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Assessment of the Finnish wolf population relies on multiple sources of information. This paper describes how Bayesian inference is used to pool the information contained in different data sets (point observations, non-invasive genetics, known mortalities) for the estimation of the number of territories occupied by family packs and pairs. The output of the assessment model is a joint probability distribution, which describes current knowledge about the number of wolves within each territory. The joint distribution can be used to derive probability distributions for the total number of wolves in all territories and for the pack status within each territory. Most of the data set comprises of both voluntary-provided point observations and DNA samples provided by volunteers and research personnel. The new method reduces the role of expert judgement in the assessment process, providing increased transparency and repeatability.

Citizens, community groups and local institutions participate in voluntary biological monitoring of population status and trends by providing species data e.g. for regulations and conservation. Sophisticated statistical methods are required to unlock the potential of such data in the assessment of wildlife populations. We develop a statistical modelling framework for identifying territories based on presence-only citizen science data. The framework can be used to jointly estimate the number of active animal territories and their locations in time. Our approach is based on a data generating model which consists of a dynamic submodel for the appearance/removal of territories and an observation submodel that accounts for the varying observation intensity and links the data to the territories. We first estimate the observation intensity using past presence-only observations made by citizens, conditioning on previously known territories. We then infer the territories using a state-of-the-art sequential Monte Carlo method, which extends earlier approaches by allowing for spatial inhomogeneity in the observation process. We verify our data generating model and inference method successfully in synthetic scenarios. We apply our framework for estimating the locations and number of wolf territories in March 2020 in Finland using one year of confirmed citizen-made wolf observations. The observation intensity is estimated using wolf observation data collected in 2011–2019, conditioning on official territory estimates and data from GPS-collared wolves. Our experiments with synthetic data suggest that the estimation of territories can be feasible with presence-only data. Our location and territory count inferences for March 2020 based on past data are comparable to the official wolf population assessment of March 2020 by the Natural Resources Institute Finland. The results suggest that the framework can provide useful information for assessing populations of territorial animals. Furthermore, our methods and findings, such as the developed data generating model and the estimation of the spatio-temporal observation intensity can be relevant also beyond the strictly territorial setting. peerReviewed

Ecological indicator approaches typically compare the prevailing state of an ecosystem component to a reference state reflecting good environmental conditions, i.e. the desirable state. However, defining the reference state is challenging due to a wide range of uncertainties related to natural variability and measurement error in data, as well as ecological understanding. This study propose a novel probabilistic approach combining historical monitoring data and ecological understanding to estimate the uncertainty associated with the boundary value of an ecological indicator between good and poor environmental states. Bayesian inference is used to estimate the epistemic uncertainty about the true state of an indicator variable during an historical reference period. This approach replaces the traditional boundary value with probability distribution, indicating the uncertainty about the boundary between environmental states providing a transparent safety margin associated with the risk of misclassification of the indicator's state. The approach is demonstrated by applying it to a time-series of an ecological status indicator, 'Abundance of coastal key fish species', included in HELCOM's Baltic Sea regional status assessment. We suggest that acknowledgement of the uncertainty behind the final classification leads to more transparent and better-informed decision-making processes.

In the Baltic Sea region, salmon are valued for the ecological, economic, and cultural benefits they provide. However, these fish are threatened due to historical overfishing, disease, and reduced access to spawning rivers. Climate change may pose another challenge for salmon management. Therefore, we conducted a problem-framing study to explore the effects climate change may have on salmon and the socio-ecological system they are embedded within. Addressing this emerging issue will require the cooperation of diverse stakeholders and the integration of their knowledge and values in a contentious management context. Therefore, we conducted this problem framing as a participatory process with stakeholders, whose mental models and questionnaire responses form the basis of this study. By framing the climate change problem in this way, we aim to provide a holistic understanding of the problem and incorporate stakeholder perspectives into the management process from an early stage to better address their concerns and establish common ground. We conclude that considering climate change is relevant for Baltic salmon management, although it may not be the most pressing threat facing these fish. Stakeholders disagree about whether climate change will harm or benefit salmon, when it will become a relevant issue in the Baltic context, and whether or not management efforts can mitigate any negative impacts climate change may have on salmon and their fishery. Nevertheless, by synthesizing the stakeholders' influence diagrams, we found 15 themes exemplifying: (1) how climate change may affect salmon, (2) goals for salmon management considering climate change, and (3) strategies for achieving those goals. Further, the stakeholders tended to focus on the riverine environment and the salmon life stages occurring therein, potentially indicating the perceived vulnerability of these life stages to climate change. Interestingly, however, the stakeholders tended to focus on traditional fishery management measures, like catch quotas, to meet their goals for these fish considering climate change. Further, social variables, like “politics,” “international cooperation,” and “employment” comprised a large proportion of the stakeholders' diagrams, demonstrating the importance of these factors for salmon management.

