Samu Mäntyniemi

Using the negative binomial distribution to model overdispersion in ecological count data

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.

Optimizing the recovery efficiency of Finnish oil combating vessels in the Gulf of Finland using Bayesian Networks.

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.

Baltic Herring Fisheries Management: Stakeholder Views to Frame the Problem

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.

Toward integrative management advice of water quality, oil spills, and fishery in the Gulf of Finland: a Bayesian approach.

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 Bayesian network for assessing the collision induced risk of an oil accident in the Gulf of Finland

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.

Experiences in Bayesian Inference in Baltic Salmon Management

Abstract. We review a success story regarding Bayesian inference infisheries management in the Baltic Sea. The management of salmonfisheries is currently based on the results of a complex Bayesian pop-ulation dynamic model, and managers and stakeholders use the prob-abilities in their discussions. We also discuss the technical and humanchallenges in using Bayesian modeling to give practical advice to thepublic and to government officials and suggest future areas in which itcan be applied. In particular, large databases in fisheries science offerflexible ways to use hierarchical models to learn the population dynam-ics parameters for those by-catch species that do not have similar largestock-specific data sets like those that exist for many target species.This information is required if we are to understand the future ecosys-tem risks of fisheries. Key words and phrases: Bayesian inference, Baltic salmon, risk anal-ysis, fishery management, decision analysis.1. INTRODUCTIONWe introduce a case of fisheries managementwhere Bayesian inference has been extensively used.Fisheries management is a field of applied science,and one could easily argue that fisheries science is

Evaluating the impact of nutrient abatement measures on the ecological status of coastal waters: a Bayesian network for decision analysis

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.

Involving stakeholders in building integrated fisheries models using Bayesian methods

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.

Human Dietary Intake of Organochlorines from Baltic Herring: Implications of Individual Fish Variability and Fisheries Management

Abstract 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.

Separating Biogenic and Adsorbed Pools of Silicon in Sediments Using Bayesian Inference

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.