A Three Species Food Chain Model with Fear Induced Trophic Cascade

Panday, Pijush; Pal, Nikhil R.; Samanta, Sudip; Chattopadhyay, Joydev

doi:10.1007/s40819-019-0688-x

Cited by 48 publications

(12 citation statements)

References 41 publications

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“…We point out that this type of three dimensional food chain models have been intensive and extensively studied by some researchers, see, e.g., [9,11,12,13] and the references therein. As far as fear effect in food chains is concerned, two recent papers [19,20] have also followed line of [30] to consider fear effect in food chain of three species; their scenario is different from ours: they considered other types of functional responses, they incorporated fear effects in the bottom and middle species, and they assumed that the top and middle species are specialist predators. The first goal of this paper is to explore the dynamics of (1.3), particularly, the impact of the meso-carnivore's anti-predation response level α on the dynamics.…”

Section: Introductionmentioning

confidence: 98%

On mechanisms of trophic cascade caused by anti-predation response in food chain systems

Wang

Zou

2020

Math Appl Sci Eng

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Motivated by a recent field study [Nat. Commun. 7(2016), 10698] on the impact of fear of large carnivores on the populations in a cascading ecosystem of food chain type with the large carnivores as the top predator, in this paper we propose two model systems in the form of ordinary differential equations to mechanistically explore the cascade of such a fear effect. The models are of the Lotka-Volterra type, one is three imensional and the other four dimensional. The 3-D model only considers the cost of the anti-predation response reflected in the decrease of the production, while the 4-D model considers also the benefit of the response in reducing the predation rate, in addition to the cost by reducing the production. We perform a thorough analysis on the dynamics of the two models. The results reveal that the 3-D model and 4-model demonstrate opposite patterns for trophic cascade in terms of the dependence of population sizes for each species at the co-existence equilibrium on the anti-predation response level parameter, and such a difference is attributed to whether or not there is a benefit for the anti-predation response by the meso-carnivore species.

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Section: Introductionmentioning

confidence: 98%

On mechanisms of trophic cascade caused by anti-predation response in food chain systems

Wang

Zou

2020

Math Appl Sci Eng

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“…Their results show that the sensitivity of individuals to predation risk leads to the different adaptability. As a typical and representative indirect effect, the fear factor is used to describe the physiological changes caused by the stress behavior of the prey population since the prey needs to be alert to predators coming at any time 14 .…”

Section: Introductionmentioning

confidence: 99%

Pattern formation of parasite-host model induced by fear effect

Ye¹,

Zhao²,

Zhou³

2022

Preprint

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In this paper, based on the epidemiological microparasite model, a parasite-host model is established by considering the fear effect of susceptible individuals on infectors. We ex-Pattern formation of parasite-host model induced by fear effect With the development of reaction-diffusion equation, the research on the pattern formation of population model has been widely concerned. Among them, the research on spatiotemporal dynamics of predator-prey model is particularly rich. Recently, Wang et al. 1 first proposed the mathematical expression of fear effect and considered the fear effect in the traditional predator-prey model. It was found that the addition of fear effect brought complex dynamic phenomena. Since then, many predator-prey models with fear effect have been studied. Considering that the fear effect also exists between uninfected host and infected host. Therefore, this paper attempts to introduce the fear effect into the epidemiological microparasite model and construct a parasite-host model with fear effect. With the help of computer, we simulate the distribution of population under different degrees of fear, and combined with other ecological factors to explore how the distribution of population will change under the interference of various factors. Our results show that the growth of pattern satisfies some laws under different ecological factors. Hopefully, this work will provide us further understanding of population dynamics in a real environment stimulated by the fear effect.

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“…In fact, all animals show many kinds of anti-predator responses, such as changes of foraging behavior, habitat usage, physiology, and so on ( [19][20][21][22][23]). To describe that, the concept of fear in the prey was introduced and studied ( [24][25][26][27][28][29][30]). In particular, Wang et al [29] for the first time proposed the following predator-prey model with the cost of fear:…”

Section: Introductionmentioning

confidence: 99%

Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect

2020

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We proposed and analyzed a predator–prey model with both the additive Allee effect and the fear effect in the prey. Firstly, we studied the existence and local stability of equilibria. Some sufficient conditions on the global stability of the positive equilibrium were established by applying the Dulac theorem. Those results indicate that some bifurcations occur. We then confirmed the occurrence of saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation. Those theoretical results were demonstrated with numerical simulations. In the bifurcation analysis, we only considered the effect of the strong Allee effect. Finally, we found that the stronger the fear effect, the smaller the density of predator species. However, the fear effect has no influence on the final density of the prey.

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A Three Species Food Chain Model with Fear Induced Trophic Cascade

Cited by 48 publications

References 41 publications

On mechanisms of trophic cascade caused by anti-predation response in food chain systems

On mechanisms of trophic cascade caused by anti-predation response in food chain systems

Pattern formation of parasite-host model induced by fear effect

Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect

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