Sensitivity of common estimators of management parameters derived from stock–recruit relationships

Local influence diagnostics are used to develop a theoretical understanding of the sensitivity of some management parameters derived from the Beverton–Holt and Ricker stock–recruit models using a common estimation method. The diagnostics provide an understanding of how characteristics of the data and model affect estimates. Sensitivity is assessed for the slope at the origin, the maximum recruitment, and the stock size corresponding to 50% of the maximum recruitment. Two types of sensitivity are considered. The first is with respect to the weighting that stock–recruit observation pairs (i.e. cases) are given in estimation. Case-weight local influence equations are developed to provide insights about why estimates change when cases are deleted. The second type of sensitivity is with respect to the stock size measurements. These are commonly assumed to be measured without error when fitting a stock–recruit model, when in fact stock size measurements often have substantial error. Local influence diagnostics are developed to assess the impact of errors in stock size, with a particular focus on measurement errors. The diagnostics are applied to 15 case-studies.