Summary
Length-at-age data for Patagonian toothfi sh (Dissostichus eleginoides) at Heard Island (Division 58.5.2) were fi tted using a von Bertalanffy (VB) growth model taking into account response-biased sampling of fi sh that were aged. Subsampling of random lengthfrequency (LF) data used to obtain the samples of fi sh for ageing used length-bin sampling involving a fi xed sample size per bin. Estimation of the VB parameters used a defi nition of the likelihood function based on variable probability (VP) sampling due to the prespecifi ed length-dependent selectivity function for trawl fi shing and the additional effect of length-bin sampling on sampling probabilities. The VB curve fi tted to the length-atage data, ignoring VP sampling and assuming normal errors with constant coeffi cient of variation using iteratively weighted least squares (IWLS), predicted substantially lower mean length-at-age for older ages compared to the VB curve fi tted using VP maximum likelihood (MLP) with length-bin relative probabilities defi ned using fi shing selectivity alone. This was due to the feature of the selectivity function of a sharp decline from ‘full’ selection at 1 000 mm length down to 1% selection for a length of 1 600 mm. When lengthbin sampling frequencies were also included in defi ning relative probabilities, the VP maximum likelihood (MLPLB) and IWLS-estimated curves were more similar. Predicted and observed values of annual growth rate (AGR) for lengths measured at release and fi rst recapture in mark–recapture studies were compared where predictions used the VB parameter estimates obtained from the length-at-age data and the Fabens (1965) form of the VB growth model. Formulae for adjusting predictions for bias imparted by the use of the Fabens model were developed and showed that the bias is relatively small for the range of release lengths in the data. Predictions of AGR using the MLPLB-estimated VB parameters were closer to, but still substantially higher than, the mean trend in observed AGR values with release length compared with those obtained using IWLS-estimated parameters. A young-age adjustment (less than 5 years old) to the VB model is also given in order to give more realistic predictions of mean length-at-age for young fish.