Integrating design- and model-based inference to estimate length and age composition in North Pacific longline catches

Age and size structure are attributes of fishery stocks important for predicting future productivity. As such, estimating age and length composition of catches has long been an important fisheries management activity. Many observer programs sample catches to obtain length measurements and otoliths (or other structures for ageing) from targeted species. In North Pacific groundfish fisheries, observers collect these data through a stratified multiphase sampling design. Sampling variance and covariance estimates for catch- or proportions-at-length or -age that reflect the randomization inherent in the sampling design provide important measures of uncertainty that correspond to measurement error components in length- or age-structured stock assessment models. We compare sampling variances and covariances of Pacific cod (Gadus macrocephalus) proportions-at-length and sablefish (Anoplopoma fimbria) proportions-at-age with those provided by the overdispersed multinomial model sometimes used in these assessment models. For example, the sampling variance estimates for 2002 Pacific cod proportion-at-length estimates in the Bering Sea - Aleutian Islands are at most 13% of the variances provided by multinomial and square-root sample size assumptions. Furthermore, some proportion estimates are positively correlated, whereas only negative correlation occurs with the multinomial distribution.