The dispersion of Scaphoideus titanus Ball adults from wild to cultivated grapevines was studied using a novel mark–capture technique. The crowns of wild grapevines located at a distance from vineyards ranging from 5 to 330 m were sprayed with a water solution of either cow milk (marker: casein) or chicken egg whites (marker: albumin) and insects captured in yellow sticky traps placed on the canopy of grapes were analyzed via an indirect ELISA for markers’ identification. Data were subject to exponential regression as a function of distance from wild grapevine, and to spatial interpolation (Inverse Distance Weighted and Kernel interpolation with barriers) using ArcGIS Desktop 10.1 software. The influence of rainfall and time elapsed after marking on markers’ effectiveness, and the different dispersion of males and females were studied with regression analyses. Of a total of 5417 insects analyzed, 43% were positive to egg; whereas 18% of 536 tested resulted marked with milk. No influence of rainfall or time elapsed was observed for egg, whereas milk was affected by time. Males and females showed no difference in dispersal. Marked adults decreased exponentially along with distance from wild grapevine and up to 80% of them were captured within 30 m. However, there was evidence of long-range dispersal up to 330 m. The interpolation maps showed a clear clustering of marked S. titanus close to the treated wild grapevine, and the pathways to the vineyards did not always seem to go along straight lines but mainly along ecological corridors. S. titanus adults are therefore capable of dispersing from wild to cultivated grapevine, and this may affect pest management strategies.

Interpolation of spatial data is a very general mathematical problem with various applications. In geostatistics, it is assumed that the underlying structure of the data is a stochastic process which leads to an interpolation procedure known as kriging. This method is mathematically equivalent to kernel interpolation, a method used in numerical analysis for the same problem, but derived under completely different modelling assumptions. In this paper we present the two approaches and discuss their modelling assumptions, notions of optimality and different concepts to quantify the interpolation accuracy. Their relation is much closer than has been appreciated so far, and even results on convergence rates of kernel interpolants can be translated to the geostatistical framework. We sketch different answers obtained in the two fields concerning the issue of kernel misspecification, present some methods for kernel selection and discuss the scope of these methods with a data example from the computer experiments literature.

The objective of the present study is the calculation of the spatial distribution of sunshine duration in the territory of Slovenia. Four maps at 1 km resolution were prepared to present the spatial distribution of sunshine duration for winter, spring, summer and autumn. The values on all four maps are 30-year mean seasonal sunshine duration, calculated from measurements from 43 meteorological stations in the period 1971–2000. The seasonal presentation was chosen due to the high inter-seasonal variability in spatial distribution of sunshine duration. The values on the maps were calculated on a mathematical horizon, to avoid the influence of geographical, urban and vegetation distortions. The interpolation model is a combination of a multivariate regression model, residual kriging and simple mathematical models. Geographical variables (altitude, latitude and longitude) are used in models to explain the spatial variability of sunshine duration. For each season, regionalisation is performed based on sunshine duration data, derived geographical data and radio-sounding data. The interpolation models are developed for each region separately and afterwards the calculated layers are merged using GIS techniques.