1. The existence of a hierarchical scheme of environmental controls on the spatial distribution of plant species was explored for three non-indigenous weeds, Fallopia japonica, Heracleum mantegazzianum and Impatiens glandulifera, in the British Isles.
2. Logistic regression analyses of the presence/absence of the three weed species examined the relative importance of 60 environmental variables, encompassing land cover, geology and climate. Analyses were undertaken using variables assessed at a hectad (10 × 10 km) or tetrad (2 × 2 km) resolution at national (England and Wales) and regional (County Durham, UK) spatial extents.
3. The ranges of all three species in the British Isles are currently increasing, and the non-equilibrium nature of their distribution limited the goodness-of-fit of logistic models. Interpretation of whether a species has expanded to occupy entirely its potential spatial range was scale-dependent, and species' distributions, when viewed at coarser spatial scales, may be more likely to be interpreted as having reached stasis.
4. Spatial autocorrelation was more evident at the finer tetrad spatial resolution for both F. japonica and I. glandulifera, but not evident at all for H. mantegazzianum. Only the distribution of I. glandulifera revealed significant spatial autocorrelation among hectads at the national scale. These patterns appear related to the different dispersal mechanisms of the three species.
5. The majority of the environmental variables identified as important at the tetrad resolution for County Durham were also important at the hectad resolution for England and Wales for both F. japonica and I. glandulifera, but not for H. mantegazzianum. However, for all three species the environmental variables identified as significant were consistent with qualitative descriptions of the species' habitat characteristics. There was no evidence of a hierarchy of environmental controls.
6. At the regional extent, scaling-up species' distributions from tetrads to hectads was relatively successful, but scaling-down was not. The coarser resolution models were too unrefined to model fine-scale distributions successfully. Similarly, at a coarse hectad resolution, regional models were poor predictors of national species' distributions. It therefore appears that scaling-up from fine to coarse resolution is appropriate when spatial extent is held constant, and focusing-down from large to small spatial extents is appropriate when data resolution is held constant.