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Invasive species control via a discrete model for the Trojan Y-chromosome strategy

Invasive species are a growing threat to ecosystems, particularly in aquatic environments. The Trojan Y Chromosome (TYC) strategy is a promising biological method for reducing invasive populations by introducing genetically modified males (supermales) that produce only male offspring, leading to population decline due to a shortage of females. In this study, we develop a novel discrete--time, age--structured mathematical model to simulate the effects of this strategy. Our model divides the life cycle of species into two stages--egg and maturity--and tracks different sub--populations, including supermales. We analyze the equilibria of the system and prove the existence and stability of extinction and positive equilibrium points. Numerical simulations show that extinction depends on factors such as fecundity, the number of supermales released, and initial population sizes. The model also reveals complex behaviors, such as bistability and thresholds for population collapse. This discrete approach offers a useful framework for understanding and optimizing the TYC strategy and can help guide future field applications of invasive species control.

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