Age-structured production model for toothfish at
South Georgia

The ASPM model used by Agnew and Kirkwood (2004, WG-FSA-04/82) has been modified through the introduction of a new annual selectivity function, modelled as a unimodal, algebraically decaying function of age, with three easily interpretable parameters.
When only a single selectivity curve was fitted for all years, the change to the new selectivity function improved the fit to length frequency data achieved last year, but the fit was still poor. The fit to the CPUE was also poor.
With selectivity parameters allowed to be estimated on an annual basis the fits are substantially improved. However, by allowing all parameters to be estimated in this way the model is over-parameterised and regularly reaches preset parameter boundaries. With one or two parameters of the selectivity estimated only once the fit to length frequencies is good but infinite populations are estimated. If the CPUE data are given high weight in the fitting, then the model has sufficient flexibility to change the selectivity to fit the CPUE very closely. Convergence problems were noted for the highly parameterised versions of this model.
Revisions to the selectivity model this year have led to an ASPM with superior performance. However, this study demonstrates that the ASPM is still not suitable for use when assessing South Georgia toothfish populations by fitting to the available catch length frequency data and CPUE data.