Common garden studies comparing trait differences of exotic species between native and introduced ranges rarely incorporate an analysis of genetic variation, but simply infer that trait shifts between ranges are genetically determined. We compared four growth-related traits (total biomass, relative growth rate RGR, specific leaf area SLA, and root to shoot ratio R:S) of five invasive Fabaceae species (Acacia cyclops, A. longifolia, A. melanoxylon, A. saligna, Paraserianthes lophantha), grown in a common garden experiment using seeds from introduced and native ranges across Australia. Chloroplast microsatellite loci were used to compare genetic diversity of native and introduced populations to determine standing genetic diversity and infer introduction history. We asked whether shifts in traits associated with faster growth due to enemy release in the introduced range were associated with levels of genetic diversity associated with introduction history. We found differences in traits between ranges, although these traits varied among the species. Compared to native-range populations, introduced-range Acacia longifolia had greater biomass and larger SLA; A. cyclops had greater RGR; and A. melanoxylon displayed lower R:S. Genetic diversity in the introduced range was lower for one of those species, A. longifolia, and two others that did not show differences in traits, A. saligna and P. lophantha. Diversity was higher in the introduced range for A. melanoxylon and did not differ among ranges for A. cyclops. These patterns of genetic diversity suggest that a genetic bottleneck may have occurred following the introduction of A. longifolia, A. saligna and P. lophantha. In contrast greater or comparable genetic diversity in the introduced range for A. melanoxylon and A. cyclops suggests introductions from multiple sources. This study has shown that a reduction in genetic diversity in the introduced range is not necessarily associated with a reduced capacity for adaptive responses or invasion potential in the novel range.