The mechanisms that facilitate success of an invasive species include both ecological and evolutionary processes. Investigating these factors can provide insight on management strategies for controlling further establishment of foreign populations in areas they would not naturally inhabit. We expand on previous work for controlling introductions of non-indigenous freshwater and marine species through ballast water discharge. This system can be modeled by a population growth function with Allee effects which incorporates spatial dispersal by a diffusion process. This approach can provide good estimates for acceptable volumes of discharge for various organisms (with differing reproductive rates) for a range of invasion risk tolerances. Additionally, repeated immigration events may lead to persistence by rescuing populations at below threshold densities or minimum volumes. In order to make our analysis more robust, we include an evolutionary subsystem to explore the effects of selection and genetic variance on traits that may increase a population’s likelihood of survival. Specifically, we allow the Allee threshold to become a dynamic parameter which is considered the result of behavioral adaptations affecting an organism’s ability to locate mates, predator vigilance, etc. Our results reveal the possibility that an introduced population that would fail to persist in the ecological context of this model has the potential to succeed through evolutionary means.