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Abstract The Trojan Y Chromosome strategy (TYC) is a promising eradication method for biological control of nonnative species. The strategy works by manipulating the sex ratio of a population through the introduction ofsupermalesthat guarantee male offspring. In the current study, we compare the TYC method with a pure harvesting strategy. We also analyze a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting or hybrid strategy may work better than the TYC method at controlling a nonnative species population. Recommendations for resource managers Where harvesting is feasible, it is as effective if not more effective than the classical TYC method. Therein managers may attempt harvesting female fish while stocking males or harvesting both male and female fishes.Managers may attempt linear harvesting, saturating density‐dependent harvesting, and unbounded density‐dependent harvesting. Linear harvesting is seen to be the most effective.We caution against the outright use of harvesting due to various density‐dependent effects that may arise. To this end hybrid models that involve a combination of harvesting and TYC‐type methods might be a better strategy.One may also use harvesting as a tool in mesocosm settings to predict the efficacy of the TYC strategy in the wild.