Chin. Sci. Bull. (2014) 59(28):3621–3629 DOI 10.1007/s11434-014-0553-6

csb.scichina.com www.springer.com/scp

Article

Ecology

Using quantile regression to analyze the stressor–response relationships between nutrient levels and algal biomass in three shallow lakes of the Lake Taihu Basin, China Xiaohua Chen • Xiaoping Li

Received: 15 January 2014 / Accepted: 13 June 2014 / Published online: 15 July 2014  Science China Press and Springer-Verlag Berlin Heidelberg 2014

Abstract Understanding the stressor–response relationship between nutrient levels and algal biomass is a prerequisite for the management of eutrophication in lakes. In this study, a quantile regression (QR) approach was used to interpret the stressor–response relationships between nutrient (e.g., phosphorus, nitrogen) concentrations and algal biomass as measured by chlorophyll-a (Chl-a) levels. QR results indicated that Lake Dianshan and Lake Changdang, which are both heavily eutrophicated, were P-limited only. In contrast, Lake Kuilei, which has significantly lower nutrient levels and algal biomass than the other two lakes, was P- and N-limited. Moreover, in Lake Kuilei, N and P levels had significant interaction effects on the algal biomass at the upper quantiles (s [ 0.68). The degree to which the lakes were P-limited increased with rises in the mean total P concentration in the lakes. QR has many advantages over ordinary least squares regression for discriminating limiting factors and, in particular, allows us to estimate changes near the upper extremes of distributions associated with limiting factors. QR is adapted to more specialized risk management problems, such as early warnings of the risk of algal blooms. The probable value-at-risk of harmful algal blooms for Lake Kuilei, Lake Dianshan and Lake Changdang is s = 0.76 (Chl-a = 9 mg/m3), s = 0.87 (Chl-a = 24 mg/m3) and s = 0.72 (Chl-a = 35 mg/m3), respectively. Given the

X. Chen  X. Li (&) State Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai 200062, China e-mail: [email protected] X. Chen Water Environmental Research Institute, Shanghai Academy of Environmental Sciences, Shanghai 200233, China

results of the stressor–response relationship analysis, we conclude that reductions in P input represent the most feasible and least costly approach for managing eutrophication in the shallow lakes of the Lake Taihu Basin. To control the magnitude and duration of algal blooms in shallow lakes, reductions in P and N inputs are required. The 95 % CI bounds of slopes indicated that the interactions of nonnutrient factors with nutrients had strong impacts on the algal biomass in lightly eutrophicated Lake Kuilei. It is suggested that, in addition to reductions in nutrient loads, several ecological measures, such as an increase in the biomass of submerged macrophytes and the reduction of hydraulic retention time by flushing, could represent important components of an integrated approach to eutrophication management in the Lake Taihu Basin. Keywords Stressor–response relationship  Limiting factors  Eutrophication  Quantile regression  Shallow lakes  Lake Taihu Basin

1 Introduction In recent decades, rapid urbanization, sewage disposal, artificial damage to wetlands and streams, and more intensive agricultural practices have increased nutrient loading in lakes worldwide. Dramatic increases in nutrient loading have fueled the accelerated eutrophication of lakes, causing harmful algal blooms, fish kills, the death of submerged macrophytes, losses of biodiversity, decreases in water clarity, and many related problems in lakes that are adjacent to areas with large human populations [1, 2]. In China, algal blooms frequently occur in shallow lakes and threaten sustainable economic development [3–5]. Most cases of lake eutrophication are caused by excessive

