ORDER-RESTRICTED BAYESIAN-ESTIMATION OF THE AGE COMPOSITION OF A POPULATION OF ATLANTIC COD

The management of a commercial fishery often requires estimates of the age composition. These estimates are typically based on age and lengt h data obtained from sampling the commercial landings from the fishery and the catches from a research vessel survey. We use data from annua l research cruises of Georges Bank conducted by the Canadian Departmen t of Fisheries and Oceans to show how inferences for Atlantic cod (Gad us morhua) can be improved. Traditionally, two-phase stratified sampli ng is used with fish length (or weight) as the stratification variable . Letting P-i. denote the proportion of fish belonging to length strat um i, and pi(ij) denote the proportion of fish belonging to age class j in stratum i, we use Bayesian methods to estimate P.(j) = Sigma(i) P -i.pi(ij), the proportion of fish that are age j. Specifications of sm oothness, expressed as unimodal order relations among the pi(ij) (with in and between the length strata), are incorporated into the prior dis tributions. Uncertainty about both the locations of the modes and the unimodality itself are included as part of the probabilistic specifica tion. With computations facilitated by using the Gibbs sampler, we sho w that the smoothness conditions provide very large gains in precision . For the data analyzed in this article, one can obtain similar precis ion by using (a) a conventional analysis or (b)an analysis with order restrictions and a sample of half the size in (a). We also show that b etter estimates of the age composition provide improved estimates of t he quantities used by fisheries managers to forecast the catches from cohorts of fish.