Functional response in coccinellid beetles (Coleoptera: Coccinellidae) is modified by prey-density experience

In the present study, we assessed functional response curves of two generalist coccinellid beetles (Coleoptera: Coccinellidae), specifically Menochilus sexmaculatus and Propylea dissecta, using fluctuating densities of aphid prey as a stimulus. In what may be the first such study, we investigated how the prey density experienced during the early larval development of these two predatory beetle species shaped the functional response curves of the late instar–larval and adult stages. The predators were switched from their rearing prey-density environments of scarce, optimal, or abundant prey to five testing density environments of extremely scarce, scarce, suboptimal, optimal, or abundant prey. The individuals of M. sexmaculatus that were reared on either scarce- and optimal- or abundant-prey densities exhibited type II functional response curves as both larvae and adults. However, individuals of P. dissecta that were reared on scarce- and abundant-prey densities displayed modified type II functional response curves as larvae and type II functional response curves as adults. In contrast, individuals of P. dissecta reared on the optimal-prey density displayed type II functional response curves as larvae and modified type II functional response curves as adults. The fourth-instar larvae and adult females of M. sexmaculatus and P. dissecta also exhibited highest prey consumption (T/Th) and shortest prey-handling time (Th) on the scarce-prey rearing density. Thus, under fluctuating-prey conditions, M. sexmaculatus is a better biological control agent of aphids than P. dissecta is.

Impact of fear on delayed three species food-web model with Holling type-II functional response

This paper deals with the investigation of the three species food-web model. This model includes two logistically growing interaction species, namely [Formula: see text] and [Formula: see text], and the third species [Formula: see text] behaves as the predator and also host for [Formula: see text]. The species [Formula: see text] predating on the species [Formula: see text] with the Holling type-II functional response, while the first species [Formula: see text] is benefited from the third species [Formula: see text]. Further, the effect of fear is incorporated in the growth rate of species [Formula: see text] due to the predator [Formula: see text] and time lag in [Formula: see text] due to the gestation process. We explore all the biologically possible equilibrium points, and their local stability is analyzed based on the sample parameters. Next, we investigate the occurrence of Hopf-bifurcation around the interior equilibrium point by taking the value of the fear parameter as a bifurcation parameter for the non-delayed system. Moreover, we verify the local stability and existence of Hopf-bifurcation for the corresponding delayed system. Also, the direction and stability of the bifurcating periodic solutions are determined using the normal form theory and the center manifold theorem. Finally, we perform extensive numerical simulations to support the evidence of our analytical findings.

Effects of Refuge Prey on Stability of the Prey-Predator Model Subject to Immigrants: A Mathematical Modelling Approach

Prey-predator system is enormously complex and nonlinear interaction between species. Such complexity regularly requires development of new approaches which involves more factors in analysis of its population dynamics. In this paper, we formulate a modified Lotka-Volterra model that incorporates factors such as refuge prey and immigrants. We investigate the effects of refuge prey and immigrants by varying the refuge factor, with and without immigrants. The results show that with Holling’s type I functional response, the proposed model is asymptotically convergent when a refuge prey factor is introduced. Moreover, with Holling’s type II functional response, the proposed mathematical model is unstable and does not converge. However, with Holling’s type III functional response in a system, the proposed mathematical model is asymptotically stable. These results point out the following remarks: The effects of refuge prey on stability of the dynamical system vary depending on the type of functional response, and when the predator population increases, the likelihood of prey extinction declines when the proportion of preys in refuge population increases. Hence, the factor of refuge prey is crucial for controlling the population of the predator and obtaining balances between prey and predator in the ecosystem. Keywords: Refuge prey, stability, prey-predator, immigrants, Mathematical modelling

Potential of Blaptostethus pallescens Poppius (Hemiptera: Anthocoridae) on Tetranychus truncatus Ehara (Prostigmata: Tetranychidae)

Efficiency, functional and numerical responses of anthocorid bug Blaptostethus pallescens Poppius on the spider mite, Tetranychus truncatus Ehara were examined under laboratory conditions. Nymphs of B. pallescens exhibited a Hollings type II functional response when females of spider mite were offered at densities of 10, 20, 30, 40, 50, 60 and 70 mites/bug. Individual fifth instar bugs consumed up to 45.3 adult females of T. truncatus in 24 h at prey mite densities of 60 mites/ bug. Studies on numerical response revealed that the nymphs of the anthocorid bug failed to complete development when the food was restricted to mite alone. Numerical response studies on adult bugs, when offered T. truncatus at densities of 10, 20, 30, 40 and 50 females showed no significant differences in the average fecundity of the female bug. Results indicate that the anthocorid predator, B. pallescens has a very high predatory potential though with a weak numerical response.

Dynamics on Effect of Prey Refuge Proportional to Predator in Discrete-Time Prey-Predator Model

Prey-predator models with refuge effect have great importance in the context of ecology. Constant refuge and refuge proportional to prey are the most popular concepts of refuge in the existing literature. Now, there are new different types of refuge concepts attracting researchers. This study considers a refuge concept proportional to the predator due to the fear induced by predators. When predators increase, fears also increase and that is why prey refuges also increase. Here, we examine the influence of prey refuge proportional to predator effect in a discrete prey-predator interaction with the Holling type II functional response model. Is this refuge stabilizing or destabilizing the system? That is the central question of this study. The existence and stability of fixed points, Period-Doubling Bifurcation, Neimark–Sacker Bifurcation, the influence of prey refuge, and chaos are analyzed. This work provides the bifurcation diagrams and Lyapunov exponents to analyze the refuge parameter of the model. The proposed discrete model indicates rich dynamics as the effect of prey refuge through numerical simulations.

Dynamical Analysis Predator-Prey Population with Holling Type II Functional Response

In this article, we investigate the dynamical analysis of predator prey model. Interactionamong preys and predators use Holling type II functional response, and assuming prey refuge aswell as harvesting in both populations. This study aims to study the predator prey model and todetermine the effect of overharvesting which consequently will affect the ecosystem. In the modelfound three equilibrium points, i.e., (0,0) is the extinction of predator and prey equilibrium,?(??, 0) is the equilibrium with predatory populations extinct and the last equilibrium points?(??, ??) is the coexist equilibrium. All equilibrium points are asymptotically stable (locally) undercertain conditions. These analytical findings were confirmed by several numerical simulations.

Fear Induced Multistability in a Predator-Prey Model

In ecology, the predator’s impact goes beyond just killing the prey. In the present work, we explore the role of fear in the dynamics of a discrete-time predator-prey model where the predator-prey interaction obeys Holling type-II functional response. Owing to the increasing strength of fear, the system becomes stable from chaotic oscillations via inverse Neimark–Sacker bifurcation. Extensive numerical simulations are carried out to investigate the intricate dynamics for the organization of periodic structures in the bi-parameter space of the system. We observe fear induced multistability between different pairs of coexisting heterogeneous attractors due to the overlapping of multiple periodic domains in the bi-parameter space. The basin sets of the coexisting attractors are obtained and discussed at length. Multistability in the predator-prey system is important because the dynamics of the predator and prey populations in the critical parameter zone becomes uncertain.