Measurement error and bias in the maximum reproductive rate for the Ricker model

Abstract

We investigated the consequences of measurement errors in spawner abundance on the estimation of alpha(tilde), the maximum lifetime reproductive rate, in the Ricker spawner-recruit model. This rate is equivalent to the slope at the origin for the Ricker model, which is crucial for the estimation of management reference points. Simulation results indicate that measurement error in spawner abundance does not lead, in general, to an overestimate of alpha(tilde), as had been previously thought. Instead, the direction, and to some extent the magnitude, of the bias is related to the range of spawner values, and we provide an analytical explanation for this phenomenon. For stocks that have been heavily exploited and have low spawner values, measurement error tends to result in an overestimate of log alpha(tilde), usually by [Formula: see text]5%. Less exploited stocks with large spawner values will have their log alpha(tilde) underestimated, commonly by –15 to –25%. Results from data-based simulations indicate that under certain conditions, empirical Bayes estimates for the distributions for alpha(tilde) among stocks, i.e., the prior distribution, can still be relatively unbiased in the presence of measurement error.