In recent years, there has been widespread concern about the ecological and genetic effects of genetically modified organisms. In salmon and other fishes, transgenic growth hormone genes have been shown to have large effects on size and various traits related to fitness. In this paper, I have shown by using a deterministic model that if such a transgene has a male-mating advantage and a general viability disadvantage, then the conditions for its invasion in a natural population are very broad. More specifically, for 66.7% of the possible combinations of the possible mating and viability parameters, the transgene increases in frequency, and for 50% of the combinations, it goes to fixation. In addition, by this increase in the frequency of the transgene, the viability of the natural population is reduced, increasing the probability of extinction of the natural population. These findings provide independent confirmation of previous concerns about the inherent risks of transgenic organisms, especially for native salmon populations potentially affected by commercial salmon production using transgenic stocks.