Biological invasions rank among the main global threats for biodiversity. The Eastern mosquitofish (Gambusia holbrooki) is considered one of the 100 world worst invasive species due to its high adaptation capability to new environments. Using the restriction-site-associated DNA tags (RADtags), introduced European locations were compared against native US mosquitofish populations to analyse genomic changes that occurred during invasive process of European locations. After filtering, 7724 RADtags containing only one SNP were retained for population studies. Comparative genomics indicated that 186 of these RADtags matched sequences in the transcriptome of Xyphophorus maculatus, the most closely related genome available. Genomic analyses showed that invasive populations show high reductions in diversity. Further, analyses of population structuring based on these data are concordant with previous analyses based on microsatellites. It is concluded that during the invasion process genetic drift was the main evolutionary force affecting patterns of diversity and population structure. While recognizing that positive selection could be masked by the strong drift during founder events, adaptive processes were evidenced in a reduced number of RADtags (<2%), with only one of these in a putative coding region. Surprisingly, balancing selection was detected in several coding RADtags, suggesting that the preservation of polymorphism in specific genes could be more important than the average population diversity for the population maintenance at any location, particularly for the survival of introduced populations