Participatory modelling increases the transparency of environmental planning and management processes and enhances the mutual understanding among different parties. We present a sequential probabilistic approach to involve stakeholders' views in the formal decision support process. A continuous Bayesian Belief Network (BBN) model is used to estimate population parameters for stakeholder groups, based on samples of individual value judgements. The approach allows quantification and visualization of the variability in views among and within stakeholder groups. Discrete BBN is populated with these parameters, to summarize and visualize the information and to link it to a larger decision analytic influence diagram (ID). As part of ID, the resulting discrete BBN element serves as a distribution-form decision criteria in probabilistic evaluation of alternative management strategies, to help find a solution that represents the optimal compromise in the presence of potentially conflicting objectives. We demonstrate our idea using example data from the field of marine spatial planning. However, this approach is applicable to many types of management cases. We suggest that by advancing the mutual understanding and concrete participation this approach can further facilitate the stakeholder involvement also during the various stages of the environmental management process. (C) 2019 The Authors. Published by Elsevier B.V.

Annual run size and timing of Atlantic salmon smolt migration was estimated using Bayesian model framework and data from six years of a video monitoring survey. The model has a modular structure. It separates sub-processes of departing, traveling and observing, of which the first two together define the arrival distribution. The sub-processes utilize biological background and expert knowledge about the migratory behavior of smolts and about the probability to observe them from the video footage under varying environmental conditions. Daily mean temperature and discharge were used as environmental covariates. The model framework does not require assuming a simple distributional shape for the arrival dynamics and thus also allows for multimodal arrival distributions. Results indicate that 20% - 43% of smolts passed the Utsjoki monitoring site unobserved during the years of study. Predictive studies were made to estimate daily run size in cases with missing counts either at the beginning or in the middle of the run, indicating good predictive performance.

Many studies underscore the importance of incorporating the effect of environmental data within a life-history-stage–specific framework for determining the recruitment and survival of small pelagic fish. The recruitment of anchovy (Engraulis encrasicolus) in the Gulf of Cádiz (NE Atlantic) is sensitive to the effect of intense easterlies, stratification of the water column, and discharges from the Guadalquivir River on early life stages. As a proof of concept, we have developed the basis for a new Bayesian model with a dual time step resolution: monthly for juveniles and adults, and weekly for earlier life stages. This dual time step resolution resolves environmental effects on prerecruits while simulating the effect of fishing on recruits. Our estimates for juvenile abundances are validated with field data. The Bayesian framework accounts for the uncertainty, thus providing consistent length-frequency estimates and a plausible environmentally driven stock-recruitment relationship., The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/ 2007-2013) under grant agreement 244706/ ECOKNOWS project and M. Rincón was funded by P09-RNM-5358 of the Junta de Andalucía.

The growth of maritime oil transportation in the Gulf of Finland (GoF), North-Eastern Baltic Sea, increases environmental risks by increasing the probability of oil accidents. By integrating the work of a multi-disciplinary research team and information from several sources, we have developed a probabilistic risk assessment application that considers the likely future development of maritime traffic and oil transportation in the area and the resulting risk of environmental pollution. This metamodel is used to compare the effects of two preventative management actions on the tanker collision probabilities and the consequent risk. The resulting risk is evaluated from four different perspectives. Bayesian networks enable large amounts of information about causalities to be integrated and utilized in probabilistic inference. Compared with the baseline period of 2007-2008, the worst-case scenario is that the risk level increases four-fold by the year 2015. The management measures are evaluated and found to decrease the risk by 4–13%, but the utility gained by their joint implementation would be less than the sum of their independent effects. In addition to the results concerning the varying risk levels, the application provides interesting information about the relationships between the different elements of the system. The growth of maritime oil transportation in the Gulf of Finland (GoF), North-Eastern Baltic Sea, increases environmental risks by increasing the probability of oil accidents. By integrating the work of a multidisciplinary research team and information from several sources, we have developed a probabilistic risk assessment application that considers the likely future development of maritime traffic and oil transportation in the area and the resulting risk of environmental pollution. This metamodel is used to compare the effects of two preventative management actions on the tanker collision probabilities and the consequent risk. The resulting risk is evaluated from four different perspectives. Bayesian networks enable large amounts of information about causalities to be integrated and utilized in probabilistic inference. Compared with the baseline period of 2007–2008, the worst-case scenario is that the risk level increases 4-fold by the year 2015. The management measures are evaluated and found to decrease the risk by 4–13%, but the utility gained by their joint implementation would be less than the sum of their independent effects. In addition to the results concerning the varying risk levels, the application provides interesting information about the relationships between the different elements of the system.

