Modelling the distribution of invasive alien species is widely used for predicting future dispersal, response to climate change, and effects of management, but little information is available on the scale dependence of spatial models. This study is focused on Heracleum mantegazzianum, a problematic invasive plant in central and north-western Europe. The main objective was to model the current distribution of this species at national (43,000 km(2)) and regional scale (4900 km(2)) using autologistic regression with a Danish data set. Presence-absence data were used in a grid system with 5 x 5 km(2) or 2 x 2 km(2) as basic units. To avoid misleading presence-absence models and unreliable probability values due to unbalanced data, the prevalence was used as cut-off value, and a favourability function was applied to the model predictions. The national model showed a widespread distribution of H. mantegazzianum with highest habitat suitability in the eastern and northern parts of the country where human population density is high, winters more severe and/or loamy soils more common. At a regional scale the distribution of H. mantegazzianum is associated with alluvial sand cover, high human population density, spring precipitation, and presence of the species in neighbour grid units. The observed widespread national distribution is likely the result of anthropogenic spread of this ornamental plant, while the locally clumped distribution suggests that H. mantegazzianum naturally spreads mainly over short distances. The current distribution in Denmark resembles an intermediate invasion stage where long-distance dispersal is less important, while spread from suitable neighbour habitats is significant. The study demonstrates that the favourability function leads to improved mapping standards for invasive species.
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