Hydra effects in stable food chain models

Pal, Debprasad; Ghosh, Bapan; Kar, Tapan Kumar

doi:10.1016/j.biosystems.2019.104018

Cited by 19 publications

(4 citation statements)

References 25 publications

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“…If

h \geq 1

extinction of the species happen. However, it is not always the case, increasing harvesting rate can raise population of the species (Pal et al, 2019).…”

Section: Numerical Simulation and Discussionmentioning

confidence: 99%

Coexistence and harvesting optimal policy in three species food chain model with general Holling type functional response

Dawed

Kebedow

2021

Natural Resource Modeling

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In this paper, we have discussed harvesting of prey and intermediate predator species. Both are subjected to Holling type I–V functional response. Conditions for local and global stability of the nonnegative equilibria are verified. The permanent coexistence criterion of the model system and existence of optimal equilibrium solution of the control problem are demonstrated. Maximum sustainable yield and maximal net present revenue are determined. To confirm analytical results, numerical solution has been carried out using the Matlab™ ODE solver ODE45 and the simulations show the model system reveals complex behavior (such as oscillations), which reflects the real situation. Recommendations for Resource Managers From our investigation of this study, we recommend to the management the following points. Coexistence of the three species with harvesting, or persistence of the model system is possible provided that good management(treatment) of some factors (such as harvesting rate, growth rate of species, etc.) are performed. The dynamics reveals complex behavior (such as oscillations), which reflects the real situation and it is sensitive to the above factors, especially the growth rate of the intermediate predator. The policy makers should recommend the optimal effort h * to be applied and the optimal stock ( x * , y * , z * ) to harvest. This indicates that maximum profit will attain while securing sustainability of the three species in the ecosystem.

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“…If

h \geq 1

extinction of the species happen. However, it is not always the case, increasing harvesting rate can raise population of the species (Pal et al, 2019).…”

Section: Numerical Simulation and Discussionmentioning

confidence: 99%

Coexistence and harvesting optimal policy in three species food chain model with general Holling type functional response

Dawed

Kebedow

2021

Natural Resource Modeling

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“…We apply the Routh-Hurwitz criteria [17][18][19] to determine the stability of the equilibrium. In order to analyze the stability of the equilibrium, it is useful to consider the characteristic equation for the eigenvalue λ. Herein, P E 1 (λ), P E 2 (λ), P E p (λ) are denoted as the characteristic polynomials of the Jacobian matrix J at equilibria E 1 , E 2 , E p , respectively.…”

Section: Linear Stability Analysis Of the Four Equilibriamentioning

confidence: 99%

“…The above two conditions of (19) can easily be achieved since there exists a local strategy S * , where S * ∈ (τ 1 , τ 2 ), such that…”

Section: The Adaptive Dynamical Systemmentioning

confidence: 99%

Coexistence and Replacement of Two Different Maturation Strategies Adopted by a Stage-Structured Population

Xue

2023

Mathematics

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Maturation strategies play a key role in the survival and development of populations. In response to changes in the external environment and human interventions, populations adopt appropriate maturation strategies. Different maturation strategies can lead to different birth and mortality rates. In this paper, we develop and analyze a stage-structured population model with two maturation strategies to obtain conditions for the coexistence of two maturation strategies and conditions for competitive exclusion. Our results also show that equality of fitness—represented by basic reproductive numbers being greater than 1 under different maturation strategies—promotes the coexistence of the two strategies. The reason why a strategy is replaced by another one is that the population adopting this strategy has weak fitness, which is measured by the basic reproductive number.

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“…Excessive exploitation behavior of predators also creates a hydra effect which is interdependent between predator-prey species (Iskin da S. Costa & Dos Anjos, 2018). For example, the exploitation of aquaculture predatory fish in intensive pond types has a tendency to destroy predator populations (Pal et al, 2019). The hydra effect is also introduced in the eco-evolution system, which shows that the rate of extinction of predatory species becomes greater with this evolution (Esteves & Caxias, 2021;Lee et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Hydra effects predator-prey bazykin's model with stage-structure and intraspecific for predator

Pratama

Siddik

Dadi

et al. 2022

DJM

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Bazykin's predator-prey population model is considered to represent the exchange stability condition of population growth. The existence of the hydra effect and, at the same time, analyzing its influence on population growth. The condition of the model divides the species into a stage structure, namely, prey, immature predators, and mature predators. The population growth of the three species has its own characteristics. This research revealed that the Holling type II and intraspecific predatory function responses together induce the Hydra effect. In the model formed, there are 12 equilibrium points, with details for every seven points of negative imaginary equilibrium and five points of non-negative equilibrium. The findings of research studies center on five points of non-negative equilibrium. All real roots that interpret the species population's growth conditions are taken and tested for long-term stability. The test results show one point of equilibrium that meets the Routh-Hurwitz criteria and their characteristic equations. In numerical simulations, the maximum sustained yield is in the local asymptotic stable state. The growth of prey trajectories increased significantly, although at the beginning of the interaction there was a slowdown in population growth. Meanwhile, the population of immature predators and mature predators was not significantly different. Both populations grow steadily toward the point of population stability. It turns out that the two populations grow inversely, the faster the rate of predation by predators, the faster the growth rate of the prey population.

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Hydra effects in stable food chain models

Cited by 19 publications

References 25 publications

Coexistence and harvesting optimal policy in three species food chain model with general Holling type functional response

Coexistence and harvesting optimal policy in three species food chain model with general Holling type functional response

Coexistence and Replacement of Two Different Maturation Strategies Adopted by a Stage-Structured Population

Hydra effects predator-prey bazykin's model with stage-structure and intraspecific for predator

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