-structured models

In this work I introduce a probabilistic stock-recruitment function, of the Cushing family, that stands as an alternative to the canonical formulas provided by Beverton-Holt and Ricker, among others. I embed this function in a mathematically tractable (dynamic linear) population model, which renders inference of abundance-at-age and unknown biological parameters (natural mortality, virgin stock's egg production rate, and steepness), as well as fisheries parameters (catchability and selectivity), easier than with canonical representations. To assist management, I provide formulas for exact and approximate reference points, associated with Maximum Sustainable Yield (MSY) and Maximum Excess Recruitment (MER). I also introduce a new summary statistic, called bottleneck abundance ratio, which requires no knowledge of steepness under the proposed stock-recruitment function. With simulated data and the concept of Pretty Good Yield, I generate bounds for MSY- and MER-based reference points and show that those based on the new function have greater resilience to uncertainty about steepness. As a case study, I apply a state-space model to the US Gulf menhaden fishery, 1964–2004. Results suggest higher than previously considered natural mortality and a discernible connection between parental stock abundance and recruitment, undetected with Beverton-Holt and Ricker models.