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This paper contributes to the characterization of the probability density of the price returns in some European day-ahead electricity markets (NordPool, APX, Powernext) by fitting flexible and general families of distributions, such as the α-stable, Normal Inverse Gaussian (NIG), Exponential Power (EP), and Asymmetric Exponential Power (AEP) distributions, and comparing their goodness of fit. The α-stable and the NIG systematically outperform the EP and AEP models, but the tail behavior and the skewness are sensitive to the definition of the returns and to the deseasonalization methods. In particular, the logarithmic transform and volatility rescaling tend to dampen the extreme returns. [ABSTRACT FROM AUTHOR]

1. It is well established that pollen-mediated gene flow among natural plant populations depends on a complex interaction between the spatial distribution of pollen sources and the short- and long-distance components of pollen dispersal. Despite this knowledge, spatial isolation strategies proposed in Europe to ensure the harvest purity of conventional crops are based on distance from the nearest genetically modified (GM) crop and on empirical data from two-plot experiments. Here, we investigate the circumstances under which the multiplicity of pollen sources over the landscape should be considered in strategies to contain GM crops. 2. We simulated pollen dispersal over eighty 6 × 6 km simulated landscapes differing in field characteristics and in amount of GM and conventional maize. Pollen dispersal was modelled either via a Normal Inverse Gaussian (NIG, currently used for European coexistence studies) or a bivariate Student (2Dt) kernel. These kernels differ in their amount of short- and long-distance dispersal. We used linear models to analyse the impact of local and landscape variables on impurity rates (i.e. proportion of seeds sired by pollen from a transgenic crop) in conventional fields and quantified their increase due to dispersal from other than the closest GM crops. 3. The average impurity rate over a landscape increased linearly with the proportion of GM maize over that landscape. The increase was twice as fast using the NIG kernel and was governed by the short-distance dispersal component. 4. Variation in impurity rates largely depended on the distance to the closest GM crop and the size of the receptor field. However, impurity rates were generally underestimated when only dispersal from the closest GM field was considered. 5. Synthesis and applications. Distance to the closest GM crop had most impact on impurity rates in conventional fields. However, impurity rates also depended on intermediate- to long-distance dispersal from distant GM crops. Therefore, isolation distances as currently defined will probably not allow long-term coexistence of GM and conventional crops, especially as the proportion of GM crops grown increases. We suggest strategies to account for this impact of long-distance dispersal. [ABSTRACT FROM AUTHOR]