The hypervolume analysis estimates the realized niche space of a species based on a random sample derived from multivariate kernel density estimates of the species' occurrence records in (Blonder et al. 2014). Two different approaches for the delimitation of the respective hypervolume are available: the first approach uses a bandwidth (herein = 1) enclosing the species records in environmental space (termed BWD hereafter), whereas the second approach delimits the realized niche space based on a multivariate minimum convex polygon (termed MMCP hereafter, see Supplementary Material S4 for a visualization of both approaches). Based on the hypervolumes of two taxa (herein native and expanding populations, as well as a set of records which could not be assigned to either of them), it is possible to compute various statistics including the volume of the realized niches per taxon, the intersection of two taxa as well as the unique volumes, the centroid distance between two taxa, and the Sorensen index [i.e., for hypervolumes A and B: S = 2*|A int B| / (|A| + |B|), Blonder 2015]. Furthermore, an inclusion test allows a projection of the hypervolumes into geographic space, representing the potential distribution of the species based on the estimates of the realized niches.