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nutrient (e.g., P, N) inputs resulting from rapid economic development and explosive population growth [6]. The Lake Taihu Basin is located in the lower Changjiang (Yangtze) River Delta in China. This basin is by far the most densely populated and most developed area in the country, representing 0.4 % of the whole territory of China, 2.9 % of the national population, and more than 14 % of the gross domestic product (GDP). The GDP per capita within the basin area is 3.5 times higher than the state average GDP per capita [7]. Unfortunately, rapid economic development has resulted in serious deterioration of the lacustrine environment. Thus, an overwhelming majority of the lakes located in the basin have become susceptible to anthropogenic alteration and accelerated eutrophication over the last three decades [4]. One of the prominent features of a developing region or basin is the great heterogeneity of the area’s freshwater ecosystems [8]. The lakes in one basin have hierarchical environmental states, including their own characteristics and landscape features, which might result in heterogeneity in water quality and trophic states among the lakes. Similarly, there may be considerable heterogeneity in the responses of algal biomass to nutrients across different lakes with different trophic states. The use of information on such heterogeneity to predict nutrient effects on algal biomass across its conditional distribution could help limnologists and managers to improve the nutrient management of lakes in a given basin [9]. In addition, algal blooms with extremely high algal biomass are extreme events in the lakes, and these events pose a threat to drinking water safety and ecological resources. Consequently, our attention focuses on the upper tail of the conditional distribution of algal biomass for the purpose of estimating the limiting relations between nutrients and algal biomass. Most commonly used regression techniques, such as ordinary least squares regression (OLSR), estimate ecological relationships based on the center of data distributions (conditional means), not including the tails of the distribution [10]. OLSR is confined to providing a measure of central tendency and omits the limiting relationships found with different conditional distributions [11–15]. As a popular alternative to OLSR, quantile regression (QR) [16] is a desirable method of handling heterogeneous data from lakes because it offers a complete view of the way that the covariates affect the response variable according to the full range of the distribution. This approach is of particular utility for distributions without symmetric or normal forms. QR is especially useful with data that are heterogeneous in the sense that the tails and the central location of the conditional distributions vary differently with the covariates [17]. Furthermore, QR requires minimal assumptions about the form of the error distribution and is helpful in modeling the maximum response instead of the mean as a

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way to understand the limiting relationships of lakes. Consequently, we applied the QR approach in this study to analyze the heterogeneous effects of nutrients on algal biomass across its entire conditional distribution in three shallow lakes (Lake Dianshan, Lake Changdang, and Lake Kuilei) located in the Lake Taihu Basin. The main objectives of this study were (1) to present how QR can be a useful analytical tool for tackling heterogeneity in algal biomass in response to lake nutrients, (2) to compare the limiting relationships between nutrient levels and algal biomass found in three shallow lakes based on QR, and (3) to provide recommendations for nutrient management and eutrophication control of the shallow lakes in the Lake Taihu Basin.

2 Study area and methods 2.1 Study area and data collection As shown in Fig. 1, Lake Changdang (31330 –31400 N, 119300 –119370 E) is located upstream of Lake Taihu. Lake Dianshan (31040 –31120 N, 120530 –121010 E) and Lake Kuilei (31210 –31300 N, 120400 –120520 E) are located downstream of Lake Taihu. Although the three lakes are all shallow, they have different basic environmental characteristics (Table 1). The Environmental Protection Department of Jiangsu Province (EPDJP) and Shanghai Environmental Protection Bureau (SEPB), China, provided all field monitoring data

Fig. 1 Basin

Sketch map of the three shallow lakes in the Lake Taihu

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Table 1 Physical characteristics and designated uses of 3 typical shallow lakes in Lake Taihu Basin Lakes

Kuilei

Lake area (km2)

Average depth (m)

Water capacity (108 m3)

Average residence time (day)

Coverage ratio of submerged macrophytes (%)

Designated uses

6.9

3.3

0.22

30

35

i, iii

Changdang

82.0

1.2

0.98

55

20

ii, iii, iv, v, vi, vii

Dianshan

62.0

2.1

1.30

29

0.4

ii, iii, iv, vi, vii

i, Primary drinking water sources; ii, emergency drinking water sources; iii, irrigation; iv, tourism; v, cage aquaculture, vi, capture fishery and vii, navigation

