Aim: We explore the impact of calibrating ecological niche models (ENMs) using (1) native range (NR) data versus (2) entire range (ER) data (native and invasive) on projections of current and future distributions of three Hieracium species. Location: H. aurantiacum, H. murorum and H. pilosella are native to Europe and invasive in Australia, New Zealand and North America. Methods: Differences among the native and invasive realized climatic niches of each species were quantified. Eight ENMs in BIOMOD were calibrated with (1) NR and (2) ER data. Current European, North American and Australian distributions were projected. Future Australian distributions were modelled using four climate change scenarios for 2030. Results: The invasive climatic niche of H. murorum is primarily a subset of that expressed in its native range. Invasive populations of H. aurantiacum and H. pilosella occupy different climatic niches to those realized in their native ranges. Furthermore, geographically separate invasive populations of these two species have distinct climatic niches. ENMs calibrated on the realized niche of native regions projected smaller distributions than models incorporating data from species' entire ranges, and failed to correctly predict many known invasive populations. Under future climate scenarios, projected distributions decreased by similar percentages, regardless of the data used to calibrate ENMs; however, the overall sizes of projected distributions varied substantially. Main conclusions: This study provides quantitative evidence that invasive populations of Hieracium species can occur in areas with different climatic conditions than experienced in their native ranges. For these, and similar species, calibration of ENMs based on NR data only will misrepresent their potential invasive distribution. These errors will propagate when estimating climate change impacts. Thus, incorporating data from species' entire distributions may result in a more thorough assessment of current and future ranges, and provides a closer approximation of the elusive fundamental niche.