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
Summary1. Climatic and anthropogenic effects often interact leading to unexpected results. For example, climate may lead to a change in the spatial distribution of a fish stock and thereby its vulnerability to exploitation. The North Sea cod stock is currently under pressure from both environmental change and human exploitation. This stock has experienced a series of poor recruitments since the late 1990s and, concomitant with the decrease in abundance, the distribution of cod has changed. While it has been suggested that the change in distribution can be linked to increasing temperatures and fishing pressure, there is little evidence for this hypothesis. 2. Using winter and summer survey catches, we investigated whether a directional shift in the distribution of cod has taken place over the years . We then examined whether the change could be linked to climatic conditions, fishing mortality, stock size or limited directional movement of cod. Using the derived models, we investigated whether fishing has increased the sensitivity of the cod population to climate-induced distribution changes. 3. A series of winters characterized by high temperatures and southerly winds during the egg and larval phases of cod led to a northward shift in the distribution of juvenile North Sea cod the following year. A concomitant northern shift of mature fish around the time of spawning was linked directly to a tendency for northerly distributed juveniles to remain northerly throughout their life. This shift of the spawners further augmented that of the new recruits. 4. Although fishing mortality on a North Sea scale was not directly correlated with the displacement of any of the age groups, fishing has severely decreased the number of fish in older age groups. This increased the sensitivity of the distribution of the cod stock to climatic changes. 5. Synthesis and applications. The centre of gravity of North Sea cod has moved north as a result of the effect of a series of warm, windy winters on the distribution of recently settled cod. The shift was followed by a northwards shift in the distribution of older age groups. Unless a series of cold and calm years combined with a reduced mortality in the southern areas allows a southern spawning population to rebuild, the cod stock is unlikely to return to its previous area of distribution. Furthermore, protecting adult cod mainly in northern areas is unlikely to result in improved recruitment to the southern North Sea.
The spatial distribution of cod ( Gadus morhua ) in the North Sea and the Skagerrak was analysed over a 24-year period using the Log Gaussian Cox Process (LGCP). In contrast to other spatial models of the distribution of fish, LGCP avoids problems with zero observations and includes the spatial correlation between observations. It is therefore possible to predict and interpolate unobserved densities at any location in the area. This is important for obtaining unbiased estimates of stock concentration and other measures depending on the distribution in the entire area. Results show that the spatial correlation and dispersion of cod catches remained unchanged during winter throughout the period, in spite of a drastic decline in stock abundance and a movement of the centre of gravity of the distribution towards the northeast in the same period. For the age groups considered, the concentration of the stock was found to be constant or declining in the period. This means that cod does not follow the theory of density-dependent habitat selection, as the concentration of the stock does not increase when stock abundance decreases.
A new age-structured stock dynamics approach including stochastic survival and recruitment processes is developed and implemented. The model is able to analyse detailed sources of information used in standard age-based fish stock assessment such as catch-at-age and effort data from commercial fleets and research surveys. The stock numbers are treated as unobserved variables subject to process errors while the catches are observed variables subject to both sampling and process errors. Results obtained for North Sea plaice using Markov Chain Monte Carlo methods indicate that the process error by far accounts for most of the variation compared to sampling error. Comparison with results from a simpler separable model indicates that the new model provides more precise estimates with fewer parameters.
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