for the three lakes. Quarterly sampling was conducted at three sites in Lake Kuilei over a nine-year period from 2003 to 2011. Bimonthly on-site sampling was conducted at four sites in Lake Changdang and six sites in Lake Dianshan in 2001, 2003, 2005, 2007, 2009, and 2011. Lake Kuilei, Lake Changdang, and Lake Dianshan produced 81, 124, and 201 datasets, respectively. TN levels were determined using the method of alkaline potassium persulfate digestion UV spectrophotometry according to state standard GB/T 11894-89. The TP level in water was measured with ammonium molybdate spectrophotometry according to state standard GB/T 11893-89. The algal Chla concentration was estimated with the method described by Strickland and Parsons [18], which consists of a filtration step with a GF/C glass paper filter, an extraction step with aqueous acetone, and a spectrophotometric analysis. 2.2 Quantile regression Quantile regression, first introduced by Koenker and Bassett [16], makes no stringent assumptions about the error distribution in the model [12] and provides new opportunities for bridging this gap by fitting statistical models to arbitrary quantiles of the conditional distribution rather than to the central tendency. QR generalizes the concept of a univariate quantile to a conditional quantile given one or more covariates. For example, for any quantile s 2 ð0; 1Þ, a specific algal concentration value of one lake is at the sth quantile if this concentration value is higher than that of 100s % of all algal concentration datasets in this lake. The algal concentration value is also said to be at the 100sth percentile. Let {y1, y2,…, yn} denote the values of the dependent variable. QR reduces outlier effects by giving different weights to positive and negative residuals and considers absolute rather than squared residuals such that X Residual ¼ min ð1Þ jyi  y^i jT; where T is a multiplier term that is equal to s (the quantile value) for positive deviations (i.e., yi  y^i [ 0) and to 1 – s for negative deviations. This asymmetric minimization fits

a regression model through the upper part of the response distribution for s [ 0.5 and through the lower part of the distribution for s \ 0.5. More detailed information on the QR method can be found in the relevant references [16, 19]. 2.3 Data analysis To assess the effects of nutrient limitations and nonnutrient factors on algal biomass in the three shallow lakes, we constructed a multivariate linear regression model as follows: Y ¼ b0 þ b1 X1 þ b2 X2 þ e;

ð2Þ

where X1 represents the log-transformed TP concentrations (LgTP), X2 represents the log-transformed TN concentrations (LgTN), the response variable Y represents the logtransformed algal chlorophyll-a concentration (LgChl-a), b0 is the intercept parameter, and b1 and b2 are partial correlation coefficients that represent the rates at which the predictor (Y) changes in response to the explanatory variables X1 and X2, respectively. Specifically, b1 and b2 are increments in the yield of phytoplankton Chl-a per unit of P and N. Values of b1 [ 0 or b2 [ 0 indicate that P or N have positive impacts on algal biomass. e is the model error term. The significance of the parameter estimates for each quantile was tested against the null hypothesis by invoking a resampling method to generate 95 % confidence intervals (CI), which furnish a potential criterion of goodness of fit for a particular quantile [20]. According to this approach, the estimated slope coefficients (e.g., b1, b2) are significant if the 95 % CI of the slope coefficients of the QR analyses does not include zero. In contrast, the estimated coefficients are not sufficiently accurate if their CI bounds include 0. QR analysis was conducted using the ‘‘Quantreg’’ package of SAS, version 9.2 (SAS Institute Inc., Cary, NC, USA. http://www.sas.com/) for the entire conditional distribution of algal biomass and nitrogen or phosphorus levels. For comparison, OLSR analyses were conducted

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using the ‘‘Reg’’ package of SAS 9.2. Calculations of basic statistics for the parameters of the data sets and nonparametric tests (e.g., Mann–Whitney U test, Kolmogorov– Smirnov Z test) were conducted using SPSS version 14.0 (SPSS Inc., http://www.spss.com).

Table 3 Summary of the results of nonparametric tests (Mann– Whitney U test) comparing total nitrogen (TN), total phosphorus (TP), chlorophyll-a (Chl-a) levels, and the TN:TP ratio of the three lakes in the Lake Taihu Basin Lake group

