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Despite their name, hierarchical stock–recruit meta-analyses are often parameterized in terms of steepness, which depends not only on the assumed stock–recruitment relationship but also on the recruit–spawner relationship. This parameterization requires assumptions about the reproductive potential of the recruit that are not desirable if the focus of the study is limited to the spawning–recruitment phase instead of the full life cycle. Thus, usage of steepness should be avoided in studies that aim to produce informative priors for the stock–recruit relationship for use in studies of other salmon stocks. An alternative key parameter for stock–recruit models is the maximum survival of eggs, which is the slope at the origin of the stock–recruitment curve when spawning stock size is defined in terms of the number of eggs. Furthermore, the current widely used practices in stock–recruit modeling could be improved by taking into account the stock-specific model uncertainty. We use the method of Bayesian model averaging to build a hierarchical stock–recruit model that allows stock-specific model structures with Beverton–Holt, Ricker, and hockey stick models as alternatives, all of which can be parameterized with the maximum survival of eggs. We illustrate our approach by analyzing nine previously published datasets for Atlantic salmon (Salmo salar).

Excessively high rates of fishing mortality have led to rapid declines of several commercially important fish stocks. To harvest fish stocks sustainably, fisheries management requires accurate information about population dynamics, but the generation of this information, known as fisheries stock assessment, traditionally relies on conservative and rather narrowly data-driven modelling approaches. To improve the information available for fisheries management, there is a demand to increase the biological realism of stock-assessment practices and to better incorporate the available biological knowledge and theory. Here, we explore the development of fisheries stock-assessment models with an aim to increasing their biological realism, and focus particular attention on the possibilities provided by the hierarchical Bayesian modelling framework and ways to develop this approach as a means of efficiently incorporating different sources of information to construct more biologically realistic stock-assessment models. The main message emerging from our review is that to be able to efficiently improve the biological realism of stock-assessment models, fisheries scientists must go beyond the traditional stock-assessment data and explore the resources available in other fields of biological research, such as ecology, life-history theory and evolutionary biology, in addition to utilizing data available from other stocks of the same or comparable species. The hierarchical Bayesian framework provides a way of formally integrating these sources of knowledge into the stock-assessment protocol and to accumulate information from multiple sources and over time.

This paper presents a sequential Bayesian framework for quantitative fisheries stock assessment that relies on a wide range of fisheries-dependent and -independent data and information. The presented methodology combines information from multiple Bayesian data analyses through the incorporation of the joint posterior probability density functions (pdfs) in subsequent analyses, either as informative prior pdfs or as additional likelihood contributions. Different practical strategies are presented for minimising any loss of information between analyses. Using this methodology, the final stock assessment model used for the provision of the management advice can be kept relatively simple, despite the dependence on a large variety of data and other information. This methodology is illustrated for the assessment of the mixed-stock fishery for four wild Atlantic salmon (Salmo salar) stocks in the northern Baltic Sea. The incorporation of different data and information results in a considerable update of previously available smolt abundance and smolt production capacity estimates by substantially reducing the associated uncertainty. The methodology also allows, for the first time, the estimation of stock–recruit functions for the different salmon stocks.

In this paper, we demonstrate how information from broodstocks can be combined with lab information on alevins to obtain annual stock-specific mortality estimates from early mortality syndromes (EMS) using a probabilistic approach, how a hierarchical model structure can be used to predict these mortality rates for related, partly sampled, or unsampled stocks, and why these estimates should be used to remove the effect of this mortality on stock–recruit estimates. The approach has been illustrated for Atlantic salmon (Salmo salar) stocks in the Baltic Sea affected by the M74 syndrome. Results indicate that data on the proportion of M74-affected females, commonly used to approximate M74 mortality, overestimate actual M74-related mortality because of a declining trend in mortality among offspring of these females. The stock-specific M74 mortality estimates are used to account for nonstationarity in the stock–recruitment relationship caused by this fluctuating mortality. Because hierarchical meta-analyses assume exchangeability, the effect of M74 mortality is removed before including these stocks within hierarchical stock–recruit analyses of Atlantic salmon stocks, which are commonly unaffected by M74 mortality. Failure to remove the effect of M74 mortality on the stock–recruit data results in underestimation of the stock's productivity and resilience to exploitation, especially in the case of stocks with steep stock–recruit curves.

