Analysis of the Trojan Y-Chromosome eradication strategy for an invasive species

A Gender-Selective Harvesting Strategy: Weak Allee Effects and a Non-hyperbolic Extinction Boundary

Recently a gender-selective harvesting strategy has been proposed for possible control of aquatic invasive species, wherein females of the invasive species are harvested, whilst stocking the males (abbreviated as FHMS strategy) (Lyu et al. in Nat Resour Model 33(2):e12252, 2020). We consider the FHMS strategy with a weak Allee effect, and show that its extinction boundary need not be hyperbolic. To the best of our knowledge, this is the first example of a non-hyperbolic extinction boundary in two-compartment mating models structured by sex. The model possesses a rich dynamical structure, with several local co-dimension one bifurcations occurring. We also show the occurrence of a global homoclinic bifurcation, which has applicability for large scale strategic bio-control.

On Large and Small Data Blow-Up Solutions in the Trojan Y Chromosome Model

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.

Using YY supermales to destabilize invasive fish populations

A plausible biocontrol strategy for the eradication of invasive species involves augmenting wild populations with genetically modified supermales. Supermales contain double YY chromosomes. When they are augmented into a wild population, destabilization and eventual extinction occurs over time due to a strongly skewed gender ratio towards males. Here, we employ a mathematical model that considers an Allee effect, but we have discovered through simulation that the presence of supermales leads to an increase in the minimal number of females needed for survival at a value higher than the mathematically defined Allee effect. Using this effect, we focus our research on exploring the sensitivity of the optimized supply rate of supermale fish to the initial gender ratio and density of the wild populations. We find that the eradication strategy with optimized supply rate of supermales can be determined with knowledge of reproductive rate and survival fitness of supermale fish.

THE OPTIMAL IMPLEMENTATION OF THETROJAN Y CHROMOSOMEERADICATION STRATEGY OF AN INVASIVE SPECIES

Invasive aquatic species continue to be a persistent problem around the world. The Trojan Y Chromosome (TYC) eradication strategy has recently been developed to help fight the problem in aquatic systems by targeting only the invasive species, sparing native marine stock. It involves rearing genetically modified samples of the invasive species and introducing them into the environment to alter the sex ratio of the invasive population. The paper is devoted to finding the optimal implementation of the TYC eradication strategy of an invasive species as well as a modified, potentially more cost-effective strategy. The modified TYC strategy (MTYC) eliminates one round of exposure to sex hormones compared to the TYC strategy. After introducing both strategies, the optimal control problems for each are formulated. The two strategies are compared through numerical simulations. Our results illustrate that the MTYC strategy, with lower implementation costs, is a better strategy option when trying to minimize the overall effective cost in most scenarios.

Stochastic models for the Trojan Y-Chromosome eradication strategy of an invasive species

The Trojan Y-Chromosome (TYC) strategy, an autocidal genetic biocontrol method, has been proposed to eliminate invasive alien species. In this work, we develop a Markov jump process model for this strategy, and we verify that there is a positive probability for wild-type females going extinct within a finite time. Moreover, when sex-reversed Trojan females are introduced at a constant population size, we formulate a stochastic differential equation (SDE) model as an approximation to the proposed Markov jump process model. Using the SDE model, we investigate the probability distribution and expectation of the extinction time of wild-type females by solving Kolmogorov equations associated with these statistics. The results indicate how the probability distribution and expectation of the extinction time are shaped by the initial conditions and the model parameters.