Species distribution modeling is widely applied to predict invasive species distributions and species range shifts under climate change. Accurate predictions depend upon meeting the assumption that ecological niches are conserved, i.e., spatially or temporally transferable. Here we present a multi-taxon comparative analysis of niche conservatism using biological invasion events well documented in natural history museum collections. Our goal is to assess spatial transferability of the climatic niche of a range of noxious terrestrial invasive species using two complementary approaches. First we compare species' native versus invasive ranges in environmental space using two distinct methods, Principal Components Analysis and Mahalanobis distance. Second we compare species' native versus invaded ranges in geographic space as estimated using the species distribution modeling technique Maxent and the comparative index Hellinger's I. We find that species exhibit a range of responses, from almost complete transferability, in which the invaded niches completely overlap with the native niches, to a complete dissociation between native and invaded ranges. Intermediate responses included expansion of dimension attributable to either temperature or precipitation derived variables, as well as niche expansion in multiple dimensions. We conclude that the ecological niche in the native range is generally a poor predictor of invaded range and, by analogy, the ecological niche may be a poor predictor of range shifts under climate change. We suggest that assessing dimensions of niche transferability prior to standard species distribution modeling may improve the understanding of species' dynamics in the invaded range.