Research Document - 2005/091

Properties of three estimators of recruitment overfishing

By Shelton, P.A.

Abstract

Three limit reference point estimators which may indicate recruitment-overfishing are evaluated using stock-recruit data simulated from a Beverton-Holt model with lognormal error. The estimators are the spawner biomass corresponding to 50% of maximum recruitment from Beverton-Holt and changepoint regression model fits to the simulated data, and the spawner biomass corresponding to the intercept of the 50^th percentile recruitment value and the 90^th percentile of the recruit to spawner biomass ratio (Serebryakov method). The sensitivity of the estimators to a range of data contrast in SSB values and recruitment noise levels is evaluated for data series 20 and 30 years in length. In addition to examining the limit reference points, estimates of the slope of the spawner-recruit relationship near the origin are evaluated for the three methods, since the slope is important in determining population resilience and recovery rates. It is concluded that the LRP estimated from the Beverton-Holt fit to data generated from a Beverton-Holt model is least sensitive to low data contrast and high noise, but that the ability of the nonlinear estimation procedure to find plausible parameter estimates deteriorates with increasing noise and at both low and high levels of data contrast. In comparison, when data are generated from a Beverton-Holt model, both the changepoint regression and Serebryakov methods tend to give risk-prone estimates of the LRP in the sense that the limit reference point is lower than the true spawner biomass corresponding to 50% of maximum recruitment and application in fisheries management may thus not prevent recruitment-overfishing. Estimates of the slope parameter from changepoint regression tend to be lower than the true slope while estimates from Berverton-Holt and Serebryakov methods may be positively biased at high levels of noise. Changepoint regression therefore provides a relatively risk-averse estimate of population resilience.

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