SPATIAL DEPENDENCE OF RANDOM SETS AND ITS APPLICATION TO DISPERSION OF BARK BEETLE INFESTATION IN A NATURAL FOREST

Abstract

A large spatio-temporal data set monitoring the annual progress of bark beetle infestation in the Bavarian Forest National Park (Germany) is statistically analysed by means of complex image analysis algorithms. The infestation data were obtained by color-infrared (CIR) aerial image interpretation and cover 10 subsequent years (2001–2010). Newly emerged infestation patches are hypothesized as spatially correlated to locations of previous year’s infestation. Both areas, source patches and subsequently emerged patches, are considered as two disjoint random sets. Their spatio-temporal dependence is analysed by two methods: the classical approach based on the measurement of cross-covariance functions, and a second one based on nearest neighbor distances. The resulting characteristics can be interpreted as pre-disposition probabilities of bark beetle infestation depending on distance to sources. Both methods show a strong short-range preference, which decreases with increasing distances.

Keywords

• cross-covariance function
• ecological data
• Ips typographus
• pre-disposition
• image analysis
• Euclidean distance transform
• Fast Fourier transform