Can steepness of the stock–recruitment relationship be estimated in fishery stock assessment models?

Steepness of the stock–recruitment relationship is one of the most uncertain and critical quantities in fishery stock assessment and management. Steepness is defined as the fraction of recruitment from a virgin population obtained when the spawners are at 20% of the virgin level. Steepness directly relates to productivity and yield and is an important element in the calculation of many management reference points. Stock–recruitment relationships have traditionally been estimated from time series of recruitment and spawning biomass, but recently interest has arisen regarding the ability to estimate steepness inside fishery stock assessment models. We evaluated the ability to estimate steepness of the Beverton–Holt stock–recruitment relationship using simulation analyses for twelve US Pacific Coast fish stocks. A high proportion of steepness estimates from the simulated data and the original data occur at the bounds for steepness and the proportion decreased as the true steepness decreased. The simulation results indicate that, in most cases, steepness was estimated with moderate to low precision and moderate to high bias. The poorly estimated steepness indicates that often there is little information in the data about this quantity. However, reliable estimation is attainable with a good contrast of spawning stock biomass for relatively unproductive stocks when the model is correctly specified.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Estimating steepness inside the model did not result in convergence issue. ► A high proportion of estimates from the simulated data occurred at the bounds. ► This proportion decreased as the true or assumed steepness decreased. ► The precision and bias of estimates were improved with increased depletion. ► Reliable estimation is attainable when the model is correctly specified.