The paper presents an effort to build a biologically realistic, age structured Bayesian model for the stock assessment of data poor fisheries where only aggregated catch data is available. The model is built using prior information from other areas and ecologically or taxonomically similar species. The modeling approach is tested with data poor fisheries on the Cyclades islands in Greek archipelago. The two most important species in the area are selected: bogue (Boops boops) and picarel (Spicara smaris). Both are hermaphroditic. The only data available is the total catch from 1950 to 2010. Information was gathered about natural mortality, recruitment, growth, body size, fecundity, and sex ratio. There were significant problems in finding reliable prior information and a uniform prior was used for fishing mortality. The models at their present stage are not used to give management advice. The biological characteristics of the species in that area should be further studied. However, the posteriors of biological parameters reflect the best available knowledge on these species and they could be used in future studies or in simpler biomass dynamics models as priors.

Understanding and managing ecosystems affected by several anthropogenic stressors require methods that enable analyzing the joint effects of different factors in one framework. Further, as scientific knowledge about natural systems is loaded with uncertainty, it is essential that analyses are based on a probabilistic approach. We describe in this article about building a Bayesian decision model, which includes three stressors present in the Gulf of Finland. The outcome of the integrative model is a set of probability distributions for future nutrient concentrations, herring stock biomass, and achieving the water quality targets set by HELCOM Baltic Sea Action Plan. These distributions can then be used to derive the probability of reaching the management targets for each alternative combination of management actions.

We introduce a Bayesian probability model for making inferences about the unknown number of individuals in a sample, based on known sample weight and on information provided by subsamples with known weights and corresponding counts. Inherent in the Bayesian approach, the model allows for an incorporation of prior information that is often available about the sample size and other uncertain parameter values. As a result, the model provides an estimate of the number of individuals in the sample in the form of a posterior probability distribution that includes both the prior information and the interpretation of the observed data. Such a result cannot be obtained using the frequentist approach. The model presented here can be applied to a wide range of similar problems. Here our main focus is stock assessment, where the task is the conversion of the catch weight into the number of individuals in the catch. The model is easy to use due to availability of general purpose MCMC simulation software, and it can be used either in a standalone fashion or embedded into more complex probability models.

A participatory Bayesian approach was used to investigate how the views of stakeholders could be utilized to develop models to help understand the Central Baltic herring fishery. In task one, we applied the Bayesian belief network methodology to elicit the causal assumptions of six stakeholders on factors that influence natural mortality, growth, and egg survival of the herring stock in probabilistic terms. We also integrated the expressed views into a meta-model using the Bayesian model averaging (BMA) method. In task two, we used influence diagrams to study qualitatively how the stakeholders frame the management problem of the herring fishery and elucidate what kind of causalities the different views involve. The paper combines these two tasks to assess the suitability of the methodological choices to participatory modeling in terms of both a modeling tool and participation mode. The paper also assesses the potential of the study to contribute to the development of participatory modeling practices. It is concluded that the subjective perspective to knowledge, that is fundamental in Bayesian theory, suits participatory modeling better than a positivist paradigm that seeks the objective truth. The methodology provides a flexible tool that can be adapted to different kinds of needs and challenges of participatory modeling. The ability of the approach to deal with small data sets makes it cost-effective in participatory contexts. However, the BMA methodology used in modeling the biological uncertainties is so complex that it needs further development before it can be introduced to wider use in participatory contexts.

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).

