Co-existence thresholds in the dynamics of the plant-herbivore interaction with Allee effect and harvest
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Author list: Asfaw MD, Kassa SM, Lungu EM
Publisher: World Scientific Publishing
Place: SINGAPORE
Publication year: 2018
Journal: International Journal of Biomathematics (1793-5245)
Journal acronym: INT J BIOMATH
Volume number: 11
Issue number: 4
Number of pages: 27
ISSN: 1793-5245
eISSN: 1793-7159
Languages: English-Great Britain (EN-GB)
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Abstract
In the interaction between plants and herbivores that live in the same ecosystem, understanding the conditions in which co-existence equilibrium occurs answers a major question in Ecology, In this interaction, plants serve as food for herbivores on the food chain. Then the livelihood of herbivores highly depends on the availability of food, in this case the availability of plants. Moreover, the abundance of the plant density alone does not guarantee the non-extinction of the herbivore population as they are assumed to reproduce sexually. With this motivation, in this paper a predator-prey mathematical model is reformulated such that the death rate of the herbivore population is dependent on the plant density and their emergence is also governed by the Alice effect. Using the mathematical theory of dynamical system, threshold conditions are obtained for the non-extinction of the herbivore population and a trapping region is obtained to ensure co-existence of the population. Moreover, it has been shown that the dynamics of the population is significantly sensitive to the feeding rate and the harvest rate of the herbivore population.
Keywords
Allee effect, equilibrium points, harvest, Predator-prey, Sensitivity analysis, threshold
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