Statistics

Variables TN

3 Results

Dianshan vs. Changdang

3.1 Comparative analysis of nutrient level and trophic states in the three lakes

Kuilei vs. Changdang

Basic statistics for levels of TN, TP, Chl-a and the TN:TP ratio of the three lakes are shown in Table 2. Normality tests of stressor–response variables were performed using SPSS. A Kolmogorov–Smirnov Z test indicated that the P value was far less than 0.05 and, hence, that the null hypothesis of normality was rejected. It can be concluded from the above statistics that all the data for TN, TP, and Chl-a presented non-normal distributions and exhibited heavy tails, which suggested that neither conventional linear regressions based on stringent assumptions nor step function models would fit this type of stressor–response relationship very well. Lake Kuilei and Lake Dianshan had the lowest and highest concentrations of nutrients, respectively (Table 3), and the nutrient concentrations of Lake Changdang were intermediate between those of the other two lakes. The average TN and TP concentrations in Lake Dianshan were more than three times higher than those of Lake Kuilei. The average TN concentrations in Lake Dianshan were two times higher than those of Lake Changdang, and the average TP concentrations in Lake Dianshan were approximately 30 % higher than those of Lake Changdang. The ranking of the lakes for algal productivity was very different from the ranking for nutrient levels. Lake Changdang had the highest algal biomass, with Chl-a levels that were more than twice as high as those of Lake Dianshan and three times as high as those of Lake Kuilei. According to the results of the nonparametric test (i.e., the

Kuilei vs. Dianshan

TP

Chl-a

TN:TP

U

5,513

11,081

10,178

8,696

Z

-10.625

-5.014

-5.924

-7.417

P

\0.001

\0.001

\0.001

\0.001

U

5,455

1,787

4,370

3,937

Z

-4.053

-10.463

-5.949

-6.704

P

\0.001

\0.001

\0.001

\0.001

U

1,123

928

11,259

11,151

Z

-13.377

-13.619

-0.959

-1.092

P

\0.001

\0.001

0.338

0.275

Mann–Whitney U test) (Table 3), most environmental variables differed significantly by lake (P \ 0.001); only the differences in algal Chl-a levels (P = 0.338) and in the TN:TP ratio (P = 0.275) of Lake Kuilei and Lake Dianshan were not statistically significant. The mean nutrient levels at the inlet sites were higher than the mean nutrient levels at all sites for all three lakes. This finding indicates that the nutrient levels of the lakes depend on external nutrient input loading and suggest that the lakes with higher external nutrient input loading have much higher nutrient levels. 3.2 The impacts of P and N on algal biomass in the three lakes based on OLSR and QR To find a line that represent the ‘‘best’’ and unique linear relationship between algal biomass and nutrients (e.g., P, N), OLSR simply yields a unique set of estimated values for the three parameters (i.e., b0, b1, b2). The unique values of b1 (slope of LgTP) obtained with OLSR were 0.33, 0.37, and 0.48 for Lakes Kuilei, Changdang, and Dianshan, respectively. These results indicated that P has positive impacts on algal biomass in the three lakes. The unique

Table 2 Total nitrogen (TN), total phosphorus (TP), chlorophyll-a (Chl-a) levels and TN:TP ratio for the three lakes in the Lake Taihu Basin (mean ± SD) Lake Kuilei Changdang Dianshan

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Monitoring scope

n

TN (mg/L)

TP (mg/L)

Chl-a (mg/m3)

TN:TP

Three sites

81

1.05 ± 0.42

0.06 ± 0.02

9.21 ± 6.60

22.54 ± 12.67

One inlet site

36

1.16 ± 0.41

0.07 ± 0.02

9.72 ± 6.75

21.85 ± 13.70

124

1.67 ± 1.20

0.15 ± 0.08

29.10 ± 28.00

13.52 ± 12.24

One inlet site

Four sites

38

2.25 ± 1.25

0.19 ± 0.10

32.20 ± 29.20

15.48 ± 12.55

Six sites Two inlet sites

201 72

3.52 ± 1.85 3.81 ± 1.92

0.19 ± 0.09 0.21 ± 0.11

13.12 ± 12.33 12.8 ± 11.24

22.36 ± 10.39 21.7 ± 11.22

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values of b2 were -0.05, -0.98 and -0.57, respectively, suggesting that there was a negative relationship between algal biomass and N in the three lakes. Unlike OLSR, QR detailed the behavior of the algal biomass in response to P and N over the entire conditional distribution (0 \ s \1) rather than a unique result. As shown in Fig. 2, the profiles of the variation in the estimated parameters based on QR were similar for Lake Dianshan and Lake Changdang. The intercepts (b0) were positive and increased with increasing quantiles. The slope of LgTP (b1) remained positive and displayed a U-shaped structure, with lower values at the middle of the distribution and higher values at the ends of the distribution. For Lake Dianshan, the slope of LgTP (b1) entered the increasing domain at s = 0.40 (Chl-a = 7 mg/m3) and ascended especially sharply for s [ 0.87 (Chl-a [ 24 mg/m3). For Lake Changdang, the slope of LgTP (b1) entered the increasing

