Integrated assessments that use catch-at-age or abundance-at-age data for model calibration require an ageing error matrix as input in order to adequately account for uncertainty in the data resulting from the imprecision of age determination using annual ring counts from otoliths. This paper describes the methods and results used to provide an ageing error matrix to the HIMI toothfish integrated assessment using repeat readings by 4 readers of a set of 203 reference otoliths sampled from the HIMI fishery. The methods of sampling, preparing, reading, and modelling random reader error for this reference set of otoliths are described. A total of 933 readings were taken and errors were defined as the nearest integer (NI) value deviations, denoted as integer errors (IE), from the mean age for an individual otolith. Since the true age of the fish is unknown, only imprecision and relative differences between readers could be quantified. Linear mixed model analyses indicated that the mean IE ranged between readers only slightly (+/- 0.27 yr) whereas frequencies of random IEs, treated as classes, between readings were relatively high for +/-1 yr relative to the zero IE frequency, and less so for the +/-2 yr and greater classes. These frequencies depend on the readability score of the otolith and its average age and were modelled in two stages. In the first stage the frequency of the absolute value of IE, the AIE, considered as 0, 1, 2, 3, 4, 5 yr and greater, classes for each of the 4 readability classes and 7 aggregate age classes were modelled using continuation ratios and predicted proportions in each AIE class obtained for a given readability score and age. Proportions of the AIE 1 yr error class decreased relative to the AIE 0 class as readability improved while, in general, it increased as age increased. To model any degree of asymmetry in IEs, a binomial/logistic model of the proportion of non-zero IEs that were negative was fitted for given readability and age. This probability decreased from around 0.7 to 0.4 for ages 5 and 21 yr respectively, but did not depend on readability. The construction of the ageing error matrix is described and combines the modelled probabilities for AIE and negative IE while taking into account logical constraints. This two stage approach makes efficient use of the data since only half the number of combinations of error class by readability by age class are required compared to modelling IE classes directly. This approach differs from other studies of ageing error in that it takes into account the otolith readability score and the integer nature of ring count data.

Abstract: