CCAMLR

Length-at-age data for the Patagonian toothfish (Dissostichus eleginoides) caught by trawl in Heard Island fishery were fitted using a von Bertalanffy (VB) growth model taking into account variable probability (VP) sampling of fish that were aged. Sub-sampling of random length frequency (LF) data used to obtain the samples of fish for ageing used length-bin sampling involving a fixed sample size per bin. Estimation of the VB parameters used a definition of the maximum likelihood which took into account VP sampling due to length-dependent selectivity of trawl fishing and also accounted for the additional affect of length-bin sampling on sampling probabilities. Estimation of the trawl selectivity curve is described elsewhere and assumed known for this study with its most important feature being a sharp decline in selectivity from 100% at 1000 mm down to 1% by 1600 mm. The VB curve fitted to the length-at-age data assuming normal errors with constant coefficient of variation using iteratively weighted least squares (IWLS) substantially under-predicted mean length-at-age for older ages compared to VB curve fitted using the same error model and VP maximum likelihood (MLP) with length-bin relative probabilities defined using fishing selectivity alone. When length bin sampling frequencies for aged fish relative to those for the LF sample were also included in defining 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 first recapture in mark-recapture studies were compared where predictions used the VB parameter estimates obtained from the length-at-age data and the Fabens form of the VB growth model. Formulae for adjusting predictions for bias imparted by the use of the Fabens model were developed based on assumptions about the distribution of age at first capture 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 the mean trend in observed values with release length than 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. 

This paper develops a Bayesian mark-recapture model for estimating both fishing and natural mortality, and integrates catch-at-age data into the estimation model, to aid in distinguishing between natural and fishing mortality. The model essentially follows tagged cohorts, with the estimated parameters being the  fishing and natural mortality vectors for that particular cohort.

The model was tested against simulated data, and performed as expected. Mark-recapture data from toothfish at South Georgia was analysed with the model. The ages covered by the analysed cohorts ranged from 5 to 13. In the model runs, while fishing mortality-at-age was estimated, only one value of the natural mortality was permitted, as allowing both to vary can produce either non-sensical or nonconvergent results. For all the cohorts the model was applied to, a consistent picture emerged. Both natural and fishing mortality were estimated to be lower than those estimated in previous stock assessments using both mark-recapture and catch data. There was additionally some suggestion of agestructure in the natural mortality-at-age.

Trawl surveys are used in CCAMLR waters to estimate abundance of juvenile toothfish (Dissostichus eleginoides) and icefish (Champsocephalus gunnari). Documentation of some past trawl surveys has been insufficient to allow members of WG-FSA to fully interpret the survey results. This document suggests a standard pro-forma for reporting trawl survey results to WG-FSA based on survey reports for bottom-trawl surveys for hoki (Macruronus novaezelandiae) in the New Zealand EEZ.