not-yet-known not-yet-known not-yet-known unknown Invasive species are a major challenge to managers worldwide due to their ability to rapidly change their niche space and behavior in order to reproduce and survive in a novel environment. One globally distributed invasive species, the Pacific oyster, Crassostrea (Magallana) gigas, first arrived in Sweden in 2006. To date, they have not colonized the low salinity waters of the Baltic Sea, and it has generally been assumed that the inability of Pacific oysters to reproduce in low salinities has acted as a barrier. We have studied differences in fertilization rates among oysters along the invasion range, and examined heritability of salinity tolerance through classic mating designs across five different salinity levels. We found that fertilization rates in low salinities increased with proximity to the range front, and that there was a strong heritable component to these differences. We then used whole genome sequence data to identify genomic regions that diverged significantly from expected Mendelian inheritance in larval full-sib families that survived in low salinities. Our results show that a chromosomal region containing coding sequences for all histones forming the nucleosome, as well as a region containing LSU and SSU subunit ribosomal DNA in the sperm, are involved in low-salinity tolerance at fertilization and early development. We also found no evidence of recent bottlenecks or reductions in genetic diversity along the invasion front compared to more established populations. We therefore conclude that the Pacific oyster has the potential to adapt further to low-salinity conditions and may invade the Baltic Sea.