1. 1.暨南大学生态学系水生生物研究所，广东 广州 510632
2.中国科学院南京地理与湖泊研究所，江苏 南京 210008
3.中国—丹麦科研教育中心，北京 100190
4.中国科学院大学，北京 100049
5.安徽师范大学地理与旅游学院，安徽 芜湖 241003
• 收稿日期:2020-11-28 修回日期:2020-12-29 出版日期:2021-03-19
• 通讯作者: 王荣 E-mail:dww_running@163.com;rwang@niglas.ac.cn
• 基金资助:
中国科学院南京地理与湖泊研究所“一三五”自主部署项目“气候变化对典型浅水湖泊生态系统弹性的影响及机理”(NIGLAS2017GH01);中国科学院青年创新促进会(Award 2017364)

### The Influencing Factors of Critical Transition in Shallow Lakes Revealed by Model

Wenwen DENG 1 , 2( ), Rong WANG 2( ), Zhengwen LIU 1 , 2 , 3, Wenxiu ZHENG 2 , 4, Chenxue ZHANG 2 , 5

1. 1.Department of Ecology and Institute of Hydrobiology，Jinan University，Guangzhou 510632，China
2.Nanjing Institute of Geography and Limnology，Chinese Academy of Sciences，Nanjing 210008，China
3.Sino-Danish Center for Education and Research，Beijing 100190，China
4.University of Chinese Academy of Sciences，Beijing 100049，China
5.School of Geography and Tourism，Anhui Normal University，Wuhu Anhui 241003，China
• Received:2020-11-28 Revised:2020-12-29 Online:2021-03-19 Published:2021-03-19
• Contact: Rong WANG E-mail:dww_running@163.com;rwang@niglas.ac.cn
• About author:DENG Wenwen (1995-), female, Huizhou City, Guangdong Province, Master student. Research areas include eutrophication process. E-mail: dww_running@163.com
• Supported by:
the Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences "One Three Five" Independent Deployment Project "The impact and mechanism of climate change on the resilience of typical shallow lake ecosystem"(NIGLAS2017GH01);The Youth Innovation Promotion Association, CAS(Award 2017364)

Eutrophication can cause critical transitions in shallow lakes and severely impair ecosystem services. Phosphorus is one of important environmental factors that cause critical transitions in lake ecosystems. Exploring the mechanisms of phosphorus dynamics in lakes is a key to lake management. This paper simulated the phosphorus concentration variations in lakes using a phosphorus kinetic model， and discussed the specific impacts of main model parameters on simulation output. Based on literature reviews， we discussed in detail the effects of different types of climate change and human activities on the critical transition time， hysteresis length， and restoration rate of lakes. The paper indicated that changes in factors such as climate change induced temperature warming， weakened light intensity， increased wind/waves and human activities caused biological disturbances and water level fluctuations would not change the threshold of transition or the time of transition， but would significantly delay the recovery time， decrease the recovery threshold and extend the lag period and the steady state. For the management of lake ecosystems， we suggested that it be important to consider the different impacts from different external perturbations on the process of critical transitions to avoid harmful tipping point.

Table 1 Meaning and setting of phosphorus kinetic model parameters

Table 1 Meaning and setting of phosphorus kinetic model parameters

（a）模型参数的物理意义；（b）模型输出的湖泊生态系统折叠交叉模式及湖泊生态系统稳态转换
Fig.1 Schematic diagram of phosphorus kinetic model parameters and critical transition of lake ecosystem
（a）Schematic diagram of the model formula；（b）Collapsed catastrophe model of the lake ecosystem and critical transition of lake ecosystem

（a）模型参数的物理意义；（b）模型输出的湖泊生态系统折叠交叉模式及湖泊生态系统稳态转换
Fig.1 Schematic diagram of phosphorus kinetic model parameters and critical transition of lake ecosystem
（a）Schematic diagram of the model formula；（b）Collapsed catastrophe model of the lake ecosystem and critical transition of lake ecosystem

(a) 湖水磷浓度随时间变化的曲线( P-t图)；(b) 湖水磷浓度和外源驱动的关系( P-α图)
Fig.2 Schematic diagram of phosphorus kinetic model results
(a) The curve of lake water phosphorus concentration with time ( P-t diagram); (b) The relationship between lake water phosphorus concentration and external driving force ( P-α diagram)

