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How climatic variability is linked to the spatial distribution of range sizes: seasonality versus climate change velocity in sphingid mothsAim To map the spatial variation of range sizes within sphingid moths, and to test hypotheses on its environmental control. In particular, we investigate effects of climate change velocity since the Pleistocene and the mid‐Holocene, temperature and precipitation seasonality, topography, Pleistocene ice cover, and available land area. Location Old World and Australasia, excluding smaller islands. Methods We used fine‐grained range maps (based on expert‐edited distribution modelling) for all 972 sphingid moth species in the research region and calculated, at a grain size of 100 km, the median of range sizes of all species that co‐occur in a pixel. Climate, topography and Pleistocene ice cover data were taken from publicly available sources. We calculated climate change velocities (CCV) for the last 21 kyr as well as 6 kyr. We compared the effects of seasonality and CCV on median range sizes with spatially explicit models while accounting for effects of elevation range, glaciation history and available land area. Results Range sizes show a clear spatial pattern, with highest median values in deserts and arctic regions and lowest values in isolated tropical regions. Range sizes were only weakly related to absolute latitude (predicted by Rapoport's effect), but there was a strong north‐south pattern of range size decline. Temperature seasonality emerged as the strongest environmental correlate of median range size, in univariate as well as multivariate models, whereas effects of CCV were weak and unstable for both time periods. These results were robust to variations in the parameters in alternative analyses, among them multivariate CCV. Main conclusions Temperature seasonality is a strong correlate of spatial range size variation, while effects of longer‐term temperature change, as captured by CCV, received much weaker support.