The multiplicative model described by Robson can be used to obtain estimates of annual standardized catch rate and its variance by including years in the model. The corresponding estimate of standardized effort is the ratio of the total catch and the estimated catch rate. If the error is assumed to be lognormally distributed then these estimators have well defined statistical properties.Key words: effort standardization, catch rate, multiplicative model, stock assessment

A variety of tools are available to quantify uncertainty in age-structured fish stock assessments and in management forecasts. These tools are based on particular choices for the underlying population dynamics model, the aspects of the assessment considered uncertain, and the approach for assessing uncertainty (Bayes, frequentist or likelihood). The current state of the art is advancing rapidly as a consequence of the availability of increased computational power, but there remains little consistency in the choices made for assessments and forecasts. This can be explained by several factors including the specifics of the species under consideration, the purpose for which the analysis is conducted and the institutional framework within which the methods are developed and used, including the availability and customary usage of software tools. Little testing of either the methods or their assumptions has yet been done. Thus, it is not possible to argue either that the methods perform well or perform poorly or that any particular conditioning choices are more appropriate in general terms than others. Despite much recent progress, fisheries science has yet to identify a means for identifying appropriate conditioning choices such that the probability distributions which are calculated for management purposes do adequately represent the probabilities of eventual real outcomes. Therefore, we conclude that increased focus should be placed on testing and carefully examining the choices made when conducting these analyses, and that more attention must be given to examining the sensitivity to alternative assumptions and model structures. Provision of advice concerning uncertainty in stock assessments should include consideration of such sensitivities, and should use model-averaging methods, decision tables or management procedure simulations in cases where advice is strongly sensitive to model assumptions

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Abundance estimates from bottom trawl surveys are important elements in the evaluation of stock status. The reliability of stock assessment results are greatly influenced by the precision of the survey abundance estimates. In this study, a new stratified random design, based upon historical spatial distribution, for estimating the abundance of ages 5-12 Atlantic cod Gadus morhua on the eastern Scotian Shelf off Nova Scotia was evaluated. Gains in precision from the new design, relative to simple random sampling, were mainly due to the improved allocation of trawl sets to strata, whereas the gains solely due to the new stratification scheme were minimal. We conclude that any reasonable stratification scheme that is flexible enough to allow for the optimization of the allocation of sets to strata should perform well. In our study, the allocation scheme was based upon the historical spatial distribution of abundances. Although annual changes in spatial distribution would require revision of the allocation strategy, we found that averaging results over several earlier years was more robust than just using the most recent year's data. The new design has been used for an annual March survey of this Atlantic cod stock from 1986 to the present. Comparisons of the results from the 1986-1990 period with those from 1979-1984, which stemmed from the traditional depth-based stratification, indicate that the new design is more efficient with respect to gain in precision than the old design. Finally, we note that the simple random sampling variance is smaller in a July series of surveys of this stock than in the March series and this difference can be exploited to give more precise stratified surveys in July than in March.

One of the primary uses of bottom-trawl survey data, with respect to fisheries management, is the estimation of abundance of the species involved. Stratified-random surveys have been conducted on the eastern Scotian Shelf since 1970. The precision of abundance estimates for Atlantic cod (ages 5-12) from these surveys was found to be inferior to what would have been obtained if simple random surveys had been conducted. These results were primarily due to suboptimal allocation of stations to strata. Historical data were used to devise alternative sampling strategies. This analysis indicated that the number of strata could be reduced considerably without loss of precision. An additional and important benefit of the smaller number of strata would be increased flexibility for allocation. With the present level of sampling, it would be necessary to reduce the number of strata to achieve proportional allocation of stations or to approximate optimal allocation.