Oil transport has greatly increased in the Gulf of Finland over the years, and risks of an oil accident occurring have risen. Thus, an effective oil combating strategy is needed. We developed a Bayesian Network (BN) to examine the recovery efficiency and optimal disposition of the Finnish oil combating vessels in the Gulf of Finland (GoF), Eastern Baltic Sea. Four alternative home harbors, five accident points, and ten oil combating vessels were included in the model to find the optimal disposition policy that would maximize the recovery efficiency. With this composition, the placement of the oil combating vessels seems not to have a significant effect on the recovery efficiency. The process seems to be strongly controlled by certain random factors independent of human action, e.g. wave height and stranding time of the oil. Therefore, the success of oil combating is rather uncertain, so it is also important to develop activities that aim for preventing accidents. We found that the model developed is suitable for this type of multidecision optimization. The methodology, results, and practices are further discussed.

There are several potentially mobile pools of silicon in sediment, e.g. biogenic Si (BSi), dissolved Si and adsorbed Si (AdSi) which makes the studying of a single pool very difficult because of the interference caused by other Si pools. In order to evaluate the impact that different Si pools have on the Si cycle of water ecosystems, it is important to have reliable estimates of the pool sizes. The objective of this study was to estimate the joint concentration distributions of two pools, AdSi and BSi, in, of a small catchment area in southern Finland. The potential correlation between BSi and AdSi was studied to find out if the AdSi pool can be inferred from the total pool (BSi + AdSi). The potential error caused by simultaneous extraction of AdSi in BSi determinations was also investigated. Because all extraction methods include variability due to measurement imprecision and inter-sample variation, the different sources of variation were explicitly separated to be able to infer the underlying true variation of AdSi and BSi within the study area. We have utilized Bayesian inference for this task.

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.

Mäntyniemi, S., Romakkaniemi, A., Dannewitz, J., Palm, S., Pakarinen, T., Pulkkinen, H., Gårdmark, A., and Karlsson, O. 2012. Both predation and feeding opportunities may explain changes in survival of Baltic salmon post-smolts. – ICES Journal of Marine Science, 69: 1574–1579. The survival of wild and hatchery-reared post-smolts of salmon (Salmo salar) in the Baltic Sea has declined since the 1990s. Direct observations of the processes affecting survival are, however, lacking. Here, the importance of food availability and predation in regulating post-smolt survival is analysed. Based on previous studies, the following explanatory variables were selected: (i) availability of herring (Clupea harengus membras) recruits in the Gulf of Bothnia (Bothnian Sea, Bothnian Bay) in the northern Baltic Sea; (ii) sprat (Sprattus sprattus balticus) and herring abundance in the southern Baltic Sea; and (iii) abundance of grey seal (Halichoerus grypus) along the post-smolt migration route. Bayesian analysis was used to estimate the relative probability of each of the 32 combinations of these variables and revealed that the model including grey seal abundance and herring recruits per post-smolt had the highest posterior probability and a high coefficient of determination. The results suggest that the declining trend in post-smolt survival is explained by the increased number of grey seals, whereas the annual variation in survival coincides with variation in the recruitment of Bothnian Sea herring. However, it remains uncertain whether the observed correlations arise from direct causalities or other mechanisms.

Juntunen, T., Vanhatalo, J., Peltonen, H., and Mäntyniemi, S. 2012. Bayesian spatial multispecies modelling to assess pelagic fish stocks from acoustic- and trawl-survey data. – ICES Journal of Marine Science, 69: 95–104. A Bayesian spatial model was constructed to estimate the abundance of multiple fish species in a pelagic environment. Acoustic- and trawl-survey data were combined with environmental data to predict the spatial distribution of (i) the acoustic backscattering of fish, (ii) the relative proportion of each species, and (iii) their mean length in the Gulf of Finland in the northeastern Baltic Sea. By combining the three spatial model layers, the spatial distribution of the biomass of each species was estimated. The model consists of a linear predictor on environmental variables and a spatial random effect given by a Gaussian process. A Bayesian approach is a natural choice for the task because it provides a theoretically justified means of summarizing the uncertainties from various model layers. In the study area, three species dominate pelagic waters: sprat (Sprattus sprattus), herring (Clupea harengus), and three-spined stickleback (Gasterosteus aculeatus). Results are presented for each model layer and for estimated total biomass for each species in 2 × 2 km lattices. The posterior mean and central 95% credible intervals of total biomass were sprat 45.7 kt (27.7–71.6), herring 24.6 kt (9.7–41.3), and three-spined stickleback 1.9 kt (0.9–3.2).

