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The Trojan Y Chromosome Strategy (TYC) is the only genetic biological control method in practice in North America for controlling invasive populations with an XX–XY sex determinism. Herein a modified organism, that is a supermale or feminised supermale, is introduced into an invasive population to skew the sex ratio over time, causing local extinction. We consider the three species TYC reaction diffusion model, and show that introduction of supermales above certain thresholds, and for certain initial data, solutions can blow-up in finite time. Thus, in order to have biologically meaningful solutions, one needs to restrict parameter and initial data regimes, in TYC type models. 

Blue mussels (Mytilus edulis) are important keystone species that have been declining in the Gulf of Maine. This could be attributed to a variety of complex factors such as indirect effects due to invasion by epibionts, which remains unexplored mathematically. Based on classical optimal foraging theory (OFT) and anti-fouling defense mechanisms of mussels, we derive an ODE model for crab–mussel interactions in the presence of an invasive epibiont, Didemnum vexillum. The dynamical analysis leads to results on stability, global boundedness and bifurcations of the model. Next, via optimal control methods, we predict various ecological outcomes. Our results have key implications for preserving mussel populations in the advent of invasion by non-native epibionts. In particular, they help us understand the changing popluation dynamics of local predator–prey communities, due to indirect effects that epibionts confer. 

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.