Biological invasions are largely considered to be a "numbers game", wherein the larger the introduction effort, the greater the probability that an introduced population will become established. However, conditions during transport - an early stage of the invasion - can be particularly harsh, thereby greatly reducing the size of a population available to establish in a new region. Some successful non-indigenous species are more tolerant of environmental and anthropogenic stressors than related native species, possibly stemming from selection (ie survival of only pre-adapted individuals for particular environmental conditions) during the invasion process. By reviewing current literature concerning population genetics and consequences of selection on population fitness, we propose that selection acting on transported populations can facilitate local adaptation, which may result in a greater likelihood of invasion than predicted by propagule pressure alone. Specifically, we suggest that detailed surveys should be conducted to determine interactions between molecular mechanisms and demographic factors, given that current management strategies may underestimate invasion risk.