Genomics approaches allow the empirical evaluation of standing genetic diversity across geography and environment in several species. The patterns of neutral population genetic structure reveal the history of migration and gene flow defining the scale of isolation by distance and environment, which has fundamental implications for tracking invasion and managing ecosystems. We have surveyed thousands of individuals of a model invasive species Brachypodium hybridum and foundation species Eucalyptus melliodora, at scores of collection sites across the southeastern range of Australia. Multiple inbred colonizing lines of B. hybridum can be traced back to their native Mediterranean and West Asian range while a few locations have novel genetic diversity available to local selection, suggesting that limiting introduction is a higher priority than limiting expansion of naturalized populations. Although Eucalyptus forests are highly fragmented across their range, we found very little evidence of historical structure and isolation by distance explained only 4% of genetic variation. This suggests that a focus on local provenancing of a few remnant trees could be maladaptive given current land use and accelerating climate change causing a reduction of genetic diversity in this foundation species. These tools, when deployed for conservation, can lead to better management strategies than current reliance on null models of clonal invasion or local adaptation.