Co-existence thresholds in the dynamics of the plant–herbivore interaction with Allee effect and harvest

Asfaw, Manalebish Debalike; Kassa, Semu Mitiku; Lungu, Edward M.

doi:10.1142/s1793524518500572

Cited by 10 publications

(5 citation statements)

References 25 publications

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“…In this study, numerical simulations are performed by the use of MATLAB software using secondary data obtained from [2,14]. These simulations are performed to analyze the effect of harvesting of species and Allee effect on the ecosystem where time is in years.…”

Section: Numerical Simulation Of the Modelmentioning

confidence: 99%

“…In the absence of pathogens, we have susceptible plants, herbivores and their natural enemies. Performing numerical simulation for this population dynamics using data adopted from [2,14] where,r = 20, k = 10000, c1 = 1.22, θ = 0.4, p2,c2 = 0.2, d = 0.2 where we get the graphs in Fig. 3, Fig.…”

Section: Simulation Of Susceptible Plants Herbivores and Their Natura...mentioning

confidence: 99%

“…For instance, plants produce their own food from water and sunlight, whereas animals feed on other species in order to survive. Therefore, the law of nature for all living things in every ecosystem is based on the struggle for food, with the weak being eliminated from the ecosystem while the strong species survive [1,2,3]. Interactions between species have an impact on an ecosystem biomass, productivity, and population size of each species [4].…”

Section: Introductionmentioning

confidence: 99%

“…Allee effect and harvesting of species have been incorporated in the interaction of the plant-herbivore models [1,2,11]. However, the models did not incorporate plant pathogen and natural enemies of herbivores.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Modelling of Plant-Pathogen-Herbivore Interaction Incorporating Allee Effect and Harvesting

Barasa

Apima²,

Wanjara³

2022

JAMCS

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Plant-pathogen-herbivore model describe interaction between plants, pathogens and herbivores. Plants are invaded by pathogens and herbivores while the herbivores are harvested by natural enemies such as predators and human. On the other hand, the abundance of food does not guarantee exponential growth of species who reproduce sexually and plants governed by carrying capacity. Therefore, the Allee effect may be crucial for sustaining such species. In this paper, a model of plant-pathogen-herbivore interactions that takes Allee effect and harvesting into account was developed and analyzed. The stability analysis showed that the ratio intrinsic growth rate to the environmental carrying capacity of susceptible plants must be greater than certain threshold value to raise sufficient plant biomass to sustain other species. Numerical simulations shows that all species coexist when intrinsic growth rate of plants is greater than the harvesting rate and when conversion rate of what is eaten by herbivores to newborn ones is greater than that of their natural enemies. It also shows that in the absence of susceptible plants, herbivores migrates in search of food, while others deteriorate and dies out. Furthermore, regardless of the availability of susceptible plants, the herbivores population crashes to extinction if the herbivore population is less than the lower limit required to keep the herbivores existing in the ecosystem. In the interest of conservation of all species and the environment, policy developers will greatly benefit from understanding the solutions to address clearing land for human settlement, human activities and herbivore or their natural enemies hunting. In addition, monitor species closely, especially those that reproduce sexually by establishing and maintaining the least number required to keep the species existing.

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Section: Numerical Simulation Of the Modelmentioning

confidence: 99%

Section: Simulation Of Susceptible Plants Herbivores and Their Natura...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical Modelling of Plant-Pathogen-Herbivore Interaction Incorporating Allee Effect and Harvesting

Barasa

Apima²,

Wanjara³

2022

JAMCS

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show abstract

“…Harvesting of species have been incorporated in the interaction of the plant-herbivore models for instance, in [11]. However, the models did not incorporate the natural enemies of herbivores such as carnivores.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Plants, Herbivore and Natural Enemies of Herbivores Interaction with Harvesting

Barasa,

Apima

2023

ARJOM

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Plant-herbivore-natural enemies of herbivores interaction is one of the basic interactions that drives of the ecosystem yields. In this interaction, plants are the primary food source for herbivores while natural enemies of herbivores depends on herbivores for food and on plants for shelter. Harvesting of every species which is common in many habitat may affect the population densities of the species and even the entire ecosystem. Therefore, conservation and maintenance of the harvested species is critical for ecosystem balance. In this paper, a model of plant-herbivore-natural enemies interactions with the constant effort harvesting of every species was developed and analyzed. The positive invariant set, the conditions of existence and locally asymptotically, stability of the equilibria were determined using the stability theory of ordinary differential equations. The results shows that the species being harvested would become extinct if harvesting effort exceeded a threshold value for the given population. While maintaining the coexistence of populations in the ecosystem requires sensible harvesting practices. Therefore, it is fair to choose a reasonable harvesting effort to allow all species to coexist in order to govern the species’ dynamic behavior. The insights of the solutions of this study are of great essence to ecologists and policy developers in environmental conservation. The authorities to pay attention to the minimum number required based on the area coverage in deciding when to harvest and also be cautious to the amount and effort of harvesting in view of conserving the species and the environment.

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Stochastic plant–herbivore interaction model with Allee effect

2019

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Co-existence thresholds in the dynamics of the plant–herbivore interaction with Allee effect and harvest

Cited by 10 publications

References 25 publications

Mathematical Modelling of Plant-Pathogen-Herbivore Interaction Incorporating Allee Effect and Harvesting

Mathematical Modelling of Plant-Pathogen-Herbivore Interaction Incorporating Allee Effect and Harvesting

Mathematical Modeling of Plants, Herbivore and Natural Enemies of Herbivores Interaction with Harvesting

Stochastic plant–herbivore interaction model with Allee effect

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