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The Trojan Y Chromosome (TYC) strategy is a biological control method for controlling invasive populations with an XX–XY sex determinism, wherein a modified organism is introduced into an invasive population to skew the sex ratio over time, causing local extinction. However, the classical three compartment TYC model possesses blow-up solutions, for large initial conditions [Takyi EM, Beauregard MA, Griffin T, Bobo L, Parshad RD, On large and small data blow-up solutions in the Trojan Y Chromosome model, Axioms 11(3):120, 2022]. We investigate model improvements via accounting for a modified logistic term, female mating preference, competition between males and supermales and pair formation. Each one of these models is dynamically explored and is shown to possess global in-time non-negative solutions, in any parameter and initial data regime, and the models are also effective in facilitating extinction of the invasive wild type. [ABSTRACT FROM AUTHOR]

In this study, the Z-type control method is applied to an intraguild crop-pest-natural enemy model, assuming that the natural enemy can predate on both crop and pest populations. For this purpose, the indirect Z-type controller is considered in the natural enemy population. After providing the design function for the crop-pest-natural enemy model with Z-control, we find the analytical expression of the update parameter. The findings indicate that the uncontrolled system can produce chaos through period-doubling bifurcation due to crop over-consumption by the pest population. We draw a Poincaré map to confirm the occurrence of chaos and compute the maximum Lyapunov exponent. As the observations further indicate that the pest population can be controlled by using an indirect Z-control mechanism in the natural enemy population, we postulate that, if natural enemy abundance can be governed by the update parameter, any desired pest population abundance can be achieved through the proposed Z-type controller, thus controlling the pest. To verify these assertions, extensive numerical simulations are performed to explore the potential for practical application of the proposed Z-type controller. [ABSTRACT FROM AUTHOR]

The literature posits that an introduced predator population is able to drive its target pest population to extinction, if supplemented with high quality additional food of sufficient quantity. We show this approach actually leads to infinite time blow-up of the predator population, so is unpragmatic as a pest management strategy. We propose an alternate model in which the additional food induces predator competition. Analysis of this model indicates that depending on the competition parameter c , one can have global stability of the pest-free state, bistability dynamics, or up to three interior equilibria. As c and the additional food quantity ξ are varied standard codimension one and codimension two bifurcations are observed. We also use structural symmetries to construct several nonstandard bifurcations such as saddle-node-transcritical bifurcation (SNTC) in codimension two and a cusp-transcritical bifurcation (CPTC), also in codimension two. We further use symmetry to construct a novel pitchfork-transcritical bifurcation (PTC) in codimension two, thus explicitly characterizing a new organizing center of the model. Our findings indicate that increasing additional food in predator–pest models can hinder bio-control, contrarily to some of the literature. However, additional food that also induces predator competition, leads to rich dynamics and enhances bio-control. [ABSTRACT FROM AUTHOR]

Classical language dynamics explain language shift as a process in which speakers adopt a higher status language in lieu of a lower status language. This is well documented with English having out-competed languages such as Scottish Gaelic, Welsh, and Mandarin. The 1961–1991 Indian censuses report a sharper increase in Hindi/English Bilinguals compared to Monolingual Hindi speakers, suggesting that English is on the rise in India — and is out-competing Hindi. However, the 1991–2011 data show that Bilingual numbers have saturated, while Monolingual Hindi speakers continue to rise exponentially. To capture this counter-intuitive dynamic, we propose a novel language dynamics model of interaction between Monolingual Hindi speakers and Hindi/English Bilinguals, which captures the Indian census data of the last 50 years with greater accuracy, than other well-known language dynamics models. We thus provide a first example of a lower status language having out competed English, a higher status language. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cannibalism is an intriguing life history trait, that has been considered primarily in the predator, in predator-prey population models. Recent experimental evidence shows that prey cannibalism can have a significant impact on predator-prey population dynamics in natural communities. Motivated by these experimental results, we investigate a ratio-dependent Holling-Tanner model, where cannibalism occurs simultaneously in both the predator and prey species. We show that depending on parameters, whilst prey or predator cannibalism acting alone leads to instability, their joint effect can actually stabilize the unstable interior equilibrium. Furthermore, in the spatially explicit model, we find that depending on parameters, prey and predator cannibalism acting jointly can cause spatial patterns to form, while not so acting individually. We discuss ecological consequences of these findings in light of food chain dynamics, invasive species control and climate change. [ABSTRACT FROM AUTHOR]

Population ecology theory is replete with density-dependent processes. However, trait-mediated or behavioral indirect interactions can both reinforce or oppose density-dependent effects. This paper presents the first two species competitive ODE and PDE systems, where the non-consumptive behavioral fear effect and the Allee effect, a density-dependent process, are both present. The stability of the equilibria is discussed analytically using the qualitative theory of ordinary differential equations. It is found that the Allee effect and the fear effect change the extinction dynamics of the system and the number of positive equilibrium points, but they do not affect the stability of the positive equilibria. We also observe standard co-dimension one bifurcation in the system by varying the Allee or fear parameter. Interestingly, we find that the Allee effect working in conjunction with the fear effect can bring about several dynamical changes to the system with only fear. There are three parametric regimes of interest in the fear parameter. For small and intermediate amounts of fear, the Allee + fear effect opposes dynamics driven by the fear effect. However, for large amounts of fear the Allee + fear effect reinforces the dynamics driven by the fear effect. The analysis of the corresponding spatially explicit model is also presented. To this end, the comparison principle for parabolic PDE is used. The conclusions of this paper have strong implications for conservation biology, biological control as well as the preservation of biodiversity. [ABSTRACT FROM AUTHOR]