The statistical characteristics of total nitrogen(TN) and total phosphorus(TP) nutrient input and their responses during the lake eutrophication process are of increasing concern.An increase in the mean(μ) and/or variance of TN and TP input may increase the probability of exceeding the critical threshold at which algal blooms proliferate. Dianshan Lake,a shallow temperate lake in the Taihu Plain,is an important source of drinking water for Shanghai and is subject to a subtropical monsoon climate.Its trophic state transitioned from eutrophic to hypereutrophic in 1999,causing the lake to suffer from bluegreen algal blooms ever since.Beginning in 2004,some restoration measures have been taken to reduce nutrient inputs into the lake.However,the immediate reduction of nutrient inputs did not instantly reduce the frequency of algal bloom events. In order to understand nutrient input and their responses in a lake ecosystem from a statistical point of view,the frequency distributions of TP,TN and chlorophyll a(Chl a),and the TP-Chl a relationships during two different trophic stages(eutrophic stage: 1986—1999;hypereutrophic stage: 1999—2009) of the lake were analyzed based on long-term data from 1985 to 2009.The means and variances of these parameters were compared with those after restoration measures were undertaken on the lake in 2004. The means and variances of TN and TP increased with the eutrophication process.The probabilities of TN and TP values exceeding the Surface Water Standard for Class V Waters(TN = 2.0mg/L;TP = 0.2mg/L) increased from 62.8% and 12.1% during the eutrophic stage to 91.4% and 51.9% during the hypereutrophic stage,respectively.The increase in Chl a concentration was even greater,with the probability of exceeding the limit of 15 μg/L increasing from 0.5% during the eutrophic stage to 67.5% during the hypertrophic stage. The log-log relationship between TP and Chl a was calculated as per Organization for Economic Co-operation and Development(OECD) methods using three data sets: 1985—1986,2000—2004 and 2004—2008.All of the observed patterns fit the TP control paradigm well,which indicated that TP had been the primary limiting factor.Over the 24-year eutrophication period examined,the slope of the TP-Chl a log-log relationship increased from 0.54 during the 1980s to 0.83 in the early 2000s and then further to 2.46 by 2008,which might indicate an increasing of proportion of bluegreen algae and the frequency of their blooms. After restoration measures were undertaken in 2004,mean TP stayed constant and the discrete degree(variance decreased to 50%,whereas the probability of Chl a exceeding 15 μg/L continued to increase by an additional 20%.Under the hypereutrophic condition,a reduction in peak nutrient values or variance only had a limited contribution to primary algal production.Further study on the effects of TN and TP reductions in eutrophication control is necessary. Here,we showed that statistical parameters such as mean,variance,slope and frequency distribution of nutrients and their responses were able to describe the eutrophication process of Dianshan Lake.These characteristics also offer statistical support for lake restoration assessments,risk assessments for Harmful Algal Bloom and nutrient criteria and standard development.