American Institute of Mathematical Sciences

2018, 15(3): 765-773. doi: 10.3934/mbe.2018034

Analyzing the causes of alpine meadow degradation and the efficiency of restoration strategies through a mathematical modelling exercise

 1 Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000, China 2 Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada 3 North-West Plateau Institute of Biology, the Chinese Academy of Sciences, Key Laboratory of Ecology Restoration in Cold Region in Qinghai Province, Xining, Qinghai 810001, China

* Corresponding author

Received  May 20, 2017 Revised  September 1 2017 Published  December 2017

Citation: Hanwu Liu, Lin Wang, Fengqin Zhang, Qiuying Li, Huakun Zhou. Analyzing the causes of alpine meadow degradation and the efficiency of restoration strategies through a mathematical modelling exercise. Mathematical Biosciences & Engineering, 2018, 15 (3) : 765-773. doi: 10.3934/mbe.2018034
References:
 [1] The Grassland Monitoring Report of China, 2015, Ministry of Agriculture of the People's Republic of China, 2016. [2] W. Fu, J. Zhao and G. Du, Study on sustainable development of alpine grazing ecosystem on Qinghai-Tibetan Plateau, Grassl. Turf, 33 (2013), 84-88. [3] R. Long, Functions of ecosystem in the Tibetan grassland, Sci. Technol. Rev., 25 (2007), 26-28. [4] L. Wen, S. Dong, Y. Li, X. Li, J. Shi, Y. Wang, D. Liu and Y. Ma, Effect of degradation intensity on grassland ecosystem services in the alpine region of Qinghai-Tibetan plateau, China, Plos One, 8 (2013), e58432. doi: 10.1371/journal.pone.0058432. [5] Y. Lan, The degradation problem and strategy of alpine meadow in Qingzang Plateau, Qinghai Prataculture, 3 (2004), 27-30. [6] T. Akiyama and K. Kawamura, Grassland degradation in China: Methods of monitoring, management and restoration, Grassl. Sci., 53 (2007), 1-17. doi: 10.1111/j.1744-697X.2007.00073.x. [7] Y. Lan, Some important problems of ecological restoration of "San jiang yuan" area in Qinghai province, Territ. Nat. Resour. Study, 3 (2005), 51-52. [8] X. Wang and X. Fu, Sustainable management of alpine meadows on the Tibetan plateau: Problems overlooked and suggestions for change, AMBIO: J. Hum. Environ., 33 (2004), 169-171. [9] H. Zhou, X. Zhao, Y. Tang, S. Gu and L. Zhou, Alpine grassland degradation and its control in the source region of the Yangtze and Yellow Rivers}, China, Grassl. Sci., 51 (2005), 191-203. doi: 10.1111/j.1744-697X.2005.00028.x. [10] R. Harris, Rangeland degradation on the Qinghai-Tibetan plateau: A review of the evidence of its magnitude and causes, J. Arid Environ., 74 (2010), 1-12. doi: 10.1016/j.jaridenv.2009.06.014. [11] Q. Chen, Grassland deterioration in the source region of the Yangtze-Yellow rivers and integrated control of the ecological environment, Acta Prataculturae Sin., 16 (2007), 10-15. [12] W. Li, W. Cao, J. Wang, X. Li, C. Xu and S. Shi, Effects of grazing regime on vegetation structure, productivity, soil quality, carbon and nitrogen storage of alpine meadow on the Qinghai-Tibetan Plateau, Ecol. Eng., 98 (2017), 123-133. doi: 10.1016/j.ecoleng.2016.10.026. [13] J. Luo, J. Zhou, W. Zhao, L. Dong and J. Zheng, Effect of fences on functional groups and stability of the alpine meadow plant community in the Qinghai-Tibet Plateau, Pratacultural Sci., 34 (2017), 565-574. [14] Y. Chang, B. Zheng, L. Guo and X. Cai, Theoretical analysis and multi-agent simulation of the ecosystem in Tibet, in Sixth International Conference on Natural Computation 7 (eds. S. Yue, H. Wei, L. Wang and Y. Song), IEEE, (2010), 3656–3659. doi: 10.1109/ICNC.2010.5584047. [15] X. Liao, Theory, Methods and Application of Stability, Huazhong University of Science and Technology Press, Wuhan, 1999.

