Native geographical range extent has frequently emerged as a correlate of invasiveness, especially for plant species. We tested whether dimensions of the native range (measured by the area-of-occupancy and its scaling patterns) of 720 Australian eucalypts (genera Angophora, Eucalyptus and Corymbia) could explain introduction and invasion success. We also compared our results with a previous study on 979 Australian acacias (previously grouped in Acacia subgenus Phyllodineae) to investigate whether features of their native ranges explained the much higher invasion success in this group compared to eucalypts. From nine databases we found records that 373 eucalypts have been introduced to areas outside their native ranges; 82 of these have become naturalised, and eight are invasive. A similar proportion of Australian acacias have been introduced, but almost three times as many are invasive (384 species introduced, 71 of which are naturalized and 23 invasive). Eucalypts with large native ranges are more likely to have been introduced and subsequently naturalise, as is the case with acacias. Unlike acacias, however, the native range size of invasive eucalypts was not significantly greater than naturalised (but not invasive) species. Intriguingly, the human preference for introducing species with larger ranges was much greater for acacias than for eucalypts as the geometric mean range sizes of introduced, naturalised and invasive acacias are 2.04, 1.88 and 3.59 times those of eucalypts at the same stage. Moreover, the percolation exponent (i.e. the slope of occupancy scaling) becomes more extreme towards the end of the introduction–naturalization–invasion continuum, decreasing for acacias but increasing for eucalypts, with acacias, except for non-introduced species, having a lower exponent than eucalypts. The selection preference of acacias during introduction is thus for species that can rapidly expand their range; in contrast, slow-spreading eucalypts have been selected for dissemination. In other words, humans appear to have selected for highly invasive acacias but against introducing highly invasive eucalypts.