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domain at s = 0.56 (Chl-a = 20 mg/m3) and increased especially sharply for s [ 0.72 (Chl-a [ 35 mg/m3). In contrast, the slope of lgTN (b2) remained negative throughout all conditional quantiles (0 \ s \ 1). These results indicated that the algal biomass in the two lakes was positively and negatively associated with the P and N levels, respectively. The variations in all estimated parameters for Lake Kuilei were very different from the variations for the other lakes. Both b0 and b1 had inverted U shapes, with high values at the middle of the distribution and low values at the ends. The b1 values remained positive for most quantiles when 0.09 \ s \ 0.85 and ranged from 0.21 to 0.77. The b2 value was positive, ranging from 0.09 to 1.15 along the entire conditional distribution and increased dramatically from 0.13 to 1.14 in the upper quantiles of s [ 0.76 (Chla [ 9 mg/m3). Therefore, both P and N levels were positively correlated with Chl-a concentrations.

Fig. 2 Estimated intercept (b0) and slopes (b1, b2) of the bivariate regression of algal Chl-a on P and N levels obtained with QR and OLSR. The estimated coefficients obtained with QR (solid curve) are presented with their 95 % confidence bounds (shaded in gray). The coefficients obtained with OLSR (central dotted line) are also given with their 95 % confidence bounds (upper and lower parallel dotted lines). a1, a2, a3 Lake Dianshan; b1, b2, b3 Lake Changdang; c1, c2, c3 Lake Kuilei

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The mean values of b1 (slope of LgTP) obtained with QR were 0.27, 0.35, and 0.50 for Lakes Kuilei, Changdang, and Dianshan, respectively (Table 3). The mean values of b1 increased with mean TP concentrations (0.06, 0.15, and 0.19 mg/L) in Lake Kuilei, Lake Changdang, and Lake Dianshan, respectively. Thus, the degree of P-limitation increased with increasing TP levels for the three lakes. The 95 % CI widths are useful indicators of the significance of the effects of N or P levels or of non-nutrient factors omitted from the regression models on algal growth. The CI of b1 for Lake Dianshan did not include zero for any quantiles or for the entire conditional distribution, indicating that P was significantly positively correlated with algal biomass in all cases. The CI of b1 for Lake Kuilei and Lake Changdang excluded zero only in certain cases (when 0.22 \ t \ 0.68 and s [ 0.735, respectively, Table 4, Fig. 2b2); in these ranges, P levels had a significant positive impact on algal biomass. However, N and P levels had strong interacting impacts on algal growth in Lake Kuilei at the lower (s \ 0.22) and upper quantiles (s [ 0.68). For Lake Changdang, non-nutrient factors (e.g., temperature, wind, and flushing rate) that were not included in the regression models may have had strong interactive impacts with P levels on algal growth at s \ 0.735. Consequently, Lake Dianshan and Lake Changdang are significantly P-limited, with the former more limited than the latter. Lake Kuilei was co-limited by P and N. A comparison of the results of OLSR with those of QR shows that the estimated regression coefficients from OLSR were very close to the mean value of the parameters from QR for both Lake Dianshan and Lake Changdang.

However, the OLSR and OR results of Lake Kuilei were strongly divergent. The slope of LgTN (b2) of Lake Kuilei had a unique negative value of -0.05 in the OLSR model but ranged from 0.09 to 1.15 and had an average value of 0.33 in the QR model.

4 Discussion 4.1 The advantages of QR over OLSR for discriminating limiting factors of lakes We specifically concentrated on the use of QR as a tool to detect limiting relations between nutrients (e.g., P, N) and algal biomass determined by Chl-a. The QR results indicated that the nutrient level and other environmental factors contributed to the heterogeneity in the algal biomass responses. We can conclude that QR has many advantages over OLSR for discriminating limiting factors. The use of QR makes it possible to avoid various problems associated with OLSR. Ordinary least squares regression is estimated under the stringent assumptions of equal variance and a normal or Gaussian distribution of residuals [21]. However, it is rare for environmental variables to obey this assumption [22]. In contrast, QR requires no assumptions of the properties of variances and distribution forms of the residuals and therefore allows an investigation of causality for any percentile of the response [10–12, 16, 23]. These considerations suggested that a QR can yield a better explanation than could a typical OLSR for heterogeneous stressor–