(a) 湖水磷浓度随时间变化的曲线( P-t图)；(b) 湖水磷浓度和外源驱动的关系( P-α图)
Fig.2 Schematic diagram of phosphorus kinetic model results
(a) The curve of lake water phosphorus concentration with time ( P-t diagram); (b) The relationship between lake water phosphorus concentration and external driving force ( P-α diagram)

(a) ~ (c)分别是指改变 α的斜率后对应的磷输入速率随时间变化的图（ α-t图）、湖水磷浓度随时间变化的图（ P-t图）、湖水磷浓度随磷输入速率变化的图（ P-α图）；(d)和(e)分别是指改变 r值大小所对应的湖水磷浓度随时间变化的图（ P-t图）、湖水磷浓度随磷输入速率变化的图（ P-α图）；(f)和(g)分别是指改变 s值大小所对应的湖水磷浓度随时间变化的图（ P-t图）、湖水磷浓度随磷输入速率变化的图（ P-α图）；(h)和(i)分别是指改变 σ值大小所对应的湖水磷浓度随时间变化的图（ P-t图）、湖水磷浓度随磷输入速率变化的图（ P-α图）
Fig.3 Results of the phosphorus kinetic model
(a)~(c) Respectively refer to the graph of the change of phosphorus input rate with time after changing the slope of α ( α- t graph), the graph of the change of water phosphorus concentration with time ( P- t graph), and the phosphorus concentration of water graph of change with phosphorus input rate ( P- α graph);(d) and (e) Respectively refer to the graph of changes in water phosphorus concentration with time ( P- t graph) and the graph of changes in water phosphorus concentration with phosphorus input rate ( P- α graph) corresponding to changes in the value of r; (f) and (g) Respectively refer to the graph of the change of phosphorus concentration in water with time ( P- t graph) and the graph of the change of phosphorus concentration in water with phosphorus input rate ( P- α graph) when the value of s is changed;(h) and (i) Respectively refer to the graph of the change of phosphorus concentration in water with time ( P- t graph) and the graph of the change of phosphorus concentration in water with the phosphorus input rate ( P- α graph) corresponding to the size of σ value

(a) ~ (c)分别是指改变 α的斜率后对应的磷输入速率随时间变化的图（ α-t图）、湖水磷浓度随时间变化的图（ P-t图）、湖水磷浓度随磷输入速率变化的图（ P-α图）；(d)和(e)分别是指改变 r值大小所对应的湖水磷浓度随时间变化的图（ P-t图）、湖水磷浓度随磷输入速率变化的图（ P-α图）；(f)和(g)分别是指改变 s值大小所对应的湖水磷浓度随时间变化的图（ P-t图）、湖水磷浓度随磷输入速率变化的图（ P-α图）；(h)和(i)分别是指改变 σ值大小所对应的湖水磷浓度随时间变化的图（ P-t图）、湖水磷浓度随磷输入速率变化的图（ P-α图）
Fig.3 Results of the phosphorus kinetic model
(a)~(c) Respectively refer to the graph of the change of phosphorus input rate with time after changing the slope of α ( α- t graph), the graph of the change of water phosphorus concentration with time ( P- t graph), and the phosphorus concentration of water graph of change with phosphorus input rate ( P- α graph);(d) and (e) Respectively refer to the graph of changes in water phosphorus concentration with time ( P- t graph) and the graph of changes in water phosphorus concentration with phosphorus input rate ( P- α graph) corresponding to changes in the value of r; (f) and (g) Respectively refer to the graph of the change of phosphorus concentration in water with time ( P- t graph) and the graph of the change of phosphorus concentration in water with phosphorus input rate ( P- α graph) when the value of s is changed;(h) and (i) Respectively refer to the graph of the change of phosphorus concentration in water with time ( P- t graph) and the graph of the change of phosphorus concentration in water with the phosphorus input rate ( P- α graph) corresponding to the size of σ value

Table 4 Phosphorus kinetic model results and their corresponding influencing factors

Table 4 Phosphorus kinetic model results and their corresponding influencing factors