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Analysis of a stochastic tri-trophic food-chain model with harvesting

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Abstract

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.

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Acknowledgments

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.

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Authors and Affiliations

  1. School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, People’s Republic of China

    Meng Liu & Chuanzhi Bai

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Meng Liu

Authors
  1. Meng Liu
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  2. Chuanzhi Bai
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Correspondence to Meng Liu.

Additional information

The National Natural Science Foundation of China (Nos. 11171081, 11301207 and 11571136), Project Funded by China Postdoctoral Science Foundation (2015M571349), Natural Science Foundation of Jiangsu Province (No. BK20130411), Natural Science Research Project of Ordinary Universities in Jiangsu Province (No. 13KJB110002), Qinglan Project of Jiangsu Province (2014), Science and Technology Support Plan Project of Huaian (HAR2015013).

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Liu, M., Bai, C. Analysis of a stochastic tri-trophic food-chain model with harvesting. J. Math. Biol. 73, 597–625 (2016). https://doi.org/10.1007/s00285-016-0970-z

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