Table 4 Statistics of all estimated parameters obtained by multivariate QR and OLSR for the three lakes Methods

QLSR

Parameters

b0 b1 b2

QR

b0

b1

b2

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Statistics

Constant

Lakes Dianshan

Changdang

Kuilei

1.60

1.62

1.29

95 % CI band

Never included 0

Never included 0

Never included 0

Constant

0.48

0.37

0.33

95 % CI band

Never included 0

Never included 0

included 0

Constant

-0.57

-0.98

-0.05

95 % CI band

Never included 0

Never included 0

included 0

Mean Range

1.55 0.94–2.47

1.58 0.84–2.66

1.25 -0.20–1.67

95 % CI band

Never included 0

Never included 0

Did not include 0 when 0.14 \ s \ 0.82

Mean

0.50

0.35

0.27

Range

0.28–0.85

0.10–0.77

-0.53–0.58

95 % CI band

Never included 0

Did not include 0 when s [ 0.73

Did not include 0 when 0.22 \ s \ 0.68

Mean

-0.51

-1.00

0.37

Range

-0.85 to -0.29

-1.27 to -0.77

0.09–1.14

95 % CI band

Never included 0

Never included 0

Did not include 0 when 0.25 \ s \ 0.50

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response relationships between nutrients and algal biomass in the lakes. Ordinary least squares regression is confined to providing a measure of central tendency and obtains a unique solution to find a line that represent the ‘‘best’’ relationship between algal biomass and nutrients (e.g., P, N). Accordingly, previous literature [24, 25] has provided conclusive evidence that OLSR cannot correctly reflect the underlying ecological theory, such as the Law of the Minimum or Law of Limiting Factors. In contrast, QR allows us to examine the behavior of the response variable over its entire conditional distribution (0 \ s \ 1) and to make use of all the available information [11, 12, 16, 19, 21]. One interesting feature of QR models is their ability to estimate changes near the upper extremes of distributions associated with limiting factors and offers the opportunity to view the maximum as the best possible estimate for the limiting relationships [11]. An upper regression quantile (e.g., s [ 0.8) should provide an approximation that is more consistent with the ecological theory of limiting factors than estimates based on the center of data distributions [10]. A controlling factor can be identified as limiting if its slope tends to be steeper for upper quantiles [26]. For Lake Dianshan and Lake Changdang, the slope of LgTP (b1) remained positive and increased markedly with the higher quantiles when s [ 0.5, suggesting P-limitation. The slope of LgTN (b2) of Lake Kuilei with QR increased dramatically in the upper quantiles (s [ 0.76), which suggested that N-limitation occurred in Lake Kuilei. OLSR is notoriously sensitive to even a single outlier, which often causes misleading results [27]. However, QR requires no stringent assumptions and therefore is insensitive or robust to extreme values of outlying dependent variables. For example, Lake Kuilei obtained a unique negative b2 value of -0.05, suggesting that there was a negative relationship between algal biomass and N in the lake. However, QR obtained multiple b2 values ranging from 0.09 to 1.15, showing positive impacts of N on algal biomass. In our study, the slope of LgTP (b1) of Lake Kuilei obtained with OLSR overestimated the rates of change of the response of algal biomass to P at the lower and upper quantiles. In contrast, the values of b1 for Lake Dianshan and Lake Changdang obtained by OLSR underestimated the rates of change of algal biomass in response to P in the two tails. 4.2 Implications for eutrophication management of shallow lakes in the Lake Taihu Basin Our application of the QR model provides new insight into the possible eutrophication management of lakes in the Lake Taihu Basin. QR can estimate multiple rates of change of algal biomass in response to nutrients and clearly

