1. Nonnative ("invasive," "exotic," "naturalized") species frequently are vilified. However, some philosophers and ecologists have questioned whether nonnative species and assemblages are objectively, ahistorically identifiable as different entities relative to native species and assemblages, once selection biases are taken into account. 2. We used an unprecedented dataset of morphology, phylogeny, and assemblage content for 336 species of Anolis lizard to compare morphological and phylogenetic characteristics of variability and central tendency between native assemblages and those that include nonnative species. 3. Equivalence tests demonstrated significant similarity between native and nonnative assemblages in trait variability, phylogenetic dispersion, and mean trait values except for body size; logistic and zero-inflated regression failed to distinguish native and nonnative assemblages. For most traits, similarity was not due to assemblages being structured randomly but rather to both native and nonnative assemblages including similar species. 4. Without historical information, a naïve observer would be unable to identify Anolis assemblages as native or nonnative based on morphological assemblage structure or most mean assemblage trait values, but would have some success categorizing assemblages based on average body size of species in the assemblage. 5. Significant phylogenetic and morphological clustering in native assemblages likely reflects source pools composed of close relatives that share traits, as well as some environmental filtering effects; the slightly less phylogenetically clustered but equally morphologically clustered nonnative assemblages are less constrained to proximal source pools but still probably subject to filtering. Differences between native and nonnative assemblages in mean body size likely reflect assemblage youth. The ontological status of nonnative species is discussed in light of these results.