A comparison of the Trojan Y Chromosome strategy to harvesting models for eradication of nonnative species

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 of supermales that 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.

Optimal control and analysis of a modified trojan Y-Chromosome strategy

“…This suggests that it is important to include intraspecies competition and the Allee effect to appropriately determine the overall cost of the TYC eradication strategy. In addition, this indicates that the overall cost of the strategy is smaller than previously predicted [18]. Lastly, a stochastic model is proposed to investigate the influence of noise in the birth and death rates on the objective function's value.…”

“…An optimal introduction rate of supermales is determined through optimal control theory and was chosen to minimize an objective function that measures the total amount of wild population and introduced supermales. The optimal introduction rate for the classical model was given in [18]. Here, we compare the influence of including the intraspecies competition for mates and the Allee effect on the optimal introduction rate.…”

“…5. Therefore, the inclusion of intraspecies competition and the Allee effect greatly influence the overall cost of the TYC strategy and indicate the strategy is less costly than previously considered in [18]. In the case, of the TYC model that includes intraspecies competition for mates and does not consider the Allee effect obtains an objective value of −381.3074, which is still considerably lower than the classical model.…”

“…In this section, we will numerically simulate the optimal control for the modified TYC model with strong Allee effect. The following unscaled parameters used for simulation are provided from a least squares approximation of population experiments of guppy fish in [18], namely, β = 0.0057, δ = 0.0648, K = 405, α = 24, and time interval of (0, 200). In scaled variables: r ≈ 17.8125, a ≈ .06, 0 < t < 12.96.…”

“…Therefore, the acceleration of the declining population can be used as an indicator as to when to begin rapidly reducing the introduction rate. As a basis of comparison, the optimal µ in unscaled variables for the classical model was determined in [18] (see Fig. 5), which is shown in Fig.…”