Investigating the uncertainty of age determinations for Patagonian toothfish (Dissostichus eleginoides) and the implications for stock assessment

We revised the method of Candy et al. (2012) to estimate the ageing error matrix (misclassification matrix) to address some issues regarding true ages not being the mode at the extremes of the matrix and a lack of smoothness in the probabilities for ages above 25 years. Positive errors now aggregate into the plus group, negative errors are truncated below the minimum age, and fish with true ages greater than the plus group are incorporated into the final row of the misclassification matrix. We expanded the reference collection to include an additional 50 otoliths with a mean age above 25 years. The revised method was applied to the expanded reference collection to re-estimate the misclassification matrix.We assessed misclassification matrices obtained using the revised Candy method along with two other methods of accounting for ageing error, approximation by a Gamma distribution and a constant coefficient of variation (c.v.) of 0.1. We compared the misclassification matrices with the observed age determinations from the expanded reference collection. We then used estimates of spawning stock biomass (SSB) and year class strength (YCS) from the CASAL assessment of the HIMI fishery to evaluate the effects of these three methods along with assuming no ageing error. The Gamma and revised Candy methods both provided satisfactory representations of the observed age determinations. The constant c.v. method provided a poor representation of the observed ages, underestimating the variability at the younger age classes and over estimating the variability at the older age classes. Estimates of SSB were similar for the revised Candy and Gamma methods. The constant c.v. method and assuming no ageing error produced similar estimates of SSB that were consistently lower than those from the revised Candy and Gamma methods. Not accounting for ageing error gave the most precise and least variable estimates of YCS while the Gamma method gave the least precise and most variable estimates. Estimates of YCS from the constant c.v. method and the revised Candy method were between the other two methods in terms of year to year variability and precision. The poor agreement of the constant c.v. method with observed ages and the similarity of SSB estimates to those obtained assuming no ageing error would suggest it is not appropriate for use in the HIMI assessment and we would caution others to assess its impact before applying it to their assessments. Estimates of SSB from the Gamma method were consistent with the revised Candy method, suggesting this method may be of use where there is insufficient data to estimate ageing error directly.