# American Institute of Mathematical Sciences

June 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 11, 2017 Published  December 2017

As an important ecosystem, alpine meadow in China has been degraded severely over the past few decades. In order to restore degraded alpine meadows efficiently, the underlying causes of alpine meadow degradation should be identified and the efficiency of restoration strategies should be evaluated. For this purpose, a mathematical modeling exercise is carried out in this paper. Our mathematical analysis shows that the increasing of raptor mortality and the decreasing of livestock mortality (or the increasing of the rate at which livestock increases by consuming forage grass) are the major causes of alpine meadow degradation. We find that controlling the amount of livestock according to the grass yield or ecological migration, together with protecting raptor, is an effective strategy to restore degraded alpine meadows; while meliorating vegetation and controlling rodent population with rodenticide are conducive to restoring degraded alpine meadows. Our analysis also suggests that providing supplementary food to livestock and building greenhouse shelters to protect livestock in winter may contribute to alpine meadow degradation.

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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