RESEARCH ARTICLE
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Pasture–livestock dynamics with density-dependent harvest and changing environment
Harald Bergland,
John Wyller,
Evgenii Burlakov,
Corresponding Author
Harald Bergland
School of Business and Economics, University of Tromsø—The Arctic University of Norway, Harstad, Norway
Correspondence Harald Bergland, School of Business and Economics, University of Tromsø—The Arctic University of Norway, Campus Harstad, P.O. Box 1063, N-9480 Harstad, Norway. Email: harald.bergland@uit.no
Search for more papers by this authorJohn Wyller
Applied Mathematics Section, Faculty of Science and Technology, Norwegian University of Life Sciences, Ås, Norway
Department of Mathematics, Natural Sciences and Information Technologies, Derzhavin Tambov State University, Tambov, Russia
Search for more papers by this authorEvgenii Burlakov
Department of Mathematics, Natural Sciences and Information Technologies, Derzhavin Tambov State University, Tambov, Russia
International Complex Research Laboratory for Study of Climate Change, Land Use and Biodiversity, University of Tyumen, Tyumen, Russia
Search for more papers by this authorHarald Bergland,
John Wyller,
Evgenii Burlakov,
Corresponding Author
Harald Bergland
School of Business and Economics, University of Tromsø—The Arctic University of Norway, Harstad, Norway
Correspondence Harald Bergland, School of Business and Economics, University of Tromsø—The Arctic University of Norway, Campus Harstad, P.O. Box 1063, N-9480 Harstad, Norway. Email: harald.bergland@uit.no
Search for more papers by this authorJohn Wyller
Applied Mathematics Section, Faculty of Science and Technology, Norwegian University of Life Sciences, Ås, Norway
Department of Mathematics, Natural Sciences and Information Technologies, Derzhavin Tambov State University, Tambov, Russia
Search for more papers by this authorEvgenii Burlakov
Department of Mathematics, Natural Sciences and Information Technologies, Derzhavin Tambov State University, Tambov, Russia
International Complex Research Laboratory for Study of Climate Change, Land Use and Biodiversity, University of Tyumen, Tyumen, Russia
Search for more papers by this authorAbstract
We model pasture–livestock interactions by means of a predator–prey model, with the biomass vegetation as prey and the herbivores as predators. The harvesting rate is a sigmoidal function of the livestock density. We identify the necessary biological and harvest conditions for different equilibria of this model to exist. The system possesses no interior equilibrium points for the mortality rate exceeding a certain threshold. For the regime of low and moderate values of the mortality rate and a high consumption rate per animal, a unique finite and asymptotically stable state exists. We incorporate the effect of forage resource deterioration over time, causing extra decrease in the herbivore population and in the biomass density. We also include the effect of fluctuations in the availability of fodder by allowing for a seasonal periodic variation in the conversion efficiency. This results in extra oscillations superimposed on the general trends of the unperturbed system.
Recommendations for Resource Managers
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Depending on biological and harvest conditions, the system possesses up to three equilibrium states.
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Forage resource deterioration over time causes an extra decrease in the herbivore population and in the biomass density.
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A seasonal periodic variation in the conversion efficiency results in oscillations mainly in the herbivore density superimposed on the general trends of the unperturbed system.
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