In fisheries stock assessment, the amount of information available from a specific stock is often limited, and the resources to gather new data can be insufficient. This is especially the case when management advice is required for by-catch species which are not always well monitored. However, information is often available from other stocks of the same or closely related species. Also, potential correlations between the life history parameters may contain information which is not usually taken into account in stock assessments. Utilizing all available information can be a cost-efficient way to diminish the amount of uncertainty about key parameters for a case with limited data or when constructing an informative prior for a new case study. In hierarchical modeling, different hierarchical levels can be used to connect closely related and more distant stocks. For example, a lower level of hierarchy can link the stocks within the same species, and a higher level, stocks of related species. We use length-weight and length-fecundity datasets from the FishBase database. Using these datasets, we demonstrate how Bayesian hierarchical correla- tion analysis can improve understanding of fecundity and formalize available knowledge about length-weight and length-fecundity relationships in terms of informative priors for future analysis.

A Poisson process is a commonly used starting point for modeling stochastic variation of ecological count data around a theoretical expectation. However, data typically show more variation than implied by the Poisson distribution. Such overdispersion is often accounted for by using models with different assumptions about how the variance changes with the expectation. The choice of these assumptions can naturally have apparent consequences for statistical inference. We propose a parameterization of the negative binomial distribution, where two overdispersion parameters are introduced to allow for various quadratic mean-variance relationships, including the ones assumed in the most commonly used approaches. Using bird migration as an example, we present hypothetical scenarios on how overdispersion can arise due to sampling, flocking behavior or aggregation, environmental variability, or combinations of these factors. For all considered scenarios, mean-variance relationships can be appropriately described by the negative binomial distribution with two overdispersion parameters. To illustrate, we apply the model to empirical migration data with a high level of overdispersion, gaining clearly different model fits with different assumptions about mean-variance relationships. The proposed framework can be a useful approximation for modeling marginal distributions of independent count data in likelihood-based analyses.

We followed a long-term (up to 503 days) microbial mineralization of dissolved organic carbon (DOC) from lake water in a bioassay and described the kinetics of biodegradation with a new model based on a reactivity continuum approach. The biodegradability of DOC was expressed as the probability of biodegradation, which was assumed to follow a beta distribution. We compared the performance of our beta model to five earlier models: the simplest first order kinetic model, two G models, the power model and the gamma model. The simplest first order kinetic model described the decreasing microbial mineralization of DOC poorly (r 2 = 0.73), but the other models explained the observed kinetics of biodegradation well (r 2 > 0.95). When we assessed the extrapolation power of models beyond the length of the bioassay by reducing the amount of data, the predictive power of the G models was poor. Instead, the beta model predicted the biodegradation kinetics consistently and correctly based on even only three observations in time. The beta model provided also long-term predictions (up to 5,000 years) along the observed long-term mineralization trajectory of organic carbon in sediments. Additionally, the beta model formulated the biodegradability continuum of DOC, which was skewed towards low biodegradability. During the bioassay, the skew towards low biodegradability increased as the most biodegradable parts of DOC were consumed. The beta model describes the biodegradability continuum quantitatively and can predict biodegradation in a realistic manner, thus, improving our understanding about the biodegradability and the role of natural organic matter in the environment.

Mäntyniemi, S., Kuikka, S., Rahikainen, M., Kell, L. T., and Kaitala, V. 2009. The value of information in fisheries management: North Sea herring as an example. – ICES Journal of Marine Science, 66: 2278–2283. We take a decision theoretical approach to fisheries management, using a Bayesian approach to integrate the uncertainty about stock dynamics and current stock status, and express management objectives in the form of a utility function. The value of new information, potentially resulting in new control measures, is high if the information is expected to help in differentiating between the expected consequences of alternative management actions. Conversely, the value of new information is low if there is already great certainty about the state and dynamics of the stock and/or if there is only a small difference between the utility attached to different potential outcomes of the alternative management action. The approach can, therefore, help when deciding on the allocation of resources between obtaining new information and improving management actions. In our example, we evaluate the value of obtaining hypothetically perfect knowledge of the type of stock–recruitment function of the North Sea herring (Clupea harengus) population.

