Growth models for D. eleginoides for the Heard Island plateau region (Division 58.5.2) calibrated from otolith-based length at age data and validated using mark-recapture data

Length-at-age data for the Patagonian toothfish (Dissostichus eleginoides) caught by trawl in Division 58.5.2 were fitted using von Bertalanffy (VB) and segmented-linear models using a likelihoods that either did or did not incorporate fishing selectivity and the length-bin sampling frequencies for ageing relative to those for random length frequency (LF) samples to give the variable probability (VP) of sampling lengths. A segmented linear trawl fishing selectivity function was used where the upper-arm was estimated, as described elsewhere, from comparisons of longline LF samples to that for trawls for seasons where both fishing methods were used. Due to the small number of fish in the aged sample that were older than 20 years the general trend in the data of length with age did not exhibit obvious asymptotic behaviour so we compare the fit of the VB model to a segmented linear model. We also adjust the VB model by incorporating a multiplicative term that reduces the VB length-age trajectory below an estimated young-age to give a more realistic predicted length at age zero than that for the unadjusted model. We also tried fixing the t0 and L? parameters of the VB model to give age zero length of 30 mm and asymptotic length of 2000 mm but the fit to the data was very poor. The Akaike Information Criterion indicated that the 2-segment linear model gave the best fit to the length-age data. We compare predictions from these models with growth increments obtained from mark-recapture data for a large sample of recaptured fish. Mean annual growth increment from mark-recapture data for days at liberty greater than 175 days was 36.6 mm yr-1 while that predicted from the 2-segment linear model for lengths above 557 mm was 37.6 mm yr-1. Mean annual relative growth rates for mark-recapture data corresponded most closely to predictions from the VB model fitted by maximising the VP likelihood. For the 5 to 25 year age range predicted lengths from this VB curve and the 2-segment linear model were almost identical.