A Bayesian state–space mark–recapture model is developed to estimate the exploitation rates of fish stocks caught in mixed-stock fisheries. Expert knowledge and published results on biological parameters, reporting rates of tags and other key parameters, are incorporated into the mark–recapture analysis through elaborations in model structure and the use of informative prior probability distributions for model parameters. Information on related stocks is incorporated through the use of hierarchical structures and parameters that represent differences between the stock in question and related stocks. Fishing mortality rates are modelled using fishing effort data as covariates. A state–space formulation is adopted to account for uncertainties in system dynamics and the observation process. The methodology is applied to wild Atlantic salmon (Salmo salar) stocks from rivers located in the northeastern Baltic Sea that are exploited by a sequence of mixed- and single-stock fisheries. Estimated fishing mortality rates for wild salmon are influenced by prior knowledge about tag reporting rates and salmon biology and, to a limited extent, by prior assumptions about exploitation rates.

We introduce a Bayesian probability model for the estimation of the size of an animal population from re- moval data. The model is based on the assumption that in the removal sampling, catchability may vary between indi- viduals, which appears to be necessary for a realistic description of many biological populations. Heterogeneous catchability among individuals leads to a situation where the mean catchability in the population gradually decreases as the number of removals increases. Under this assumption, the model can be fitted to any removal data, i.e., there are no limitations regarding the total catch, the number of removals, or the decline of the catch. Using a published data set from removal experiments of a known population size, the model is shown to be able to estimate the population size appropriately in all cases considered. It is also shown that regardless of the statistical approach, a model that assumes equal catchability of individuals generally leads to an underestimation of the population. The example indicates that if there is only vague prior information about the variation of catchability among individuals, a very high number of suc- cessive removals may be needed to correctly estimate the population size. Resume : Nous utilisons un modele de probabilite bayesien pour estimer la taille d'une population animale a partir de donnees de retrait. Le modele se base sur la presupposition que, dans un echantillonnage par retraits, la capturabilite peut varier d'un individu a un autre, ce qui semble necessaire pour decrire de facon realiste de nombreuses populations biologiques. Une capturabilite individuelle heterogene engendre une situation dans laquelle la capturabilite moyenne de la population decroit graduellement a mesure que le nombre de retraits augmente. Avec cette presupposition, le modele s'ajuste a n'importe quelle serie de donnees de retrait; il n'y a donc pas de limites en ce qui a trait a la capture totale, au nombre de retraits ou au declin de la recolte. L'utilisation de donnees de retrait publiees obtenues sur une popula- tion de taille connue montre que le modele est capable d'estimer la taille de la population de facon adequate dans tous les cas etudies. De plus, independamment de l'approche statistique utilisee, un modele qui presuppose une capturabilite individuelle uniforme sous-estime la population. L'exemple montre que, s'il n'existe que des informations prealables vagues sur la capturabilite individuelle, il faudra peut-etre un nombre tres eleve de retraits successifs pour pouvoir estimer correctement la taille de la population. (Traduit par la Redaction) Mantyniemi et al. 300

We developed a Bayesian probability model for mark–recapture data. Three alternative versions of the model were applied to two sets of data on the abundance of migrating Atlantic salmon (Salmo salar) smolt populations, and the results were then compared with those of two widely used maximum likelihood models (Petersen method and a model using stratified data). Our model follows the basic principles of stochastic models presented for stratified data. In contrast to the earlier models, our model can deal with sparse data. Moreover, even weak dependencies between the studied parameters and the possible factors affecting them can be used to improve the plausibility of the estimates. The assumptions behind our approach are more realistic than those of earlier models, taking into account such factors as overdispersion, which is expected to be present in the mark–recapture data of salmon smolts because of their schooling behavior. Our examples also show that assumptions about the model structure can have a substantial impact on the resulting inferences on the size of the smolt run, especially in terms of the precision of the estimate.