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.

This study examines the extent to which Finnish human dietary intake of organochlorines (PCDD/Fs and PCBs) originating from Northern Baltic herring can be influenced by fisheries management. This was investigated by estimation of human intake using versatile modeling tools (e.g., a herring population model and a bioenergetics model). We used a probabilistic approach to account for the variation in human intake of organochlorines originating from the variation among herring individuals. Our estimates were compared with present precautionary limits and recommendation for use. The results show that present consumption levels and frequencies of herring give a high probability of exceeding recommended intake limits of PCDD/Fs and PCBs. Furthermore, our results clearly demonstrate that in the risk management of dioxinlike organochlorines, regulating fishing (in this case increasing fishing pressure) is a far less effective way to decrease the risk than regulating the consumption of herring. Increased fishing would only slightly decrease organochlorine concentrations of herring in the Finnish fish market.

This study presents a state-space modelling framework for the purposes of stock assessment. The stochastic population dynamics build on the notion of correlated survival and capture events among individuals. The correlation is thought to arise as a combination of schooling behaviour, a spatially patchy environment, and common but unobserved environmental factors affecting all the individuals. The population dynamics model isolates the key biological processes, so that they are not condensed into one parameter but are kept separate. This approach is chosen to aid the inclusion of biological knowledge from sources other than the assessment data at hand. The model can be tailored to each case by choosing appropriate models for the biological processes. Uncertainty about the model parameters and about the appropriate model structures is then described using prior distributions. Different combinations of, for example, age, size, phenotype, life stage, species, and spatial location can be used to structure the population. To update the prior knowledge, the model can be fitted to data by defining appropriate observation models. Much like the biological parameters, the observation models must also be tailored to fit each individual case., The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement n° 244706/ECOKNOWS project and from the Academy of Finland (through a grant to AK).

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.

We review a success story regarding Bayesian inference in fisheries management in the Baltic Sea. The management of salmon fisheries is currently based on the results of a complex Bayesian population dynamic model, and managers and stakeholders use the probabilities in their discussions. We also discuss the technical and human challenges in using Bayesian modeling to give practical advice to the public and to government officials and suggest future areas in which it can be applied. In particular, large databases in fisheries science offer flexible ways to use hierarchical models to learn the population dynamics parameters for those by-catch species that do not have similar large stock-specific data sets like those that exist for many target species. This information is required if we are to understand the future ecosystem risks of fisheries., Published in at http://dx.doi.org/10.1214/13-STS431 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We developed a hierarchical Bayesian integrated life cycle model for Atlantic salmon that improves on the stock assessment approach currently used by ICES and provides some interesting insights about the population dynamics of a stock assemblage. The model is applied to the salmon stocks in eastern Scotland. It assimilates a 40-year (1971–2010) time-series of data compiled by ICES, including the catches in the distant water fisheries at Faroes and West Greenland and estimates of returning fish abundance. Our model offers major improvements in terms of statistical methodology for A. salmon stock assessment. Uncertainty about inferences is readily quantified in the form of Bayesian posterior distributions for parameters and abundance at all life stages, and the model could be adapted to provide projections based on the uncertainty derived from the estimation phase. The approach offers flexibility to improve the ecological realism of the model. It allows the introduction of density dependence in the egg-to-smolt transition, which is not considered in the current ICES assessment method. The results show that this modifies the inferences on the temporal dynamics of the post-smolt marine survival. In particular, the overall decrease in the marine survival between 1971 and 2010 and the sharp decline around 1988–1990 are dampened when density dependence is considered. The return rates of smolts as two-sea-winter (2SW) fish has declined in a higher proportion than return rates as one-sea-winter (1SW) fish. Our results indicate that this can be explained either by an increase in the proportion maturing as 1SW fish or by an increase in the mortality rate at sea of 2SW fish, but the data used in our analyses do not allow the likelihood of these two hypotheses to be gauged.

We present a method by which the knowledge of stakeholders can be taken into account in stock assessment. The approach consists of a structured interview process followed by quantitative modelling of the answers. The outcome is a set of probability models, each describing the views of different stakeholders. Individual models are then merged to a large model by applying the techniques of Bayesian model averaging, and this model is conditioned on stock assessment data. As a result, the views of interviewed stakeholders have been taken into account and weighed based on how well their views are supported by the observed data. We applied this method to the Baltic Sea herring (Clupea harengus) stock assessment by interviewing six stakeholders and conditioning the resulting models on stock assessment data provided by the International Council for the Exploration of the Sea.

