Using YY supermales to destabilize invasive fish populations

Bhattacharyya, Joydeb; Roelke, Daniel L.; Walton, Jay R.; Banerjee, Soumitro

doi:10.1016/j.tpb.2020.04.003

Cited by 9 publications

(7 citation statements)

References 26 publications

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“…The dynamics defined on the sliding segment Σ S is determined by the differential equation (7), which admits pseudoequilibrium of the Filippov system (4) (cf. Fig.…”

Section: Model Equationsmentioning

confidence: 99%

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Non-smooth dynamics emerging from predator-driven discontinuous prey dispersal

Bhattacharyya¹,

Chattopadhyay

2021

Nonlinear Dyn

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In ecology, the refuge protection of the prey plays a significant role in the dynamics of the interactions between prey and predator. In this paper, we investigate the dynamics of a non-smooth prey-predator mathematical model characterized by density-dependent intermittent refuge protection of the prey. The model assumes the population density of the predator as an index for the prey to decide on when to avail or discontinue refuge protection, representing the level of apprehension of the prey by the predators. We apply Filippov's regularization approach to study the model and obtain the sliding segment of the system. We obtain the criterion for the existence of the regular or virtual equilibria, boundary equilibrium, tangent points, and pseudo-equilibria of the Filippov system. The conditions for the visibility (or invisibility) of the tangent points are derived. We investigate the regular or virtual equilibrium bifurcation, boundarynode bifurcation and pseudo-saddle-node bifurcation. Further, we examine the effects of dispersal delay on the Filippov system associated with prey vigilance in identifying the predator population density. We observe that the hysteresis in the Filippov system produces stable limit cycles around the predator population density threshold in some bounded region in the phase plane. Moreover, we find that the level of apprehension and vigilance of the prey play a significant role in their refuge-dispersion dynamics.

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“…The dynamics defined on the sliding segment Σ S is determined by the differential equation (7), which admits pseudoequilibrium of the Filippov system (4) (cf. Fig.…”

Section: Model Equationsmentioning

confidence: 99%

“…4). The pseudo-equilibria E P i = (x P i , L) (i = 0, 1) of the system (4) satisfies the differential equations (7), where…”

Section: Model Equationsmentioning

confidence: 99%

Non-smooth dynamics emerging from predator-driven discontinuous prey dispersal

Bhattacharyya¹,

Chattopadhyay

2021

Nonlinear Dyn

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“…A mathematical model for the TYC strategy was first pioneered in [16], and has been well investigated [11,19,[21][22][23][24]. Prior work on TYC [25][26][27][28], shows that depending on the introduction rate of the supermale/feminized supermale, and initial data, eradication is always possible. These results rely on the assumption that solutions remain positive for all non-negative initial data.…”

Section: Introductionmentioning

confidence: 99%

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

Parshad

Beauregard

Takyi

et al. 2022

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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.

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“…In (b) and (c), supermales interact with males and females at different µ introduction rates and extinction occurs quicker. Initial condition is given as [50,50,30,10,50]. Thus we see that supermale introduction in classical pair formation models can cause a faster decay in solutions, than without.…”

mentioning

confidence: 87%

“…In the event that the sufficient conditions of [149] are not met, the shape of the Allee threshold remains an open problem [7]. In particular, in cases where a strong Allee effect has been introduced into TYC type mating dynamics, we still see a hyperbolic extinction boundary [6,10], but this might be due to a lesser exploration of the parameter space. 24.…”

Section: The Extinction Boundarymentioning

confidence: 99%

Some mathematical problems in population ecology

Takyi

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Using YY supermales to destabilize invasive fish populations

Cited by 9 publications

References 26 publications

Non-smooth dynamics emerging from predator-driven discontinuous prey dispersal

Non-smooth dynamics emerging from predator-driven discontinuous prey dispersal

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

Some mathematical problems in population ecology

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