INCORPORATING SAMPLING VARIATION AND RANDOM READER ERROR INTO CALCULATION OF EFFECTIVE SAMPLE SIZE IN THE APPLICATION OF AGE LENGTH KEYS TO ESTIMATION OF CATCH-AT-AGE PROPORTIONS

Catch-at-age proportions are generally incorporated into an integrated assessment as observations that contribute to the objective function via a multinomial likelihood. The multinomial likelihood requires a nominal sample size for each fishery and year combination. A method is described for estimating an effective sample size (ESS) that can be used as the nominal multinomial sample size. The method accounts for both the variation associated with sub-sampling of the random length frequency (LF) sample for ageing, and random reader error when ageing fish. The catch-at-age ESS is estimated by dividing the ESS for the LF sample, where this ESS is obtained from the haul-level LF data, by an over-dispersion parameter estimate obtained from simulated samples of age frequency data. These samples are obtained using Monte Carlo multinomial replicates of the observed age length key (ALK) with each ALK used to generate a replicate age frequency sample. For each replicate a random draw of the ageing error matrix is taken and applied to the age frequency sample, thus combining both sources of variation. The over-dispersion parameter is estimated from the fit of a log-linear Poisson generalized linear model to the replicated length frequency data. Using simulated data to include only sampling error, the over-dispersion parameter declined from a maximum of around 6 to 8 down to close to 1 as the aged sample fraction increased from 1% to 10%. When random ageing error was combined with sampling error the corresponding values were lower, with a corresponding range of around 4 down to 1. This reduction is due to the way the ageing error matrix ‘smooths-out’ peaks in the true (i.e. without ageing error) age frequency data.