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)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(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.

Statistics for Patch Observations

“…To the author's knowledge this is the first time non-parametric RACS summary functions have been explicitly correlated with LPI concepts. Kautz et al (Kautz et al, 2011) provide an example of the power of non-parametric RACS very similar to LPI without directly referring to LPIs. Otherwise previous use of RACS in relation to LPIs have been for simulation studies (Hargis et al, 1998) and model fitting (Diggle, 1981;Sadler, 2006).…”

“…(Molchanov, 1984;Ayala and Simó, 1995;Kautz et al, 2011). (Stoyan and Mecke, 2005) observed in a rectangular region; hatched regions denote locations inside the random set.…”

“…The RACS framework has also been used to test the spatial dependence of beetle infestation (Kautz et al, 2011) and the relationship between tree deaths and bore locations (Chang et al, 2013). Numerous other examples exist (Descombes, 2012).…”

Fine fluorescent powder marking study of dispersal in the spruce bark beetle, Ips typographus (Coleoptera: Scolytidae)

“…It is commonly considered to be a secondary pest of Norway spruce (Szujecki, 1987;Forster, 1993;Schwenke, 1996), but may occasionally infest also pine and larch. Dispersal of adults is a minor but key part in the life cycle, which may crucially infl uence the survival and reproductive success of the spruce bark beetle (Hawkes, 2009) and colonization of host trees (Kautz et al, 2011a). Before a host tree is infested, the adults exhibit a series of consecutive behaviours.…”

“…Ips typographus prefers weakened, damaged or dying trees, predominantly older than 60 years. Favourable climatic conditions, frequently in combination with the late removal of infested timber, may lead to an outbreak of spruce bark beetles (Kautz et al, 2011a;Lausch et al, 2011). During such outbreaks, Ips typographus population density increases exponentially and emerging adults are able to infest and kill even healthy trees on a large scale, which changes Ips typographus into a primary pest (Reeve, 1997).…”