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References:
 [1] The Grassland Monitoring Report of China, 2015, Ministry of Agriculture of the People's Republic of China, 2016. [2] W. Fu, J. Zhao and G. Du, Study on sustainable development of alpine grazing ecosystem on Qinghai-Tibetan Plateau, Grassl. Turf, 33 (2013), 84-88. [3] R. Long, Functions of ecosystem in the Tibetan grassland, Sci. Technol. Rev., 25 (2007), 26-28. [4] L. Wen, S. Dong, Y. Li, X. Li, J. Shi, Y. Wang, D. Liu and Y. Ma, Effect of degradation intensity on grassland ecosystem services in the alpine region of Qinghai-Tibetan plateau, China, Plos One, 8 (2013), e58432. doi: 10.1371/journal.pone.0058432. [5] Y. Lan, The degradation problem and strategy of alpine meadow in Qingzang Plateau, Qinghai Prataculture, 3 (2004), 27-30. [6] T. Akiyama and K. Kawamura, Grassland degradation in China: Methods of monitoring, management and restoration, Grassl. Sci., 53 (2007), 1-17. doi: 10.1111/j.1744-697X.2007.00073.x. [7] Y. Lan, Some important problems of ecological restoration of "San jiang yuan" area in Qinghai province, Territ. Nat. Resour. Study, 3 (2005), 51-52. [8] X. Wang and X. Fu, Sustainable management of alpine meadows on the Tibetan plateau: Problems overlooked and suggestions for change, AMBIO: J. Hum. Environ., 33 (2004), 169-171. [9] H. Zhou, X. Zhao, Y. Tang, S. Gu and L. Zhou, Alpine grassland degradation and its control in the source region of the Yangtze and Yellow Rivers}, China, Grassl. Sci., 51 (2005), 191-203. doi: 10.1111/j.1744-697X.2005.00028.x. [10] R. Harris, Rangeland degradation on the Qinghai-Tibetan plateau: A review of the evidence of its magnitude and causes, J. Arid Environ., 74 (2010), 1-12. doi: 10.1016/j.jaridenv.2009.06.014. [11] Q. Chen, Grassland deterioration in the source region of the Yangtze-Yellow rivers and integrated control of the ecological environment, Acta Prataculturae Sin., 16 (2007), 10-15. [12] W. Li, W. Cao, J. Wang, X. Li, C. Xu and S. Shi, Effects of grazing regime on vegetation structure, productivity, soil quality, carbon and nitrogen storage of alpine meadow on the Qinghai-Tibetan Plateau, Ecol. Eng., 98 (2017), 123-133. doi: 10.1016/j.ecoleng.2016.10.026. [13] J. Luo, J. Zhou, W. Zhao, L. Dong and J. Zheng, Effect of fences on functional groups and stability of the alpine meadow plant community in the Qinghai-Tibet Plateau, Pratacultural Sci., 34 (2017), 565-574. [14] Y. Chang, B. Zheng, L. Guo and X. Cai, Theoretical analysis and multi-agent simulation of the ecosystem in Tibet, in Sixth International Conference on Natural Computation 7 (eds. S. Yue, H. Wei, L. Wang and Y. Song), IEEE, (2010), 3656–3659. doi: 10.1109/ICNC.2010.5584047. [15] X. Liao, Theory, Methods and Application of Stability, Huazhong University of Science and Technology Press, Wuhan, 1999.
The stability regions of equilibria in the $C-A$ plane.
Bifurcation diagrams of Model (2) showing the globally stable equilibria only. Left: $C< \theta K$; Middle: $\theta K<C<K$; Right: $C>K$.
Variation of coordinates $x^{*}, y^{*}, z^{*}, u^{*}$ of $E_{5}$ and values of $A$, $\theta$ when one of the parameters $d_{1}, r, K, d_{3}, d_{4}, q$ increases (all other parameters are fixed).
 Parameter $d_{1}$ $r$ $K$ $d_{3}$ $d_{4}$ $q$ $x^{*}$ $-$ $-$ $-$ $\nearrow$ $-$ $-$ $y^{*}$ $-$ $-$ $-$ $-$ $\nearrow$ $\searrow$ $z^{*}$ $\searrow$ $-$ $-$ $-$ $\nearrow$ $\searrow$ $u^{*}$ $-$ $\nearrow$ $\nearrow$ $\searrow$ $\searrow$ $\nearrow$ $A$ $\nearrow$ $-$ $-$ $-$ $-$ $-$ $\theta$ $-$ $\nearrow$ $-$ $\searrow$ $-$ $-$
 Parameter $d_{1}$ $r$ $K$ $d_{3}$ $d_{4}$ $q$ $x^{*}$ $-$ $-$ $-$ $\nearrow$ $-$ $-$ $y^{*}$ $-$ $-$ $-$ $-$ $\nearrow$ $\searrow$ $z^{*}$ $\searrow$ $-$ $-$ $-$ $\nearrow$ $\searrow$ $u^{*}$ $-$ $\nearrow$ $\nearrow$ $\searrow$ $\searrow$ $\nearrow$ $A$ $\nearrow$ $-$ $-$ $-$ $-$ $-$ $\theta$ $-$ $\nearrow$ $-$ $\searrow$ $-$ $-$
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