Estimating recruitment variability and productivity in Antarctic krill

Abstract

Three alternative forms of the spawner-recruit relationship – the Beverton-Holt and two expressions of the Ricker function - and a fourth form representing annual recruitment deviations without an explicit relationship to spawning biomass, were applied in an integrated assessment model for Antarctic krill. Model data were from the international krill fishery and U.S. AMLR surveys in the Commission for the Conservation of Antarctic Marine Living Resources (CCAMLR) Subarea 48.1, the area around the Antarctic peninsula where the majority of recent fishing for krill has taken place. Sensitivity tests using pre-specified values for the standard deviation of the logarithm of annual recruitment residuals (σR) and productivity (steepness, h) for the relationship between spawning biomass and subsequent recruitment indicated that neither the Beverton-Holt nor Ricker functions were superior to configurations of the model that did not assume a spawner-recruit relationship. As the predictive power of the spawner-recruit functions was reduced by increasing the value of σR the fit to the data improved. All the functions fitted the data best when σR was large enough so that random recruitment with respect to spawning biomass was produced. The alternative functions produced the same time series of recruitment and spawning biomass estimates when they were determined by the data rather than forced towards an assumed relationship. Although the Beverton-Holt and Ricker models were poor predictors of the data, cross-correlations of the recruitment predictions with the spawning biomass predictions from the best models indicated that recruitment was statistically correlated with spawning biomasses in the previous two to four years. The highest correlation (0.58) was with spawning biomass three years previously. Correlations in the reverse direction, with spawning biomass following recruitment were insignificant. These results suggest that recruitment variability does not influence subsequent spawning biomass in krill. They leave open the possibility that krill spawning biomass could influence subsequent recruitment, but not as modeled in the Beverton-Holt or Ricker functions with a one-year lag and the pre-specified von Bertalanffy growth.