Comprehensive problem framing that includes different perspectives is essential for holistic understanding of complex problems and as the first step in building models. We involved five stakeholders to frame the management problem of the Central Baltic herring fishery. By using the Bayesian belief networks (BBNs) approach, the views of the stakeholders were built into graphical influence diagrams representing variables and their dependencies. The views of the scientists involved concentrated on biological concerns, whereas the fisher, the manager, and the representative of an environmental nongovernmental organization included markets and fishing industry influences. Management measures were considered to have a relatively small impact on the development of the herring stock; their impact on socioeconomic objectives was greater. Overall, the framings by these stakeholders propose a focus on socioeconomic issues in research and management and explicitly define management objectives, not only in biological but also in social and economic terms. We find the approach an illustrative tool to structure complex issues systematically. Such a tool can be used as a forum for discussion and for decision support that explicitly includes the views of different stakeholder groups. It enables the examination of social and biological factors in one framework and facilitates bridging the gap between social and natural sciences. A benefit of the BBN approach is that the graphical model structures can be transformed into a quantitative form by inserting probabilistic information.

How can uncertain fisheries science be linked with good governance processes, thereby increasing fisheries management legitimacy and effectiveness? Reducing the uncertainties around scientific models has long been perceived as the cure of the fisheries management problem. There is however increasing recognition that uncertainty in the numbers will remain. A lack of transparency with respect to these uncertainties can damage the credibility of science. The EU Commission’s proposal for a reformed Common Fisheries Policy calls for more self-management for the fishing industry by increasing fishers’ involvement in the planning and execution of policies and boosting the role of fishers’ organisations. One way of higher transparency and improved participation is to include stakeholders in the modelling process itself. The JAKFISH project (Judgment And Knowledge in Fisheries Involving StakeHolders) invited fisheries stakeholders to participate in the process of framing the management problem, and to give input and evaluate the scientific models that are used to provide fisheries management advice. JAKFISH investigated various tools to assess and communicate uncer- tainty around fish stock assessments and fisheries management. Here, a synthesis is presented of the participatory work carried out in four European fishery case studies (Western Baltic herring, North Sea Nephrops, Central Baltic Herring and Mediterranean swordfish), focussing on the uncertainty tools used, the stakeholders’ responses to these, and the lessons learnt. It is concluded that participatory modelling has the potential to facilitate and structure discussions between scientists and stakeholders about uncertainties and the quality of the knowledge base. It can also contribute to collective learning, increase legitimacy, and advance scientific understanding. However, when approaching real-life situations, modelling should not be seen as the priority objective. Rather, the crucial step in a science–stakeholder collaboration is the joint problem framing in an open, transparent way.

Molecular markers have been demonstrated to be useful for the estimation of stock mixture proportions where the origin of individuals is determined from baseline samples. Bayesian statistical methods are widely recognized as providing a preferable strategy for such analyses. In general, Bayesian estimation is based on standard latent class models using data augmentation through Markov chain Monte Carlo techniques. In this study, we introduce a novel approach based on recent developments in the estimation of genetic population structure. Our strategy combines analytical integration with stochastic optimization to identify stock mixtures. An important enhancement over previous methods is the possibility of appropriately handling data where only partial baseline sample information is available. We address the potential use of nonmolecular, auxiliary biological information in our Bayesian model.

Environmental managers must make decisions about complex problems that have a high degree of uncertainty such as, which nutrient abatement measure optimally improves the condition of an ecosystem. Although data and models that provide information on this subject exist, their knowledge may be fragmentary and difficult to interpret. We present a user-friendly modelling tool that integrates results of different models and data-analyses. It can be used by decision-makers for assessing the probabilities of different nutrient abatement scenarios for achieving specific targets set by the Water Framework Directive for Finnish coastal waters in the Gulf of Finland. The results suggest that significant reductions in nutrient loads are required to achieve good ecological status in Finnish coastal waters, and in the event of increased precipitation these targets may be less likely to be attained. Moreover, different approaches to the status classification lead to very different conclusions.