Pasture-livestock dynamics with density-dependent harvest and changing environment
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.
This is the pre-peer reviewed version of the following article: Bergland, H., Wyller, J. & Burlakov, E. (2019). Pasture–livestock dynamics with density‐dependent harvest and changing environment. Natural Resource Modeling, 32(4), e12213, which has been published in final form at https://doi.org/10.1111/nrm.12213. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.