Abstract. 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.

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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.

We introduce a Bayesian probability model for the estimation of the size of an animal population from removal data. The model is based on the assumption that in the removal sampling, catchability may vary between individuals, 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 successive removals may be needed to correctly estimate the population size.

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.