Habitat structure and prey aggregation determine the functional response in a soil predator–prey interaction

AbstractIn the present article, we investigate the impact of fear effect in a predator–prey model, where predator–prey interaction follows Beddington–DeAngelis functional response. We consider that due to fear of predator the birth rate of prey population reduces. Mathematical properties, such as persistence, equilibria analysis, local and global stability analysis, and bifurcation analysis, have been investigated. We observe that an increase in the cost of fear destabilizes the system and produces periodic solutions via supercritical Hopf bifurcation. However, with further increase in the strength of fear, system undergoes another Hopf bifurcation and becomes stable. The stability of the Hopf-bifurcating periodic solutions is obtained by computing the first Lyapunov coefficient. Our results suggest that fear of predation risk can have both stabilizing and destabilizing effects.

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A Fractional-Order Predator-Prey Model with Ratio-Dependent Functional Response and Linear Harvesting

10.20944/preprints201910.0340.v1 ◽

2019 ◽

Author(s):

Agus Suryanto ◽

Isnani Darti ◽

Hasan S. Panigoro ◽

Adem Kilicman

Keyword(s):

Functional Response ◽

Fractional Order ◽

Equilibrium Points ◽

Stability Criteria ◽

Predator Prey ◽

Predator Prey Model ◽

Proposed Model ◽

Prey Interaction ◽

Ratio Dependent ◽

Predictor Corrector

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

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Prey body mass and richness underlie the persistence of a top predator

Proceedings of The Royal Society B Biological Sciences ◽

10.1098/rspb.2019.0622 ◽

2019 ◽

Vol 286 (1902) ◽

pp. 20190622 ◽

Cited By ~ 2

Author(s):

Laura Melissa Guzman ◽

Diane S. Srivastava

Keyword(s):

Food Web ◽

Functional Response ◽

Body Mass ◽

Prey Species ◽

Handling Time ◽

Predator Prey ◽

Prey Diversity ◽

Prey Interaction ◽

Range Of Values ◽

Food Web Model

Predators and prey often differ in body mass. The ratio of predator to prey body mass influences the predator's functional response (how consumption varies with prey density), and therefore, the strength and stability of the predator–prey interaction. The persistence of food chains is maximized when prey species are neither too big nor too small relative to their predator. Nonetheless, we do not know if (i) food web persistence requires that all predator–prey body mass ratios are intermediate, nor (ii) if this constraint depends on prey diversity. We experimentally quantified the functional response for a single predator consuming prey species of different body masses. We used the resultant allometric functional response to parametrize a food web model. We found that predator persistence was maximized when the minimum prey size in the community was intermediate, but as prey diversity increased, the minimum body size could take a broader range of values. This last result occurs because of Jensen's inequality: the average handling time for multiple prey of different sizes is higher than the handling time of the average sized prey. Our results demonstrate that prey diversity mediates how differences between predators and prey in body mass determine food web stability.

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Does altering patch number and connectivity change the predatory functional response type? Experiments and simulations in an acarine predator–prey system

Canadian Journal of Zoology ◽

10.1139/z05-072 ◽

2005 ◽

Vol 83 (6) ◽

pp. 797-806 ◽

Cited By ~ 5

Author(s):

P J Lester ◽

J M Yee ◽

S Yee ◽

J Haywood ◽

H MA Thistlewood ◽

...

Keyword(s):

Functional Response ◽

Panonychus Ulmi ◽

Type Ii ◽

Response Type ◽

Predator Prey ◽

Amblyseius Fallacis ◽

Type Iii ◽

Prey Interaction ◽

Patch Connectivity

In multipatch landscapes, understanding the role of patch number and connectivity is key for the conservation of species under processes such as predation. The functional response is the most basic form of the predatorprey interaction. Two common response types exist: a decelerating curvilinear increase in prey consumption with prey density to a plateau (type II) and a sigmoidal-shaped curve (type III). Type II responses have been observed for a variety of predators, though only type III responses allow long-term persistence and are demographically stabilizing. We tested the hypothesis that the functional response type can change from a type II to a type III with increasing patch number and (or) decreasing connectivity. The predatory mite Amblyseius fallacis (Garman, 1948) has previously been shown to have a type II response when feeding on Panonychus ulmi (Koch, 1839). We examined this predatorprey interaction using experiments that varied in patch number, and simulations that varied in both patch number and connectivity. In no experimental or simulation trial did altering patch number or connectivity change the predator's functional response from type II to type III, even with an 80-fold decrease in patch connectivity. How do predators with this demographically destabilizing functional response persist? Hypotheses regarding metapopulations and alternative prey are discussed.

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A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting

Mathematics ◽

10.3390/math7111100 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1100 ◽

Cited By ~ 8

Author(s):

Agus Suryanto ◽

Isnani Darti ◽

Hasan S. Panigoro ◽

Adem Kilicman

Keyword(s):

Functional Response ◽

Fractional Order ◽

Equilibrium Points ◽

Stability Criteria ◽

Predator Prey ◽

Predator Prey Model ◽

Proposed Model ◽

Prey Interaction ◽

Ratio Dependent ◽

Predictor Corrector

We consider a model of predator–prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity and boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon’s theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurrence of Hopf bifurcation around the interior point is also shown analytically. At the end, we implemented the Predictor–Corrector scheme to perform some numerical simulations.

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