Empirical and theoretical analyses of correction of time-series bias in stock-recruitment relationships of sockeye salmon (Oncorhynchus nerka)

Abstract

Using data from 30 sockeye salmon (Oncorhynchus nerka) stocks and Monte Carlo simulations, we examined the importance of time-series bias on estimates of optimal harvest rate, optimal escapement, and sustainable yield. We compared the performance of the least-squares procedure for fitting a Ricker curve with an existing bias-correction method. Simulations showed that the effect of time-series bias is greatest for low-productivity stocks that exhibit a high degree of autocorrelation among residuals of the stock-recruitment relationship. A strong inverse empirical relationship between autocorrelation and stock productivity among the 30 stocks suggests that time-series bias is a more important concern for low-productivity northern stocks than for more productive southern stocks. The corrected method reduced bias in optimal escapement estimates under a limited set of conditions but at the price of increased variance in the estimates. For a constant escapement goal policy, using the bias correction thus resulted in sustainable yields slightly lower than or equal to expected values for 28 of the 30 stocks compared with yields obtained using the standard least-squares estimation method. We demonstrate the value of using a decision theoretic approach to evaluate the performance of estimation methods.