Analysis of a stochastic tri-trophic food-chain model with harvesting
- 981 Downloads
We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each species. The results show that persistence and extinction of a species only depends on the demographic impacts of environmental stochasticity on the species and species at lower tropic levels; however, the mean abundance of a species depends on the impacts of environmental stochasticity at all trophic levels. Then we consider stability in distribution of the model. Finally, we provide a necessary and sufficient condition for existence of optimal harvesting strategy and give the optimal harvesting effort and maximum of sustainable yield. The results show that the optimal harvesting strategy is closely related to the stochastic noises in the model.
KeywordsStochastic control Optimization under uncertainties Management of natural resources
Mathematics Subject Classification60H10 60H30 92D25
We are very grateful to Professor Sebastian Schreiber and anonymous referees for their careful reading and valuable comments, which led to an improvement of our paper. We also thank Dr. H.Qiu and Q.Wu for helping us to improve the English exposition.
- May RM (1975) Stability and complexity in model ecosystems. Princeton University Press, PrincetonGoogle Scholar
- Moon JW (1970) Counting labelled tress. Canadian Mathematical Congress, MontrealGoogle Scholar
- Murray JD (2001) Mathematical biology I. An introduction, 3rd edn. Springer, New YorkGoogle Scholar