Performance of a Bayesian state-space model of semelparous species for stock-recruitment data subject to measurement error

Measurement errors in spawner abundance create problems for fish stock assessment scientists. To deal with measurement error, we develop a Bayesian state-space model for stock-recruitment data that contain measurement error in spawner abundance, process error in recruitment, and time series bias. Through extensive simulations across numerous scenarios, we compare the statistical performance of the Bayesian state-space model with that of standard regression for a traditional stock-recruitment model that only considers process error. Performance varies depending on the information content in data, as determined by stock productivity, types of harvest situations, and amount of measurement error. Overall, in terms of estimating optimal spawner abundance SMSY, the Ricker density-dependence parameter β, and optimal harvest rate hMSY, the Bayesian state-space model works best for informative data from low and variable harvest rate situations for high-productivity salmon stocks. The traditional stock-recruitment model (TSR) may be used for estimating α and hMSY for low-productivity stocks from variable and high harvest rate situations. However, TSR can severely overestimate SMSY when spawner abundance is measured with large error in low and variable harvest rate situations. We also found that there is substantial merit in using hMSY (or benchmarks derived from it) instead of SMSY as a management target.