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presents the information at the upper extremes of the response distribution (often in a state corresponding to an ongoing algal bloom). Therefore, the use of QR eliminated the need for an excess of arbitrary decision-making by environmental management [11]. Moreover, QR is adapted to more specialized risk management problems, such as the formulation of an early warning of the risk of algal blooms. As shown in Table 2 and Fig. 2, the incremental rates of change (b1) of the response of algal biomass to P in the upper distribution obtained with QR are twice the central value obtained with OLSR. The most obvious effects on algal biomass were at the upper quantiles and not at the mean biomass. Therefore, we suggest that a management policy for lakes developed from mean-based measures of effects may not be as useful as a policy based on the concept of limiting factors. Algal biomass would increase explosively within a very short time and produce disastrously damaging algal blooms when the slopes entered the sharply increasing domain. Consequently, the initial points of the dramatically ascending domain in the upper tail of the distribution can be viewed as the value-at-risk of algal blooms. The quantile s = 0.76 (Chl-a = 9 mg/m3) can be considered the value-at-risk for Lake Kuilei. The value-atrisk of Lake Dianshan is s = 0.87 (Chl-a = 24 mg/m3). The value-at-risk of Lake Changdang is s = 0.72 (Chla = 35 mg/m3). According to the results of the QR, Lake Dianshan and Lake Changdang were significantly P-limited. However, Lake Kuilei was co-limited by P and N to a certain extent. Furthermore, the degree of P-limitation increased with increasing TP levels in all three lakes irrespective of the TN:TP ratio. The P-limited status of the lakes was further demonstrated by Cheng et al. [28], who found that the relationship between Chl-a levels and TP levels was characterized by regression coefficients ranging from 0.54 to 0.83; P is usually the primary limiting nutrient in freshwater systems worldwide [29]. Our finding that P was the limiting nutrient in these three lakes is corroborated by studies of 45 other shallow lakes in the Changjiang (Yangtze) area of China. These studies concluded that P, rather than N, determines the amount of total phytoplankton in the lakes over a prolonged period of time [30]. Therefore, reducing P inputs represents the most feasible and least costly approach for managing the eutrophication of the shallow lakes in the Lake Taihu Basin. The first step should be to reduce external P loading [31] because the lakes with higher nutrient levels at the inlet sites have correspondingly higher mean nutrient values (Table 2). In terms of the light-eutrophicated Lake Kuilei, more attention should be paid to the evidence that N-limitation was stronger than P-limitation. N-limitation commonly occurs during the summer months when the availability of N is a key growthlimiting factor for the blooms of toxic Microcystis spp. [32,

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33]. Therefore, although P load reduction is important, N load reduction is essential for controlling the magnitude and duration of algal blooms [34]. In addition to P and N, other environmental factors, including physical, chemical and biological factors, can be important limiting factors for algal biomass [35–38]. The 95 % CI bounds of both b1 and b2 with QR in Lake Kuilei showed that the relationships between the two nutrient factors and algal biomass were not significant at low or high s. The interactions of non-nutrient factors with nutrients had strong effects on algal biomass in light-eutrophicated Lake Kuilei. For example, the coverage rate of submersed plants in Lake Kuilei was greater than 30 %; these plants compete for nutrients with algae. Submerged macrophytes can obviously suppress the growth of algae through nutrient competition and allelopathic effects [39]. In comparison, as a result of excessive nitrogen, the coverage ratio of submerged macrophytes in Lake Dianshan decreased from 61.05 % in 1987–1988 to 0.38 % in 2010 [40], which possibly magnified the P-limitation on algal biomass in the lake. Furthermore, algal blooms are often exacerbated by low flushing rates or long residence times [41]. Lake Changdang had the longest hydraulic retention time of the three lakes. This characteristic might explain the finding that this lake showed the strongest P-limitation. Both Lake Dianshan and Lake Kuilei, which have much shorter hydraulic residence times, have significantly lower mean Chl-a concentrations than Lake Changdang (P \ 0.001). Consequently, nutrient abatement strategies should not be considered to represent a stand-alone tool for eutrophication management [42–45]. Once nutrient reduction has been achieved, other ecological measures such as the increase in biomass of submerged macrophytes and the reduction of hydraulic retention time by flushing can be important components of an integrated approach to eutrophication management in the Lake Taihu Basin. Acknowledgments This work was supported by the National ‘‘11th Five-year Plan’’ Water Special Project of Ministry of Science and Technology of China (2009ZX07106-001). We highly appreciate Environmental Protection Department of Jiangsu Province (EPDJP) and Shanghai Environmental Protection Bureau (SEPB), China, for their help in providing all field monitoring data of lakes. Conflict of interest of interest.

The authors declare that they have no conflict

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