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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inference is used to estimate the epistemic uncertainty about the true state of an indicator variable during an historical reference period.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.

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.

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.

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 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.

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.

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.

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.