scholarly journals Study on evolution of a predator–prey model in a polluted environment

2021 ◽  
Vol 26 (6) ◽  
pp. 1052-1070
Author(s):  
Bing Liu ◽  
Xin Wang ◽  
Le Song ◽  
Jingna Liu
Keyword(s):  
Body Size ◽  
Function Analysis ◽  
Fitness Function ◽  
Rapid Evolution ◽  
Evolutionary Model ◽  
The Body ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

In this paper, we investigate the effects of pollution on the body size of prey about a predator–prey evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment. Firstly, an eco-evolutionary predator–prey model incorporating the rapid evolution is formulated to investigate the effects of rapid evolution on the population density and the body size of prey by applying the quantitative trait evolutionary theory. The results show that rapid evolution can increase the density of prey and avoid population extinction, and with the worsening of pollution, the evolutionary traits becomes smaller gradually. Next, by employing the adaptive dynamic theory, a long-term evolutionary model is formulated to evaluate the effects of long-term evolution on the population dynamics and the effects of pollution on the body size of prey. The invasion fitness function is given, which reflects whether the mutant can invade successfully or not. Considering the trade-off between the intrinsic growth rate and the evolutionary trait, the critical function analysis method is used to investigate the dynamics of such slow evolutionary system. The results of theoretical analysis and numerical simulations conclude that pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution leads to a smaller body size of prey due to natural selection, while the opposite is more likely to generate evolutionary branching.

Qualitative analysis of a predator–prey model with rapid evolution and piecewise constant arguments

2017 ◽  
Vol 10 (07) ◽  
pp. 1750101 ◽  
Author(s):  
Lie Wang
Keyword(s):  
Qualitative Analysis ◽  
Rapid Evolution ◽  
Flip Bifurcation ◽  
Differential Model ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Linearized Stability

The qualitative analysis of a predator–prey model with rapid evolution and piecewise constant arguments is investigated in this work. The discrete model, which determines the dynamical behavior of the corresponding differential model, is achieved by calculation. First, the sufficient conditions for the existence and local stability of the equilibriums are concluded from the linearized stability theorem and latent root method. Second, the global stability of the equilibriums is discussed through the Poincaré–Bendixson theorem. Furthermore, it is proved that the system has at most one limit cycle. Third, by using the bifurcation theory it is found that the model can undergo the saddle-node bifurcation; the flip bifurcation; and the Neimark–Sacker bifurcation. From the qualitative analysis it can be found that the exponential growth rate and the ratio between the fast and slow timescales have profound influence on the dynamic behavior of the model. Finally, numerical examples carry out to justify the main results in this work.

scholarly journals Behavior and body size modulate the defense of toxin-containing sawfly larvae against ants

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jean-Luc Boevé
Keyword(s):  
Body Size ◽  
Large Body ◽  
The Body ◽  
Larval Body ◽  
Predator Prey ◽  
Sawfly Larvae ◽  
And Behavior ◽  
Toxic Peptides ◽  
Laboratory Bioassays

AbstractThe sawfly larvae of most Argidae and Pergidae (Hymenoptera: Symphyta) species contain toxic peptides, and these along with other traits contribute to their defense. However, the effectiveness of their defense strategy, especially against ants, remains poorly quantified. Here, five Arge species, A. berberidis, A. nigripes, A. ochropus, A. pagana, A. pullata, plus three Pergidae species, Lophyrotoma analis, Lophyrotoma zonalis, Philomastix macleaii, were tested in laboratory bioassays on ant workers mainly of Myrmica rubra. The experiments focused on short-term predator–prey interactions, sawfly survival rate after long-term interactions, and feeding deterrence of the sawfly hemolymph. The larvae of Arge species were generally surrounded by few ants, which rarely bit them, whereas larvae of Pergidae, especially P. macleaii, had more ants around with more biting. A detailed behavioral analysis of Arge-ant interactions revealed that larval body size and abdomen raising behavior were two determinants of ant responses. Another determinant may be the emission of a volatile secretion by non-eversible ventro-abdominal glands. The crude hemolymph of all tested species, the five Arge species and L. zonalis, was a strong feeding deterrent and remained active at a ten-fold dilution. Furthermore, the study revealed that the taxon-specific behavior of ants, sting or spray, impacted the survival of A. pagana but not the large body-sized A. pullata. The overall results suggest that the ability of Arge and Pergidae larvae to defend against ants is influenced by the body size and behavior of the larvae, as well as by chemicals.

scholarly journals Self-limitation in a discrete predator–prey model

2008 ◽  
Vol 48 (1-2) ◽  
pp. 191-196 ◽  
Author(s):  
Francisco J. Solis
Keyword(s):  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Dynamics of an Eco-Epidemic Predator–Prey Model Involving Fractional Derivatives with Power-Law and Mittag–Leffler Kernel

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 785
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Isnani Darti
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Derivative ◽  
Equilibrium Point ◽  
Power Law ◽  
Equilibrium Points ◽  
Essential Difference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Infected Prey

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana–Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag–Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.

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