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1. Using two sources of data to estimate butterfly species richness, the potential influences of 11 environmental variables on the richness gradient of butterflies in western/central Europe and northern Africa were examined with multiple regression and spatial autocorrelation analysis. A measure of water–energy balance, actual evapotranspiration, explained 79% of the variance in butterfly species richness using data derived from range maps, and 72% of the variance using data derived from grid-based distribution maps. All other variables explained less than 4% of the variance in the regression models and differed depending on the data source. 2. The spatial analysis indicated that actual evapotranspiration successfully removed most of the spatial autocorrelation in both richness data sets at all spatial scales, confirming the ability of the model to account for the spatial pattern in butterfly richness. 3. Plant species richness, a rarely tested variable hypothesised to be an important determinant of herbivore diversity, was weakly associated with butterfly richness, suggesting that it has little or no direct influence on butterfly richness. 4. A historical variable, the length of time that areas have been exposed for recolonisation after the retreat of the ice sheet following the last ice age, was also not associated with richness patterns, indicating that butterfly richness is in equilibrium with contemporary climate. 5. It was not possible to confirm a result reported for Canadian butterflies that land cover diversity is a strong predictor of butterfly richness, possibly because of methodological differences in the studies, differences in the range of climates found in Canada and the western Palearctic, or because of the highly modified landscape characteristic of Europe. 6. Water–energy balance offers a parsimonious explanation for the butterfly richness gradient in this region, operating partially indirectly via effects on plant productivity and partially directly via physiological effects on butterflies, and this conclusion is robust to differences in the types of distribution maps used to estimate richness patterns. [ABSTRACT FROM AUTHOR]